Thanks Michael and hello again everybody. As Michael said this is going to be unit 4 of our financial management course and so as always let's just take a quick review of the course learning objectives that apply to this unit. We've talked about a couple of these before but again just a reminder that one looking for you to have an ability to actually demonstrate a degree of accounting and financial literacy. Which means that you can talk about and discuss what's going on in the financial system of your company. The ability to apply the results of financial analysis specifically to making decisions to make a determination on how well you're doing and whether changes are required. And last we touch base on capital last week to calculate the cost of a firm's debt and equity. Otherwise known as their capital plan or the debt to equity ratio. There's a cost to the money we use and we'll be talking a little bit about that and some of the topics we're going to cover today. The course layout again consists of 7 units and prior presentations we covered the first 3 today we're covering unit 4 or talk about the idea of risk and return which is a basic and critical discussion point for any time you're looking to make an investment. Now we have learning objectives for each of the units and so for unit 4 here's the objectives that we have and that we think are important and the material relates to these objectives explain why accepting greater risk requires an expectation of greater return. The greater the risk the greater the return you want to make. Recognizing the impact that interest rates have on investment financing. Remember interest rates are the cost of debt and so it does have a direct impact on potential returns for an investment. Calculating the risk of an investment will find this is not an exact science but there are things we can do to at least identify and perhaps do some analysis of what kind of risk are we accepting with an investment. Well take a look at how firms evaluate risk in their investment decisions. Excuse me we'll talk a little bit about stocks and how they're valued after all stocks are representation of how the market views the how well the firm is performing. Now the financial topics that we'll talk about for unit 4 are these and we'll talk about financial risk specifically measuring risk. We'll talk about a couple of specific kinds of risk that's the market risk and the firm specific risk. Both are important there is a distinction between the 2. We'll talk about a risk premium and one way we can look at positionary ourselves to achieve a desired return given an amount of risk that the firm is taking. Touch base briefly and stocks just a brief overview of the difference between preferred in common stock the implications for those shareholders what it means to the firm and then one of the things that plays a part in somebody's decision to invest in a firm could also be their dividend policy is the firm paying dividends to the pay dividends regularly dividends increasing over time. So there's a lot to a lot to review this morning and so before I get started let me just pause and see if there are any questions from topics that we covered previously or before I get started on risk. Great. So there there is a little problem with listening to Michael who's controlling our video today. So I'll just step in for him and say that if you have any questions you can leave them into the chat if there are questions on prior units or as we go through this today if we don't get your question during the presentation. We will get back and answer those questions so please feel free to leave those. So going forward. Let's talk and open up the discussion on the idea of risk. We're all familiar with risk. We're familiar and risking our in our day to day lives. We make an investment and there's a potential that we're looking to get something back from that investment. Couple simple examples that are maybe applicable to our audience today. You make an investment by studying or not studying for the final exam. What's the expected return? Well I'm guessing you'd looking to pass the course and the risk not getting a passing grade. The amount of investment you make equated to the amount of time you put in how many minutes and or hours are you studying for the exam and it has a direct impact on the potential results or one of my personal favorites you purchase a health club membership. Why we're expecting to maybe get some weight loss and improve physical conditions. The risk of that investment of course is you don't achieve weight loss and or your physical condition does not improve. So we're all kind of used to the idea of risk and expected return. Let's talk about financial risk. In a business decision we're going to invest money for some future gain. How do we define financial risk and I've mentioned this in prior discussions it's worth repeating. Financial risk is the potential that the actual return on the investment you make will be less than the expected return. Now think about this for a minute because it's important. Let's assume that you're going to make an investment in a project and you have an expected return of 8%. Now maybe that 8% is simply the amount of return required for you to break even. Not even get ahead but you're going to break even on this investment. Well the risk of that investment is that the actual return is less. And in this case it could represent a loss or suppose your expected return is 8% and that's a couple of percent over the cost of your investment and the return is 10. Well you're doing better than the expected rate but that's financial risk. It's that what actually occurs isn't what you wanted to occur or isn't what you expected to occur. Now when we talk about taking risk there's a range of how much risk people and or firms are willing to accept. We've got folks that are risk seeking. They will prefer investments that have more risk. Why because they have expectations of return. Consider you there is a new mine open up they believe that there's a potential that they will find gold in that mine. You make an investment. It could be that you're going to invest a lot of money but your expectation of return is very great. Why because there's a lot of risk here. They could wind up getting into the mining operation and find out there is no gold. We have people that are risk neutral. In this case they'll consider investment opportunities with greater or less degrees of risk. They're going to evaluate an opportunity and make determinations on a case by case basis. And then there are some who are actually risk adverse. We're not looking to take any risk. Now this doesn't mean this is not bad. It's a matter of evaluating what your financial position. So let me give an example that maybe some of you can relate to. As you are younger and starting out in your careers you may be willing to take more risk in making investments because you're looking to maximize your return. And you know that you have time to recover if your return is not what you expected. As you get older as you get towards retirement and you're looking to just ensure that you have a steady flow of income you may not be looking to make investments that are very risky. And so we might look to make investments that are risk free or they carry little to no risk. Okay. Hopefully that makes sense. Businesses are the same. Companies that have a good amount of cash ready to invest. They are financially sound might be willing to take more risk for investment projects because of the position they're in. Less so if the company is facing any financial difficulties. Okay. So let's talk just a second about this idea of risk free investing and is there such a thing. Well nothing in life is 100% guaranteed. But from an investment standpoint we do know that there are some things we some places we can put our money that are relatively risk free. For example I can invest some of my money every month into a savings account at a local bank saving money for the future. That's relatively risk free. Unless there's an overall bank crash which happens infrequently then my money is probably secure. I can also invest in T bills or T bonds that are issued by the United States government. These are issued by the U.S. Treasury. They have a guaranteed interest rate. All right. A guaranteed dividend to be paid at some point in the future or over time. And we consider that to be relatively risk free given the history and the stability of the U.S. Treasury. Now because these are risk free going back to the rule of the greater the risk the greater the expectation of return. There's no great expectation of return on these investments. Savings accounts may pay a couple of percent a year. Your money's safe. You're earning a little bit but you're not making any great return. And you're going to find the same thing with T bills and T bonds because they are secure and because they're guaranteed. Typically the rates that are earned are less than you would expect in the general market. OK. So that's what we consider risk free investing. The reason this is important is when we consider a company making an investment. It starts with the fact that they've identified that there is cash available in the firm. So we have a million dollars that we can invest. We have two things that we can do here. The firm can make a decision to take that million dollars and make a risk free investment and get a certain percent of return. Or they can invest in a new project a new product line new equipment with an expectation of a higher return. But obviously because it's new it's riskier. And so the firm just like an individual makes a decision at that point on whether or not how much risk they are willing to take. Should they stake with something that is risk free or assume more risk with their investment. Now there's 2 basic kinds of risk that I just want to touch base on this morning. One is market risk.  The market risk is systematic. And by that I mean that general risks that affect the entire market not individual to a unique investment or unique business. Consider things like oil prices rise. And as oil prices rise there's an impact on crossover transportation everywhere which can affect every business and that's going to have an impact on the overall market risk or what the market return is. So one thing we think about especially if we have shareholders is that shareholders obviously can invest or divest in the market. If you have a portfolio of stocks there's an expectation of what the market is returning for you today. One way to attract investors or to perform better for our investors is to invest in projects with an expectation of return that's greater than what the market is returning. That's giving our investors more than what they could get in the general market. And that's market risk. The other type of risk and specific to investors is firm specific risk. This is unsystematic and that means that it's unique to a firm a company or it could even be an industry. But it's not the overall market. So a firm has firm specific risk. If when Apple goes out and advertises they're launching the next the next version of the iPhone. There's a market risk firm specific risk to them because they tend to release a new product every year or so. And depending on how the market views what's new in the new iPhone it may or may not meet sales expectations. So a new product offering may or may not be accepted by the marketplace. Now a shareholder does have a way to reduce the impact of firm specific risk. And that's the concept of a diversified portfolio. So let's step back a minute and go into stock investing one on one. A portfolio is simply your collection of stocks that you've invested in. Now you could have built a portfolio where you've invested all of your money in energy producing companies. Or in my world you've put all your eggs in one basket. That is not a diversified portfolio because if something happens to the energy sector your entire portfolio is impacted. A diversified portfolio says you actually pick choose and select a variety of stocks from different industry segments different markets different sizes. So what you're doing is you're spreading the risk of any one company over the potential risk of your portfolio. Now at this point I hope I haven't lost anybody but I will say that there is a ton of information online regarding market portfolios and diversified portfolios. For those that want to get a tad more specific know that you can actually take your portfolio of stocks at any given time and you can do a weighted average analysis of the returns of each stock looking at the percentage of each stock that makes up your portfolio and you can actually calculate the weighted average return of your portfolio. This becomes interesting if in fact you note that your return on your portfolio or the risk is increasing or the return is decreasing. That's a good indication that it's time to rebalance your portfolio. Now before I leave this remember that we talk about investors. Excuse me. Individual investors having a portfolio. Well companies have a portfolio of investments as well. Think about a major firm. Some of the companies that I worked for that made investments in technology equipment marketing and advertising programs new product launches expansions of distribution networks entry into new. So companies can have a diversified portfolio of investments as well. And by the way they can also look at analyzing or reviewing what the average return of their portfolio is. And this is one way that companies that are actively involved in lots of projects look to diversify or increase their investments in one project over another. OK. So what applies to an individual certainly applies to a company just on a much larger more complicated scale. Now I mentioned in the beginning that there is a concept called risk premium. The risk premium says that we can if we identify what the market is returning. If we look at what our cost of capital is and remember we talked prior to this presentation about the weighted average cost of capital. That's what it costs the firm for the capital plan that they put together. I remember that's made up of two two components. One is debt. One is equity. Debt is money that we borrow from the lender that has a cost. And we know what that cost is. It's the interest on the debt. If we choose to use equity there's a cost to that equity even though shareholders have put money into the firm or the owner has put money into the firm to make investments. There's a cost to that and that cost is what the expected return is. So remember we talked about the fact that your investors can have investments in the overall market return. If the market is returning 7% to investors then we probably want to set our cost of equity at a minimum of 7%. That should be the least that an investor would expect to get from our firm and what we're doing. However again in a quest to ensure that we are always maximizing the return to owners and shareholders creating value in the firms that we're managing. I can put a risk premium and say that while the overall market is returning 7% we're going to only look at and invest in projects that have a return of 9%. We have a risk premium. We're looking to get projects that are returning better than the average return for our shareholders. This is a key as we consider our investment decisions. Remember when we talk about the cost of capital. That's a number that we very often use as the discount rate when we're discounting future cash flows. So let me drag future cash flows. We make an investment in a project. We forecasted that that's going to be a loop. I'm sorry. That last sentence I I lost you there. Like the zoom picked up and I lost the end of that last sentence. OK, so if we if we consider the cost of capital and we talked about discount rates. Remember we've got that concept of future cash flows. I invest in a new product because over the next five, six years, seven years, I'm expecting to get cash flow as a result of that. Well, that cash is in the future. Remember that we discounted future cash flows to bring it back to the present value and that discount rate is the cost of capital in those cases. OK. Now. If there's a risk premium, think about what happens for a second. If I'm discounting future cash flows by seven percent, I put on a risk premium of nine percent. That means that that present value of those future cash flows is now worth less. In effect, I'm really challenging the expectations of what's going to happen in the future. I'm going to make it more difficult. I want to really ensure that the return is going to be reasonable and meet the expectations of shareholders. And that's why we might use a risk premium. Now, the other way we consider a risk premium is as the company itself sits back and looks at an investment opportunity, we're making an assessment of how risky we think the project is. Now, some will not be as risky as others. I spent a great deal in my career, for example, working at United Technologies Carrier Air Conditioning Company, World's largest manufacturer of air conditioning and heating systems. Been around for a hundred years. Thousands of lines of products have been produced by this company. If we were looking at rolling out a next generation of home air conditioning, the risk of that not being successful is fairly understandable and fairly low. If on the other hand, as as a former vice president of marketing at Carrier, I said, I think we should roll out a line of computers, that would be very risky. Nobody would recognize Carrier Air Conditioning Company as a source of computers. Even if we had the technology, just the task of showing the market that this was a viable product would be extraordinary. So when a company looks at a potential new project and says, well, this might be a tad riskier than what we're used to do, again, they can add a risk premium. So when we calculate the discount rate we're going to use to evaluate future cash flows, we'll start out with the cost of capital and we will add a risk premium amount, 2%, 5%, 8%, reflecting how risky the investment is. If I bump up the discount rate to 8% and after evaluating future cash flows, I still have a positive NPV. And you all remember what net present value is from last week. If it's positive, we said we'd make the investment. Well, if I've really stressed the potential return and use that risk premium, and it's still positive, I'm becoming more sure that it might be a reasonable investment to make. Okay, now there's risk, there's all kinds of risks that we face in business. And one of the key things that any company must do is manage risk. So let's talk a little bit of about one where the risks might come from, and how we go about managing risks. As a former CEO of a company, I know that risk comes constantly and in many forms. There is risk about our pricing plans and product demand. We put together a program that says we can raise our prices to a certain extent for next year. Based on our research and our understanding of our customers, this will have little to no impact on sales. It's a big risk. And whether or not new price increases will be accepted by the market. Or even what the demand for a new product will be. If you're doing business across borders, as I did business in some 30 or 40 countries around the world, a key issue is currency exchange rates. We're constantly looking to forecast what the currency transaction costs will be, but it's a forecast. Anybody who deals in currency knows that currency rates go up and down every day. We have input costs. We go into the market and we talk a lot about preparing our strategic and business plan. We forecasted prepared proformas. Part of that was forecasting our expenses for next year. There's a risk that our forecast is wrong. There's a major impact. Suddenly there's a huge impact in increasing taxes. Or as we've seen around the world today, the cost and the impacts of the supply chain. So that's another risk that's a potential issue. We forecasted our net operating profit after taxes or notepad. We have an expectation. We set an expectation in the market about our profitability. Free cash flow. Businesses require free cash flow. That's having an adequate amount of cash to meet the day to day, week to week operating activities of the business. That to equity ratio, which we've talked about as the capital plan and we forecast what we expect to be our cost of debt and what our cost of equity will be. But there's a risk that those forecasts are off. Suppose there's a sudden increase in the cost of interest. Can have a major impact on the projects that we have and the projects we're looking to invest in. And of course there's interest rates, which we just talked about. Interest rates fluctuate like everything else. One of the things a firm will do is not only understand the interest they're paying today, but what's the potential interest in the future? Do we anticipate interest to go up or down during the next 12 months? This has an impact on decisions we're making and what we want to invest in. Now there's an opportunity here to manage this. Let me change it from opportunity to there's a requirement for management to manage risk. Risk impacts the value of the firm and the potential return to our shareholders. And remember that one of the roles of management is to constantly focus on increasing value, value of the business for the benefit of owners and shareholders. So if we can manage risk, doesn't mean we can control it, doesn't mean we can eliminate it. But if we're at least aware and we take some steps to manage risk, there are some benefits that accrue for that. One, if you really are managing your risk and you're in a reasonably good position, chances are you can use more debt. And the cost of that debt will be less.  Obviously, they do a credit review. And depending on your credit worthiness, will have an impact on the interest that you pay. The riskier you are on your financial base, the higher the interest rate will be. I mean, that's how the lender adjusts for their risk, the risk that you will default. Same thing applies to a business. If a business has a found financial base and is performing well, they can expect to negotiate lower interest rates that has an impact on the overall cost of capital. And so that means that you're in a better position to be able to develop that optimal capital plan that we talked about before. And remember that the optimal capital plan simply says that it's some percentage of debt and some percentage of equity. Given the cost of each, you've got the lowest overall cost of capital. And remember, we said we could actually determine that by varying the percentage of debt and the percentage of equity used in our capital plan. We do that and we zero in on the debt to equity ratio that will give us the lowest overall cost of capital. Typically, as a general rule, it's somewhere in the area of 60 40 debt to equity. But it varies by industry by time by the financial wellness of the firm. The some additional risks are that you can if you're if you're managing risk, you can maybe limit some of the risks that come from financial issues. I say avoid and it's possible, although after 30 semi years of experience, I've never been in a position where I was able to eliminate risks. But we do try very, very hard to limit that risk. And so on the financial issue, if we can, if we limit the impact of the risk of getting into financial difficulties, we can minimize potential impacts with suppliers who, for example, maybe we're allowing you to purchase goods and then they would send you a belt. Now we're looking for you to pay cash in advance. That's an impact on your business. If there's any indication that there are potential financial problems in the firm, they could have an impact on customers. And if you have financial difficulties, I can assure you that we are spending an exorbitant amount of management time dealing with the issues that arise from that. And as I mentioned before, there's the potential for reducing the cost of debt. Now, generally, here's a simple way to think about risk management. It's management of unforeseen events, which might have a negative impact on the firm's financial performance. Now, how's that for a vague definition of what it is? But remember, we're talking about things that could occur in the future. If they've already occurred, you're deep into the mess and you're dealing with it today. But what we're really thinking about from ownership and executive management is what's going to occur or what could occur. And we want to plan for that. So there are categories of risk. I'm going to list some. The list could probably be much larger. But for example, some of the areas of risk that a business will look to spend some time looking at will be financial risk. We talk about what some of those are financial risk of not receiving the expected return on investment, the financial risk of increasing interest rates, having an impact on a cost of capital, an increase in accounts receivable that's having an impact on our cash flow. So financial, anything financial that can impact the day-to-day operation of business. Property risk or the assets we have. We've just we're deciding to make an investment in a new plant because we believe that we're in a position to dramatically increase our sales and I need to produce more product. There's a risk in that decision. Personnel. Do I have the right people with the right skills to actually operate and manage the business? One thing that's interesting on personnel that I've noted as an avid reader of all things business is that companies are actually taking longer in the hiring process today. From the time we start the interview process to the time we offer someone a job, we're taking longer because we're recognizing how important it is to get the right people into our firm and people that we hope will be able to not only attract the right people but retain the right people. The environment. Lots of issues today on environment and being good stewards of the environment. Companies that have are associated with a negative impact on the environment. There's a huge risk associated with that today. Liability in all of its many forms. Product liability, personnel liability, business liability. Demand. I know as an executive in a company that was doing $3 billion a year, we spent an awful lot of time, money and resources forecasting what the demand for our products and services would be going forward. With all of that research and all of that time, I wish I could say that our forecast was always 100% right on. It wasn't. So there's a potential risk about how off of the forecast will you be. And competition. One thing that I've noted about competition over the last number of years is that competitors are coming more frequently and from more places. We're in a dynamic global competitive marketplace today. Good luck at trying to understand where that next competitor will come from. If I go back 30 years in my career, I could tell you who are cap six competitors were. And I was very familiar with the companies, their makeup, their locations, their products. Today, a competitor can come up that wasn't even on your radar the day before. So these are risks that firms have to deal with. So how do we do that? Well, there are some processes. There's a there's a system that we can use to manage risk. And let me give you four four point simple step by step way to do it. One, every business must identify all the potential risks that the firm might face. Now, this is a this is not an exercise in futility. In my organizations, we would sit there as we wrapped up the end of the year. We would look at what had taken place. We would try to see what we knew about going forward. And we would try to identify all those potential areas that posed a risk to us achieving the financial goals that we had set. Once you've identified all the risks, and by the way, this can be a pretty substantial list, then we have to go through and identify and quantify the degree of impact. I mean, not all risks are the same. And so certainly I want to look at what do I believe? What's the probability of a risk occurring? And how severe might that be as an impact to my to my business? So I can lay out a list and order. So maybe I at least start by looking at the top five risks, the one that have the biggest, largest potential impact in my business. And then the fun begins, because once you've done all that, and before you get depressed by looking at all the risks that your company faces, you can step back and start doing a risk mitigation strategy, which is just a business term for saying how do we reduce it? And so we typically would put together a plan or a business plan or strategy for each and every risk on that plan. That said, if this risk occurs, if this pops up, here's how we're going to go about approaching it. Now, why do we do that? We do that because you don't want to wait till you're faced with a crisis and then say, okay, so let's all get together now and talk about what we might do. The clock is ticking, folks. And so we plan in advance. We plan a preemptive strike. We have the list of projects that are on the shelf. And when risk number two pops up, we pull the plan off and we initiate the plan that we had talked about. Now, does this mean there's a perfect defense against risk? No. But it's certainly better than no defense against risk. And it's part of what management does, right? And it's dynamic. And by that, I mean that it's constantly changing. You can do your risk assessment at the beginning of the year. Does that mean you're all good till the next year? No. You're probably going to review that at least on a monthly basis or a quarterly basis because changes may need to be made. Alright, now, some simple potential actions that we can take when we identify at our risk in putting together our mitigation plans. Are some of these risks, can we offset the risk by purchasing insurance? There's a risk that if you're driving your car, you'll be in an accident. And you may be faced with a large bill to repair your car. How do I mitigate the risk of being faced with that large... I have auto insurance. Well, there's business insurance. There's business interruption insurance. There's flood insurance. There's disaster insurance. What kinds of insurance might the business be able to get to help with risk? Now, bear in mind, all of these plans come with a cost. So yes, I'm increasing cost. Also has to be taken into account in my financial risk. Let me give you an example of an insurance issue. Here in the U.S. for some period of time, going back a decade, CEOs of publicly traded companies who have a stated legal fiduciary responsibilities to shareholders to make decisions that are in their interest were potentially at risk of being sued by shareholders if decisions they made, they didn't exercise due diligence in making those decisions. Well, major corporations covered the executives for that risk with insurance policies. As a former CEO, my firm provided me with liability coverage in case of those kinds of suits. Now, the idea here being that if I was working in the best interests of shareholders and could demonstrate due diligence, then it was reasonable to try and protect protect executives from those kinds of suits. Are there certain activities that are risky for us that we could outsource? Outsourcing is commonly used today. And a matter of fact, we outsource on a global basis. Coming again from United Technologies Carrier, we had operations and facilities around the world. And we outsource production to major manufacturers around the world. Transactions and currency exchange rates. Well, again, as a global company with billions of dollars of foreign currency transactions taking place, we had an entire department in corporate finance that dealt with future contracts on currencies. So we would actually take positions in the future on what we thought currency might what the currency exchange rate might be on all the various currencies we did business in. Or maybe necessary for the firm to step back and reduce or eliminate high risk activities. Suppose you're involved in the man in a manufacturing process and the insurance company says, well, we can't ensure that that is too risky. Well, maybe that's an indication that the firm may want to either reduce that activity or eliminate it all together. Now, I've covered a lot of things on risk here. And so before I go much further and get into stocks, let me just stop for a moment and see if there are any questions. All right, well, I again, everyone, if you have any questions, leave them in chat. I we will we'll get to them. But I do have a question. And that's what I was thinking about the entire time. When we started, you said, you know, nothing's guaranteed. Don't put all your eggs in one basket. What would be like the the risk assessment for doing that? Right? Because the most efficient way would be to get your the person to have as big a basket they can and put as many eggs as possible in that basket, right? No, not as many eggs. Remember, by eggs in one basket, that means that if you have a dozen eggs in that basket and you drop it, what do you lose? All your eggs. But that's more efficient for us as a business. We have 12 but if he makes it, it's 12 eggs, right? But if you have a basket and in there you have 12 eggs, 12 oranges, five apples and two bananas. If you drop it, you'll lose the eggs, but you haven't lost your entire basket. And that's really what a diversified portfolio is. I could put on invest only in energy stocks. But if anything happens to the energy sector, the entire basket goes down. So instead to reduce the overall risk, I want to have some industry, some energy. I might want to have some consumer goods. I might want to have some technology. And that's the idea of not putting all your eggs in one bit. Mix the eggs, mix them with them. That's great. I might clip that out and do something with that answer. But I'm not seeing anything in the chat right now. But if anyone does have any questions, of course, leave them in the chat anytime. And if you're if you're watching later, leave it in the comments. I'll get to it sometime in the 24 hours stand after you. But we'll I'll hand it back over to you. We can we can go on. We're we're good, I think. Okay, great. By the way, that's a that's a good question, which students labor over every time it came up in in classes that I had, or talking with friends of mine who were investing and actually understanding that you can calculate the overall risk of a portfolio. If you want to get into all the math, I'll let you go to YouTube for that. But it is possible. But it's a great question and people labor with that who invest. Let's wrap up our discussion today with just a quick review of stock and I bring stocks into this because remember the the the stock price investors are investing in your company and they're getting a share of that business, right? If you're publicly traded, you're getting a stock. And that stock represents something for the business, it means that you've gotten some equity from investors. They've given you money. And remember they gave that to you. Why? Because they're hoping that you will take that money and invest in initiatives that will generate a return that is greater than what they would expect to get some place else. That's why they're investing in you. For the company, the stock is a source of equity. Remember our capital plan is made up of debt and equity. So welcome to equity. So we're we're looking for folks to invest in our business as a means of funding future growth and investment activities. Typically, there are in a publicly traded company, there's two kinds of stock. One is preferred and one is common. Now, preferred stock is interesting at preferred stock goes to certain individuals who invested a large sum of money in the business. They have no voting rights. So preferred shareholders do not get the vote at the annual board meeting. They don't get to vote for the board of directors. But they do have a guaranteed dividend. So as a preferred stockholder, I put my money into the firm. I invested. They have guaranteed me a 5% dividend per year on the money that I've invested. That's guaranteed. And a couple of interesting things happen with preferred shareholders. One, in the case of default, if the company goes bankrupt, the people at the top of the list to benefit from the liquidation of the firm are preferred shareholders. We go first. The other thing that happens is the dividend is not only guaranteed, but let's suppose the company is currently in some financial difficulties. We don't have the cash available to pay those preferred dividends. That means that nobody gets paid dividends.  Now, more commonly is common stock. That's stock that's bought over any of the major international stock exchanges. I go in and I buy a share of stock in a company. Now, there's no guarantee of a dividend on my share of stock. As a matter of fact, there's no guarantee of a return on that share of stock. In terms of bankruptcy, if I'm a common shareholder, I go to the bottom of the pile. So after preferred shareholders and debt holders and people the firm owns, but once that's all paid, if there's only money left over, it goes to the common stockholder. So what's the attraction here? Well, attraction is one, I can now I do have voting rights. So as a shareholder at the annual shareholders meeting, I get to vote my shares of stock. Now, if I own two shares of stock, my vote might not count much. But when you consider the fact that you have institutional investors, for example, anybody here who belongs to a as a retirement fund from a union or a job position, those retirement funds invest a certain amount of their money in the stock market. They vote lots of shares of stock. And so they can actually have an impact on decisions that the board of directors is making for the direction of the firm. They have impact on selecting the officers of the board of directors. So they can they can become very engaged. And over the last number of years, I think I can say that shareholders have become a much more involved group than they were 30 or 40 years ago. Shareholders today tend to be much better informed. They're watching businesses, they're looking at financial reports, they're looking at the market. And they're making much better informed decisions. And that's a key to remember as a president and CEO of a company recognizing my responsibility to them. Now, the other thing that sharehold that shares do is we look at the share price because it's an indicator. It tells us something. Remember that if I look at what the value of the actual value of a share of stock today in terms of dollars and cents is the book value of the company. We've talked about that in the past off the balance sheet. If I take all the firm's assets and I turn them into cash, I liquidate all the assets. I pay off all the liabilities. If there's a pool of money left, that's shareholders equity that belongs to the shareholders. Now, let's just say that that equity was $100. The company has one shareholder. It's me. I have one share of stock. So the value of that share of stock is $100. Now, that's the book value divided by the number of shares of stock that are out there. Shares outstanding. That's how you look at what the book value is. But that's not necessarily what the selling price is. If you go to the market, we'll find that stocks can have a price that is greater than or less than what the book value of that share is. And so what does that tell you? It's the market telling us something. The market is looking at your firm. They're looking at your past performance. They're looking at your financial plans. They're looking at how well you're performing financially. And they're making some determinations. They're saying we're happy with that performance. And so we're willing to pay a little bit more than the book value of that price of stock, because we think it is a good investment depending on how you define good. If in fact the market's looking at a company, looking at what you've done over the last number of years, and they see an expectation that you will continue and perhaps even grow more in the future, what do you suppose happens to the price of that share of stock? It goes up. And so what is the market doing? They're pricing the returns on that business looking forward. So it's a forward view of what's happening. If a share of stock is selling ed book or less, then the market is either one not terribly interested in what you're doing or concerned. And one might expect to see people selling their shares of stock. All right. So there's the stock market as an executive of a publicly traded company. I can assure you that I monitored the stock market. I monitored what the overall market was doing. I was keenly interested in what all my major competitors were doing, how my industry sector was performing. And of course, how we were doing compared to that, recognizing that that's one way of judging how good the decisions I was making are. Now, another thing that shareholders will look for when they invest in stock is whether or not that stock pays a dividend.  Some stocks pay no dividends. But what is a dividend? A dividend says that at the end of the year, if you go back to our first two videos on this course, we talked about the income statements, the financial package and what it said. Well, the bottom line of the income statement was net profit. After all the expenses were paid, how much money was left over? That's net profit. And remember that the business has a decision to make at that point. Let's suppose that that net profit is a million dollars. What do I do with it? Technically that million dollars belongs to the shareholders. I could return it all. The problem with that is then there won't be any money on day one of the new year. So we retain some of that money for continuing operations. And remember what we called that, retained earnings. So if I retain some of those earnings, I don't have to retain all of it necessarily. If I retain some, then what do I do with the balance of that? One thing to do with that is to pay dividends to shareholders. Now, this is so important that as an executive of a publicly traded company with shareholders, we actually planned in our business plan and as part of our pro forma statements that we would project that we needed to earn so much money above retained earnings so that we in fact could pay our shareholders dividends. So as somebody buying a share of stock, I might be interested in one, are dividends being paid yes or no? Two, if they're being paid, how often are they being paid? And three, are these dividends, can I anticipate that the dividends will actually increase year over year, which some companies strive to do? Those all impact investment decisions, your shareholders return on value, and how much equity the firm has to invest. Now, that's probably more than enough to keep everybody busy for today's lecture. Next week, we're going to go on to unit five in our course, and we're going to talk about managing capital, a key responsibility for the management of any business, and managing capital is a key responsibility for anybody that has a household. So with that, I'm going to turn it back to Michael and see if there's any questions so far. Um, there are no questions right now. But again, if anyone has a question, I'll do the thing I do where I talk a lot and give you time to do it. Um, thank you for joining us. Um, again, we'll be back next week, as said, if you haven't caught any of our videos before there, uh, linked below. And of course, this is supplemental material for, uh, Sailor Academy's course. So again, that's linked in the description below. If you'd like to like to do that. Um, but I of course, just like to, uh, thank Dr. Pearson for taking us through this. I'd like to thank everyone watching now, everyone watching later. Um, hopefully, uh, me fixing my voice hasn't made the videos worse for you guys. Um, um, uh, but I'm, uh, I'm looking here. I don't, I don't see anyone, um, having any questions right now. But, um, yeah, I think, I think, uh, I think we're just, we'll call it for now. It's, it's been a long one. You guys, you guys can, uh, you know, think about what we talked about. If you have any questions, leave them in the comments and we can talk about them next week, I think. But, uh, thank you everyone again. Again, thank you, Dr. Pearson, uh, as always, uh, for, for taking us through this. Thank you, Michael. Take care, everyone. All right. Bye, everybody.


From around the globe, it's theCUBE. Covering HPE Discover Virtual Experience, brought to you by HPE. Official intelligence, Monica Livingston. Hey, Monica, welcome to theCUBE. Hi, Lisa, thank you for having me. So AI is a big topic, but let's start just understanding Intel's approach to artificial intelligence. Yeah, so at Intel, we look at AI as a workload and a tool that is becoming ubiquitous across all of our compute solutions. We have customers that are using AI in the cloud, in the data center, at the edge. So our goal is to infuse as much performance as we can for AI into our base platform. And then where acceleration is needed, we have accelerator solutions for those particular areas. An example of where we are infusing AI performance into our base platform is the Intel Deep Learning, boost feature set, sorry, the Intel Deep Learning Boost feature set, which is in our second generation Intel Xeon scalable processors. And this feature alone provides up to 30X performance improvement for deep learning inference on the CPU over the previous generation. And we are continuing infusing AI into our base platform with the third generation Intel Xeon scalable processors, which are launching later this month. Intel will continue that leadership by including support for B Float 16. B Float 16 is a new format that enables deep learning training with similar accuracy, but essentially using less data. So it increases AI throughput. Another example is memory. So both inference and training require quite a bit of memory and with Intel Optane persistent memory, customers are able to expand large pool of memory closer to the CPU. And where that's particularly relevant is in areas where data sets are large, like imaging with lots of images and lots of high resolution images, like medical diagnostic or seismic imaging. We are able to perform some of these models without tiling. And tiling is where if you are memory constrained, you essentially have to take that picture and chop it up in little pieces and process each piece and then stitch it back together at the end, whereas that loses a lot of context for the AI model. So if you're able to process that entire picture, then you are getting a much better result that is the benefit of having that memory accessible to the compute. So when you are buying the latest and greatest HPE servers, you will have built-in AI performance with Intel Xeon scalable and Optane persistent memory. A couple of things that you said in there that piqued my memory or my interest or a 30X improvement in performance. Do you talk about that with respect to the deep learning booster? 30X is a huge factor. And you also said that your solution from a memory perspective doesn't require tiling. And I heard context. Context is key to have context to the data to be able to understand and interpret and make inferences. So talk to me about some of those big changes that you're releasing. What were some of the customer compelling events or maybe industry opportunities that drove Intel to make such huge performance gains in second generation? Right, so second generation is, these are the processors that are out now. So these are features that our customers are using today. Third generation is coming out this month. But for second generation and deep learning boost, what's really important is the software optimization and the fact that we're able to use the hooks that we built into the hardware, but then use software to make sure that we are optimizing performance on those platforms. And it's extremely relevant to talk about software in the AI space because AI solutions can get super expensive. You can easily pay two to three X what you should be paying if you don't have optimized software. Because then what you do is you're just throwing more and more compute and more and more hardware at the problem, but it's not optimized. And so what's really impactful is being able to run a vast number of AI applications on your base platform that essentially means that you can run that in a mixed workload environment together with your other applications and you're not standing up separate infrastructure. Now, of course, there will be some applications that do need separate infrastructure that do need appliances and accelerators. And for that, we will have a host of accelerators via FPGAs today for real-time low-latency inference. We have Armavidius VPU for low-power vision applications at the edge, but by and large, if you're looking at classical machine learning, if you're looking at analytics, deep learning inference, that can run on a base platform today. And I think that's what's important in ensuring that more and more customers are able to run AI at scale. It's not just a matter of running a POC in a back lab. You do that on the infrastructure that you have available, not an issue, but when you are looking to scale, the cost is going to be significantly important. And that's why it's important for us to make sure that we are building in as much performance as it's feasible into the base platform and then offering software tools to allow our customers to see that performance. Okay, so talking about the technology components, performance, memory, what's needed to scale on the technology side, we want to then kind of look at the business side because we know a lot of customers in any industry undertake AI projects and they run into pitfalls where they don't, they're not able to even get off the ground. So, conversed to the technology side, what is it that you're seeing, what are the pitfalls that customers can avoid on the business side to get these AI projects designed and launched? Yeah, so on the business side, I mean, you really have to start with a very solid business plan for why you're doing AI. And it's even less about just the AI piece, but you have to have a very solid business plan for your solution as a whole. If you're doing AI just to do AI because you saw that it's a top trend for 2020, so you must do AI, that's likely going to not result in success. You have to make sure that you're understanding why you're doing AI. If you have a workload that could be easily solved or a problem that could be easily solved with data analytics, use data analytics. AI should be used where appropriate and where to provide true benefit. And I think if you can demonstrate that, you're a long way in getting your project off the ground. And then there's several other pitfalls like data, do you have enough data? Is it close enough to your compute in order to be accessible and feasible? Do you have the resources that are skilled in AI that can get your solution off the ground? Do you have a plan for what to do after you've deployed your solution because these models need to be maintained on a regular basis? So some sort of a maintenance program needs to be in place. And then infrastructure. Costs can be prohibitive a lot of times if you're not able to leverage a good amount of your base infrastructure. And that's really where we spend a lot of time with customers in trying to understand what their model is trying to do and can they use their base infrastructure? Can they reuse as much of what they have? What is their current utilization? Do they maybe have cycles in off times if their utilization is diurnal and during the night they have lower utilization? Can you train your models at night rather than putting up a whole new set of infrastructure that likely will not be approved by management? Let's be honest. And I imagine that that is all part of the joint go-to-market strategy that HPE and Intel have together to have such conversations like that with customers to help really build a robust business plan. Yeah, so HPE is fantastic at consulting with customers from beginning to end looking at solutions and they've got a whole suite of storage solutions as well which are crucial for AI. And Intel works together with HPE to create reference architectures for AI and then we do joint training as well. But yes, talking to your HPE rep and leveraging your ecosystem I think is incredibly important because the ecosystem is so diverse and there are a lot of resources available from ISVs to hardware providers to consulting companies that are able to support with AI. So Monica, the ecosystem is incredibly important but how do you work with customers, HPE and Intel together to help a customer, whether it's in biotech or manufacturing to build an ecosystem of partnership that can help the customer really define the business plan of what they want to do to get that cross-functional collaboration and buy-in and support and launch a successful AI project? Yeah, it really does take a village but both Intel and HPE have an extensive partner network these are partners that we work with to optimize their solution. In HPE's case, they validate their solutions on HPE hardware to ensure that it runs smoothly and for our customers, we have the ability to match make with partners in the ecosystem and generally the way it works is in specific segments we have a list of partners that we can draw from and we introduce those to the customer the customer generally has a couple of meetings with them to see which one is a better fit and then they go from there but essentially it is just making sure that solutions are validated and optimized and then giving our customers a choice of which partners are the best fit for them. Last question for you, Monica. We are in the middle of COVID-19 and we see things on the news every day about contact tracing, for example, social distancing and a lot of the things that are talked about on the news are human contact tracers, people being involved in manual processes. What are some of the opportunities that you see for AI to really help drive some of these because time is of the essence yet there's the ethics issue with AI, right? Yes, yes, and the ethics issue is not something that AI can solve on its own. Unfortunately, the ethics conversation is something that we need to have broader as a society and from a privacy perspective how are we going to be mindful and respectful while also being able to use some of the data to protect society, especially in a situation like this? So contact tracing is extremely important. This is something that in areas that have a wide system of cameras installed, it's something that is doable from an algorithmic perspective and there are several partners of ours that are looking at that and actually the technology itself, I don't think is as insurmountable as the logistical aspect and the privacy and the ethical aspect and regulation around it and making sure that it's not used for the wrong purposes but certainly with COVID, there is a new aspect of AI use cases and contact tracing is obviously one of them. The others that we are seeing is essentially companies are adapting a lot of their existing AI solutions or solutions that use AI to accommodate or to account for COVID, like companies that have surveillance systems and so if they were doing facial recognition either in metro stations or stadiums or banks, they now are adding features to their systems to detect social distancing, for example, or detect if somebody is wearing a mask. The technology again itself is not that difficult but in the implementation and the use and the governance around it I think is a lot more complex and then I would be remiss not to mention remote learning which is huge now. I think all of our children are learning remote at this point and being able to use AI in curriculums and being able to really pinpoint where a child is having a hard time understanding a concept and then giving them more support in that area is definitely something that our partners are looking at and it's something that I see with my children and the tools that they're using. So instead of reading to their teacher for their reading test, they're reading to their computer and the computer is able to pinpoint some very specific issues that maybe a teacher would not see as easily and then of course the teacher has the ability to go back through and listen and make sure that there weren't any issues with dialects or anything like that. So it's really just an interesting reinforcement of the teacher student learning with the added algorithm impact as well. Right, a lot of opportunity is going to come out of COVID, maybe more accelerated than others because as you mentioned, it's very complex. Monica, I wish we had more time. This has been a really fascinating conversation about what Intel and HPE are doing with respect to AI. We'll have to have you back as this topic is just too big but we thank you so much for your time. Thank you. For my guest, Monica Livingston, I'm Lisa Martin. You're watching theCUBE's coverage of HPE Discover 2020. Thanks for watching.


So, through the numerical examples, we saw that limit p n p is a transition matrix. So, the nth power as n goes to infinity, if this exists, if the limit exists, then it converges to a matrix with all rows identical. Whatever 2-3 examples we considered, we saw that the limit existed and then we saw that the rows were becoming identical as we increase the power value of n. That means, we continue taking higher powers of p. So, we can easily show that in case limit p n exists, limit p n as n goes to infinity, if this limit exists, this will always be the case. That means, whenever this limit exists, then this will converge to a matrix whose rows are all identical. So, let us show this immediately very easily. So, limit p n, suppose n goes to infinity is, so q 1 is a row q 2 q k. Suppose, these are k rows, we are considering the system when it has k states, k possible states. So, then I can write limit p n as n goes to infinity as limit p n minus 1 into p as n goes to infinity. Then as as goes to infinity, this and this have the same value. So, this is the same matrix, they will converge to the same matrix. So, this will be q 1 q 2 q k is equal to q 1 q 2 q k p. So, this reduces to the limiting case, this reduces to the system. And from here, you can say that q i, the i th row here would be the i th row multiplied by p, post-multiplied by p. So, this is it for all i. And hence, you can see that all rows of p are, I should not say of p, what I want to say is that, if converges to p is your transition matrix. So, all rows of p raise to n will converge to. So, all rows of limit p n, I should write here, limit p n as n goes to infinity are identical. Now, if you want to solve for this, we can see that immediately. See, you know that the rows of p, the rows of p have the property because it is a transition matrix. So, all rows add up to 1. And therefore, this is not a non-singular matrix. And so here, you will have infinite solutions. To this system, you will have infinite solutions. But then, if you also require the elements of q i to be non-negative and they add up to 1. That means, we are looking for a solution, where the q i is the elements of q i form probabilities. Then, this will be a unique solution. I will denote the solution by q i is equal to pi 1, pi 2, pi k. And these will be known as the steady state probabilities. So, that means, when the system has in a steady state that means, it has gone on for a long time, it settles to a steady state. Then, the probability of being in state 1 is pi 1, probability of being in state 2 is pi 2 and up to pi k. So, this is the whole idea. And now, we will come up with a method of obtaining these values pi 1, pi 2, pi k, the steady state probabilities. So, now, let us evolve a method for computing the pi i's, the steady state probabilities. See, p n can be written as p n minus 1 into p, the nth power of the transition matrix. So, then, if I take limit on both sides, then this is limit p n and n goes to infinity and this is limit p n minus 1 and goes to infinity into p. Now, as we said, since we have assumed that the pi i's exist and so, each row of p n in the limiting value would be pi 1, pi 2, pi k. So, all the rows are identical. Therefore, on this side also, you get the matrix pi 1, pi 2, pi k, pi 1, pi 2, pi k and so on. Similarly, p n minus 1 will also converge to the same matrix and this times p. So, the limiting behavior, I can just break up this in this way and then do it and so, if this is going to the limit in the limiting value to this matrix, this will also go to the same matrix and therefore, you have these equations. Now, this system, actually, since all the rows are identical, so actually, these k equations reduce to. So, now, I am, so far, I was talking about three state processes. So, now, let me just do this much in three state for the general case and then we will come back when we want to talk of specific values and examples. We will again revert back to the three state example that we have been talking about. So, let us just talk about it in general and therefore, the system reduces to k equations. That means, I can simply just equate the first row here to the first row here. So, that means, pi 1 to pi k is equal to pi 1 to pi k times the matrix p. And now, let us write out the equations in detail here. So, pi 1, the first component here will be this multiplied by the first column of p. So, the first column p is p. So, pi 1, p 1, 1 plus pi 2, p 2, 1 and so on plus pi k, p k 1. Similarly, equate the second component here element to the second element. That means, this multiplied by the second column of p. So, that gives us this. And finally, the k-th equation is pi k is equal to pi 1, p 1 k. So, the k-th column we will take when we equate pi k with this multiplied by the k-th column. So, I have these k equations. But you can immediately see that these k equations are not linearly independent since sigma p i j, j varying from 1 to k is equal to 1. So, let us just quickly check this that all the equations that see essentially what I am saying is that your first k minus 1 equations will give you the k-th equation. So, therefore, those of you who are familiar with the word rank. So, the rank of this matrix is k minus 1 or you want to show that. So, let us add the first k minus 1 equations here. So, it will be pi 1 plus pi 2 plus pi k minus 1 and this is equal to. So, when you are adding the first k.  So, it will be pi 1 into summation p 1 j, j varying from 1 to k minus 1. And similarly, pi k into summation j varying from 1 to k minus 1 p k j. Now, since the rows add up to for the transition matrix, we have put that I mean we know this that these rows of the transition matrix will always add up to 1. So, therefore, sigma j varying from 1 to k minus 1 p 1 j is actually 1 minus p 1 k. Because this plus p 1 k is 1. So, therefore, this sum is equal to 1 minus p 1 k and similarly, I substitute for all of these sums by. So, this one will be 1 minus p k k. And now you see that when you open up the bracket. So, pi 1 plus pi 2 plus pi k. So, pi 1 plus pi 2 plus pi k minus 1 cancels out, you are left with pi k. And the other things you transfer to the side, then you immediately get pi 1 p 1 k plus pi 2 p 2 k and pi k. So, this is your kth equation. So, because the probabilities of the rows sum up to 1, therefore, these k equations are not linearly independent. So, in fact, the first k or any k minus 1 will lead you to the kth one essentially. Because here, I just chose the first k minus 1, you can choose any k minus 1 and you will be able to obtain the remaining one by adding the k minus 1 equations you have chosen. So, therefore, infinite solutions because the matrix is singular, the equation matrix is singular. And therefore, but when you impose the condition, because since we are looking for these steady state probabilities and they must add up to 1, pi 1 plus pi 2 plus pi k has to be 1. Because the system will be occupying one of the states, either 1, 2 or k. So, when you impose the condition that pi 1 plus pi 2 plus pi k is 1, then you get a unique solution. And so this is therefore, we have a very neat way of computing these steady state probabilities and we know that we have a unique solution. So, you cannot say that the probability of the long run probability of being in a particular state of the system, the probabilities are more than 1. That would not be a reasonable solution. So, now let us go back to your job assignment problem and let us try to obtain. Because I was trying to get you the, have a look at the steady state probabilities by taking the powers of p, but now here let us have this seems to be a quicker way of and a neater way of solving the, trying to get the pi's. So, because in the, when you are taking the powers, you really do not know when to stop. Or in fact, you would have to go on doing it till you see that the values are really closing in. So, therefore, this would be a better way to get your steady state probabilities. And so the three equations you see, you can see from pi 1, your, this thing, p 1, 2 is, no, no, when you are writing the equation, yeah, p 2, 1 is 0. So, here you get, yeah, the matrix is there in your earlier lectures. So, these are the three equations essentially, right, for solving pi 1, pi 1, pi 2, pi 3. So, therefore, I can, from this equation I immediately get. So, the trick would be that since, you know, I do not get a unique solution to this system. So, I will solve for pi 1 and pi 2 in terms of pi 3 and then I will apply the condition that the sum is equal to 1 to get the value of pi 3 and then I will get all the values. So, from here you see, you immediately see that half of pi 1 is 3 by 4 pi 3. So, that gives you that, yeah, where is pi 1? Yeah, half of pi 1 is 3 by 4 pi 3. So, pi 1 is 3 by 2 pi 2, right, 3 by 2 pi 3, right. And then you can substitute here for pi 1 in terms of pi 3 to get your pi 2. So, pi 2 comes out to be 5 by 4 pi 3, because this is half pi 2 and this is pi 3 minus 1 by 4 into 3 by 2 pi 3. So, which makes it 3 by 8. So, 5 by 8 pi 3, therefore, pi 2 is 5 by 4 pi 3. So, now, I substitute the values pi 1 is 3 by 2 pi 3, this is 5 by 4, 5 by 4 pi 3 and this is 1. So, therefore, how much is this? I suppose I will have to redo this thing or maybe this was right, yeah, I do not know, yeah. So, what is it? This will be 6 plus 5 plus 4. So, the value was ok. This was a mistake here, but the value at computed was ok. So, this is this, right. So, therefore, your pi 3 pi 3 is 4 by 15. And so, this gives you pi 2 equal to 5 by 4 into 4 by 15, right, by the value of pi 3. So, that makes it 1 by 3. And pi 1 would be pi 1 is 3 by 2. So, 3 by 2 into 4 by 15 which is this and 3 by 5. So, pi 1 is 2 by 5. And now, let us compare these values with what we had obtained by taking powers of P. So, our pi 1 had come out to be something because 2 values are 1 0 2 upon 256 and the other one was 1 0 3 upon 256. So, you see 2 by 5 does lie between these 2 numbers. So, this was up to 4th power, right. And when you take the 5th and 6th powers, you will see that the values will get closer and you will actually reach 2 by 5, right. Similarly, your pi 1 is 1 by 3 and this is also a number lying between 85 upon 256 and 86 upon 256, right. You can compare, right. This is between. So, 1 by 3 lies between these 2. And similarly, 4 by 15 is a number which is between 68 by 256 and 69 by 256. So, the 2 things match, but certainly that is a much better quicker way of obtaining your steady state probabilities. Now, these steady state probabilities have very useful interpretations and we will continue seeing through examples drawn when we analyze the process further. So, essentially what we have said is that pi i is the probability that in distant future, one will find the system in state i. So, the probability that your process will be that means, a particular employee in the automobile manufacturing company, that particular employee will be in let us say HR, when you know after the process has gone on for let us say 4 or 4 years of 5 years, we expect the percent, the probability that the employee would be in the HR division is 1 by 3 or the probability that he will be with sales is 4 by 15, right. So, these are the long term probabilities and as we said that the initial, that means the division or the section in which he started his career is irrelevant here, right. Then you can also interpret this as the fraction of time, the system occupies state j, fraction of time, the system is occupying the state j, okay. I am writing pi i, so it should be pi i here, sorry, this is i. So, the fraction of time, the system occupies state i, right. Now, if you run many identical processes simultaneously, then you see the pi j would come out to be the fraction of processes that you would find in state j, that means if you suppose run 100 identical processes simultaneously and you find out that that is is maybe 45 of the processes are at that particular time. Of course, you let the processes run for a long time and then after certain, at particular period time, you just find out how many of these processes are occupying state j. So, if that comes out to be 45, then your pi j would be, pi j would be approximately 45 upon 100. That will be the fraction of processes that you would find in state j. And another interesting interpretation of the pi j is, you know, it is the reciprocal of the mean number of transitions between recurrence of state j. So, this recurrence I will define formally after some time, which is also very important. So, what we are saying is that this is the reciprocal of the mean number of transitions. So, on the average, how many transitions you would be required to go from state j to j. Now, recurrence means for the first time, that means you are in state j to start off and then for the first time when you revisit j. So, that number of transitions, if you take the average of such transitions, then the reciprocal of that is your pi j. And this also we will derive in another way and of course, this part we will prove later on. So, for example, what we are saying is that since pi 2 is 1 by 3 and pi 2 is our HR section. So, we are saying on the average, three transitions will be required for this particular employee to go from HR to HR. That means if he starts his career with HR, Human Resource Section, then he will after 3, on the average, he would be requiring three transitions to get back to HR. So, this is the so many interpretations that we have, we can give and then we will see how we make use of these steady state probabilities to analyze these processes further. So, let us now, I have taken this example from again Ravindran Phillips and Solberg. So, interesting physical interpretation of state probabilities. So, what he is saying is that in the job assignment problem, you would consider the three states as three reservoirs. So, node 1 and node 2 and node 3 they are reservoirs and the arcs connecting the nodes are the pipes through which liquid can flow with valves to ensure that flow goes in the direction in which the arrows are there. For example, there will be a valve here which will direct the flow from 1 to 3 only and another valve which will direct the flow from 1 to 2 and then another valve which will just direct the flow from 1 to 1. So, this is the idea. So, just think of this as representing a reservoir with these pipes connecting them with the reservoirs and then the valves to ensure that the flow goes in the direction in which the arrows are there. And then the probabilities Pijs that means for example, the probability 1, 4 associated 1, 2 would be the fraction of the liquid that is there in 1 in reservoir 1 which will be sent to 2. Similarly, if you look at 2 to 3 then it is the half the liquid which is there in reservoir 2 will be sent to from 2 to 3 and so on. So, these probabilities then can be interpreted as the fraction of a liquid in reservoir. So, Pij is the fraction of the liquid in reservoir i that will pass to reservoir j in 1 unit time. So, it will take 1 unit of time for the flow that means half the flow from here to here in 1 unit of time will go from 2 to 3 because the probability is half. So, if we think of the system made like this then what you do is you pour 1 unit of liquid into the system according to these initial probabilities that means 1 fourth of the liquid is put in reservoir 1, 1 fourth is put in reservoir 2 and half the liquid is put in reservoir 3. And then the liquid is allowed to flow according to this plan and then what we are saying is the dynamic equilibrium. So, what we have discussed that the probabilities will converge and they will become irrespective of how much liquid was initially poured into the reservoirs. So, finally, dynamic equilibrium will be attained and liquid will continue to flow, but the liquid in each reservoir will equal the steady state probabilities. So, our steady state probabilities I do not have the numbers here, but whatever we had computed pi 1, pi 2, pi 3 as. So, for example, I remember pi 2 was 1 by 3. So, pi 2 would be the that means reservoir 2 will have one third of the liquid and then pi 1 would represent the amount of liquid that is in reservoir 1 and pi 3 will be the amount of liquid present in reservoir 3. So, this is the interesting part and so what is being said is that actually equilibrium will be attained and the liquid will continue to flow according to this plan, but each reservoir will settle down to even though the starting amounts were this, each reservoir will settle down to the amount of liquid according to these steady state probabilities. And what do we mean by so equilibrium means that for each reservoir the flow out will be equal to the flow in. Then only the whatever there is the liquid is there steady state liquid that is there in the reservoir will be maintained, which is according to your pi 1, pi 2, pi 3. So, flow out from reservoir I would be so the probability that you are in reservoir I into then pi j summation over j. So, from I it can go to reservoir 1 to 2 to 3. So, this is the probability that the amount liquid flow out from reservoir I and the amount and this you can when you are summing up you are summing up with respect to j. So, pi i can come out and this will be sigma j pi j, but sigma j pi j is 1 all these probabilities and the i th row will add up to 1. So, this is pi i and the flow in from other reservoirs that the flow is coming in. So, that will be pi k into p k i the flow is coming from the k th reservoir to the i th reservoir. And so then this is the probability of being in the k th reservoir. So, this is sigma pi k p k well I am talking of probabilities, but here we are saying this is the amount that is there in the k th reservoir. And so this is the fraction which is going to i. So, I should actually interpret the whole thing in terms of this particular example. So, here also I should not refer to pi i as the probability of being in i, but this is the amount of liquid that is there in the i th reservoir and the p i j fraction of this liquid is being sent to the j th reservoir. So, therefore, flow out. So, from the i th reservoir this much is the liquid and from this these are the fractions of this liquid which are being sent to different reservoirs. So, this is the flow out and this is the flow in. So, please just interpret it this way ignore my earlier remark. So, this is sigma pi k p k i and so the 2 must be equal and therefore, you again get these if you do it for all i then you will immediately get this equation pi is equal to pi p. So, I thought this was the interesting way of looking at the steady state probabilities and some of these will fix certain ideas in your mind. Then, another example from Sheldon Ross that I want to because I really want to spend time on these steady state probabilities. So, that you get the ideas you know understand them properly. Now, here this is an example where it is a production system and these are the probabilities of transition probabilities. So, we have 4 states 1, 2 and 3, 4. Now, the states 1 and 2 are considered as acceptable or you can say when the system is up and 3, 4 are not acceptable which you have to interpret as your system is down. That means there is a breakdown the machines are not functioning. So, there are 4 states and this is your transition matrix from state i to state j and questions to be answered. Now, the questions that we want to answer are the rate at which the production process goes from up to down that means rate of breakdown. So, when it is up that means when the machines are working and then there is a breakdown. So, you want to know the rate at which the process the production process goes from up to down and another question will be the average length of time the process remains down. That is also very important because you want to know with this kind of transition matrix you want to know for how long the process will remain and of course, you always talk in terms of average length of time the process remains down when it goes down. So, when there is a breakdown for how long will it remain in that state before it comes up, but now the new thing is that you have two states which are describing the up situation and two states which are describing the down situation. So, therefore, I took up this example to again show you of course, we will compute the pi i's and then I will show you the how to compute answer this and there are many more questions that have to be answered. So, the third question you want to answer is the average length of time the process remains up when it goes up. So, these are three questions we will try to answer by computing these steady state probabilities. So, we write down the equations for finding the steady state probabilities. So, pi 1 is equal to this pi 1, pi 2, pi 3 times the first column. So, you get this equation then pi 2. So, you can just by looking at the transition matrix P then you can see that these are the four equations that we will obtain. Now, interestingly the second column here is all 1 by 4, 1 by 4, 1 by 4, 1 by 4. So, when you write the second equation this you immediately get the solution for pi 2 because all these add up to 1. The steady state probabilities have to add up to 1. So, this immediately comes out that pi 2 is equal to 1 by 4. So, I have used it already here and now since I have the value of pi 2 I should be able to immediately compute the values of pi 1, pi 2 and pi 3. So, what I do is here that is not I have to now after having got pi 2, I can now see from here even here. So, I thought that it was immediate that you could compute after you have pi 2 then yes see here you see that is where 1 has to be little clever and use inspection. So, here this is pi 1, pi 3 and pi 4 and again the coefficients are 1 by 4. So, this I can write as 1 by 4 into 1 minus pi 2 see and I have the value of pi 2 already as 1 by 4. So, this again immediately gives me pi 1 as 1 minus 1 by 4 is 3 by 4 into 1 by 4. So, 3 by 16. So, your pi 1 is 3 by 16. Now, I have the values of pi 1 and pi 2. So, then from here I can immediately get pi 3 because bring this here. So, this will be 3 by 4 pi 3 and I substitute the values of pi 1 and pi 2. So, this will be 1 by 2 into 3 by 16 plus 1 by 2 into 1 by 4 that gives me 7 by 32. So, pi 3 will be when you multiply by 4 by 3 gives you 7 by 24 and then once you have you now have pi 2 pi 3 and pi 4 is on this side when you bring it it will be half pi 4 and so again substituting for pi 2 and pi 3 you get these values and so you get pi 4. So, this was quick work. Now, this is certainly faster than computing second, third, fourth powers of P which is a 4 by 4 matrix. So, lot of multiplications if you start taking the different powers. Now, let us try to answer the questions rate of breakdown. So, rate of breakdown is a transition probability of transitioning from up to down. That means, up means when your machines are working or any one of the machines is working and then any one breakdown will mean there is a breakdown. So, that means, you are transitioning from up 1 and 2 which are up states to the down states which are 3 and 4. So, that means, you want to say that if you are in state 1 so that is a probability into your transition from 1 to 3 or 1 to 4. So, that is P 1 3 plus P 1 4 and if you are in state 2 then the transitioning from up to down is 2 3 plus 2 4 P 2 3 plus P 2 4. So, we have all these numbers for the probability of rate of breakdown will be 9 by 3 2 because any one of the breakdown say this means you are going from up to down. So, any one breakdown or two breakdown whatever it is the probability is 9 by 32 and that is your rate of breakdown. Now, you want to answer the second question which is the average length of time. The average length of time the process remains down when it goes down and the other one is the average length of time it is up when it goes up. So, both the things. So, let us define u bar as the average time the system is up and d bar is the average time the system is down. Then your rate of breakdown is now we are redefining or talking in now. So, then we will make the equations and then try to find out u bar and d bar this is the idea. So, rate of breakdown is 1 upon u bar plus d bar because you know see this is the average time it is up and average time it is down. So, one breakdown at the rate of 1 upon u bar plus d bar because this is the total time and it is up and then down average time. So, therefore, 1 upon this will give you the rate of breakdown because 1 breakdown for this much period 1 breakdown for this much period and therefore, the rate is 1 upon u bar plus d bar.  Now, let us try to find out. So, the definition of u bar will be pi 1 plus pi 2 this is because this is the you are either in state 1 or in state 2 that is when it is up. So, this is the this is the probability of being in state 1 or state 2 and then. So, this is the proportion of time and this is your rate of breakdown 1 upon u bar plus d bar which we have already computed as this from here right this is your rate of breakdown. So, that is this and so, this gives you your u bar and then we compute d bar and we will continue with the exercise. So, therefore, we saw that u bar will turn out to be 7 by 16 which is pi 1 plus pi 2 divided by u bar plus d bar which was your rate of breakdown. So, that was 9 by 32. So, then we multiply and it will be 32 by 9. So, this u bar comes out to be 14 by 9 that means, this is the average amount of time for which the system will be up right and since u bar plus d bar is 32 by 9. So, to get d bar we will simply say d bar plus u bar minus u bar which is 14 by 9. So, that comes out to be 18 by 9 which is 2 units of time right. So, therefore, what we have been able to answer the three questions that were asked the first was what is the rate of breakdown. So, this is 9 by 32 or 28 percent of the time the breakdowns occur and then the breakdowns on the average last for 2 units of time. So, that means, once the system is down then it will remain down for 2 units of time and then the third question was the average amount of time for which it is up when it is. So, then there is an average amount of time for 14 by 9. So, 14 by 9 it is up when the system is up right. So, it will remain up for 14 by 9 times. So, now the thing is certainly the system is not in a very satisfactory situation because your breakdowns on the average the breakdowns are remain for 2 units of time whereas, your actual production time is only 14 by 9 which is less than 2 units of time. So, certainly the system is not in a very healthy state and so this again gives a warning to the manufacturer to do something about it because the way the transition probabilities are given this is what your conclusions are. So, I hope you understand see the way we computed this because we had to define U bar and D bar and then of course, the other reason I took this example was that you know there were 2 states which were defining the up system and 2 states which were defining the down system and therefore, we had to the computations were not just straight forward. So, I thought that will be a good example to discuss in this course. So, once we have talked about the state probabilities pi i's which we were answering as to the know because this and of course, we have also computed this. So, for that means number of transitions required to go from i to j this was the answer and the pi i's gave you the pi i's gave you the long term probabilities of the system occupying a particular state and then of course, we also said this is the fraction of time that the system will be in state i. So, pi i's I gave you these interpretations of pi i. Now, this other kind of questions that are needed which are now the first passage and first return probabilities. So, this is also very important because you want to know how long will it take to reach a certain state and so, when you say how long will it take to reach a certain state. See the statement it means here that you know that that will be the for the first time that you reach the state. So, that means you starting from a state i and then you are wanting to say that how long will it take for you to reach state j. So, obviously the moment you reach state j you have answered that question. So, therefore, this will be what we mean by this is that the for the first time that you reach state j from i. So, that is the understanding. So, that means now for example, if n transactions occur before state j is reached from state i. So, suppose we want to just you know surmise or say that n transactions have taken place before state j is reached from state i and then we want to know the probability that n transactions will be required from going from i to j. Then you might say that would pi j raise to n be the answer for this probability because pi j n also tells you the probability of transitioning from i to j in step 1. Let us see now there is a difference because you see when you talk about pi j n then it does not say that you may reach j before and a number of times before you finally reach j in n steps. The various graphs that I drew for you earlier showed that you may know like you had you started from state 1 then you stayed in state 1 and state 1. So, this was your you know transition probability from 1 to 1 in 2 steps or in 3 steps you stayed in state 1. So, here that is fine. So, this was your p 113 p 113 of course, also included that you could go from here to here remain here and then come here or you could stay here then go here and go here. So, this is fine this particular path that you are taking no you are not coming back to state 1 before. So, starting from state 1 you are reaching here without going to state 1 beforehand. So, therefore, this is the kind of path you are looking for, but whereas when we were computing your p 113 we had all possible paths to reach from 1 to 1 in 3 steps that is what you are doing. Say for example, if you consider p i j 4 then p i j 4 I could go to 4 in step 2 also that means from i I could go to j as I said and then you could again go to j and then j this would also be there. Then you will have i to j and then you could go to k and then to j and this way. So, so many paths, but nobody is stopping you from. So, when you compute the probability p i j 4 remember we said it includes all possible paths for of going from i to j and so you could revisit j in between number of times because you have to enumerate all possible paths. So, therefore, this is not the answer what we are looking for. So, we need to make some more definitions and some more terminology has to be introduced to compute these probabilities. So, the first passage and first return probabilities we want to compute. So, essentially what we are looking for is that for the first time I reach j from i. So, in between I should not have touched state j and when the first time it occurs I want to compute the probabilities of such and so what we will do is we will make these definitions here. So, again f i j n I am defining as the first passage probability and so I need to I have written first passage here, but I will define it here. So, first passage probability of going from state i to state j and remember x n was the state in which the system is at time n. This is we have been using this notation when we were describing the transition probabilities and the Markov process. So, now what are we asking for we are saying that f i j n is equal to the probability of x n equal to j, but x n minus 1 is not j x n minus 2 is not j and x 1 is not j it is only x naught sorry x naught is x naught is i. So, starting from i in between all these n minus 1 transitions that take place you do not ever touch j, but it is only in the n th transition that you reach j. So, probability of that is what we are defining by f i j n. So, that means probability of reaching j from i in n transitions for the first time.  So, now we want to compute f i j n that is probability of going from i to j for the first time in n steps n transitions for the first time. So, we should not have visited j in between the less than n steps and so this we will obtain by writing p i j n which is the total probability of going from i to j in n steps all possible parts which may imply revisiting j number of times and then finally, coming back to j. So, p i j n minus in sigma k varying for 1 to n minus 1 you see because you want to reach for the first time from i to j in n steps. So, your k can be allowed to vary from 1 to n minus 1 only and then this will be f i j k. So, for the first time you have visited from i to j in k steps and then once you reach j and then again you can go to many other states come back to j or stay in j whatever it is from in n minus k steps. So, for example, if you look at p 113 then what we are saying is that you can you know continue staying here in state 1 for all the 3 transitions or you can go somewhere here come back and then again revisit here and whatever possible paths you can or you can go this way this way this way. So, many other paths you can think of so we are ruling out all those paths. So, we are subtracting so that means you have visited from i to j in k steps for the first time and then in the remaining n minus k you again from j go to other places or remain in j and then come back to j. So, we subtract all these then we get the probability that f i j we subtract these from p i j n. So, we get the probability that probability of visiting j from i for the first time in n steps and then we will see lot of applications and implications of these probabilities. So, this is what we how we write down the expression for f i j n. So, let me and of course, when j is equal to i then f i i n would be the probability of going back to i from i for the first time. So, you started from state i and then when you for the first time you reach state i again in n steps of going. So, I should say from in n transitions. So, this will be f i i n and that will be the probability of recurrence of i state i in n steps. So, f i i i n and I use the word recurrence earlier and I said we will define it later on. So, that n we will of course, be talking in detail about these first passage times and first return time. So, first return probability is your recurrence probability probability of recurrence, but here of course, we are saying in terms of n transitions and then you would want to know the probability of ever returning to state i and so we will compute that also. So, now the number of transitions to go from i to j for the first time. So, transitioning from i to j for the first time is called the first passage time. So, the number of transitions required to go from i to j for the first time we will define it as a first passage time and you can see that this is also a random variable because you do not know how many transitions you will require to go from i to j for the first time. So, first passage time is a random variable and if i is equal to j then the first passage time is called the first recurrence time. So, this will be when you want to come back to the same state starting from a particular state you want to come back to it for the first time that will be your first recurrence time. So, first passage times and first recurrence times are random variables and therefore, you can redefine this again f i j n is a probability that first passage time from probability of first passage time from i to j in n steps. That means your random variable. So, f i j n is the probability of the first recurrence of the first passage time equal to n. So, f i j n will be because this is the time first time you return you go from i to j and when this value is equal to n you want to compute the probability of first passage time equal to n is your f i j n. This is how we will define. We will go through now a very interesting journey when we want to compute these f i j n and f i i n and in fact you would finally want to talk about f i j. So, that means that will be when for the first time you return from transition from i to j. So, without the n because here this is transitioning the first passage time when it is equal to n that means the probability of the first passage time equal to n.  So, we will continue with this discussion.


Good morning and welcome to today's products and focus. The US 30 has continued to push on that a little bit higher, getting closer to potential resistance now at 69.69 as we head into the start of the FOMC meetings that are expected to last today and tomorrow with a slightly double stance potentially expected and you can see slight moves in cable your dollar and dollar yen reflecting that more double stance but the fact is that we could still have you know the lower interest rates in the US for longer is the rhetoric that people are expecting to come out and the US there is slowly grinding on the little higher in the back of them so looking at the UK 100 not such a pretty picture we've had a lot of volatility there overnight as can be seen with this candle I'm still bouncing around 63.90 this is pretty not a great technical setup candles are kind of showing a lot of you know indifference as to the direction but a lot of extreme volatility 21 pure SMA still acting as a potential cab if we continue to get drift and the US 30 the US markets look quite healthy actually versus the the Germany 30 in UK 100 but this this is gonna be problematic so we might have a lot of pressure on here any break below 63.90 opens up to 62.70 looking in Japan 2 to 5 probably not benefiting from that opposite move in dollar yen as people start buying the yen I'm actually seeing a little bit of gold buying as well as the market begin to drift off I prefer slightly Japan to do five heck resistance 54 88 that has been in place now for the last four sessions but these long-legged candles are indicative of the fact that the Japan to do five is not yet the side which direction it really wants to go but we do have quite a staunch resistance level there to break through but that will be very much guided by what's happening with dollar yen so dollar yen drifting lower towards 107 spot 36 obviously double double FOMC is not going to help dollar yen we still seem to be hugging that 21 period SMA which is definitely providing support right now you can see the last three sessions it's it has not gone below it but as this continues on the trend obviously is for hitting this potential support up one of them in spot 36 technicals are relatively neutral we didn't get across over the MACD so we'll just have to wait and see how that one pans out better look at the economic data I remember there's not really a huge amount of exciting stuff happening until well until tonight and then you've got the other data coming on Wednesday we do have a CCI data coming out at 2 p.m. UK time and we do have some durable goods orders from the US as well fast-forwarding on to on to Wednesday there not a huge amount apart from obviously the end of therefore emcee and then Thursday we've got UK nation wide house price index and we've got GDP and jobless claims which will be a bit more of a catalyst so switching on to crude oil with Texas obviously Goldman's rate cut on crude and the lack of demand is our kind of glut of supply is really hurting with Texas crude we actually brought below $80 yesterday we ended up slightly higher on the day but the pressure is still on still looking at $77 as a potential support $77.40 gold still kind of an exciting but at least we're having a little bit of positivity to the game bouncing off that 21 period SMA trading between two ranges at 1218 and 1241 not really much to report right there I think many people will be looking at gold at this stage your dollar in cable your dollar had a little bit of a bounce yesterday also trained between two ranges the dovishness on the US dollar is we put to rest or ramified tonight but we are in the middle of two ranges one spot 2746 and one 2661 finishing up with cable cable moving slightly higher again this probably looks like a consolidated area there between these couple of ranges pretty much this area we'll see a little bit of curvature across there but one spot 6009 remains potential support trend is going to be higher that's the same for your dollar and cable and I give you a bit of a flavor of what to expect so again a decent amount of fundamentals actually due out if you take and the consideration what we've got here on Tuesday and the fact the FOMC starts tonight ends tomorrow so we'll have a bit more of an idea the clear idea about US interest rates and what's going to be happening with US dollar next keep your eye on the chart form as ever make insides part of your layer and join me again tomorrow to find out what happened next