Welcome, everyone, to Bogle Heads On Investing, podcast number 43. Our guest this month is Eduardo Rapetto, Chief Investment Officer of Adventist Investors, and former Chief Investment Officer and Chief Executive Officer of Dimensional Fund Advisors. Hi, everyone. My name is Rick Ferry, and I'm the host of Bogle Heads On Investing. This episode, as with all episodes, is brought to you by the John C. Bogle Center for Financial Literacy, a 501C3 non-profit organization that you can find at BogleCenter.net. Your tax-deductible contributions are greatly appreciated. The Bogle Heads Investment philosophy is to keep it simple, and that usually means starting a portfolio with a total stock market index fund, a total international index fund, and a high-quality fixed-income allocation of some type. For most investors, this is all they need to achieve their financial objectives. Sometimes I'm asked, what's next? What's beyond a total stock market and a total international? My answer is, if you wish to take a little extra risk in your portfolio for the potential of a higher return, then look at small cap value investing, but not just any small cap value fund or small cap value index fund. You want a fund that's low-cost and highly concentrated in small cap value factors. The company that pioneered small cap value investing using concentrated factor strategies was Dimensional Fund Advisors, more commonly referred to as DFA. Eduardo Rapetto, our guest today, was the Chief Investment Officer and the Chief Executive Officer of DFA until 2017. Then in 2019, Eduardo joined Advantus Investors, a new company by American Century Investors, where he became the CIO and continued to refine factor strategies for their ETFs, mutual funds, and directed accounts. Whether you believe in this or not, or whether you want to include it or not, this is a very interesting discussion as we go behind the scenes with one of the brightest minds in the industry. With no further ado, let me introduce Eduardo Rapetto. Welcome, Eduardo. I really appreciate you coming on the Bogle Heads-on Investing Podcast today. It's a pleasure. It's always a pleasure to speak with you. Thank you. We kind of go back a ways. I can remember being in your office at DFA, pleading with you to start ETFs at DFA. That was a few years ago. That's probably 10 years ago or something like that, I don't remember. It was a while back. Yeah. Anyway, now both the DFA and your new company have ETFs. So before we go down that road, let's talk a little bit about your very interesting background. Go back as far as you would like to tell us how you got to go from where you started to where you are today. So yeah, I have a weird background. The first thing is I was born in Argentina. Argentina, if you know, was a developed market, then was an emerging market, then was a frontier market. And I don't think that this is a frontier market anymore. It's not even that. But I was always a geek. So like in numbers and whatnot, I started engineering. Then I got a master's at Brown in engineering, mechanical engineering. And then I got a PhD from Caltech here in California in aeronautical engineering. Yeah. Let me interrupt you because you didn't just get a PhD. You won the ballhouse prize for the best PhD thesis of the year.   Let's put it that way. OK, all right. Be modest, too. Yeah, I was lucky. Look, I have an amazing advisor and I was an amazing school. And so, look, this was a long time back in 98, I finished in my PhD. So and I was doing things that were extremely interesting. Yeah. But my heart was not to continue in academia. I used to have a boss back. He was a mathematician, a PhD in mathematics. And he went to research in just in mathematics into Wall Street. And he always told me, eh, you will like this. You will like investing. You will like the whole environment and and the cutting edge science, because a lot of the things that we study in science are very applicable in investment. And so I always have that bug in my mind. And so I had the opportunity to switch instead of continuing in academia and become a professor and whatnot. And I switch. And so I'm moving to finance. And I got a job in a DFA in the research group. How did you link up with DFA? That's that's the most weird thing. You know, a lot of things are random in life. So I was at Caltech and the DFA was looking for someone to work in research with Ken French and Jim Fama.  And yeah, the FFA was small. I think that I was employee 107. And I think at the time, the FFA had around 25 billion. It was a great opportunity to work with some magnificent people in a small company where you were able to get involved in basically all the different aspects, not only research, but the legal aspects of what you were doing, the portfolio management, the trading aspect, the marketing aspect. So it was a magnificent opportunity. I was lucky. And interesting, though, that DFA would look at you, given your background. I mean, clearly the forward thinking of the David Booth and Gene Fama, Ken French, who are both on the board of directors, they're decided with you, with no financial background, really, that you were the guy who they're going to bring in. And they kind of overstepped all the PhDs in economics. Well, I don't know who else was applying to be fair. I think you're giving me more credit than I deserve. Look, I was living in California. My wife's from California, and the job was in California. So it was a perfect match for me. And I was very, very lucky on that. And I was extremely lucky to work with the talented people like you mentioned. You know, it was like doing a second PhD when you started working with Ken and Gene, because you had to read and read and do research. But that's what you are trained when you do a PhD from a top university, no matter what's the field, the training is training how to learn, how to get to the cutting edge of the science and then try to push it a little bit more. That's a PhD program. And so working with these professors was basically the same, getting to the cutting edge of the science and then try to push in it a little bit forward. And that's what I was doing. And by 2007, you became the co-chief investment officer with David Booth at DFA. And I think I'm not mistaken. That's probably when I first met you back then, about 15 years ago. And then in 2009, you became the co-CEO. And at this time, wasn't DFA moving to Austin? Yes, DFA opened an office in Austin in 2007. Yeah. And so I told my wife, let's move to Austin. She agreed. So we went there, we have three kids. So I became, I was CIO and then became co-CEO with David. What's a great honor, no? Sure, absolutely. And you got on the board of directors and you became a director of the mutual funds. But then in 2017, I've heard you use the word retire. I use the word resign.  Yeah. Yeah. So my wife is from LA, no? Her parents are here, LA. So in 2015, before my oldest one started high school, the family wanted to move back to LA because the grandparents are not getting younger. Let's put it that way. And if we were staying in Austin, we would have to stay there at least for another 10 years because we have three sons. And we didn't want to move kids when they are in high school. So the family decided to move in 2015 to Los Angeles. And so I was going back and forth to Texas on top of going everywhere. I was put in 250,000 miles a year between going to Texas, if going, going everywhere around the world. So you see, it was probably not the right balance. And I was never home, never seen the family. And so it was not the right balance. So I basically resigned without any job in mind. You can call it retire. And it was not a permanent retirement, I guess. But well, you started doing research, one of your papers on value and profitability and international and emerging markets that you co-wrote during this period of time. But if I'm the same time as it was being peer reviewed and published, you then decided to take a job with Aventus, which was a new company. Now did the company form because you were coming on board? What did it form? And then you came on board. So let me speak a little bit about how that happened. I was not working, but like you, when you work a long term in the industry, you get to know a lot of people and people have magnificent ideas. And some people at American Central Investment in Kansas City that I know them for a long, long time, they wanted to start something new, something that is more systematic, low cost, because there is a big need for something like that in the market. And they reach out if I wanted to help them and they were willing to do it based in LA, where I live. So that's great. And one of the things that I have as a condition is that the investment strategies, let's call funds, what they were going to be, they have to be low fees. That's what they wanted. They wanted to start something systematic, organized from day one so that you have all the checks and controls on cost so you can be low fee and still have a very good business. So I agreed to work together with American Century and start Avantis. So Avantis was going to be a standalone company where the people in Avantis own a piece of that and American Century owns another piece of that. But we decided not to do that. Why? Because that was going to impose more cost. And that was going to make us have higher expense ratios. So what we did is we created Avantis as a unit inside American Century. So I'm an employee of American Century, but they have a business card that is called Avantis because we manage money different than the traditional American Century manager. And I report to the CEO of American Century. So we're a unit that is a little bit outside of American Century, but we are part of American Century. But all our operations, legal, compliance, HR, think about all the support functions that you need to have a professional asset management company are done by American Century personnel. Yeah. Where is the trading done? Is it done through American Century or are you doing it on your own? Depends on what, you know, when you do ETFs, you know, a lot of the trading is happens in kind, in and out. So if that's the part, we do it on our own. Whenever we need to trade stocks, we work with American Century trading desk that is segregated that were trades in a different way of trading that we think we don't have to demand liquidity to trade and we can be very efficient. And you have different products. I mean, most of your money, I believe, is in ETFs, but you also have traditional mutual funds and you have private individual accounts. But can you break that down? You've got about 10 billion under management right now, which is a great number just getting started over a couple of years. How much of that is ETFs? How much of it is mutual funds and how much of private accounts? The vast majority of the money, but the vast majority of the money is ETF. And why that? Because for most investors, an ETF is a better bet. And you know that. Well, I know that, but why do you know that? That's an inside joke, by the way, between Eduardo and me. So it goes back a long, long way because I spent years trying to convince dimensional fund advisors they should have ETFs. Both of us know that ETF is by far a better vehicle, not only because of tax advantages, but also because you're same on cost of different time, for example, in certain cases, you don't have to pay some taxation when you buy securities like stamp duties when you buy securities in other countries. So ETF is a much better vehicle. But for some investors, let's think about 401k plans. Yeah, the ETF really doesn't work because the operations of the 401k plan is different. So it works for the brokerage window, but not for the default options. Correct. Our goal is to try to help everyone with the right vehicle. We have no biases. But I have looked at the performance of an ETF and a mutual fund. Same strategy, the same might be small cap value, large cap value, whatever it is where you have an ETF and you have a mutual fund. And there are slight differences in return between them. But the fee is the same. So maybe you can explain why that is. Yeah, yeah, that's a great question. If you were running an index fund and you have pre-described holdings so you have securities and weights in both of them, the performance probably will be the same with small differences. But if you're running a strategy that is trying to use today's information, the performance will be slightly different between both. Why? Because a lot of the trading that happened in the mutual fund happened depending on when the cash flows come. You know, if you give me money today, I'm going to invest in the securities that are great to have in the portfolio today. But if I don't have money today, I have money tomorrow. I may have to wait for tomorrow to do so. You have the regular trading and rebalancing, but you have an effect of cash flows that forces more one direction than another. It's more in a mutual fund, you always have to carry cash. Why? Because you have a redemption in a mutual fund. I have to have cash to send it to you tomorrow. Yeah. And I cannot sell securities tomorrow to raise money to wire on the same day because certain men of those securities is two days later. So you have to carry cash in the mutual fund. And not much, but you have to have the same cash. If that cash that you carry is not enough, you have to hit the line of credit in order to be able to wire the money. So even though the strategies are the same, there is more difference in how you have managed them in order to deal with the different set of clients' transactions. Yeah. And if you think about that, the ETF is way more efficient because the ETF, when you purchase an ETF, high-receive securities is in kind. So I'm always interested. And when you redeem, you receive securities in kind. So the long-term shareholders don't have to bear the cost of the redemption. So there is always going to be a difference in performance between the ETF and the fund, but those differences should be small. Now, when can those differences become very big or bigger, let's call it, when the market moves a lot? If you have a day that the market moves 10 percent, and you have a purchase in that it represents a 1 percent of the fund, or 2 percent of the fund in cash flow, well, that money is not invested until tomorrow morning. So the market moves 10 percent. Right there, you can see that you have 20 basis points in difference in performance because you are carrying cash overnight. And it's not your cash. I mean, generally, if the investors are in it for the long-term, it's not their cash that's causing this. It's some other investor's cash that's causing that. Yes, it's not the long-term investors. In ETF, the long-term investor is kind of protected from the actions of people coming in and out. In a mutual fund, no, you are commingling and cash is coming in, cash is going out. So you are exposed to the actions of other shareholders. And that causes difference in performance. Now, Vanguard has a unique structure, and I know they have a patent on this, but their ETF and their open-ended mutual fund are just share classes of the same pot of money. And that patent, someday, I thought it was last year, but maybe this year, is actually going to come off patent. And in which case, is it beneficial or would it be beneficial for other fund companies to adopt that patent where there's one pool of money, and then there's an ETF share class and there's a mutual fund share class? What's the advantage and disadvantage of doing it the Vanguard way? That's a great question. We thought about that to say, do we want to have a big pot of money, a big fund, where one share class is an ETF and the other share class is a mutual fund? And we decided not to do it. Let's go through the logic. Let's suppose that you have a mutual fund share class, a mutual fund, yeah, and with a mutual fund share class. And I decide to attach to that mutual fund an ETF share class. Yeah? If you are the mutual fund shareholder, you are going to be very, very happy about that because you have people coming in kind in and out, dealing with your capital gains, and not imposing any costs on you because they're coming in kind. It's not that they give you cash and the portfolio manager had to trade and the cost is spread out about across all the shareholders. No, if you have a mutual fund and you attach an ETF share class, the mutual fund shareholders will be ecstatic, will be very happy about that, yeah? Right, I agree. Let's go to the other case. I have an ETF share class and I put a mutual fund share class on the side. Will the ETF shareholders be happy? No, they will not be happy. Why? Because people coming in the mutual fund are coming in cash and who pays for those transactions? Everyone. Even the ETF shareholder. So the ETF shareholders paid their way in, paid their way out, but they also have to pay a fraction of all the people coming in and out on the mutual fund. So it's not really fair to them. And so on top of that, if you have the shareholders and mutual fund redeeming a lot of money, the ETF shareholders may take the tax bill that they are not expecting because there are cash transactions in the mutual fund share class. So what we decided is to have different pools of money, one for ETF and one for mutual fund. If you want a mutual fund, you know what you're facing. You're having a coming vehicle and you're exposed to the actions of other shareholders, externalities, due to other shareholders, but you trade at NAB and it's for some people that's easier. And a 401k, as you said, you have to do it that way. In a 401k, you have to do it. If you go to the ETF, you're going to pay your way in and that way out when you buy in the market based on the spreads and whatnot, but you're going to be protected from the actions of other shareholders because of their time purchase and redemption mechanism. So by separating them, we give people a pure benefit of one or the other and they can decide what's better for them. They're not going to be blindly surprised by the action of the other pool of money that is coming in and out in a different way that they are. Okay, let's go into a different topic and then has to do with how you invest money. You invest money using factors.  So the factor basically is a way to understand the performance of securities. For example, let's suppose that small-cap securities have a better expected performance in large-cap securities. So a factor is the difference in performance between the small-cap securities and large-cap securities. Okay, let me stop for a second. Why would small-cap have a expected higher return than large-cap? Well, that's a good question because let's speak of another factor and then we go back to a small-cap. A small-cap is probably the one that you cannot justify. A company because just being small should not have a premium because you can have a small-cap company with extremely high price and that's not going to have a premium. So let's speak about the value factor. That's easier. What is the value factor? If you can buy a security that has low price relative to a fundamental, let's say the book value of a company, well, that company tends to have a premium relative to a company that has a high price relative to the fundamental. It's like you're buying something on an discount at a lower price. Okay, but why would a company with a low price to earnings, low price to book, low price to cash flow, low price to something or just low price, why would we expect that to have a higher rate of return? That's a great question. So we have to start with the premise. It says we believe that the market is pricing all the securities and we cannot find a better price than what the market has. There's an assumption of different kinds. But we also believe that there is no need for the market to put the same return for every security. Different securities will have different returns. Different returns will have different discount rates. Yeah? The discount rate is a factor of the perceived riskiness of a security, correct? It can be risked or it can be something else. It can be behavioral, you know. Some people just, for whatever reason, dislike a lot a certain set of companies. And if there is enough people that dislike a lot those set of companies, those companies will trade at a little bit lower price. And so that's a higher discount rate. Let me push back just to hear on this. Because I want to make sure I understand it because there's this thing between risk and behavior that always goes back and forth with these factors. But to me, if it's true that there are a lot of people who just don't like these companies, they don't like them for a reason. And isn't it true that they don't like them because they see more risk there and lower returns and that's why they don't like them? So isn't it a fundamental factor? It may or may not be. But the fact that a certain client moves away from certain set of securities certainly will push the price of those securities lower. And that suddenly, you have a higher discount rate because if the price is lower relative to the fundamental, you have a higher discount rate. But let's go a little bit deeper in why there is a premium. Because you're asking is why certain security have a premium, a higher return than others? And so let's think about that. Let's suppose that I give you two options to work. So you work with us for one week and if you work us for one week, I give you $100. That's option one. Option two is if you work with us for one week, I give you $0 or $200. 50-50 depending on the weather of the last day. So 50-50 probability gives you $0 or $200. The expected payment for you is the same. It's $100. So in one, you get $100 for sure. In the other one, you get an expected $100. But you can get $0 or $200. Will you take that deal? In general, you will not take the second deal. You will take the $100 for sure because the other one, you can finish with $0 or $200. So now I'm going to try to spice it for you. I'm going to give you $0 or $250. So now the expected payment to you is not $100 and $100. It's $100 and $125. 50% 0, 50% to 50. So I'm incentivizing you with the premium to take the more risky outcome. At some point, if I keep on increasing the incentive, at some point, you are going to say, I take the risky outcome. So whenever you have a risky investment, it's not that the expected outcome is the same as a less risky investment. The more risky investment will have a return that is a little beyond just the same expectation. It will have a premium because that premium is what incentivizes you to take a little bit of that risk. Because if you do a perfect risk adjustment and you have the same, same expected outcomes, you will never take the risky investment. So there has to be a premium, a little bit more return. So when you're speaking about security, how low price relative to fundamentals, and we're saying that's a value investment strategy, why there is a premium? Because not every security has the same expected returns. There is no need, there is no logic for that. So when you're looking for security that is low relative to fundamentals, what you're trying to do is identify those securities that are having higher discount rate, higher spectrum returns. And then put a diversified portfolio together of just those securities. Yes, but you can see that when I, what you were mentioning, hey, you're saying low price relative to fundamentals, but what we're trying to do is try ways, systematic ways, mechanical ways if you want to think about that, to identify what securities have high discount rates because the discount rate is your expected return. So what security has these high expected returns? Now, every model is incomplete. The models don't describe reality. But what financial science has been doing over time is trying to make better and better models, trying to understand what variables matter most. And that's why you have so many factors because people start looking at different variables and they say, well, this variable explains something about returns and this other variable explains about the other return. And I think that you have like 400 factors now. Yeah, I think it's a paper called the factor zoo. The vector zoo, yes. So the issue that we're facing now is there's so many factors, how we put all these together. And there are many different peoples put these together in different ways. Some people do optimization. So let's put all these factors optimized and we see what happens at the end. But you know, as well as me, whenever you put the big soup of estimated numbers in an optimization, you get very weird outcomes. So the factor zoo. So we've got, I talked about large versus small. And that factor was strong decades ago. But it seems to me since the proliferation of small cap index investing, in other words, became much, much easier to invest in a big massive mega portfolio of small cap stocks. It wasn't so easy 50 years ago. It's easy now to do that. And that led to the term, well, led to factor decay. In other words, it went away. It was easy to identify these small cap companies. It was easy now to package them together into these index funds, mutual funds, extended market small cap funds, whatever. And because of that, I believe, and I might be wrong about this, but I believe that caused this factor to decay to the point where there really isn't a big premium anymore, as you mentioned earlier. What you are observing, it's absolutely right. Now, the question is not if it has decay. The question is, was it there on day one? And why is that? Let's suppose that we go to the soup one day and we see that animals with stripes are zebras. That doesn't mean that every animal with a stripe will be a zebra because a tiger will have stripes. So the fact that people observe that the small caps up to 81, I think it was, have a premium, that can have been a random outcome. And the fact that we don't see much of that after that period, it may be because that's reality. And why I was pushing back in the small cap premium? Because when I was speaking about value, I was telling you, you have a low price related to fundamentals. You are looking for companies that have high discount rates. Any high discount rate will push the price down. So there is a logic there. And just to clarify, a discount rate means you need to get a higher rate of return. It's a cost of capital. Exactly. The company has to get a higher rate of return for you to invest in that company because you perceive true or not, you perceive that there's more risk there. So you need to get a higher rate of return. Yeah. If a company is going to produce a dollar in the future, you are not going to pay that dollar in the future with the dollar today. You are going to pay 70 cents today to get the dollar in the future, 50 cents today to get the dollar in the future. So the lower the number that I'm paying today for the dollar in the future is the higher discount rate. Higher discount rate. So when you have a strategy that is trying to buy low price securities related to fundamentals, what you are really trying to capture is that high discount rate, that higher expected return due to the low price today.  If not, you can divide a large company in a bunch of pieces and suddenly you have a premium. And more logically, let's suppose that you have a small cap company. Yeah. If I have that small cap company and that company has a very, very high price, relative to fundamentals, that company should not have a premium because the price is too, too high relative to fundamentals. So the small cap premium is highly debatable. Let's put it that way. Well, let's go ahead today and move on to some other factors because we talked about small cap potentially not being there anymore or maybe wasn't there to begin with. We talked about the value factor, price to book, price to some fundamental. You also, at your company, are looking at profitability as a factor. So tell us about profitability. Yes, that's a great question. So imagine that you are going to buy a company. How much you're going to pay for that company? You know, I'm buying Rick's company. What, how much I have to pay? Well, I have to pay for the equity that you have in your company. Yeah. But I also have to pay for your cash flows. But since your cash flows are in the future and they're uncertain, I'm going to discount those future and I'm going to pay less today for those future cash flows than the value of those future cash flows. So the price that I'm paying for your company is your equity plus a discounted value of your future cash flows. Yeah. So remember what I'm interested is in that discount rate. Yeah. And what variables I know, I know the price because Bloomberg telling me the price every minute. I can't have a proxy for the equity in the company and I have a proxy for the cash flows of the company. And these three variables, because of the valuation framework that I mentioned with you, are related to the discount rate to the expected returns. A company that has higher expected returns will have a lower price for the same equity value and for the same cash flow expectations than a company that has a lower expected returns. So the higher expected returns, the lower the price, keeping the other two variable content, keeping the equity and the cash flows. So I need to take into account not only the equity that I can use book value as a proxy for equity, I also need to take into account the cash flows of the company. I have to take both, the both set of financials, the balance sheet and the income statement, both set of financials to identify what companies have high discount rate, high expected returns. When you're selecting the securities then for your funds, is it a fixed formula where you're using some percentage of book value, some percentage of profitability together in your model or is it a variable thing where it moves? No, it's fixed, it's fixed. So look, there is enough uncertainty in life that if you have it fixed, it's already there is uncertainty to add a variable component. There is no way for us to have so much precision. So we want to use the main drivers of selecting securities that are how much money the company is making, what's the equity position of the company, what's the price related to these two variables. And once we have that, we have enough information to put together a well diversified portfolio that in our opinion has high expected returns. Trying to be more clever than that and just changing the weight of the securities with market conditions or the factors or the components with market conditions or everything else is just adding noise with not really known outcome. So I'm going to say one thing but then I'm going to move right on to something else. So what I was getting at was you don't do what's called factor rotation where you're trying to go from one factor to another to another to another. Companies are very hot on doing factor rotation and they're saying that well if we move at this time from this factor to that factor to over to this factor that somehow some way they're going to get an excess return from rotating their portfolio around and highlighting different factors at different times and you don't find any value in that at all. No, that's not predicting where the market is going to be. It's the same. If you can predict the performance of a given factor, it's the same thing. You can predict the performance of the market. Imagine who we could do that. That would be great but the markets that's not how it works. The performance of market is unpredictable because there are news that we don't even know that they're coming and they will come. I don't know what will be but it will come something new tomorrow. So you have your list then you come up with your portfolio of what you would like to buy but there's another factor that we haven't talked about yet. It's called momentum and this is looking at the price and seeing if it's moving down or moving up and we don't want to try to catch a falling knife is a phrase that we hear often with a quantitative analysis. So could you talk about how you use momentum in your portfolio management? Yeah, so momentum is fascinating. It's a little bit like small caps. When I was telling you small caps there is no logic for the system in small caps. There is a logic while the premiums are large in small caps the value premium in small caps is larger than the value premium in large caps. There is a logic for that but the existence of a small cap premium there is no logic. For momentum it's the same. Momentum is something that we observe but we don't understand why it happens and there are two competing visions of why that happens. So what is momentum? A security that has extremely bad performance will continue to have for some short period of time good performance. And a security that has extremely good performance will continue to have for some short period of time good performance. So how do we use momentum? If we have a value strategy whereby in security we have low price. Yeah? How does security become low price? One probability is because the price is going down the security has very bad performance. Well, we can go and buy the security immediately or you can say wait, don't buy it now wait a little bit until the price stabilizes and so that's what we do. We decide not to buy immediately not to jump into this security that have extremely bad performance and we decide to wait a little bit until the price stabilizes. And so we try to prevent buying securities in downward momentum. Yeah? The opposite for upward momentum if you have a security that is a small value for example and it's in upward momentum we are willing to slightly overweight that security and if the security starts going up in price and instead of being a small cap now becomes a mid cap security instead of selling it immediately we may be willing to hold it a little bit longer. Why? Because the momentum premium is very very strong but it's very short-lived. So if I can get a little bit of push because of upward momentum just by holding the security a little bit longer. So we incorporate momentum downward and upward momentum in our strategies but we are very very careful how we do it because if you are not you finish with a very very high turnover. Let me ask a question about factor premiums. Now you have a multi-factor model where you're using profitability and value combined to come up with what you would expect to be a premium over beta expect to be a premium over the market return. Do you have a way of determining what that premium should be going forward or what are we looking for and a long-only portfolio not a long and short but just a long-only portfolio? Yeah no long only I don't think any one of us needs a short portfolio so we're all happy to have a long only. This is a great question so the question is can we know at any point in time how much the market is discounting future cash flows? And the answer is no and why not? That's where behavioral finance gets together with rational markets. In different periods of time for the same level of risk people may be willing to take a lower price or a higher price. We change the market change in periods of high anxiety people are priced humongous discount rates the prices are very very depressed. In other periods the price is higher and so the market is having lower expect returns and you cannot really know at any point in time how big or how small is that premium. What you know is that it's a premium but there is a research that is very interesting that shows look look at the long-term average of these premiums that's probably as good as it gets. Now some people say that if you look at the market historical market performance relative to treasury bills for example probably was higher than what we should expect in the future. I would agree. Some people say that because now the market now more people embrace investing in the market there is more of us that are buying securities that were the wearer in the past and so if you have a higher clientele basically more people willing to take a little bit of that risk we're increasing the price and we're reducing expect return. That is a logic. I think another piece of logic is are treasury bills correctly priced if you're going to use that as the risk-free rate. Based on where treasury bills are currently priced I think that the premium could be high but if treasury drills were correctly priced based on where the inflation rate is I think that the premium might be a lot lower. So I don't know if treasury bills are the right risk-free rate to use even though that's what's being used in the models. Yeah you are right about what is the risk-free rate is interesting and but you know we're not just speaking about short-term periods we're speaking about long-term periods and so if we think about that expect returns of the market maybe a little bit smaller than what we have seen in the past there is more willingness of people to embrace the market and embrace market risk and there is more people to do that then you would expect premiums to be a little bit smaller is that the same for value investing and when I say value I think the generalized ways of value like what we do I think that there is no information about more people embracing this than before then maybe it's more than historical premiums then maybe not. Now the traditional way of defining value like if you are looking low-priced to book without looking at it and at the cash flows of the company that probably is not the right way to do it and so science has evolved from there so better I think it's better if people evolve from that Let me ask a question about US versus international because you did this paper on using value and profitability in international markets is it different outside the US is it different in emerging markets than in the US market and how do you have to change your formula? Okay so if you remember I told you a story about the evaluation of the company and so what is the value of the company the price of the company is the equity plus the cash flows is counted by some discount rate but I never told you that that valuation is only valid in the United States I think that that valuation was valid with the Babylonians who are selling and buying donkeys and for it's going to be the same in the future when we are selling and buying water or oxygen if we ever live in Mars so this is an evaluation framework the beauty of evaluation framework that is valid in all the different environments is different from a pattern a pattern may be valid here and not somewhere else so the way that we do things is based on evaluation framework to understand what factors or what matters in the spectrum returns of a company and basically it works all around the world it works in the US it works in international it works in emerging markets so the research is very robust from that point of view because you have a research that you can apply with the evaluation framework everywhere now when you're speaking about the variables itself you have to adapt to realities for example in the United States companies report financial squirtily but in some countries reports only twice a year and so you have to adapt to the data and try to make the best that you have with the data of the different countries in order to have the model use the right set of information let me ask a question about small cap value funds I personally have a small cap value tilt in my portfolio I don't yet have an international small cap value tilt and one of the questions I have is why are there no global small cap value index funds or ETFs you know I've been asked that many times it's more we we may be thinking about doing one outside the United States not for U.S. investor for outside in the United States and why we don't have one in the United States we have as you know we have a U.S. small value strategy an international small value strategy and an emerging markets meet an small value strategy and we do meet an small together in the emerging just because you have more liquidity and the number of securities but we don't have one that puts the three of them together why is that because different investors want to have different allocation to the U.S. versus the emerging versus international and if we put all together then constrain the investors to the side which one to buy how to weigh them now yeah I understand but think about this when you buy an ETF yeah what is your fixed cost do you pay ticker charges no you don't pay ticker charges so buying three ETFs is the same as buying one because you don't have ticker charges so given that you don't have ticker charges just buy three securities instead of buying one and that gives you the freedom to decide how you want to weigh them okay I will push back here because you have a global real estate portfolio a real estate but you you but you just finished saying you should have a U.S. small value in an international small value but yet you have a global real estate fund so explain why yeah that's a great question so you say you can have a U.S. a real estate an international real estate and I will tell yes you are right we can have a U.S. an international now an international real estate market is much much smaller than the U.S. real estate market yeah 30 percent versus 70 you go international versus U.S. yes yes so an ETF for international real estate that will have a very very small allocation in someone's portfolio we said no let's put it all together in real estate and let's give that to someone because I maybe I'm wrong but we said no one worries too much about how much U.S. or not U.S. or someone wants a full U.S. real estate or they are happy to have a global real estate so we say let's provide global the global real estate market has been developing if you know U.K. REITs I think they are 15 years old JREITs so it's developing at some point we may split it or have two versions or whatnot but for now we decide that global probably is the right decision I can give you the pros and cons of a global small cap value fund the pros are man it's a lot more convenient than buying three funds just buy one small value covers the world I'm happy what's the disadvantage well the disadvantage is taxes and the foreign tax credit if you're going to put it in your taxable account because since less than 50% of the portfolio is going to be an international you don't get the foreign tax credit so in a taxable portfolio you still have to divide it up between a U.S. small value and an international small value so you get the tax credits on the international small value but if this was going to go into an IRA account or a Roth account of some form which I could see a global small cap value into a Roth account that it would make sense at least from my standpoint as an advisor where I get this factor exposure using one fund there is a there is a need for it I believe out there so just plugging that you're not the first one telling us that to be fair but I also go through that and look if you have three ETFs you don't have ticket charges in custodians but you have three funds and I don't want three funds I want something simple anyway let's go to the next thing you know what we've evolved we have the factor zoo now okay we also have things like artificial intelligence and we have machine learning and behavioral finance can be thrown into that as well are you looking at these things to incorporate them into your world and how you do things you know the whole thing of machine learning neural networks and all these is fascinating because what it's trying to do it's trying to emulate how the brain works in learning or a collection of entities works in learning in order to to learn without having a pre predefined model yeah so but isn't that what the market does yeah the market the market is a big machine learning machine that does machine learning and the market is is a network of this you know a loose network of people interacting in order to increase some benefit for everyone collectively everyone but individually each one of the individuals each one is just trying to incorporate the information that they come in order to come with prices so the whole market is a big machine learning network now if I were an acting manager picking stocks and I think that I can do better than the market and find what securities and underpriced and securities underpriced probably will invest a lot of money there and say oh I'm going to be better than everyone else and find all the undervalue securities and all the other value securities that's not us so I'm not going to dispute the market price and create my model and then I will say my model is better than the market because the market is as good as it gets you know whatever our model is is going to be so part of them to the market in my opinion so the market gives us a price of the securities what we do is try to use that price in order to identify what securities have been priced at higher discount rates so they have higher expected returns and what security have been priced at lower expected returns there may be things that are interesting in machine learning to apply even to what we do and for example we were speaking about finding factors or finding drivers of the expected return you could have imagined that all these factor research could have been done with machine learning so we can have a machine learning trying to find what variables that are related to valuations have different levels of impact in the expected returns of the security and that could have been done but that's what the professors you know and researchers around the world have been done in a loose way so yeah you can use it but the lot has been done even we don't call it machine learning let me ask a question that was posed to me it has to do with ESG so ESG has popular in Europe for sure maybe becoming a little more popular here in the United States than in the past but it's very hard to find a small cap value ESG fund for the people who want factors and want ESG any interest there we are getting into the responsible investment business so we're going to launch a couple of strategies three strategies that have high exposure to a small volume in in the near future let's put it that way let's go into the last topic and that has to do with fixed income you do have a few fixed income funds and you do run a strategy based on the yield curve trying to enhance the return based on yield curve in other words you say the yield curve is telling you something could explain your fixed income investment strategy and why it there may be an expectation for a higher return than just doing a a regular straight index fund there is a couple of things that are very very interesting when you think about fixed income let's speak first about indexing you know that how the index work the index that an index manager follows in fixed income incorporates every bond as there have been issues so if you issue a bond that bond is incorporated in the index automatically now if you recap to issue a bond are you going to issue in a way that increases your cost or reduces your cost of servicing that debt you're going to try to minimize your cost so you're going to issue in the conditions say duration or whatever it is that minimize your cost yeah yes but if you are minimizing your cost you're also minimizing my specter returns if I'm the investor in that bond so the automatically inclusion of bonds it's really a detriment for an index in fixed income now you mentioned we use something else we need to have like inequities we need to have an idea what bonds will have higher specter returns than others given the same credit quality and everything the same and we do that by using the yield curve so what do we mean by that let's suppose that you have a bond and you hold it to maturity and let's suppose that the bonds of default yeah what is your expected return on that bond your expected return of that bond is your yield to maturity assuming you can reinvest the income at the yield to maturity rate let's assume that it's zero coupon life is easy life is easy zero coupon zero coupon so your zero coupon bond that has a yield to maturity of two percent your average return if you hold that bond to maturity is two percent a year correct but your return from year to year it's not going to be two percent that's great because if you have a three-year bond under the typical yield curve the yield curve is has lower yields to maturity for shortened durations and higher yields to maturity for longer duration so if I have a three-year bond that gives me yield to maturity two percent one year from now that bond will be shorter to maturity so on expectation we have a lower yield to maturity than today so you can see the yield to maturity was the average return to maturity but that means that doesn't mean that every year is the same in general the longer portion of that holding period will have higher returns than the shorter portion of that holding period so you can use information in the shape of the yield curve to decide when that bond has higher than average returns related to the yield to maturity and when it's going to have lower the specter returns yield to maturity and we use that information to create portfolios in geekish fixed income what you're talking about is a horizon return yes if you're going to use it for two years you're going to keep it for two years and then you're going to sell it you're going to do what we call riding the yield curve yes this two percent bond that you purchased because the last year the yield to maturity on that bond might only be a half a percent and you bought that two percent as a three-year after the first two years if you sold it you're going to get a return on that that's much higher than the two percent yield so the horizon yield might be two and a half or two point seven or whatever it is exactly that's exactly what we're saying see I remember from my CFA days all of that stuff that's exactly what we're doing instead of trying to get an average income to maturity we're happy to get an income from some people's time and a capital appreciation due to the change in the shape of the yield curve and the convexity as another geekish word has a lot to do with this too I mean there are some bonds that this happens rapidly and there are some bonds where it takes more time absolutely and that's why the way we do it is we have an estimated yield curve for different issuers for every issue we have an estimated yield curve depending on the sector the credit quality and whatnot based on market information we don't make predictions remember and then we use that estimated yield curve for every issuer to compute the specter return of the bond for a horizon like you mentioned and then we use that information to create a portfolio very interesting well I wonder what's been fantastic having you on Bogleheads on Investing I thank you very much for your time today and wish you a lot of luck and I know you just passed 10 billion and hopefully you get to 100 billion quickly thank you very much this concludes Bogleheads on Investing episode number 43 join us each month as we have a new guest and talk about a new topic in the meantime visit Bogleheads.org and the Boglehead wiki check out the Bogleheads new YouTube channel Bogleheads Twitter Bogleheads Facebook and find out about your local Bogleheads chapter and tell others about it thanks for listening


the power of chi. You guys wanna see the power of chi? Yeah, totally good. So, how do you do this? Easy way of doing it is, put your finger like this, okay sign, but with your pinky, okay? The other one's okay sign with your index finger. Now put the index finger in your pinky, and open up your pinky, do that a few times. Okay, now don't let it open, just can't give it some pressure so it's hard for you to do it. It's hard for you to open it. Do that a few times. So now you have a base of how strong your fingers are, right? Okay, so what I'm gonna do, everybody's got a base of how strong your fingers are? Okay, so do the same thing, do exactly the same thing, and then I'm just going to, you're opening this one, right? I'm just gonna catch you. So is it harder to open it? Yeah. Your fingers stronger? Yeah. Where is it? At least about a quarter, I'm assuming. 25 to 50% stronger? Yeah. Okay, so now just go normal, and then establish a base again. Okay, so now you got a base, right? Yeah. Okay, do it again. Now it's stronger, right? Yeah. How much more strong? Do the same thing? About there, about there. Okay, what else wants to do it? So somebody, you got a base, get a base of how strong your fingers are. You should be able to open it. It's just so tight that you can't open it. So now you got a base, right? Yeah. Okay, so see if it works. Slightly stronger? Yeah. How much more strong? About maybe one and a half. One and a half, so 50% stronger? Who else wants to do it? Okay, so you got a base, show me how to do it. So you open it. You feel how strong your fingers are, right? There you go. So you're opening it, you're opening it. Stronger, right? Yeah. How much stronger is it, you think? About 30, 40%. About 25% stronger? What do I do? I just touch you. Where's my hand? I'll touch you here. Okay, let's try something else. Wanna see something cool? Okay, same thing. We'll come over here. Do the same thing. Do the, get a baseline, and then let's get Gemma to do it. Gemma, come here for a second. You wanna give us a hand? Lovely Gemma is gonna give us a hand. Okay, so you can establish your baseline. What do I stab him? No, you don't stab him. I'm scared, no. What, wait, hold up. Okay, you got a baseline, right? Now, you do the same thing. You just put your hand, touch him there. Your hair? Yeah, and then you see if it's stronger. Don't have to press too hard. Oh, don't, that's bad. That hurts, don't want to stab. Yeah, it's bad. Okay, is it strong? Just keep your hand there. Just keep your hand there. Stronger? Whoa, yeah. Good, yeah. A little bit stronger? How much more stronger? Well, yeah, about 20% or something. 20%? Yeah. Okay, so one last time. Yes? Hands actually get sore. I don't know. Okay, I'll do it this time. Okay. So, you got baseline? Yeah. Stronger, right? Yeah. How much stronger? Yeah, about, yeah, 30%, 50% of it. So it's a little bit more than her, right? Yeah. Okay. So, if you want to know what my secret trick is, stay tuned to the next video. I'll show you. Oh. Come next class and I'll show you how to do the next.


Now, just a little note about this lesson six, technically it's due today, but if there is stuff that you did not understand, it is much more important that you figure out how to do it than hand it in, incomplete it. In other words, I'm not going to take marks off if you hand this in Monday or Wednesday. I'm going to be around today after school, tomorrow after school, Friday after school, et cetera, et cetera, et cetera. So I've had a request for question number three, I'll do three eight. And I think I can do it this way. I think I was clever, yes I was, so I can copy it. That was smart of me. You try it, Caitlin? Okay, first thing is, I'm not really going to use this 19.6. What I'm going to do first thing, because I notice it's at an angle, is I need to find the components, the components, the components, the components. So I will redraw this because it's really small. This is 19.6, there's VX, there's VY initial. Not a great drawing, it looks like VY isn't quite vertical, but I know it's supposed to be, so I'm just going to live with it. And this is going to be, what was the angle, 30 degrees right there. And Caitlin, I think you end up with VY being 19.6 times the sign of 30. Is that correct? Or are you okay with that? I'm skipping a couple of steps because I want to get an actual lesson done today. And I think VX ends up being 19.6 times the cosine of 30. And I think this ends up being 9.8, and I have no idea what VX ends up being. What did you get for VX? Nice and loud, sorry, 16.97, is that right, folks? Yep, people nodding. Now I've done the groundwork, I'm going to break this up into horizontal and vertical. I'm going to write down two things right away, horizontal acceleration is zero, vertical acceleration is negative 9.8, and I'm going to write down two more things. VX is 16.97, VY initial is 9.8. So far so good, Caitlin? I know one more thing, I know a distance, a displacement. Look carefully, did they give me a vertical displacement or a horizontal displacement in this question? They did, so what did you put for the vertical displacement? Oh, you did get the negative? You did get the negative? Excellent. It's very important to remember that the displacement is negative. Why is the displacement negative, John? Because you're ending up below from where you started, okay. It looks like I have three pieces of information under the vertical column, so now I'm going to tackle the rest of this vertically. What I really am trying to find is time of flight.  Or if you want to, you can find VY final at impact, remembering that it's going to be negative and then solve for T. Would you like to use the quadratic formula, method one, or would you like to use method two, okay? So if I find VY final, that's going to be VY final squared equals VY initial squared plus 2AD. That's going to be V final squared equals 9.8 squared plus 2 times negative 9.8 times negative 14.7. That's going to be 9.8 squared plus 2 times negative 9.8 times negative 14.7. Oh, missed the decimal. 8.7 squared VY final by a wonderful fluke happens to end up being the same as the angled velocity. That's just a fluke with the numbers. And John, that's also why your two errors canceled out this morning when you were doing it. As it turns out, VY final is 19.6, although that's not quite right. What direction am I traveling when I hit the ground, Caitlin? Negative 19.6. I don't like the fact that it flukes into the same, I'm worried you'll think, oh, that's the same as the angle velocity, no, we never use the angle velocity again once we find the components. It just happens with these numbers by a strange and a wonderful fluke, the angled component of the initial velocity just happens to be the speed vertically that hits the ground at 2. Is that okay? Now that I know VY final, I can find T. T is going to be VF minus VI all over A. That's going to be negative 19.6 minus 9.8 all over negative 9.8. And T works out evenly strangely enough, I think, to three seconds. Is that right? Is that okay so far? Now that I have time over here, I also know time of flight. It's three. And now I say, aha, I have three things. I can find any fourth thing that they want, a V, a D, or whatever, and this question wanted the range, which means they want me to find DX, which happens to be VXT plus a half AXT squared, VIT plus a half AT squared. But what was A? This whole thing is going to cancel. Yeah, the range is going to be 16.97 times three. 16.97 is really close to 17. 17 times three is 51, so I'm guessing the answer is just shy of 51, or it might even be 51 to two sig figs. 50.9, yeah, there you go. Is that okay? Do you see where you zigged? Ah, squared, yes, yeah. Range is horizontal distance, which is DX. Another word for range is horizontal distance, sorry. I know, in a projectile, that's why they call it a firing range. Like in a projectile, the range is range to target. I know, where do we get to math 12 when inverse and inverse don't mean the same thing as in physics? I know. Sorry, you're learning more things and you're realizing that knowledge gets splintered and not everyone uses the same terminology for everything. Okay, English is weird. We say fat chance will mean your chances are thin. No. Alright. Someone, not number 10, is that what I heard? Someone just got that. Oh, we do. I'm going to hold off on number 10 because I think I'm getting to it fairly similarly today. Okay? And I heard someone say number five. I'm going to hold off on number five because I'm going to be getting to that one today. Okay? Okay. So, as far as I'm going to be sending out an email update to you and your parents this weekend, it will not have lesson six on it. I'll probably type it in, but I won't activate it. Whittle away at this. This is physics 12. By the way, welcome to Two Dimensions. I think I said it at the beginning of the year, physics 12 was 11 done, but in Two Dimensions and Components. Okay? Let me hit pause. So, projectile motion, by the way, where it says kinematics lesson five, let's be clever and let's call it kinematics lesson six. I'll have to resave these and change the titles next year. And some of this is review. We said when we launch an object into the air, we'd call it a projectile. Projectiles travel in a parabolic trajectory, but it's easier to use vectors. By the way, there is something called vector mathematics, which lets you do these without components all in one fell swoop, but it's yucky. You'll probably end up doing it that way, those of you that take first year university physics next year, because in Three Dimensions doing components three times is a lot of work. So you'll try and find a way where you can do it all in one step. We break each projectile's velocity into vertical and horizontal components. Example one, right now, get your calculators out if you haven't already, break that velocity into its vertical and horizontal components. I'll freeze the screen. I'll do it up here. See if you get the same thing as me. And I get that. See if you get the same thing. Yes? Now, if I was using this to find more stuff, I would carry extra sig figs. But we've said this year if they ask you a question, give your final answer to two or three sig figs. So I gave that to three sig figs and I quit. But if they then said do something with it, either I'd have the number on my calculator and I'd use the longer decimal version. Or instead of typing VY, I might just later on in my calculator type 24 sine 36. And that way I'm not rounding off at all. And it's not that much extra typing. Summary of the changes, summary of what we want to know. So horizontal motion, VX is constant. The horizontal velocity is constant. This means that the horizontal acceleration is zero, which means that becomes that. This means that if you know the time of flight, you can find the horizontal distance, also Brett called the range of the projectile, I know. Or if you know the range, you can find the time of flight. Vertically, VY is changing, but AY is constant, negative 9.8 meters per second squared. D equals that. Couple of handy things. At the top of its arc, the vertical component is zero for a split second. That sometimes comes in handy. By the way, does this mean that the total velocity is zero at the top?  Incoming. And back. At the top right there was the velocity zero. No, one component was, which component was zero at the top? Vertical was the horizontal component zero. So we can answer this question now, hopefully without me having to throw something in another person. Does this mean that the velocity is zero? I say to you, no. Because there's still a horizontal component. Other handy things. If you start from ground level and end at ground level, your initial vertical equals negative your final vertical. What goes up must come down, and it comes down at the same velocity. As long as it's the same height, same height. Ground to ground. Lastly, if you're starting from a vertical height like a cliff, the ground is below you, which means your final vertical displacement will be what, John? Negative. So, a projectile is launched from ground level at an initial velocity of 200 meters per second at an angle of 38 degrees. Dulp. Lea, dulp stands for draw a little picture. It's an acronym that I use. So whenever I say dulp, what I'm saying is let's draw something. There. 200. There's VX. There's VY. And the angle is 38 degrees. Good to see you back as well, sir. Good, find the X, find VY. This to me, I won't call it a no-brainer because you're having to trigger some thinking, but to me, this is as close as you'll get to three marks. I will, on your test, on at least one question, say, find the vertical and horizontal components. Hopefully you can do that almost in your sleep. Some of you, the way you're yawning, probably are doing it in your sleep. Not to mention any names. And do you get 158 meters and 123 meters per second or meters per second? Are my answers right? Oh, wow. I put them in brackets, but I was doing them in my head with no calculators, so there is a chance that some of these might be wrong. Sorry, doing them in my head is not showing any work, only on a calculator while watching TV. It wasn't the best way to make up an answer key. Now, Kara, you may have noticed often next to VY, I'll put a little I for initial. Why don't I put a little I for initial next to VX?  But VY does, so I might want to remind myself, this is what I'm starting out at vertically. And it's going to be getting smaller, smaller, smaller, smaller. Zero for a split second, getting bigger, bigger, bigger, bigger, but negative. Okay. Find the time of flight. Well, the first thing that we would do is we would break this up into horizontal and vertical. And you can abbreviate them H and V if you want to. You can abbreviate them Hori and Verdi, whatever, but something that's clear to you, in fact, I've seen some kids abbreviate it as X and Y, but to me, since we use the phrase horizontal and vertical, H and V would make more sense. And let's list our data right away. Let's defic. Lea, defic is another acronym. Defic stands for data formula insert crunch, and it's another approach that I use in physics as well. So I know AX is zero, AY is negative 9.8, I know that VX is 158, I know that VY initial is 123. How many pieces of information do I have under horizontal? Two. How many pieces of information do I have under vertical? I can't solve. There has to be something else, and there is. What else do I know? I know something else about vertical. Oh, what's my displacement? Ah, since I'm starting and ending up at the same height, I know that that's zero. How does that help me find T? Do I have an equation that has A, V, I, D, and T in it? I do. Which one? The quadratic, the squared, the T squared one. That's one. D equals VIT plus a half AT squared. If I plug in all my numbers, I get this. Zero equals 123T minus 4.9T squared. Mr. Duck, yes, Connor, where did the negative 4.9 come from? Where did the negative 4.9 come from? Half of 9.8. That one I've done so often, and I also know two times 9.8 is 19.6, because that shows up in the VF squared equals VI squared plus 2A. What kind of an equation is this? It's a quadratic. How do I know it's got a squared? How do I solve this one? I don't use the quadratic formula. I could. Am I wrong? If you've got your quadratic solver, knock yourself out. If this one factors, what's the first thing that I always, always, always, always, always, always, always, always, always, always, someone's got me always, always, always, someone's got me always look for when it says factor. You guys, I heard it. Always look for a GCF first. And if they didn't drum that into you in grade nine, well, then you never had me in math nine, and you didn't because I don't teach math nine right now. Always, always a GCF. First of all, because if there is a GCF, it almost always makes everything else smaller and easier to factor, and you'll catch the subtle one. There is a greatest common factor here. There is something that appears in both of those terms on the right. What? I heard it. What? You can factor out a T. Put your pencils down, look up. If I gave you this in grade nine, I'm sorry, in grade 11, zero equals 4x squared minus 5x. That's a quadratic. How do I know? It has a squared GCF. What's the GCF? You would have said, okay, factor out an x and it's 4x minus 5. What are the roots without doing any extra work? What are the roots? What did you learn last year as shortcuts? What did this give you as a root? I heard it. And what about here, Matt? It was change the sign of the constant divided by the coefficient. Change the sign divided by the coefficient. What if they had been really mean and if they had done this, 7x minus 3x squared? What kind of an equation is that? It's a quadratic. How do I know? It's got a squared. Yes? Factor out the x. You would say, oh, this is x bracket, 7 minus 3x. What are the roots? What's the first one? This is the easy one, zero. What about here? The rule is change the sign of the constant term divided by the coefficient. That's what you were doing with your shortcut here. It's just last year they almost always put the x first and then the constant term and so you probably didn't actually go through those steps. You just saw the root. But for what it's worth, it's change the sign of the constant term divided by the coefficient. Got it? Make sense?  What are the roots? What's the root here? This is the easy one, zero. By the way, what we're saying is at time zero, you're at a height of zero. What's that really saying? The projectile was launched from around the, oh, mathematically that popped out, too. What's the second root? Louder, I think you're right. Change the sign, divide by the coefficient. Whatever the heck that is is a decimal, please. By the way, the reason I'm showing you that is if you're launching from the ground, it is still a quadratic but you don't need to use the quadratic formula and I think that's way faster, Jeanette, way faster. It is negative 123 divided by negative 4.9, someone? Equals 25.1 seconds, which is what I said. That's a unique situation where your quadratic will still stay a quadratic but not a yucky quadratic. If you're starting on ground, ending at ground. There are other ways you could have found the time of flight. You could have found the time to the top because at the top, how fast are you traveling at the top vertically? Zero and then doubled it to get back to the ground and you know what you would have got? 25.1. But you would have had to do two separate little solving of things and this got us there in one shift. Is that okay? D says, find the range. Okay. You know what another expression for the range is, Brett? That. Oh, by the way, what did we say the time of flight was? 25.1. I would walk over here where my horizontal section is and I would make a little note, hey, T was 25.1 and then I would smile because how many different quantities do I have on the horizontal side? Now? Three. Now I can solve for any fourth one. In this case, they want me to find the range, the horizontal range. I'm looking for an equation that has A, V, T, and D in it and it's our old favorite, our old stand by, our old reliable, D equals VX, T plus a half AX, T squared. And once again, woohoo! And I get 158 times 25.1, what do you get for the range? You get 3,960, almost four kilometers, sorry, 50, okay, so 3.96 times 10 to the third. If we go to three six things, E, find the maximum height, am I going to solve this vertically or horizontally? Am I going to solve this vertically or horizontally and there's an obvious answer screaming out of me in the way the question is phrased? Why vertically? Height, that's a vertical word, yep, okay. I still have my vertical stuff listed right here, except T is not going to be 25.1. Maximum height, the top, what else do I know at the top? I know one more nice thing at the top, VY final is zero. And they would like me to find DY, the height, the vertical displacement. And from up here, I know AY is negative 9.8 and I know that VY initial is 123. Do I have an equation that has VFDA and V initial in it? Which one, Mitchell? Did you say the letter T, because if you said the letter T, I don't see a letter T sitting anywhere here in part E, so I don't think I can use it. I'm looking for an equation that has VFDA and now, here's what Mitchell said. Why wouldn't you just take half of the T? Here's why, if I got that wrong and I take half of it, I guarantee I'm getting this one wrong too. That to me is bad test writing. I'll use what they give me whenever I can. Right now in here, the only one I've had to calculate is my component and I can do that in my sleep. I'm going to use the one equation that uses these without time, because that way I'm not using perhaps bad data to find a bad answer. Which one? Yeah. Can you get the D by itself, please? No. Why don't you forget to say out loud, VF squared minus VI squared, all over 2A, yes I'm yelling again, Joe. If you're scaring me, get used to it. Zero squared minus 123 squared, it was 123, right, yeah. All over 2 times negative 9.8. Caitlin, do I need to square root this one? This answer? Do I need to square root my final answer? No, just making sure that I dig that little, you know, put my thumb on that little bruiser. How many numbers are on top, Kara? In my fraction, how many numbers are on top? Two, rackets around the top, yes. How many numbers are on the bottom? Rackets around the bottom, yes. You want to practice these on your calculator.  Dumb. Do you get 772 meters? So far so good. Next page. Caitlin, look at part C of example two. That's the question, question five that you were asking me, basically. It's going to be the same idea, finding a final velocity if you know the time, okay. In fact, look at part C in example two. It's similar to the one in example 10, but in example 10, the question 10 that you asked me, instead of giving you the time and saying find the final velocity, they gave you a horizontal distance which you could use to find the time and then find the overall velocity. Trust me. A projectile, it says, is launched from a 45 meter high cliff at an angle of 64 degrees with the horizontal. And with an initial velocity of 36 meters per second. Dump. Let's draw a little picture. There's my cliff. There's my projectile, 36 with an angle of 64 degrees, and this height here is 45 meters. That's a pretty good picture. You'll notice I did it nice and big. I've learned to make dumbness strikes when I do small little midget pictures. What does part A want me to find? Range. Can't do it yet. In fact, you know what I need to do before I go further at all? Let's find the components. Let's do that right over here. I'll freeze the screen. Try it yourself. I went for sig figs because they didn't ask me to find the components, so it's not a final answer, so I'm going to keep some extra decimals.  It can't be that they get this reaction anymore. Your TV at home is never on? Well, talk to your parents. Maybe there's a reason for that. Now what would I do? Now what would I do? What did they ask me to find? Range. I can't find the range. You know why I can't find the range? To find the range, I have to find something else first. Time. You know what this question is really asking me to find, really asking me to find time of flight. How am I going to do that? Oh, let's break our page up. Yo, let's break our page up. By the way, 15.78, I've got to get this battery replaced. It's barely ever working. Sorry. Thanks for letting me know. I got a VX of 15.78, a VY of 32.36, and I broke it up into components, and right away did my horizontal vertical. It would be nice. An easy question, Sean, would be if they'd given me the time of flight, then they could ask me to find the height and the range, and I could find those both pretty easily because they're both distances and more plug and chug. But here, they've asked me to find the range. Oh, I know one more thing, by the way, because right now, I only have two quantities in each column. I can't solve for anything. What else do I know? Vertical displacement is negative 45. And since I have three things here now, I can solve for t. You can either solve for t using the quadratic formula and your quadratic solver, and I'm good with that, using d equals Vi t plus a hat of t squared. Or you can find VY final, negative when it hits the ground, and use that to find time. Who would like to use the quadratic formula approach? Who would like to use the VY final approach? Well, the vote was apparently five to two. Thank you for participating. Okay. VY final squared equals VY initial squared plus 2ad. VY final squared equals 32.36 squared plus 2 times negative 9.8 times negative 45. And Caitlin, what will I do at the very, very end? I will square root. And I get 43.9. Which is actually wrong? Kara, what did you say? I think, did you say negative? Yeah, I was reading your lips. And the second time when I said what you say and you didn't say it any louder, it's still reading your lips. Yeah. Turns out, VY final is negative 43.92. So I have VY final, VY initial, a, I can find t. What equation has VF, VI, A and T in it? By the way, I'll say this again. If you haven't clued in that it's really helpful in physics 12 to have your formula sheet out in front of you during the lesson, which is why I gave you two of them in the first place. You might want to actually clue that in because I'm also wanting you to train your eyes to look in the right place. That helps, believe it or not. At least one per table would be clever. So which equation? And I love the fact that you got the t by itself. T equals VF minus VI over A, which is going to be negative 43.92 minus 32.36 divided by negative 9.8 bracket, negative 43.92 minus 32.36 closed bracket divided by negative 9.8, 0.8. I get a time of flight of 7.78 seconds. Someone else want to double check me? Quadratic guys, if you use your quadratic solver, you should got a negative answer and then your positive answer should have been this. If not, hit me up later. 7.78 seconds, 7.78 seconds. Oh, no, wait a minute. I'm not done. Emily, what was this question you asked me to find? Part A said find t. Part A said find t. Yeah, a little faster, ready? Part A said find that, range. Which, Brett, is actually d what? Now, dx. And as it turns out, Brett, dx is just Vxt. What happened to the half at? Oh, yeah, it cancels. Notice I'm taking a few more shortcuts now, right? It's going to be Vx, which was 15.78 times 7.78 times 15.78. And I get a lovely range of 122.8. Oh, no, three sig figs. I get 123 meters. Am I right? That would be a great written question for probably five marks. Very nice. What are you wanting? At what time does the projectile reach its maximum height? Oh, height, vertical, vertical, vertical. Really quickly, let's write down. Ay equals negative 9.8. vy initial was 32.36. They want me to find time. Oh, and there's one more thing I know. At the maximum height at the top, what do I know? vy final is 0. You know what I think? I can use the good old vf equals vf. I can use t equals vf minus vi all over 8. It equals 0 minus 32.36 all over negative 9.8. How long to get to the top? You get 3.3 bracket, 0 minus 32.36, close bracket, divided by negative 9.8. Show me the goods. 3.3 seconds. That's part one of part b. Joel, what's part two of part b? What's the second question they ask? How, what? Ah, you know what that is? That's saying, hey, find dy. So I'm looking for an equation that has d in it and then has av initial and t, or av initial and vf. I think I can just use plain old d equals vit plus 1 half a t squared, right? Do I know vy initial? Yep. Do I know the time? Just figured it out. Do I know a? Oh, this is plug and chug. V initial, 32.36, t 3.3 plus negative 4.9, 3.3 squared. Where's the negative 4.9? Oh, all right. That's right, half a. And you get 98.4, right? You get 98.4? I don't think you do get 98.4. In fact, I know you don't, people who are faking it on their calculators. What do you get? Louder, Katie. You get 53.4 meters. Why is that not the maximum height? Why is the actual answer 98.4, like I wrote in brackets? Matt, we're on a cliff. What we've just figured out is how high above your starting point you reached. You made it 53.4 meters above your starting point. But how high was your starting point, according to this question? How high was the cliff? D equals 45 plus 53.4. And that's where the 98.4 meters above the ground comes from. Question, Mitch? No? Question, Brett? Sure?  You good? You good? Sorry, the drool's just chronic. OK, my bad. C, yes. Can you know what the homework's going to be? Probably number one. Probably number two. Probably number three. Probably number four. Sure, six. Couldn't you just say, oh, Mr. N- Yeah, well, I could have. We're nearly done, OK? This is going to answer your questions. Folks, you want to watch the last few minutes of the lesson because I like this question. I like part C. I like this question. I like this question. I like this question. Why would I say I like this question so many times? Did I say that? Or are you just like, really? I never would tell you that. You're just a good student who notices things that teacher has emphasized. Good. Brett says, find the velocity at t equals 2.4 seconds, OK? If it took 3.3 seconds to get to the top at 2.4 seconds, is it on the way up or on the way down? It's on the way up. Here's what I think that velocity looks like. I think that velocity looks like that. And I think it's made up of two components, the horizontal velocity and, don't write this next part down, Vy at 2.4 seconds. I think however fast it's traveling vertically after 2.4 seconds, if I add those two together, that should give me my resultant. Except instead of calling it Vy 2.4, I'm just going to call it Vy final. Because that's where it's going to appear in my equation. I know this because it doesn't change the whole time. What was Vx? I've scrolled down. What was Vx? We calculated it at the top of this question. What was Vx? I think that was Vy initial, was it not? What was Vx? OK, don't get them mixed up. 15 point what? Sorry? 7, 8? The most common mistake is kids get this concept and they go, that's Vx, Vy. They put 32.36 right there. And they do the Pythagoras. And you know what they get as an answer? They get 36 meters per second at an angle of 64 degrees. They've just gone backwards and uncomponentized their velocity. Instead, what we need to do is we need to go vertical over here for a second. And we need to realize that Ay is negative 9.8. Vy initial, what's Vy initial, Nicole? 32.36.  So I should be able to find Vy final. As a matter of fact, I have an equation that's already got it by itself. I think I can go Vy final equals Vy initial plus AT. It's going to be 32.36 plus negative 9.8 times 2.4. Question, Mitch? Is that OK? What is my after 2.4 seconds? I'm still traveling horizontally, because Vy.7.8. But what's my vertical velocity after 2.4 seconds? It's slowing down. What do you get? Sorry? Anybody else? 8.84? Probably depends whether you used a rounded off version or what. So 8.4, 8.34 meters, 8.84. Sorry, guys. 8.84 meters per second. By the way, what if I got a negative answer for Vy final? What would that tell me? It would tell me I should have drawn, instead of the blue line going upwards this way, I should have drawn the blue line going downwards this way. But it'll work still. Now, this is the velocity at 2.4 seconds. You good? How can I find this? By the way, when I had that stark realization, I probably also would have gotten a little shiver and like, oh, yeah, absolutely. I agree with that. So how can I find the magnitude of this velocity? What grade 8 math skill can I pull out of my back pocket? Well, let's do that. Velocity at 2.4 seconds is, and I'm going to do that all in my calculator. It's just I'm actually going to find the squared. What will I remember, Caitlin, before I'm done to do what? Yes. So the magnitude of the velocity I get is 18.1 meters per second. What angle will I use? Hey, how about that one right there? Jacob, can you help me out? Jacob, can you help me out? Thank you. You're back? Where were you? Oh. Jacob, opposite of Jason for hypotenuse. What trig function? What we do in Hawaii? Yes. In fact, the tangent of the mystery angle is going to be opposite over adjacent 8.84 over 15.78. How can I figure out the actual angle? Ah, nothing. How can I figure out the actual angle? Hey, inverse tan of 8.84 divided by 15.78. And I get 29 degrees. At 29 degrees. And we said last day we would say this as above the horizontal. Caitlin, does that answer your question? That's how I approach. If they want me to find the velocity in the projectile's flight at any time, I find the two components. The horizontal I've probably already found. The vertical, they're either going to tell me the time or breadth in question ten, which is a bit trickier. They told you how far to travel horizontally. And since you know the horizontal velocity, you can find how much time has elapsed. And then you'll know T. And you can plug it in to find BY final, add the components together, do the Pythagoras, and do the trig. What's your homework? 1 to 6, as well as the stuff from lesson 6. I have a couple of videos, but I'm going to show those next class because you guys are zoning out on me.