The following is a presentation of TFNN Trade what you see With Larry Pezzavento Call now toll free at 1-877-927-6648 or internationally at<PHONE_NUMBER> Now Larry Pezzavento Okay, looking good Billy Ray feeling good Lewis. We're going to cover some other things that That are important. Well, everything's important, but this is one on natural gas. This is the daily I want you to notice here. What we're looking at here is strong support You notice that we're coming down now What we're going to do now is we're going to go down into a smaller time frame to try to find a pattern That will line up to tell us that yes Maybe this would be something that we get interested in and so what we're going to do is we're going to go to the four-hour chart And we're going to bring it up and this is how I set up a trade most of you already know how I do this But there's the four-hour chart. You can see The ABCD up here at the top Okay, and now you see the corrections that we had there's a 3a2 here 3a2 here You can see the market coming down and it's getting really close to this level right here, isn't it now The 50% didn't hold it the 61% Didn't hold it and will the 78% level hold it. Well, there was no ABCD here And there was no ABCD right here So we want to find out if there's going to be something Right at that spot that's going to give us an idea that yeah, maybe we can take that risk So what we're going to do now is we're going to go down with our little tiny microscope that I got from Louis Pasteur When I helped him solve the uh, what did he do infections? I like Pasteur because he said chance favors the prepared mind. That's one of my favorite Quotes, okay, here's we are with a hourly chart now From four-hour to the hourly and now you see guess what we have folks We have a beautiful three drive to a bottom pattern. Look at the symmetry here ABCD right in here. Guess what this is This is the 78% level that we saw on the chart So now do we have the 78 plus we've got a bcd coming in right here You can't ask for anything better. This is a picture of the wheat market folks And we also what wheat market wheat we went from 604 all the way up to five six 53 almost 50 cents in In two days So anyway, that's what we're going to be watching here tomorrow So that'll be something that I'll put on the video tonight and say, okay This is something if you like natural gas and natural gas trades a lot folks. I mean huge It's in the neighborhood of crude oil. So this is not This is not something to take lightly. It's it's the real the real thing and it's good swings great stops I mean it's it's it's a real it's a real event. So if you haven't traded natural gas before I would take a look at it because Well, first of all these patterns don't work all the time, but when they do they work pretty good Now here's that same pattern In the wheat I'm just going to get up The only difference is is one is wheat and the other is natural gas But you'll see here There it is. There's your there's your drive one right here Drive two right here drive three right here. There's your abcd Bada bing bada boom. It's went off the top of the chart Went up to 653 today folks Straight up. I mean that part of that of course may be short covering, but that's neither here nor there That's where it went to so let's uh, let's keep an eye on that too for the next couple of days because a little pullback Tells us that we're most probably getting ready to be a buyer Now Go to repeat a couple things here paula web will be my guest again here in a little bit But uh, this is the one you want to focus on folks. I keep knocking on the door here, but This is the kind of door you like to have believe it or not.  So we've hit it three times in the last few days The exact 61 percent retracement of the high going back here a little over a year ago Look at the beautiful patterns on the way down a b cd abcd there again is the three drive To a bottom pattern folks The three drive to the bottom pattern is my go-to pattern when I have a really bad run of luck And luck is when you're not prepared. I understand that and I do have those So when I have trade when I trade poorly, which I more often than I'd like to admit The thing that I like to go to is to go right back into that three drive to a bottom Or three drive to a top and the reason is is when you get to this spot right here All your decisions have been made You buy it and you risk a small amount because if it goes beyond there That 1.618 level you flat out wrong and you have a zero chance of picking up any bread on that one So let's uh, let's remind ourselves of that. Okay, so there's what we're watching right here in the euro Now looking at this on a shorter time frame. I keep repeating myself But repetition is the mother of knowledge and the father of invention. Let's get this up here So you'll be able to see it. This is it on the four-hour chart Because then you can see about six weeks of data in here There we are look at you can see I didn't do all the abcd's in here But there's they're all in here But I just did the main one because that tells us we're up into this area. We've hit it once twice Three and now today it hit it again and now it's reversed quite a bit We're back down into this level right here So this is tell us but if we do get above there if we go smashing above it and we close above it That is going to be extremely bullish now. Remember the s&p when we were at that 4206 level uh on uh the 26th uh last wednesday How long was it there folks get your stop watch out? It wasn't there more than two minutes That meant that that was not a breakout that was just stops getting hit And those stops are protected. I mean no one's out looking for those stops But they that's where the market will go to and what there's nothing there it reverses and of course, you know the market reversed So that's what you want to do if it breaks out to the upside and if it does Then you've got to say all right this thing can go a long way And you don't want to stand in front of it. That's the That's the main thing now. Let's go back and talk about crude oil here because this is a something that very unusual happened here in the crude oil last night because it market dropped after the market Was in the secondary market in the evening we dropped from Drop four dollars a barrel folks to take out the lows here of march Okay By just a little bit and then it reversed And it reversed all the way up from 64 up to 69 and jumped five dollars a barrel Hey after it's down so much you expect it to be down But the thing was if you believe in the 3a2 which we do I want to bring up the 3a2 here now in the That in the crude oil and you'll be able to see it stopped right at The 3a2 level right here and now it's going this gives us a price objective up here Which is quite a bit higher but uh 10 dollars off the bottom But at least it hit the exact 3a2 now if this fails Then all bets are off and we're going to be going Down but right now that hit it and rallied two dollars a barrel or two thousand dollars so Very very important to follow the patterns when they work and when they don't work don't follow them Go look at something else. Let's take a break eight seven seven nine two seven six six four eight Currencies commodities and bond markets are as important as ever right now with how they're driving the volatility in equity markets across the globe Which is why it's a great time to try out teddy keg stats tiger forex report Teddy keg stat breaks down the forex markets every monday using his 30 plus years of experience as a trading veteran of futures Forex stocks and options teddy releases his weekly tiger forex report every monday morning with coverage of all the major currency pairs Including the dollar index the euro dollar pound dollar dollar swiss Dollar yen as well as many more and he also has weekly coverage of the crude oil market and the 30 year t bonds As they both influence forex markets tremendously when you sign up for the tiger forex report You also gain instant access to teddy 60 minute webinar archive He just hosted forex strategies and fundamentals What is behind the tiger forex report for all the details and to start your 30 day tiger forex report subscription today Visit the front page of tfnn.com tfnn educating investors Tfnn has just launched their new trading room the tiger's den hosted at discord Tfnn has been educating traders for more than 20 years with live programming hosted by a variety of professional traders during market hours And now they are expanding their reach with the tiger's den available to all tigers and tiger's for just one dollar for the year There's no catch or added costs when you join our community of traders in the tiger's den You can look over the shoulders of tom o bryan and the other tfnn hosts while they analyze charts during their live tiger tv programs And join an interactive trading community with hundreds of members exchanging ideas Interact with other tigers and tigers as they share trading ideas news analysis and discuss the market action all trading day Even at night and on the weekends the tigers den at discord is accessible on mobile or tablets as well So it's always at your reach to sign up today and become a part of this educational community of traders Just visit the front page of tfnn.com Are you looking for a way to consistently add winning trades to your portfolio? Tom o bryan is here to help Tom o bryan has been successfully trading markets for over 30 years A frequent contributor to td ameritrade network and cnbc Tom o bryan founded tfnn over 20 years ago to help educate investors just like you Tom's daily market newsletter market insights is published every morning when the market's open to give you the competitive informational edge you need to succeed These newsletters are packed full of tom's advanced technical analysis and are geared to deliver comprehensive strategies for a successful portfolio Get tom o bryan's newsletter market insights today and try all of our products and newsletters 30 days risk-free with our money back guarantee at tfnn.com tfnn educating investors O bryan has won<PHONE_NUMBER> internationally at<PHONE_NUMBER> Okay, folks. I've put up a chart here of a three minute chart in the s&p Someone asked the question do these patterns work on any time frame and the answer is yes Because mandel brought when he talked about his fractal analysis, which he's the father of Everything depends on this A b c d pattern all you have here is a smaller a b c d pattern coming in right here and that forms another a b c D to the upside that's really what you're That's all you're following. There's other a b c d's in here, but I just wanted to show you the really clear ones That's what you're supposed to look at when you're trading is find the ones That are very very easy to see and put those on Right now. There's not too much that's easy to see in here. Sure. There's some a b c d's, but they're not clear like these are So that's why you want to focus on that. Okay Very very important at least from my perspective. That's uh, that's the way I uh try to try to look at things So I don't really have anything more to say than that um, I've been asked to Talk just a tiny bit more about that german dachs Try trade that was up here earlier today And then I'll also do the footsie since we're going to redoing these again. Paula Webb will be my guest at the break But here is the uh, this is the german dachs Tom who guard trades this uh every day You can see the a b c d patterns that are here. This one comes in Right at the 61 percent retracement Then the market goes up and makes a very strong a b c d Stops right there and and look how often it stays there folks It stays there for well over several hours That's either distribution or its Distribution or accumulation But this one was distribution the reason why you know that Is if you take a look at the four minute chart You'll see that the market had a very substantial break to the downside in typical a b c d there's your a b c right at your 61 And then down and then you had a very good rally In fact, this rally right here stopped right at the 61 percent retracement was equal To this rally right here. In other words, if you measured it up To there and moved it over And measured it here and moved it over it would stop right at the 61 percent retracement. So That's how you start to look at them Interday I I just try to prepare the trades and I'm trying to find and when I put those on those are the ones that I try to I try to look at and I had to read I'm going to bring this chart up here because I think the chart here that jeff sent us On the dow Jones emini is extremely important and I want to bring it to your attention again Here it is is what we're looking at There is the one three five pattern folks. This was given to me by Roy Longstreet and his son bill all I did was help them with the ratios They watched the time from this high to this high to this high Is where you would expect the market to reverse and that's exactly what's happened Now what's happened here? You see we had this big up move then the down move then the up move So everybody that's bought it here in the last two days is now setting underwater So all the market has to do is to close sharply lower today or tomorrow And they're going to trap a lot of people and that's going to make the market Accelerate to the downside and you can see here After point three, there's point one. There's point three. There's point five There's where the big drop happened now if this drop equals that one You're talking serious money down in here. Of course that will lead to what we think will be Very very bullish scenario On a longer term basis now. Let's look at another one that Cb told us just chuck was kind enough to send us this chart This is the sp y and this is not this was earlier this morning and it is not It's rallied of course from there, but it's done a perfect abcd pattern. That's exactly what it's done And I remember this is the cash s&p So it was perfect. It stopped went down below these lows by just a little bit and stopped this makes We get really strong today folks. We're going to go higher And that's the whole key is to watch it because if it does that It's going to go a lot higher not just a little bit higher But a lot higher probably way above that 42 4206 that we saw on friday very very important to Pay attention to that I wanted to go over one other thing and that is that gold trade That I did yesterday because it was absolute perfect trade It well it was even though that it Didn't make any near near what it could have been if I'd have been a buyer of the pullback But there was the number and the market backed all the way Down into this level right here. We backed off $17 that's one half the harmonic number and then folks it took off We got up to here right near the close and then right after the close they went into the overnight session and this thing jumped went up to 2081 that was $16 higher than my 78 percent level But I had taken some profits here and then I'd moved my stop to 41 I figured if I got to 2041 Late in the day it probably wasn't going to break anymore So my second one only made a few bucks on but out of the first one I did relatively to relatively. Okay, and I trade two Sometimes I'll take scalp them off. Sometimes I'll take one off But I'm here to make money and if I think it's time and I make a decision I try to find the ones that line up the best and those are the ones that I try to do That's uh, that's neither here nor there. So I hope that helps Because I am far from infallible as a matter of fact. There's there's just no question about that Let's take a look here at one market that is extremely weak And they just keep beating it up and they beat it up again today here. And that is the russell 2000 which is the uh small cap. This is one of the reasons why that banking index Is so bad because these are come from the regional banks These are the stocks that the regional banks led money to and as you can see here We were we're way down below here already folks We got down to this level whether we're going to close there and I don't know but look at this We hit the 3821 to three times Over a three week period and it couldn't get one tick above it Boy, if that wasn't telling you that the market was weak the s and p It went higher so to the nas so to the nasdaq and so to the dow Jones But not the russell and the russell is the second Most actively traded you got the s and p 500 first E mini and then you got the russell e mini then you have the nasdaq e mini and then you have the dow Jones e mini That's why when you're watching these things you got to be determined which one you're going to be looking at Take a look at the price of Microsoft folks msft that thing is only down three or four dollars from its high I mean, that's nothing. I mean that that's a tremendous Tremendous move here And and no follow through to the to the downside. So And I think microsoft I know apple has the earnings out today and of course I think 80 out of 80 percent of the time when the earnings come out that Stock gaps up, but the 20 percent that it doesn't that's a big thing to to remember here So stay tuned. We're going to have paul and douglas's. I guess tomorrow will be mike more More analytics. So we'll be right back The gold report As a precious metal gold is still king It continues to hold the most effective safe haven and hedging properties across the global major trading hubs of the london otc market The us futures market and the shanghai gold exchange the gold report tom o'brien publishes his weekly gold report every monday morning for subscribers consisting of coverage of the xa u hui gdx the dollar bonds the south african rand As well as 25 different mining equities with specific buy sell recommendations The gold report New subscribers get a 30-day money back guarantee. So you have nothing to risk subscribe To tom o'brien's gold report newsletter now at tfnn.com Sharpening your skills as an investor is like getting better at playing a musical instrument You have to practice sure, but you also need excellent instruction from experts at tfnn You'll get advice and guidance from the authority and technical market analysis And it's not just dry tedious text either tfnn airs live financial content streamed live on tfnn.com and tfnn's youtube channel with tiger tv Live every market day from 8 30 a.m. To 4 p.m. Eastern for free Each host is an experienced trader and gives their take on the market while taking calls and questions live from around the world From the moment the market opens until the closing bell sounds tiger tv has eight different shows with expert hosts To help you make the right moves with your money Watch online at tfnn.com or on tfnn's youtube channel and become the investor. You were born to be tfnn educating investors Are you looking for a way to consistently add winning trades to your portfolio? Tom o'brien is here to help Tom o'brien has been successfully trading markets for over 30 years A frequent contributor to tdm air trade network and cnbc Tom o'brien founded tfnn over 20 years ago to help educate investors just like you Tom's daily market newsletter market insights is published every morning when the market's open to give you the competitive informational edge you need to succeed These newsletters are packed full of tom's advanced technical analysis and are geared to deliver comprehensive strategies for a successful portfolio Get tom o'brien's newsletter market insights today And try all of our products and newsletters 30 days risk-free with our money back guarantee at tfnn.com tfnn educating investors This segment is brought to you by think or swim for more information Just click the think or swim banner on the front page of tfnn.com Okay, folks proud to say that we have paula tea on the line again paula tomosini web douglas pt tell me tell me the tomosini part. I I call i've been calling her pt since uh, oh my gosh. I don't I can't I spent so many years. I I can't even remember at work. I was born Yeah, well since you were born that's true Just being the teenager that you are now word is a tomosini Is that your uh Well tom tomosina was my mother's name and it's also my middle name And yeah, uh, I there was one time when my mother was over and you were you were in town And you said hey tomosini and you may not remember but my mother and I both Looked at you and said what?  So she appreciated that well, you've uh folks uh paula and mark has entertained my family for Uh christmas and easter And thanksgiving for so many years. Well all the years we've been here together here, uh In uh in arizona and also uh in california, but bt. I don't know. I was just thinking about when we first met Uh, I was walking along michigan avenue I hadn't known you more than two days and I was bucking up on a trade I don't remember which one it was and probably an air trade But anyway, I had had lots of money in my pocket and I stopped at a louis vitton Store to buy you a purse because you kept saying you want the louis vitton purse And and I had no idea these things cost like 800 dollars You know, so you said one at 800 so I bought you this purse and uh, I don't know if you still have it or not, but by golly, I Walked in and I and I was when you were so happy to get it. I said, well, okay. It was worth it But i'm not kidding you paul. I had I had uh Reprecussions and the second thoughts of that for weeks 800 dollars for a leather purse. Are you kidding me? My mother would have rolled over in her grave I know that's uh, no, we've we've had some fun through the years. That's for sure Anyway, here's a question I have for you a person wants to start trading Of course, they won't start with the psychology part, which is the most important But if you if someone called you and said I want to be a trader. What would you tell paula? And you get you probably get these calls all the time, don't you? Well, yes, I do as a matter of fact and Obviously one of the things I ask them right away is if they have a methodology If they have a good platform or you know a system Um, I kind of go through the the nuts and bolts of it first And if they don't have a methodology, obviously as you know, larry, I refer them over to you Uh for some some training, uh, you know, hopefully and um Most of the time they have a good platform I would say probably 80 of the time they don't have a system and a lot and and the trouble is that a lot of new traders They want to create their own system But since they don't really know anything about trading It's really difficult for them to understand how to create a system so and I kind of usually try to talk them out of that but Gently but um, and then the other thing, of course, I just tell them, you know You need to at least read at least one of our books, whether it's the discipline trader or trading in the zone and If they really don't know that much about the markets then, you know Our third book the complete trader because that that kind of gives you the background on how the markets work together It talks about, you know price action volume open interest price movement all of that because most of today's traders if they're younger than let's say 40 They grew up on computer games and video games. So they are convinced that trading is just A computer game that they're they're going to attempt to beat So that that's a really big misconception these days So that's that's kind of the overview of what I try to impart to them How would the person purchase that book? Do you have it online or is it hard copy or how would they buy it? Well, all of our books are on amazon and barns and noble Obviously if they want a uh, a personally signed copy by mark douglas I still have some in inventory. Those are a little more pricey, of course, but um They they they were signed by him personally. So I do have some of those But yeah, all of our books are on amazon and barns and noble and if and if you have any trouble You know purchasing it or whatever Or they're out of stock just you know contact me Let me know the best way to the best way to contact you is polytweb.com or 760 636 4 2 9 0 i'm in the office seven days a week for you guys And anybody calls me from larry show gets the family and friends discount That's the you know that you know, we're really lucky though because we get to do what we like to do and uh And what I think confucius said find a job that you Uh really enjoy doing in your own vacation the rest of your life And of course we've been had that and we've traveled so many places together Uh, this just has been really really great. One other question I had here This is from somebody in wichita, kansas and he said he has a problem with his relatives Saying that he is nothing more Than a gambler that he should be playing blackjack or because it's something like that And I I tried to give him my what what would how would you respond to that? Well first and foremost You can't convince anybody who's not a trader that what you're doing is a worthwhile business adventure You're not going to be able to convince them of that because they have no concept of what trading is about Second of all, I know you'd love for your families To support you but you knew that going into it So You're just going to have to Not talk about trading You know call yourself an investor Which which they can understand and you can say well i'm investing in in our financial future And this is how i'm going to do it. You don't have to go into great detail Just say I am investing in our financial future and and that may that may help Well, I've tried everything else. I always tried people that hey, we've got jeff from new jersey on the line Jeff you have a question for paula? Hi larry thanks for taking my call. I wanted to tell paula about a psychological Aid that I came up with for myself that made a big improvement To my training and I I wanted to see what paula thought about Okay So The problem that I was having is that When i'm in a trade I'm completely focused on the trade and I have trouble Observing myself To catch myself from doing something I don't want to do like breaking one of my rules or Taking the type of trade I don't want to take But you know I did in my past so My problem is just I don't have a big enough brain to focus on my trade and to observe what i'm doing at the same time And then when the trade's over and I lose money, then I realize how what did I do that for that was stupid But if I could realize it before I took the trade that would be better So what I did was I I started a log And the log has why i'm entering the trade and also why i'm exiting the trade And so what that did for me is that when i'm Oh, are we breaking jeff? Yeah, I want you to stay with us We got another one. We want to continue with your trick for trading. This is important We'll be right back folks with jeff and paula t Tomasini web douglas on the line Sharpening your skills as an investor is like getting better at playing a musical instrument You have to practice sure, but you also need excellent instruction from experts at tfnn You'll get advice and guidance from the authority in technical market analysis And it's not just dry tedious text either tfnn airs live financial content streamed live on tfnn.com And tfnn's youtube channel with tiger tv live every market day from 8 30 a.m. To 4 p.m. Eastern For free each host is an experienced trader and gives their take on the market while taking calls and questions live from around the world From the moment the market opens until the closing bell sounds tiger tv has eight different shows with expert hosts to help You make the right moves with your money Watch online at tfnn.com or on tfnn's youtube channel and become the investor. 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If you trade china a shares now may be time to take a closer look trade chau or chad Directions daily csi 300 china a share bull and bear etf's china a shares in either direction Visit direction investments.com today an investor should consider the investment objectives risks charges and expenses of the direction shares carefully before investing The prospectus and summary prospectus contain this and other information about direction shares to obtain a prospectus or summary prospectus Please contact direction shares at eight six six four seven six seven five two three The prospectus or summary prospectus should be read carefully before investing an investment in the funds is subject to risk Including the possible loss of principal the funds are designed to be utilized only by sophisticated investors such as traders and active investors distributor four side fund services LLC This program is brought to you by vista gold traded on the nyse american and tsx under the symbol vgz We're back folks. We're speaking with paul t web and also with the jeff out of new jersey and he has a Continue on with your trick to get you to do the right thing that I like that idea Okay, thanks um Right. So what I did is I started a log Which in which I would record why I entered a trade and why I exited the trade And what the fact that had is that when I went to do the trade it You know, I was mindful that I had to fill in that log And that triggered me to think about what I'm doing so if I uh Didn't want to take a particular kind of trade that I used to take When I went to take you know, I saw the opportunity on the chart and I went to take the trade And then it's like, all right. What am I going to put in the log? It's like, oh my god I'm going to take one of these trades again. I only go one two So I it prevented me and then also in exiting a trade Um, sometimes I would exit through the fear And not realize it until I was out My brain, you know would come up with a good excuse to get out But when I was out I was like, you know what I exited early I didn't want to exit out early But when I started keeping that log when I went to exit it's like, okay What am I going to put in my log while I'm exiting? It's like, you know what? I don't have a good reason I don't have a valid reason for exiting and I would not and I would hold on longer Until I hit my target So that was it's been a really good aid in and being mindful about what I'm doing and avoiding Uh, you know breaking my rules and making mistakes So I wanted to see what you solved your own problem That's the main the best way to do it because that sounds good to me Yeah, I mean this is something that mark and I have been teaching since we did our first workshops in the early 1990s And as a matter of fact, you know, we used to sell our daily trading journal To help traders understand the the benefits of of keeping not just track of your trades But you have to keep track of what you're thinking and if you don't know what you're thinking then Then you can't be effective as a trader. So, you know keeping keeping that journal That's good. That's really good way to go Speaking of journals, I wasn't Hurting myself in any way, you know by by doing that like detracting from From paying attention, you know, you're reinforcing what you should be doing and that's exactly what you want to do You did the exact right thing Absolutely. Yeah, that's for sure. I think that's a good confirmation. I appreciate that. Yeah Speaking of that event Palatine if you remember Robert st. John one of the three biggest bond traders in Chicago Uh, who happened to be they worked together for so long. They became very good friends. Mike Mark and uh, and robert and robert was the greatest trader for the first hour of the day You remember that paula he would he would make two or three million dollars in the first hour And then he would give back two million dollars the last five or six hours of trading And mark worked work with him for a year and they finally made him convinced you only work one hour a day He said well, that doesn't sound fair. He said well, you make all your money In one hour. What do you want to do the rest of the time? You know just walk around the board of trade go buy a hot dog or do something and once you start working one hour a day He was consistent as heck. He was just really good for that one hour Which was the opening hour, which was the time to be, you know trading, but that was the big deal He only worked an hour a day Right Yeah, he went from He went from his uh brokerage firm about ready to kick him out He had two mortgages on his homes and in within one year. He was up three four million Yeah, and paid everything off. I I remember that very very much and then he later on just trading one hour Yeah, I know Well, listen, sweetie, I want you to uh hang in there because we're like we said on the other part of the show We're going to be doing something together here in arizona It's going to be a quote called the friends and family Trading we're going to trade live money and we're going to give the money back to the people that if we make any And if we don't you'll have to track me down in mexico because i'll be on my way No, we'll have some fun. We did this uh in 1999 and we for three days and we were very successful So we're going to do it again. I think we should resurrect it after 24 years And we'll get rich anderson to help us and also Mr. Z And maybe i'll even get somebody else if i can get Byron out here to give us a little philosophy and stuff would be good But uh paul will be talking to us about the psychology of the stuff right out of the words of the master The new age of trading psychology It sounds good. I like that a lot of new material. Yeah, so that that that book can be bought at Amazon or barn any of our books amazon and barn's a noble or get my office a call And anybody who wants any services through me coaching or a one-on-one workshop You know, you get the the friends and family discount from the larry show There you go one percent Right off the top No, listen. Thank you paul. It's easy for joining us dear and we'll talk to you soon We'll get we'll get cracking on uh this thing for September or talk october probably around october 1st Would be uh, because that's before the snowbirds get here and it'll be really easy to get in and out and everything So we'll we'll get it done Hey, thanks for joining us dear.  Okay paul a tea Hold on one second here. I don't hold on Let me get this next chart up here that I want to talk about because this is the most important chart We're having a little bit of bounce here towards the mid-afternoon here in the market, but this thing really looks bad folks This is the one you got to be They're telling you lies and the lies you're going to see it right here There this is the regional banking index from the nasdaq Uh, this the small cap regional banks look at that something's wrong folks They they're telling us now that these three banks that we had silicone valley Signature bank and then also the federal bank out of los angeles Uh, I don't know what the name of the bank was frb Yeah, federal reserve bank out of los angeles and uh, there's something republic bank, sorry, but uh, they're They're not telling you the truth every one of these stocks is down today all 50 of them now Something's there folks because there's more sellers and buyers that markets going down So pay attention to that And you know our market doesn't look that good either after that chart that in fact Jeff was just on the line and that chart that he shows you, you know, if if this is halfway Even close to being right you're looking at some pretty serious corrections here In the in the old stock market here today So let's remind ourselves of that. Okay, look at this this three drive. Look at that or 135 pattern The price objective is you know taking out the october lows and look how quickly it can come down with news like this All it takes is another couple of banks here there There were three or four of them today. They're down 30 40 percent That's not good. How'd you like to be a stockholder? I wouldn't even want to be a Apollo a what do you call a depositor for heaven's sakes? Even though they're supposed to be guaranteed to whatever I think it's whatever value you have in there That's what they said. Hey, we got to take a break here I think to pay a few bills and when would we get back and when we get back We will Talk about the euro one more time because the euro to me Is the key to the whole thing of what's going on in the euro because if we can get above those numbers That we'll post here when we come back from the break That'll tell us that uh-oh money talks and bs walks And what we have to do is to follow that but it's got to close and close strong above that 111 We'll be right back eight seven seven nine two seven six six four eight If you're looking for potential trading setups in the stock market then rocket equities and options report is a newsletter You should try tom. Yo, brian delivers options and equity trades when the markets present them using a combination of fundamentals And technicals sign up for rocket equities and options report today with a 30-day money back guarantee So you have nothing to risk for all the details and to start your subscription today visit the front page of tfnn.com tfnn educating investors You might think that if you want to be successful at trading in the stock market You're going to need a crystal ball. After all it's impossible to predict the future, right? Like any endeavor in life before you decide it's impossible get some advice from the experts You might find that it's not so impossible after all for daily market overviews that give you direction on the key indices Selective stocks and commodities Subscribe to the opening call newsletter at tfnn.com The opening call newsletter is written by basal chapman Creator of the trading methodology known as the chapman wave The chapman wave up down sequence gives you an edge in identifying price turns Finding the peaks and valleys and stock prices get the opening call newsletter by basal chapman and your inbox every day First time subscribers also get a 30-day money back guarantee If you're not satisfied, let us know and you'll get a full refund within 30 days of signing up tfnn.com educating investors Everything in the universe is governed by the fibonacci sequence This mathematical principle is responsible for everything from the most aesthetically pleasing artwork to patterns in the stock market To stay on top of stock patterns You can take advantage of sign up for the fibonacci 24 7 newsletter at tfnn.com When you subscribe you'll get a weekly report from veteran day trader larry pezzavento On stocks you need to pay attention to and you can trust larry's analysis After all he's got 45 years experience as a day trader larry will also provide daily charts videos And data on the key markets that he's tracking expect notifications from larry on market movement You need to act on at any time first time subscribers also get a 30-day money back guarantee If you're not satisfied, let us know and you'll get a full refund within 30 days of signing up Subscribe to the fibonacci 24 7 newsletter today tfnn.com educating investors Tfnn has launched the tiger's den hosted at discord tfnn has been educating traders for more than 20 years With live programming hosted by a variety of professional traders during market hours The tiger's den available to all tigers and tigers for just one dollar for the year There's no catch or added costs when you join our community of traders sign up today and become a part of this educational community of traders Just visit the front page of tfnn.com Catch tom o brian professional trader and educator founder of tfnn also a special guest on cnbc Tom will bisect and dissect the markets the tom o brian show next on tfnn Okay, folks for the last time today. I posted the chart of the euro versus the u.s. Dollar This to me is the key to what's going on because this is the money moving the u.s. Dollar index 53 percent of it is the Euro itself You know, we're looking at what 29 countries in europe All of them with different currencies and stuff, but they go by the euro with all their different, uh, I forget what those little coins are They some of them don't even use coins anymore. I don't believe but anyway, that's where the real key lies. I believe now the euro right now has had a had a pretty big break to the downside and We've gone from Well, we haven't even been able to rally up to a to a 382 retracement yet today As fact is I ought to just bring this up so you folks can all see it together because this is what we're watching and This could be a really big move folks And and again it might it might fail So what we're going to do now is i'm going to put that 382 in here Just to show you that sometimes these things line up Just the way you like to see him and here we go. We'll get it up here Take a quick look at it. Oh dear. I know we can switch this over easy enough and there it is But remember if it gets back above that level then it's good But so you've come down and you made your abcd on the day There's your abcd and then the rally back It's been right up to the 382 So what we want to be watching now is to see if this is going to be Uh, just like gold remember gold backed off a little bit and then when blasting above it Well, the key level is up in here. This is at this 111 level close above 111 It's lights out u.s. Dollar. I mean it's going to be in big big trouble. I mean it's It has no friends at all above that 111 that means u.s. Dollar is going to be above below par Hey, take a break. See you tomorrow live every day in an attitude of gratitude and may god bless


I think I'm quite interested in what Tony Sharrock has presented. I'm not too sure I caught the methodology quite closely, but it's something I would be very interested to read, and I don't know when the book is coming out or whether there are some papers based on that that are already available somewhere that one can download. The specific question I have is, why do you focus on the billionaires? Because the Forbes dataset, I've used it to basically to try and look at how economic growth in Africa is generating more millionaires, but I looked at the millionaire numbers rather than the billionaire numbers. What happens if you drop the barrel and looking at billionaires, but you have a continuum from, say, a couple of millions to billions, and you try and plot that so that you don't lump Africa as one country, but you distinguish them to see what is happening. Thank you. Could you identify yourself? Who are you? My name is Nicholas Gepa. I'm with Oxfam, and I'm also with the University of Johannesburg. Thank you. Thank you very much, Nicholas. Yes, please. Okay. I have a question for Andrea. You showed that education is the main driving force for Latin American inequality change. When I'm looking at surveys, because in household surveys, normally we don't look so much at technical education, just regular education, but looking in Brazil, I was surprised to see a big jump that no one is talking very much about on the trends of vocational education. And the second thing is when you mention lack of land reform, etc., when you see a Piketty's book, you see most of wealth is housing, urban housing. In the past, it was land, inequality hold, wealth holdings. And as I showed, there seems to be a change in Brazil. I'm not very secure about that. We're just starting to look at this data. But a change in the wealth distribution in terms of housing. So I would like to see your opinion. I would also like to ask Professor Schorach about these household surveys. They are not good to get top incomes, but they are reasonably good to get housing information. So you can estimate housing wealth from these surveys. Of course, not for the top ones, but to get your impression on how useful standard surveys are to capture housing wealth. Thank you. Thank you very much, Professor. So the next question we have, we have two there, please. The microphone is heading towards you. The person who grabs it first gets the next question. Please identify yourself, sir. Yes, John Linden Lane from Rutgers University. My first question is regarding to the first paper, which I'm very interested. During this period of time during Latin America, there was the pursuit of low inflation policies. You didn't touch on it as much, but how much did that play in the drop in the inequality that you observe? My comment is that obviously high inflation affects people differently, and with low inflation, we also get higher quality of measurement. There's sort of a double, two questions here. How much improvement of measurement and the quality of the data that statistical agencies are generating nowadays is causing or our statistical findings and quality is changing. And how much do you think the low inflation policies, that some of the... Low inflation. Inflation targeting like Chile and Peru in the 2000s started inflation targeting. And is there any way that you could, from your data that you've got, could tell us what contribution that has had on your analysis? Okay, thank you, John. We'll take one more in the current round and we'll ask for some responses, so we don't forget. So please identify yourself, sir. My name is José María Larrua and came from Universidad de San Pablo in Spain. My question is for Andrea Cornia. It's just if you could expand a little bit more the cases of Honduras and Costa Rica, because I think that they're both a contra egalitarian trend recently. So what happened in... More widely in Central America, this is not following the example of the connoisseur. Thank you. Okay, thank you very much. We'll come back for another round in a minute or two. So, gentlemen, questions on Africa's billionaires versus millionaires, the issue of land reform and housing wealth in Latin America, the validity or worth of household surveys or not, the consequences of low inflation for Latin American inequality and Honduras and Costa Rica, are they outliers and what do we know? So, Andrea, please. Now, the data which we have used to measure the educational improvements are general enrollment and secondary education. And now I think that you raise an important picture because, including in Europe, there is a big debate whether there should be a general secondary education or vocational education. In Italy, for instance, there is a drive towards the reintroduction of vocational education in the secondary, which is what Germany does on a bigger scale than anybody else. But I don't know. I mean, I haven't really tried to do that. My guess would be that with the very rapid technological changes which are still ongoing and with more limited progress in secondary education, positive but gradual progress in secondary education, going back to some, at least for some of the students' population, to vocational education would have a positive effect. And I come from Bologna City where the most famous school was not the university which is the oldest in Europe. It was a mechanical school which was not able to graduate the students because they would go away, they would be recruited instantaneously. And then the expansion of the educational system has gone in the past towards general education. So everybody has to go to the lycee. Now, the land versus urban housing. I think that is a good point. I'm familiar with the wealth surveys done by Jim Davis, Tony, Lenny and all that. And in fact, I was struck myself by seeing that 70, something like 67% of the wealth is represented by housing. So the argument would be, well, land matters less because in the total amount of wealth, so letting me in my houses doesn't matter if we give them land. That problem for the urban population would be okay. But for the rural population, I don't know. So if I go to Paraguay, Paraguay there is a major issue of land with actually with all these bad Brazilian soldiers that they go in and then occupy Manu Militari, the land to produce social for experts. And I think that Lugo tried to redistribute the land but did not have enough political muscle to do it. And I guess that President Lula has always become, at least in Europe, an icon. It's like Virgin Mary, Lula, and then now also Pope Francis. So he, in a way, apparently probably wanted me, I don't know. I don't know what went through his brain. But I remember well that when he was campaigning he had promised to give land titles to... Now, of course, many people they also say, well, okay, and now Brazil is urbanizing. So it's becoming less of an issue. But I mean, if you go to Guatemala, Honduras, many of these countries, a nice piece of land reform would be quite useful. Now, the issue of inflation I think is a very good point. And inflation, we, basically inflation has been stabilized in the 90s, in the 80s and 90s. So, and of course, if you want to stabilize inflation, normally if you follow the standard IMF package, basically repress the economy, you must adopt the contractionary measures.  So one could say, well, you know, the Washington consensus did the dirty job of reducing inflation and balancing the books, then let the others now do the good things. Now, during the 2000, inflation has remained pretty low now with the exception of Venezuela. And since 2010, Argentina, when the country, basically the National Statistical Institute has been taken by the government and producing fake data. So the rate of inflation in Argentina is about 30%. And the government continued to say it was 10%. Now, if you want to reduce inflation, if you don't use an administrative method which may be useful or sometimes are not, basically you have to use contractionary monetary policies or contractionary fiscal policies, which will worsen inflation, which will worsen inequality. So now we try the econometrically, it doesn't come out anything significant. Now, the improvement, they did it. Now, let in America, country to Africa, for instance, because now I'm studying these problems in Africa, it has a very good data set. So they said, like, the work done by Leonardo Gasparini and Guigermo Cruces in Universidad de la Plata in Argentina is really to be recommended. They took, they went back, Cepale has done a lot of good work as well, but I think that what the La Plata people did, they took the service and they applied the same procedures for inflation. So, you know, and I think that this difference in procedures can explain up to two, three, four points in genius. So if they use the same methodology, then we have reasonable data from 1990 onwards. So I don't think that there is any problem with that concerning the service, except for concerning financial wealth.  Probably you go to the Bahama, no, to the Virgin Islands and that is the real issue now. I think that the issue of international fixation. Really, Central America has been doing on average less well. Now, and Costa Rica, which was like the icon of Central America, was like the good country. People, even this morning, Amartya Sen mentioned Costa Rica, but Costa Rica is one of the few countries in Latin America which had an increase in income inequality. It also had a shift in political regime towards the center-right, the more conservative regime. And I think that that is not the problem, but the problem is that the economy is moving towards manufacturing and so perhaps the Christmas model here applies. Now, Honduras had bad distribution, worsening distribution until 2005 and then an improvement from there onward. And El Salvador, which fought the civil war, which ended in 2001, I think, in 2002. And basically had a very, very large improvement in equality with the upper party, which is a very conservative party. I think the prime minister was one of the guy leading the death squad or something like that. So it was very difficult to explain how inequality fell in El Salvador. And I think that what the authors of the case studies show is that migration, I think migration has been... And normally in theory, the hump theory of migration says migration is disequalizing, but now so many El Salvadorians have gone abroad. So now even the poor migrate. So remittances tend to accrue also to poor families and also the amount of people who has left have reduced the number of unskilled labour who are available in the economy. So if you have a migration of the Salvadorian scale, then you can have a very large reduction of income inequality with almost no impact of the CCT type problem, which are being very modest. Okay. Thank you, Andrea. Tony. Thanks. First question about why do we use billionaires rather than millionaires. I wasn't clear enough. I used billionaires because that's the only data we have. If there was estimates of the number of millionaires in the world, that's what I would use. But there are, I think our estimates are, there's something like 30 million dollar millionaires in the world. You're not going to get accurate numbers on that. The billionaires though, someone sits down and puts resources and does some reasonably accurate, I think, estimates. I mean, the Forbes, if you read the Forbes pages and so on, they even have people sending in their certified accounts, I mean, to Forbes. Some people are so vain that they want to make sure they're on the list and stay on the list.  So the, you know, we're talking about modest numbers and presumably they have quite good estimates of people that are quite close to the billionaire range. We use that, we use the billionaire as our observation, but then we use, we assume it's a Pareto distribution, so all you need with a straight line is two points. And one of them is the billionaires and one of those distributions. We just fit it to the, you know, we're just saying, assume it has a Pareto tail at some point and assume that the billionaire data is correct. Then I can generate estimates for everything. We estimate what's the number with 100 million, what's the number of 10 million, what's the number of millionaires for every country in the world. It's what we do every year and we've been doing it. It's just now we've got a more consistent way, I think, to avoid, you know, year on year variations, which are a bit erratic. I also have to say, you know, we generate those numbers, we also generate now median wealth in each country in the world back to the year 2000 in a sort of comparable way. So obviously for African countries, there's very few that have billionaires, but quite a few, pretty well all of them are going to have some millionaires and we will give those numbers clearly. It's the countries which have more, where they have better data, when you get to a point where you've got no billionaires, you've got no wealth distribution, you've got no wealth data, you know, you're limited in what confidence you can have in the numbers, but we try our best to get the best estimate based on what we have, the information we have available. The second question about housing, I think it's an interesting one. The problem, as it turns out, the evidence suggests that people are actually quite accurate in, when you ask surveys and they ask them their housing wealth, they're quite good at responding. Indeed, the estimates, the evidence suggests that they actually even give inflated values, but the numbers you get out are maybe five or 10% higher than the true value of their housing. There's quite a lot of evidence. There's various people that have done studies to compare that. It's not housing wealth that's under-reported, and the whole real wealth is probably, isn't the problem area. It's financial wealth and it's to do with, and even worse, I think, debts.  So you get, this is where you have the problem areas. The problem, though, is if you're looking at that as a trend, because the housing wealth is only, is housing non-financial wealth globally is around about 45% of the total now. Historically, what's happened is in the year 2000, financial wealth was about 55% of gross wealth, 55% to 45%, the ratio then went down until they were pretty well equal in the year around about the crisis. In fact, I think there was one year in which financial wealth went below non-financial wealth. But since 2008, non-financial wealth has been pretty flat globally, and it's financial wealth that expanded. So the gap has gone up to roughly what it was before. It's interesting, because of the, as I told you, these trends that it looks like, inequality went down up to the crisis, and then it's gone up again. This is exactly what you'd expect on the basis of portfolio differences, because richer people have a higher proportion of financial assets. So if financial assets are declining relative, if asset prices are changing such that financial assets are losing value, then you'd expect that to be equalizing. And if financial assets are going up, which they have been. This last year, we're just about to the report this year, stock markets have been booming. This is the last 12 months or 18 months have been probably the biggest rise in personal wealth in the globe ever. Stock markets have just soared. The US, which rose last year by 22%, is the median. It's actually just slightly below the median for the countries in the world. More than half the countries did better than 20% increase in market capitalization. So we had this huge increase in financial assets, but this has been true since the financial crisis. It's just booming. It's interesting because of, sort of Piketty's intervention has raised questions about what is happening globally. And one suggestion is, and this is really quite irrelevant, I think, to the discussion here. One suggestion is income inequality has gone up. So more income has gone to richer people. Richer people don't spend as much. So what do they do with this extra cash? They look around for investments. So they've been channeling this extra money that's been coming along. They've been channeling into investments. What's that done? It's driven down interest rates. You look at interest rates since 1980, they're just declining. We're now at historically low interest rates, as we know. But of course, if interest rates are low, asset prices go up. So housing prices go up, and also all stock markets. So you could think that what has been happening, and this is the macroeconomic effects of increasing inequality, is that it's been driving down interest rates, driving down asset prices, which is then of course fed back to the people that own the assets. Of course, what's happened at the low end, the people who don't have such high incomes, everyone else has been galloping ahead. Their income has not been going up. So what have they been doing? They've been borrowing more. So this increase in debt has been fueled. The people that have benefited are funding. They're actually lending the money to the people who have not done so well and they're just building up debt. And again, you've only got to look at all these things. This is what's happening, and this is really one of the worries in the world, that whether this sort of trends can be sustained. And of course, all of this also is funded a little bit by quantitative easing by the central banks, because they are buying up all these assets and forcing down these interest rates. So when all this comes to an end, we don't really know, but it's going to be interesting to see whether the whole thing unravels or whether or not, you know, whether there's another option. Thank you, Tony. Since we started late, we've got a little bit of time to take out of the coffee break, but we can have another very quick round. Please be very concise and point it in your questions. I'll take three more. So the gentleman over there, please. We'll get the microphone to the gentleman there if you could identify yourself. I've had no female questioners so far, and I've got two males lining up. So I'm going to take the next one over there. So please identify yourself. Hi, I'm Johar Honkla from Statistics Finland. First of all, I would like to congratulate my former boss from 96th Andrea for a very interesting presentation. Glad to see you're still doing fine. My question is to Tony Sharks. Now, I appreciate a lot what you're doing. It seems an impossible task to construct a global distribution of wealth. Now, you have data limitations, and you were discussing about financial and non-financial wealth. My question is on the estimation of real wealth. To my understanding, there are very little countries which have balance sheet data on non-financial assets. And even worse, I've looked at your report. The countries for which you have balance sheet data on real assets are countries which have relatively low home ownership rates like Germany, Netherlands, France. And you use this data to estimate the real wealth for countries which have much higher home ownership rates. So my question is, how do you account for the differences in home ownership rates? Because for this, you have really good data. Okay, thank you, Johar. If you could take the lady now at the back if you could identify yourself, please. Hi, I'm Tanya Pohan Sangra Zhang from Chulalonggong University in Thailand. I have one response to the second presentation. I think the wealth pyramid is really interesting, mainly because I've been interacting with demographers. And I'm not sure whether we can borrow some of the techniques, for example, right now in that pyramid in each layer, not only the number of the population that's shown, also some other categories like proportion of people who finish secondary education or proportion of people with a certain level of asset holding, such as land holding. So I'm not sure how much contribution that would be, but it may be interesting to show other dimensions of inequalities within the pyramid as well. Okay, thank you. I'm going to take one last question. I'm going to go inie-minie-minie moment. I'm going to take James Foster at the very front. So microphone to James Foster, please. Apologies, sir, but you will be able to ask over a coffee break. James, James, there we are. Now, hello. Yes, one thing that I was interested in was, in the first talk, everything comes down to education. And in the second talk, nothing comes down to education. In other words, education or human capital isn't included in your definition of wealth, but as you know and remark in the report, it's three times the value of the wealth that you're talking about. Has there been any discussion or attempt to incorporate education as part of wealth per se, human capital as part of wealth per se? So that's my main question. I'll just ask two other little questions. Is it really appropriate to use the Lorenz curve to measure wealth inequality or should some absolute notion be used instead? So that's just one of my measurement questions. I've been thinking about that for a long time, that wealth is different than inequality being stock versus flow, lots of other things. Yes, and zeros are there as well, and negatives like crazy. So these are really big problems. And then finally, just in terms of education, you are using schooling clearly for your discussion of education and equality. Is there anything on the front of introducing quality into those numbers? I'm actually going to sneak the gentleman there back in because he nearly got the microphone, so he deserves to ask the question. Please identify yourself. Thank you very much. My name is General Wu from Australia. Just a very brief comment on the billionaire number. A, this number is very small in each country. So if someone becomes bankrupt, then it creates a lot of distortion. B, those guys are also very mobile. They can change their nationality anytime. I was thinking it was better to look at the other side of the distribution. They poised 10% or 5% instead of they reached 1%. The number of the poised 5% in each country. Thank you. Okay, so back to the panel for some very brief responses. First, let's start with Tony first. Tony. Thank you. Okay, let's just... First question about real assets and whether there's a bias there to countries which have low home ownership rates. I'm not quite sure how... I don't think we'd really bias that. And I'm not quite sure... I think we might think about that question rather than something which we do throw in other variables. So there's a sense in which we may pick that up. We are all the time, I think, trying to revise our numbers and see whether we can improve. But we are at least limited by the fact by what data is available. So I'm sure in 20 years' time people will be doing much better than we are. But in the meantime, we'll do what we can and we'll just sort of keep adjusting. But we'll think about that and see whether we can add some of the variables in, I think, to see what difference it makes. The wealth pyramid question about whether we can have other dimensions. In a sense, we do in our report. We have, for example, we give a breakdown by regions and so we could easily break it down by lots of other factors. We don't have any... Remember here, I told you at the beginning, we're generating a synthetic database. So we do not have any other characteristics of individuals. You can go back and you can generate for countries where we do have survey data, we could get that, but otherwise we don't. So we're a bit limited there. Of course, if you want to take a country and go and process their wealth data, then you would be able to do other things as they do. So I'm not sure we don't... If we had other dimensions, what we'd like more than anything, I think, is age because we don't... We just have no information other. We're just generating what we think is a number and we don't even break that down by age, but we would like to do it by age. We'd probably like to do it by gender and then we might get on to things like education level, but that's a long way ahead. About James' question about human capital, this always comes up really. I mean, how you define wealth, if you start to sort of add in human capital, you get something which is almost a sort of a neurotized version of income. And so I think there is an advantage for keeping the thing separately. The usual definition is something that's marketable. The questions about definition are tricky. And often the trickiest question is to do with what you do about pension wealth. And because there's different sorts of pension wealth, there's funded pension, state pensions versus private pensions. So that is a really kind of complex area. If you can, if you like, add in... You can add in these other things, but you end of the day, you say, is that really helping you understand the world? On the whole, I think people do have an interest in the wealth of people, what their assets are, what they're doing with it, how they've made their wealth. And that is what we try to respond to. As James also mentioned, though, that the wealth inequality is interesting because we can have negative numbers. And in fact, we do get quite a few negative numbers. And indeed, negative numbers are growing. More countries are having negative numbers. And part of that is there's lots of debts at the bottom, payday loans, student debts are getting enormous in lots of countries. And one of the problem countries we've had is Denmark, because they have 30% of their population, has negative wealth. And indeed, if you look at the Lorenz curve, it doesn't actually go above the x-axis until you get into the 60th or 70th percentile. And it gives you a genie more than 100. At least we did have. That was partly our processing, but if you look at the report last year, you'll find that Denmark has a genie of 105 or something. And we get people writing to us all the time saying, it can't be right. The genie is between zero and 100. Of course, that is true. We're not using the Lorenz curve anymore. I've just told you. So there's a sense in which moving to this sort of diagram in which we're plotting this curve is much below or along the lines that you're suggesting. If you wanted to keep it in terms of wealth rather than wealth relative to the mean at the bottom, then you'd be able to plot what's happening over time and seeing how the curve is shifting. But if you're interested in analyzing inequality and inequality trends and trying to, let's say, combine the use-the-forbes-type top-tailed information for different years, then I think I would recommend that one goes ahead in the way that I've proposed. Thank you. The last question was about billionaires. Yes, there's a small number. Again, we're not interested just in billionaires. I'm just using it as a point, as a sample point. It's used as saying we're treating it as if it's accurate. It is true that, you know, people can move around. On the whole, we use the forbes definition. It is on what their nationality is, not where they're resident. So if people move to a different country, the forbes data doesn't treat Abramovich as a UK billionaire. The Sunday Times does in crude terms. We're taking the citizenship definition, largely because that seems to be more relevant in terms of if we're using that as a predictor of what the wealth is in that country, the few people at the top who happen to move to another country. They made their money in Russia. That's where the other big wealth holders are like to be. Some of them will have moved. That's true, but I think it's a big problem for Russia. It's a big problem for India. I think there's quite a few transient Indians. And I think probably will be, you know, I can imagine it being a problem for other countries as well in the future. So this issue about, as I mentioned, is one which I think will have to be addressed in the future. Okay. Thank you, Tony. So, Andrea, any brief responses before we break for coffee? Yes. I think that the Latin American story boils down not only to education because there are also policies in the labor market, taxation, public expenditure, macroeconomics and so on and so forth. But basically the educational policies already since the 1990s, basically they affected very strongly the distribution of human capital and therefore the ratio between skilled and skilled wages because they increased the number of people with sufficient education. Now, the quality of education, maybe we don't have data. They're not easy to measure because we don't have a distribution. We have tests, but you don't have then a distribution of people with the quality taken into consideration. But I think that one of the argument is that the quality of education has been falling as we, I think, that has been shown because of massification of education and that may have contributed to the decline of the wages of the skilled laborers. Okay. Very well. Okay. Thank you very much, Andrea. So it remains for me to thank our two excellent speakers who've certainly given us a lot of food for thought to adjourn for coffee. Remember that the next sessions will begin shortly and when you next get a call from Forbes reminding you to fill in that billionaire form, please do it accurately. Okay. Thank you very much.


In our previous lecture, we introduced the method which we call direct proof, which if you're trying to prove a statement which is conditional in form, so you're trying to prove the statement P implies Q, the template for the proof is the following. You assume the statement P is true, maybe unravel some definitions, bridge some logical gaps, and then you conclude that the statement Q is true as well, based upon the assumptions you made here. This is the method of direct proof. In this video, I want to provide some more examples of how do you prove something directly, unlike in the previous video where we actually sort of step-by-step wrote the proof together. In this video, I'll show you the proof already finished or de-polished, but try to motivate where this proof came from. And much like in the previous video, we're going to be focusing on conditional statements about integers and real numbers, trying to focus on arithmetic and algebraic properties that you may already be familiar with, as opposed to introducing sort of novel mathematical concepts. So consider this proposition here. If N is an even number, then N squared minus 6N plus 5 is an odd number. So this is an if-then statement. So if we wanted to prove this by direct proof, what we're going to do is we're going to assume N is an even number and then work to argue that N squared minus 6N plus 5 is an odd number. Now what is in, so that's exactly how we start this. Suppose that N is an even number. What does it mean for N to be an even number? What that means is there exists some integer k such that N equals 2k. So the very first thing I did was state the assumption. Assume that N is an even number. And then I decided to unravel the definition. What does it mean to be an even number? Well, there exists some integer k such that N equals 2k.  Well, what does it mean to be odd? It means that there is some integer of, there's some way of writing my number as 2M plus 1. That's what we're looking for here. So we can see that. We have N equals 2k. We want to end up with some type of 2M plus 1. How would we accomplish that? Well, the idea is if I take, if I take the expression N squared minus 6N plus 5 and replace each of the Ns with 2k, maybe algebraic manipulation will allow me to then produce something of the form 2 times M plus 1. Okay, that's what we're going to do. So we start off with the value we're trying to consider for our conclusion. N squared minus 6N plus 5. Replace each of the Ns with a 2k. So we get 2k quantity squared minus 6, minus 6 times 2k plus 5. So let's do some algebraic calculations here. 2k quantity squared is the same thing as 4 times k squared. With the negative 6 times 2k, that's equal to negative 12k, you have a plus 5 right here. Now, notice my goal is I want to write this as 2, 2M plus 1, where M is any integer. I don't care what it is. It just needs to be an integer. So I need to find a 1 and I need to find a 2. So one way to try to do that is I'm just going to produce a 1, right? That is, there's a 5 here. 5 is just 4 plus 1. And so I'm just going to extract the 1, set it by itself, and then leave the plus 4. Because everything other than the plus 1 should be part of the 2M. And so that's exactly what we see right here. I have everything plus 1, okay? Now, this thing right here should be 2M. If this statement is true, that's got to be my 2M. Is this an even number? Sure enough, look at the coefficients. I don't know what k is, but 4, 12, 4, I can factor out a 2 from each of those coefficients. So I end up with 2 times 2k squared minus 6k plus 2. And then you add a 1 to that. And so you don't necessarily have to declare the symbol M. It doesn't need to be specified here, but it's like, okay, as the number 2k squared minus 6k plus 2 is an integer, the following form then tells us that n squared minus 6n plus 5 is in fact a non-number. And this improves our proposition by this method of direct proof. In summary, we started with our assumptions, we unravel definitions, we bridge the gap between the 2s, and then we finish with proving the statement we've set out to do, the conclusion of the conditional. Let's look at another example. This time we'll look at some real numbers. Let x and y be positive real numbers. So that, of course, means that x and y are going to be greater than 0. We then want to show, so this right here is basically just defining the set of objects we're going to consider. So the conditional statement actually follows here. If x is less than or equal to y, then the square root of x is less than or equal to the square root of y. This first statement was necessary so we know what we're describing. Are we describing integers? Are we describing real numbers? Are we describing ration numbers, complex numbers? In this case, the scope of our inquiry is only for positive real numbers. The conditional statement is right here. So you don't have to restate that x and y are positive numbers. That's already established. Instead, our conditional is right here, p implies q, so we start by assuming p. So the very first sentence will be, suppose that x is less than or equal to y. Our very last sentence will be that the square root of x is less than or equal to the square root of y. And then from there, we're going to apply some definitions when necessary and try to unravel these things. Now it is important to note here that y is the numbers being positive, important here. We'll get to that in a second, but let's start off with the thing we do know. We do know that x is less than or equal to y. If we start to manipulate this algebraic inequality, perhaps we can then produce the inequality we're looking for. After all, the statement has the form if an inequality is true, then another inequality that uses the same variables is also true. So maybe we can manipulate this one somehow or another. Notice that if you were to subtract y from both sides, you would turn this inequality to this one right here. But when we write a proof, we have to make sure we draw the picture with words, right? We can't necessarily use these little informal notations like we would if I was giving a lecture or in a classroom, much like this video is a recording of. So we describe it with words. Suppose x is less than or equal to y. Then we would say something like subtracting both sides by y, we have that x minus y is less than or equal to zero. Now there's a lot of liberty on how you can express such a statement. You have to always keep in mind who is your audience? Who are you writing to? Currently, this video is intended for students of a class similar to SUU's math 3120. This is a class for students transitioning into advanced mathematics and so this proof is written with that intention in mind. Now if you're writing to a very different audience, if you're writing to like mathematical scholars, you might not say this at all. You might say something like, suppose x is less than or equal to y, then x minus y is less than or equal to zero. You might not give any justification why the two statements are related, understanding that your audience would be able to feel the difference. Like, oh yeah, just distract y from both sides or if you move y to the left hand side, it becomes this inequality like here. So always keep your audience in mind. Writing for first grade math is different from writing 12th grade math, which is different for writing college math undergraduate, which is very different for how you might write for graduate students. Writing for like a general education math class like calculus or college algebra, it's very different how I present mathematics for my advanced math students, my math majors, much like we're doing in this video. I am providing some justification here, but I probably could get away with without it, but I got to write something, right? So subtracting both sides by y, we have y, x minus y is greater than or equal to zero or this is the same thing as x, the square root of x squared minus the square root of y squared is less than or equal to zero in that situation. Now look what I did. I explained exactly what I did to get from here to here in the first step, but in the second step, I didn't actually justify it. I just said that they're the same inequality. Understanding that my audience would understand that, oh yeah, we have positive numbers. The square root of x squared is equal to the absolute value of x, and since the numbers are positive, that's equal to x. Same thing for the square root of y squared. I expect my audience to be able to do that and it's not unfair to expect that of the audience I'm presenting right now. So I can go from here to here just by saying, oh yeah, these two things are the same. Now, when I use the word or here, I don't mean it in the logical sense. I mean that this is equivalent to this or it's equivalent to that. That is, you could pick either of those two forms, but they're actually both true, right? This is just a progression. We went from this inequality to this one to this one, okay? We're going to continue to do that until we get to this one down here. Now, the reason why this one is useful, I then explain to the reader here, factoring the left-hand side we have, because now you see this as a difference of squares. That was why we introduced the squares and the square roots. You can then factor this as a difference of squares. You have the square root of x minus the square of y times the square root of x plus the square root of y. That's less than or equal to 0, okay? And then again, I did preface this.  That's appropriate in a trigonometry class when you're trying to prove a trig identity. If you're trying to prove something like, oh, sine of 2 theta equals the usual identity 2 sine theta, cosine theta. If you were actually trying to prove this, then you might have some type of statement here, statement here. I should say expressions.  That's appropriate for like, sure, like a trigonometry class. But we have to write better proofs than that. This is not just a sequence of equations, or in this case, a sequence of equalities. We have to give some explanation. You don't want it just to be mathematical symbols. There should be some English in there as well to help our audience understand what's happening here. So we give some clarity that you're factoring this, and that's where this thing came from, okay? Might it be reasonable for the audience to figure that? Yeah, but that doesn't mean you never say anything that your audience could do on their own. Because honestly, if your audience is math 31-20 students, which mine is right now, it's reasonable that I could expect them to write this proof. In which case, I might write the proof as, in the following here, the proof is trivial. Duh. It's like you guys can figure it on your own, or textbooks do this all the time. The proof is delegated to a homework assignment. It's like you get to prove it true. Yeah, sure, you can do that. But that's not going to be very instructive for students if I just say this is a trivial proof. You wouldn't learn why it's a trivial proof. And so you should give something. You've got to give something to the audience. And so it is a give and take. You don't want to give too much because then your proofs get long and verbose and difficult to read because it's too long. It's like, I get it, move on.  Finding the right balance is important here. This is all about writing composition. How do you compose it to make a well-written beautiful proof? It's give and take. An experience is how we can fill in the gaps there. So returning to the, returning to the proof here, we have the square root of x minus square root of y times square root of x plus the square root of y is less than or equal to zero. Now we can say that well, because like, let's note that the square root of x plus the square of y is greater than zero, right? Since x and y are positive numbers, the square root of x is always positive. The square root of y is always positive. The sum of two positive numbers is positive. Regardless, I know that the square root of x plus square root of y is a positive quantity. Why is that necessary? Well, if we divide both sides by the square root of x plus the square root of y, that means we divide both sides here, zero divide by anything of course is going to be zero again. I can then simplify the inequality to be this one right here. The square root of x minus the square root of y is less than or equal to zero. Remember, when you work with inequalities here, if you divide by a positive, you preserve the direction, but if you divide by a negative, it actually flips it around. That's why I need to specify this was a positive number. Be aware that writing a proof is not just about composition. It should be well composed so that it reads well, okay? We also have to worry about things like clarity. Is it clear to the reader what's going on here? If you skip too many things, then it might not be very clear. But also, if you put too many things in there, the audience might get stuck in the weeds and not understand what's going on either. That's what we were talking about earlier. We also have to worry about completeness. We have to make sure we include everything that we need to say. Now, if you start dividing inequalities by willy nilly real numbers, we should be cautious. Did you just divide by zero? Because that might actually make the statement mathematically incorrect. Is it a correct statement? But then also, in this case, since we're divided by a positive quantity, it doesn't switch the inequality around. But if you divide by a negative, it would switch the inequality around. So to be correct, to have the correct ordering right here, we have to divide by a positive. And if we don't state that, then our proof is somewhat incomplete. If there's two large gaps, then that makes the proof incomplete. Now, admittedly, the gaps we leave could be because we expect our audience to do it and it's clear how the audience is able to do it. But as students writing this, we have to be very careful. Is there a gap there because the audience can answer it and you're just choosing not to? Or is that you don't know how to fill in the gap and you're hoping no one will notice if you claim that the emperor is wearing some new clothes or something like that. We'd be cautious of such things as we write. Okay, so for completeness sake, we would specify this as a positive quantity. Therefore, this inequality implies this inequality, we get that the square root of X minus square root of Y is less than or equal to zero, for which then I say finally, that implies the square root of X is less than or equal to square root of Y. I didn't specify this time that we're actually adding the square root of Y to both sides. I mentioned it before. But really, it's like I expect by now the audience to see what happens. You move this to the other side, and then we get the inequality we wanted right there. And so that then provides the proof of this one. And we went through it very slowly explaining why things were written. Every word in this proof was mentioned for a reason. None of it was intentional to be fluff. It was every word was put in there for the following rubric, the so-called foresees. I did it for the sake of composition or for the sake of clarity, the sake of completeness, or for the sake of correctness. If any word was modified, it's possible that one of these four rubrics would have been weakened inside of this proof. Let's look at another example of a direct proof. Let X and Y again be positive numbers, then the quantity two times the square root of XY, the product, is less than or equal to X plus Y. So again, how do we start this thing? We can mention our assumptions here. So let X and Y be positive numbers. Now, you'll look at this one. It's like this one doesn't exactly look like the previous one. The previous one was like X and Y are positive numbers. Let that happen. Then you have this inequality. If X is less than or equal to Y, then the square root of X is less than or equal to square root of Y. This time, I'm starting off by actually stating that the X and Y are both real numbers. I didn't know the previous one because it was built into it. I didn't even mention it, but unlike the other ones, like I don't have anything else to say, I got to start with somewhere. So I'm just going to mention, okay, X and Y are positive real numbers. Then since they're positive real numbers, it is true that zero is greater than or equal to X minus Y squared. I want to be aware that this statement holds not because the numbers are positive, but because they're real numbers. If you take any real number in existence and you square it, it's always going to be greater than or equal to zero. If you square zero, you get back zero. If you square anything else, a positive or negative, you always get something positive. And so regardless of what the number X minus Y is, it could be positive, it could be negative, it could be zero. I know it's square will be non-negative. This is a universal statement about real numbers. The positivity is not being used there. Then because this is true, I can algebraically foil this out and get X squared minus 2XY plus Y squared. Just these two quantities are equal. And so since this is greater than or equal to zero, this will be greater than or equal to zero. Okay, I got that. Taking this inequality, I could then add 4X to both sides of the inequality. This would then give something the following. Well, zero plus 4XY would be 4XY. And then if you add 4XY here, you end up with a positive 2XY. And then on the right hand side, if we then refactor that, we end up with X plus Y squared. Okay, so now we have the inequality that 4XY is less than or equal to X plus Y squared. Then I claim by proposition 434, which be aware, the proposition 434 was the one we just proved on the previous page. If X is less than or equal to Y, then the square root of X is greater than or equal to square root of Y. Now in this situation, what meant X before is now replaced with 4XY. And what meant Y before is now replaced with X plus Y squared. And so by proposition 434, we get that the square root of 4XY, which is the same thing as two times the square root of XY. So notice those things are equal. That'll be less than or equal to the square root of X plus Y quantity squared, which will simplify to be X plus Y, like so. Thus giving us the inequality we are looking for provided the proof. Now you look at this one, it's like, wait a second, I thought this video was about direct proofs. How is this a direct proof? Well, it turns out the direct proof is a lot more subtle in this situation. By all means, sure, we started with our assumption, we ended with our conclusion, but we're not actually proving a conditional, so to speak. I mentioned beforehand in a previous video that essentially every proof you ever write is essentially a conditional, because there's always some hypotheses and some conclusion. So you can be like, oh, if X and Y are positive integers, then this inequality happens. So in that regard, it's the case, that's the case as well. But I also mentioned, where was positivity ever used? When did it ever use the fact that the numbers were positive real numbers? You didn't need it here, because that inequality would be true for any real numbers. You didn't use it here, that's just an algebraic expansion. You didn't use that here, because again, you just algebraic could manipulate the inequality, no real number was needed there. Where was it used? Aha, it's actually used quite secretly right here. The fact that the integers were positive was used in Proposition 434. If you recall, Proposition 434 says, let X and Y be positive real numbers, and then this inequality or this conditional holds in that situation. X and Y being positive real numbers were part of the assumptions of Proposition 434. If you do not have them, then you can't use the proposition. And so as your proof, as your proof writing gets more complicated and more detailed, sometimes the assumptions of the conditionals you use will not be used directly, they'll be used indirectly as hypotheses of previously proven theorems like in this case. So I want to include this example because we didn't use our hypothesis directly in this proof. We used it indirectly in another proof that we had just done previously. This is common mathematical writing. And so this is an example of the direct proof method, but the uses of the assumptions were actually inside of a proposition. If you don't use your assumptions, then it begs the question, why did you use the assumptions at all? The assumptions that are there for a reason. If you don't need them, remove the assumption and that gives you a stronger statement. We use them not directly, but indirectly as the assumptions of a different proposition. And that's something we're going to see all the time as we proof things by this method of direct proof.