Applied Portfolio Management - Class 1 - Risk & Return

hello and welcome back my name's Patrick Boyle and today we will be starting a new series are called applied portfolio management so we're gonna look at it's broken into a number of classes so we're gonna have four classes that are released this week and then we'll have more classes next week and so this week's classes will be mostly on the topic of traditional asset management and then next week's class will be all about alternative asset management so we'll be talking about hedge fund trades private equity things like that and the whole purpose of this class is for students of the market to understand what it is that people actually do when they are managing assets and sometimes that's not always so obvious that there's an awful lot of financial theory that you possibly learn as a student and it's not always obvious to you how useful that theory is or how it's used in practice and so in today's class we're gonna go through a lot of it and we're gonna see how people actually use it why it's useful and we'll talk about the pros and cons of a lot of that theory as well so here we go so week 1 we're going to be looking at art we have 4 classes as I mentioned the first one is today's class and that is on the topic of the risk return relationship which matters an awful lot in finance it's one of the key ideas that we have in finance that we pay a lot of attention to so firstly I guess I should just tell you guys a little bit about myself and kind of why I'm teaching this class so I'm a visiting professor at Queen Mary University of London and also at King's College London I've worked for 20 years in the finance industry I've worked at a bunch of different firms Bank of America or BS Nomura a bunch of investment banks and I also worked for victim leader how far out leader offer investments is a Englander millennium and a number of years ago I guess in 2011 I launched a fund called Palomar my background at least my educational background is I studied at Trinity College in Dublin and then London Business School and as I mentioned earlier I teach at Kings and Queen Mary and my background is in alternative asset management that's really what I focused my career on hedge fund strategies in quantitative finance and so today we're going to just learn all about asset management and kind of what you saw what these calculations that we do in finance how they actually are useful when used by real investor or a trader so yes some kind of background on the fund that run it's a firm called Palomar as I mentioned earlier it's a quantitative fund so I trade futures short-term futures trading and dad is a firm that's been around since around 2011 so anyhow the first thing I'm gonna talk about is just something that a lot of students always ask me about and that is are there any good books to read in the investment management space and so I've put together this slide which my students will be able to to get a copy of and also I'll put I'll put the links to these books in the description below of the video but there's a bunch of really interesting books the first one I've got up here is a random walk down Wall Street and that's a book that really kind of builds the idea of kind of why people should invest in Index products and I think there's a lot to be said for that book and the ideas inside that book it's you know it's useful for most retail investors I think for most people they neither have the time the energy to spend their time kind of doing this sort of work that that you might do if you worked at a hedge fund or at an investment management firm and so it's very reasonable to take that approach and so that's a decent book to read the next one is Roger Lowenstein book on Warren Buffett and in fact I would recommend all of Roger lahnsteins books he writes really great financial books in fact my favorite one is coming up in just a moment that I'll tell you about the next two books that I've mentioned that will actually basically everything written by Jack Swagger so Jack Swagger wrote a series of books the market wizard series I forget all their names there's about four of them in which he profiles sort of the the top kind of hedge fund or floor traders a quantitative traders I don't know what you'd really call them they for some reason they tend to be futures trader study profiles and they're just really good interviews Jack asks all the right questions really understands his topic understands risk and managed to interview some of the most interesting people in the world of finance and so I think if you're a student who wants to know what fund managers actually do or how they think this is a really excellent series of books and then the next book on the list is also by Jack Swagger and it's called market sense and nonsense and I'd strongly recommend that book quite simply it's it's I think it came out in 2013 and it's just a really good look at what Jack Swagger learned in his whole career in finance he's probably well I don't know how old he is but he's probably worked for about 40 years in the finance industry worked with some of the best traders out there investing with many of them and and and the book is just really a wonderful explanation I read it and just everything sounded right to me you know he explains kind of how people invest the mistakes they make and so on and it's it's a really interesting and good book the next next one up is a book by Nicolas in the seemed to leap you know its fooled by randomness is the book I think that he wrote that is good he's written a whole series of books you know they're okay this one's pretty good it's just a pretty interesting book on the topic of risk and you know I'd strongly recommend that one it's interesting as much the next two books are by Vic meter offer education of a speculator and practical speculation I've worked for Vic Nader Hoffer for I guess about four years and Viktor Viktor is a massively intelligent and interesting guy and both of these books are really good education of a speculator takes you through his life story the lessons he learned as a child that turned out to be useful as a fund manager many years later and you know some people I when I read the reviews some people like me absolutely loved that book there's other people who don't like it and they don't understand why he's telling you about you know playing squash and things like that and how that relates to the markets and you know if you don't like that kind of thing you you won't enjoy the book but it to me it's it's kind of what's great about the book is it tells you how he thinks and how he approaches the market and and I find that really useful he's also Viktor is a good friend of mine the in addition there's a book practical speculation and I worked with Viktor when that book was being written and helped out a little bit in in some of the work around writing it and it said that's a biased when I recommend that book or I guess what else have we got on here Denson marsh and stone and triumph of the optimists that's a really interesting book it's kind of an expense when I put a link to it I think it's around a hundred pounds in in England but you'll find it at most university libraries and that sort of thing and it's just a really fascinating book on the topic of how markets pay off you know like what how investments do and in a way that's a lot about what we'll be talking about in today's class and so they managed to back out you know over a hundred years of data on a number of markets around the world uh it's probably the most market data that anyone's had to work with and there's just some really interesting and useful conclusions from the book one of them even is you know when they look at the the returns from so many different countries around the world and you see in the long run that actually they balance out and become about equal and that's just a fascinating thing on its own because often there is an argument we'll say that a lot of the studies that are done on market data are done on US market data and so you might look at you know the returns and say well this is a country that everything went really well for is this is this reasonable to expect going forward but you know Timpson Marsham stone and they look at at all sorts of different countries returns places where history has treated them well and badly do you find in the long run they all have rather similar returns and the argument i guess you can take away from that is that that is the return that an investor might be able to expect from an investment in will say an equity or bond market or whatever it might be and so i I would recommend that book it's really interesting the next one up is kind of a book that I recommend to almost everyone it's by Roger Lowenstein once again and it's called when genius failed and it's the story of long-term capital management and it's probably the best book on the hedge fund industry that that I have read in that it's it's interesting it's a great story it's exciting it has a lot of really important people in finance and men are in there you know we've got Scholes and Martin for example were partners at long-term capital management the fund that that this book is all about and it's the story of how long-term capital management was launched how successful they were initially maybe some of the errors that they made some of the approaches to risk management that didn't work out very well and it basically tells you this whole story of the rise and fall of LTCM and I strongly recommend the book it's a book that I've even given my mom to read because it's not it's not just that it's a good sort of industry book a good investment book it's actually just a good story like it's really interesting and when Steen is a great writer what else we got on here Ivan Boesky merger mania now I've put a link to this on Amazon but in truth I think the book has been out of print for quite a while so you'll have to dig around to find a copy but it is written by Ivan Boesky who you know it's on the top of topic of merger arbitrage which was both skis trade I suppose and it's it's a really interesting book at the time there were no books that really explains merger arbitrage and then he wrote this book you know there's obviously a few caveats associated with this one because both give course it turned out a little while later that his main trade was actually insider trading rather than merger arbitrage and there's some great bits in the book where he writes about how he how he just happens to have this great instinct for when a deal is about to happen and get in ahead of it and with hindsight with hindsight we realized that it was insider trading he ended up going to prison not that long after the book was published what else have we got Howard Marks the most important thing I really enjoyed this book as well it's written by Howard Marks of oaktree asset management I think the fund is called Howard is a great writer he writes all of these letters to investors and they're almost like the Warren Buffett letters to investors they're just really well-written really interesting very thoughtful and he's compiled them all into a book and it's a great and an interesting book and I'd recommend that one to all investors as well but the next one up is called fiasco by Frank Partnoy and it is a story from the I guess mid-90s the whole structured products and derivatives industry and of course I I do teach a class on derivatives and you might have seen some of my videos and derivatives and the Frank Partnoy book is so that the story of the early days of a lot of the structured products and the derivatives trades that didn't always go well and it's one of those kind of crazy mid-90s stories of Wall Street Frank Partnoy not long after writing the book I believe he went on to be a professor I think he's at Berkeley in California and so really really smart and interesting guy and tells a great story so I'd recommend that one the next one up is I've got two books here by Michael Lewis liars poker and the big short both are but both are just really good books Michael Lewis is a great storyteller very funny like all of his books are hilarious and he's written a number of other books that are not financed based but he started out working at Salomon Brothers I guess in the 1990s as a bond salesman and so he's tells the story of the bond traders at Salomon Brothers in liars poker it's a great story and in fact it's sort of all of the people that are in liars poker turn up later in when genius failed so it's kind of a good introduction to that crew of bond traders the big short got turned into a big film as well which I recommend the book and the film they're both good and it is the story of the people who made money during the financial crisis of 2007 2008 not with not just people who made money but people who saw what was happening in the markets and managed to profit from it and so that's just a really interesting and good story of kind of contrarian investors and so on and so you know once again really entertaining book as well as being a good you know lesson in finance I suppose and then finally the newest book that I have on the list is just from a few months ago the man who solved the market by Gregory Zuckerman and that is the story of Jim Simons and Renaissance Technologies which is kind of the top quant hedge fund in the world I would say and you know that's a great book I think it's won a number of awards for being the best finance book of the year and whatever and it's just great story well written and I would strongly recommend it so that's kind of my list of books that students always ask me for and I thought rather can just write it all down and it's it's better to tell you about it and tell you why I enjoyed those books and hopefully you'll enjoy them too and I think I'll probably put these links up on my website which is on Finance dot org and you'll be able to see them there as well and so now the main topic of today's class other than of course my book reviews is is to talk about the basic financial concept of risk and reward and so this whole class is going to just be about risk and reward in financial markets what it means what it doesn't mean and how that relates to investing so we start out with this sort of example of two people to career paths you could take we've got here our rock star and we've got a dentist you know and we'll say well we'll imagine if each of them could have been either of these things you know we've got teeth I'm not sure that I would want Keith Richards dealing with my teeth but anyhow you know it could happen but we've got we've got these two two career paths that are possible and they're very different to each other because for a rock star the problem is that you have a very unpredictable career income right and obviously for Keith it worked out doesn't work out for an awful lot of people for a dentist over here we've got a very predictable career income you know once you qualify as a dentist if you're decent at your job you can turn up every day and earn a good living right but it'll never be exciting you you'll never sort of see the height that a rock star might see and so there's a big risk reward difference here and this risk reward difference is a big thing in finance as well and it's off the misunderstood concept now the reason it's a misunderstood concept is that often people think when when they hear about risk and reward in finance and they hear the expression there's no there's no return without risk they they then come to the mistaken conclusion of what that means is that in order to maximize your wealth you have to maximize your risk that essentially that risk is always rewarded and that's not what we mean in finance when we talk about risk and reward we simply mean that in order to decide to take greater risk you would only do that if there was greater reward or if there was a possibility of greater reward so it's not that you're guaranteed to get the greater reward because of course you're not that's the nature of risk is that you don't really know what you'll get but you're seeking it and there there is a likelihood right because you would never know one would naturally we'll say for example if there were two investments and one was very risky and had an expected return of 10% and the other one was entirely lacking in risk and had an expected return of 10% well anyone would any intelligence would take the one that was lacking in risk for 10% rather than that rather than the one that was high in risk for an expected return of 10% so in order to lure you into taking a greater risk an investment has to have the likelihood of a very high return if it doesn't have that likelihood then it's it's not a smart decision to take it on and so the idea here is that that the rock star idea is that yes it is a risky path there's a good chance that you just play the guitar and a bunch of bands that never go anywhere and you have a few fun stories and then you have to settle down to a sensible life but there is always that small potential then maybe things could go really well and you'd have a really exciting life and the dentist thing it's sort of the opposite where you're unlikely to have a really crazy exciting life but you're likely to have a very predictable and good income and have a pleasant life you know and so we've got a different risk return trade-off and the return the expected return is maybe higher for the the rocks are but of course the risk is much higher as well and for most people it doesn't work out so and the same thing then can be said about investment so when we move on when we move into the world of investments we move to this idea of a high tech growth stock or a utility these are the examples I'll use and we'll say our tech stock is something like uber and our utility our boring stock is is this water utility and so an investor can look at these and they look at the water utility and they'll say well nothing that exciting is gonna happen with that right like they it's a regulated business its regulated with by the government they can't jack up the price of water they can't you know do anything too exciting but they'll probably continue to be in the business that they're in forever simply because there's not really very much competition and there's there's no obvious way that things will go horribly wrong now with our tech stock here there is of course there is the chance that it'll go to zero because you know it's that that's the nature of risk is that things could go either really well or really badly and so for our tech stock like uber the kind of person who invests in it invests with this idea that the doober will just own the ride-sharing business in the future you know and so they can lose all of this money right now spending to grow their business with this idea that at some point in the future they're the only there so they're the one-stop shop for it for that business and examples of that would be things like Amazon that early on it was you know just an online bookstore but it grew and grew moved into a bunch of different businesses and is basically the wouldn't stop shop for online shopping right now so the idea with a growth tech stock like uber is really that you'll you'll take this risk that it could go to zero in order to also have the massive upside if things go really well and so that is risk and return in finance and so hopefully that makes a little bit of sense to you and so that doesn't mean that you should definitely invest in one or the other it means that you you depending on your risk appetite you can choose which you might want to invest in and even depending on what you're a future expectation for either of these businesses is you can decide based upon that but you would never invest in in a company like uber or in a water utility if you thought the expected return was the same because of course Obert can go bust and the water utility is way less likely to do so so that's really what we're saying would risk and return in finance and so that of course gets priced in finance and so we have here a question that I often ask the students in my class that if if both of these companies if we had a really exciting it doesn't have to be over it can be any exciting tech type company that's priced at $100 a share today and we've got a water utility that's also priced at $100 a share today and you can buy an option and an option is a derivative that has a payoff if something goes up a lot and no path if it doesn't an option with a strike price are sort of like I hear a call option on either one with a hundred and fifty strike price with one year to maturity so it has to go up by 50% for this option to be valuable to you at expiration which one would you pay more for now the probably the correct answer to this is is the the high tech stock the high-growth stock because the water utility nothing that exciting is likely to happen in the world of utilities over the next 12 months that will move the price up by 50% while the other stock our high tech growth stock is actually in such a volatile business that it's probably much more likely that that one will go up 50% than the other one will and so of course in the real world the option on our high tech growth stock will be much more expensive than the similarly strike option on on our water utility and hopefully that makes a little bit of sense to you so does that mean that the tech stock is the better by luck should you just the textile rather than owning the water utility that's not what it means at all because we don't know what like it's there's a huge question mark over the textile could go up a lot it could go down a lot it's volatile okay and so is it a better buy well I've got a bunch of examples up here of tech stocks from 20 years ago we've got boo calm Cosmo calm and many you probably don't recognize the pets calm sock puppet which was all over the television in the in the late 1990s and so these were all the really hot tech stocks of of 1999 and they all pretty much disappeared a year later amusingly like Cosmo calm was one of those delivery companies that's become a big thing once again you know in in London there's delivery that will deliver food to you cosmo used to do that in the late 1990s and they took on this huge valuation but they basically spent all the VC money they had didn't make any money and went to zero rather quickly bucum was a British comm company and I think they almost they were one of the fastest ones to go bust I think they kind of got their VC funding blew through it in a few weeks and it was all gone and so at the bottom here on this chart by the way these slides are all available to students and I'll possibly put them up on my website as well so you don't have to really just read them off of the screen but the chart at the bottom here is of the Nasdaq Composite Index which was to take stock index of the 1990s and as you can see just really ramped up in certain 98 99 and then went right back to where it started again you know so there was a lot of excitement and then a lot of whatever the opposite of excitement is and and that can be the nature of things in markets you know and so we don't know which of these two investments the tech stock or the water utility is the actual best investment but we do know that there's very different risk reward expectations of these two companies so risk aversion which you hear a lot about in finance just tells you that investors fer lower to higher risk for a given level of expected return right because if the return if you knew what the return was likely to be you'd always take the lowest risk way of getting it and that that just makes sense that's a sensible decision to make and so investors will only accept a riskier investment if they're compensated in the form of a higher expected return and so that really just sums up everything I've been saying up until now so then in finance a lot you see these things called indifference curves this chart here I'm sure many of you have seen this stuff before and they're basically plotting on this axis here we have expected return and over here we have standard deviation now the big thing to take away we've got all these different curves but for each of them for additional risk and risk is we usually use standard deviation to represent risk in finance for any increase in risk we have an increase in expected return now these are a bunch of different levels of risk aversion now although there are people with different levels of risk aversion they still all want more return for more risk they're not willing to take more risk without being compensated for the risk that they're taking and so these these different curves might be different investors with different risk tolerances they might even be the same investor at different times in their life so maybe when someone is 20 years old they might be very willing and and quite sensible to take plenty of risk at that age and maybe a year or two before retirement they move down in terms of they they are way less willing to take risk and actually have to be promised way more expected return in order to to step up to taking more risk because they're hoping to retire at that point and and maybe if you're if you're 20 years old you can make a big financial mistake and you've got your whole life to recover from it but if you're 64 years old and planning on retiring next year doesn't really make a ton of sense to bet the farm a crazy speculation so that is indifference curves and you've probably seen them a little bit already but I often feel they're not well explained and so the indifference curves represent an investor's preference for risk in return and each of them represents a different risk appetite so we had how many we had one two three four different curves and each of those are four different risk appetites which it's reasonable to think exists so when someone says that they're risk seeking they often don't mean that they're taking risks for the sake of risk they mean that they are willing to take risk for a higher expected return that they might seek excitement but that's different to seeking risk you don't sort of if you're gonna skydive you're gonna skydive because you expect it to be fun that is the expected return if you didn't think it would be fun thus there's no expected return you wouldn't do it it wouldn't make sense to and so hopefully that clears up that idea so expected return how do we calculate it well it's usually the weighted average of the likely payoffs of an asset so we take an asset and there's all of these likely payoffs of it and and we basically weight them by the probability of the payoff and discount them to to the present date so it's the weighted average of the likely pass of an asset now risk reflects the chance that the actual return may be different to the expected return okay so that's an important point would risk in finance is that often when people think about you know what do you mean by risk and they often say well it's it's the risk of losing money because at least in the English language that's what the word risk might mean but actually in finance it's it's simply the the chance that the return will be different to the return you're expecting that that also means it could be significantly better as well as being significantly worse and so it's worth remembering that when we talk about standard deviation we're essentially talking about that bell curve that you see in statistics and basically the wider the standard deviation the greater the the randomness well not really the randomness but the the wider the likely outcomes are some more stuff can happen with a wide standard deviation than with a very narrow standard deviation and so then we have a pure variance which is Sigma squared is a measure of dispersion of a set of data points around their mean values if we have the mean the expected return and then the variance is sort of how spread out all of the observations on average are from that so it is the mathematical expectation of the average squared deviations from the mean that's the definition of variance but essentially it just means and why do we use squared deviations it's worth noting that the often in a lot of calculations you'll see things being squared and often that's in order to cancel out the pluses and minuses you know so so it's basically telling you we've got an expected return but how wide or how far apart are the various observations in it when we look at an expected return like that so then we go to standard deviation and standard deviation is the square root of the variance because it's Sigma rather than Sigma squared so we just calculate the variance take the square root of that and we've got standard deviation and so a low standard deviation indicates that the data points tend to be very close to the mean so they tend to cluster close to the expected return and then a what high standard deviation means that they tend to be spread out over a large range of values so that's really what standard deviation is telling you now why do we use standard deviation instead of variance the reason for that is just that standard deviation is expressed in the same units of the data so if we've got an expected return of 20% then with the standard deviation you might have a standard deviation of 15 percent and that is in the same units as our expected return and so it just makes it easier for us to understand what would talking about so then we come to this idea of mean-variance portfolios that you've probably heard a little about already in finance and essentially that is when we look at all of the the possible portfolios that are out there there are varying montañés we can invest in we usually invest in a portfolio rather than a single stock and I'll explain that in a few minutes time but essentially you want to have a portfolio that gives you the best expected return for a given level of volatility and that's what we see with this curve here is we see the various levels of standard deviation at the bottom of risk and the expected return over here and of course when we add in a risk-free asset we're then able to decide to put a certain amount of money into the risk-free asset some into this risky portfolio and then we can decide how much to put into either of these two asset classes in order to come up with the risk return trade-off that is most appropriate for us so that is that sort of idea of a mean variance portfolio so standard deviation again I sort of explained this but we'll just look quickly at the bell curve here so the standard deviation is it relates to this idea of normally distributed returns and essentially what we're saying with standard deviation is that around sixty eight point three percent of the observations would be one standard deviation from the mean so if the expected return was we'll say twenty percent and there was a standard deviation of 15 percent that means that you can add or subtract 15 from that expected return and 68 percent of the observations will be within that range so that means within what is it five percent and 35 percent sixty eight point three percent of the observations will fall and within that range and then we've got ninety five and a half percent will fall within two standard deviations of mean and finally 99.7% of of observations will forward in three standard deviations of the mean now that's all assuming normally distributed returns and it's worth noting that in markets returns tend not to be normally distributed and once again we're gonna talk about that well right now I guess so I have up here I we are able to see it if not you can see it in your slides this is actually from the statistics textbook that I've just written it's actually not yet published but here we've got a plot of the sp500 returns I think there's 50 years of returns that I've plotted here that's these straight lines it's it's put together as a histogram and then we've got the sort of reddish or burgundy colored line over it is the normal distribution and so what we're trying to do here is to see how our stock price is distributed are they really normally distributed because if we're using standard DB deviation there's sort of an assumption that there's a normal distribution and of course most of you have probably already heard this idea that in finance stock prices tend not to be normally distributed and so that's what we're talking about here so as you can see here the SP returns of a higher central peak and then the shoulders are narrower so the the distribution is kind of much more stacked to the center and kind of hollowed out there in the shoulders of the distribution where the bell curve is wider but then the the real question is what about the tails of the distribution and when you look at this initially you can't really see much like you can see a few things sticking up there beyond the the tails of our log normal distribution but it doesn't really look that bad and the reason it doesn't look that bad is just that we're looking at this in in a sort of regular chart but when we move to a log chart which we have on our next screen here so the the large differences are quite deep in the tail is really what we're seeing here and what we find and so you can you can't see that on the linear scale that we looked at in the last one but when we move to a log scale here we get the following chart and as you can see what happens is that it the the normal distribution which is that solid line there actually is is fairly reasonable for an awful lot of the returns but once we get out to this sort of kind of three standard deviations are greater there's way more observations in the actual market than there are or than would be expected in a normal distribution so the example of God up here is that a +5 and a half percent move in one day would be expected to occur according to a normal distribution about once every 67,000 years that's what you would expect if the stock market was normally distributed well we actually find that what do we find I've been to there been two of these moves in the last seventy years and actually I say that we're in a very volatile market at the moment where this is shot in March 2020 and the whole coronavirus thing is going on right now markets have been insanely volatile and of course we've seen numerous you know what can I say three to ten Sigma events occurring in markets right now and of course what that is telling you it's not we're not actually in well it is a bit of a crazy time but it's also actually within the range of expectations of markets it's just not what really within the range of expectations to happen as often if markets were normally distributed and so that is the distribution of the S&P 500 when compared to a normal distribution and hopefully you find that a little bit interesting so risk and return the Sharpe ratio so the Sharpe ratio is a calculation that you'll see a lot if you work in US at my our work in finance and the Sharpe ratio is really just risk and return right so we've got here new annual minus RF so that's the annual expected return of an investment divided by the annualized standard deviation right that's all there is so it's it's expected return minus the risk-free rate so that sort of a real return and inflation adjusted return divided by the volatility of the of the risky asset and so what is the Sharpe ratio it's really just telling us the risk to return of a given investment and so if you were looking at a bunch of different investments or we'll say for example a bunch of different portfolio managers you might want to look at their Sharpe ratio and see what kind of return they have gotten historically for the risk that they're taking and that's what the Sharpe ratio is it does penalize upside volatility and that's the nature of using standard deviation as a measure of risk is that both big up moves and big tamils are equally punished in the calculation of standard deviation and it's unsuitable for non-normally distributed return profiles and that's obviously a bit problematic because on our last slide we've just explained that the markets are not actually normally distributed so let's look at where a Sharpe ratio might maybe help you make the wrong decision so we've got here two trading strategies here's the first one where you know our trader seems to make most years are sorry every second year they make money every second year they lose them so they they make money lose money make money lose money in a fairly low volatility way in a predictable way there's one year that they do a little bit better than average but most years they seem to be returning about 2% and when they ever down here they lose about 1% and so we have an annual return of seven and an annualized standard deviation of 5.8 in this example and when we do the Sharpe ratio calculation that gives us a sharp off at one point - one now our next one here we have a down year a small up year a massive up here a small down your small up your small up your small up your small up here and in this example with an annual return of 23 and an annualized standard deviation of 20 you know so this higher expected return but also higher a standard deviation and that gives us sharp ratio of 1.15 so let's look at that that's one point one five or one point two one and so which of these would you choose if you wanted to get the best risk return and it's worth noting that you you can't just look at the return right because we have to assume that you're maybe able to leave her into one of them right like if this one is better on a risk return basis you could possibly just leave her into it you could by one and a half times the amount of this as the other one right because that's something that can be done in the real world and so we've got a Sharpe ratio one point two one compared to one point one five based on Sharpe ratio this is the correct one to pick but let's look at it in a bit more detail where are we being penalized here well you can see that there's not a lot of volatility here and that in the as I said the returns are reasonably predictable in this one there is a big volatile event and that's in this period when when our trader made 20 percent in in one period right so what's going on here well the the problem is that we've got a bigger standard deviation on this one than we did on the last one but the reason is all to the upside right it's because of this huge big up move if we had a much smaller up move we would have had a way lower standard deviation and we would have picked this right but you obviously want that big return don't you like I mean that's kind of why you're in it is to get the big upside and so that's a problem with Sharpe ratio is that if we just pick based on Sharpe ratio and the fact that Sharpe ratio punishes both upside and downside volatility we've got a little bit of a problem so that then brings us to maybe another calculation so it says here the problem with the shower is that it penalizes all volatility even upside volatility and the Sharpe ratio would have picked the wrong one in in that example so that then brings us to this idea of semi variance which people use a lot in finance as well and so semi variance you can see the calculation right here n is the total number of observations below the mean or T is the individual observed values and average is the mean our target value of the data set so semi variance is basically a calculation where we're only looking at downside volatility okay so we're not we're sort of throwing out the observations when there's upside volatility because we kind of want that and we're we're just allowing it to punish us for big down moves or volatility to the downside and so if we use semi variance instead of variance we're then able to calculate something that's very similar to the Sharpe ratio that's called the Sortino ratio and the Sortino ratio just looks at downside volatility and so that's something that's used a lot in finance as well now the truth is does most practitioners will look at all of these things right if you're gonna calculate one race you'll calculate them all like we just because we've explained that there are flaws in Sharpe ratio doesn't mean you won't calculate it it just means that you'll be aware of the flaws and try to make sensible adjustments based upon your knowledge so there we go so the next thing we've got the next kind of piece of financial theory that you've probably heard a lot about that portfolio managers do use is this idea beta and so each stock can be thought of as being made up of partially market risk and partially the unique stock risk you know the risk of that individual business and it might surprise some people if they're new to finance that actually the majority of the risk is market risk and if we think about right now with this whole coronavirus thing and the way way markets are really volatile at this particular moment in time when you see a couple of days ago we had a 12 roughly fall in the sp500 which was the biggest down day since the 1987 crash okay big big move and there aren't many stocks up on a day like that even the good ones even if even if you're making a product that might be particularly suited to this time the problem is that when the market tanks stocks tank with it and so what we're trying to do when we calculate beta which is the covariance over the variance what we're trying to do is to work out what part of the stocks return is down to the movements of the market and we call that beta and then the other part the unexplained part we call that the idiosyncratic risk our stock specific risk and we call that alpha and so beta is widely used for a variety of reasons because beta doesn't just tell us exactly kind of what what what part of the move relates to the market but it sort of tells us how risky our stock might be because let's think about it if you had let's see if I have a good slide on this if you have a low beta stock so here we have the market is this blue line and the orange line is a beta 0.5 stock but that's really telling you is that if the market moves one percent usually your stock will move a half of a percent usually so that's up or down and so essentially your stock is half as volatile as the market and thus half as risky as the market now the next one here we have a beta of 1.25 stock which means that if the market moves up or down one percent your stock can be expected to move up or down one and a quarter percent and so it's more volatile than the market it moves with the market but it's more volatile it's at a more leveraged maybe to economic conditions than the average stock is and so that's kind of what beta is telling you now how are we calculating this well the idea behind beta is that we are we basically do a regression analysis which is a statistical calculation where we regress the returns of the stock against the returns of the market portfolio and there's this idea of the market portfolio now the idea of the market portfolio is that it's every possible investment that's out there you know it's it's every risk that you could possibly take with your money is in the market portfolio we bundle those all together and we do this regression analysis and we kind of compare this one stock to all possible investments now in the real world there isn't a market portfolio or at least it's not a good time series of the market portfolio so what we use is the S&P 500 mostly now in other countries maybe you use if you're looking at we'll say if you're in China you might use a Chinese stock index to regress against just because maybe that's more reasonable why the S&P 500 or is it reasonable or unreasonable to use the S&P 500 well I would argue that it's actually fairly reasonable to use this and P 500 because if we think of all the financial risks that we can take the S&P 500 is basically made up of the 500 largest publicly traded companies in the world and in there there'll be technology companies oil companies banks you know you name it there's every type of company in there there they're also international companies right like if you if you think of a big oil company they'll be all over the world so even though the S P is an American stock index it's not just leveraged to conditions in the United States it's leveraged to global conditions you know we'll say the biggest stock in in the S&P at the moment is an Apple Computer and they obviously sell their products all over the world not just in the United States they also manufacture them all over the world or at least where things are manufactured which is China but so when we look at the S&P 500 is it representative of the market portfolio it kind of is you know because you might say oh well things like gold aren't in there and it's like well gold as an asset isn't in there but gold will be represented in there by will say gold mining companies are by companies that use gold in one way or another and so the truth is that most things are represented in there and secondly it just makes a calculation and awful lot easier to use the S&P rather than to construct difficult to put together index of the market so that's that that's what we use to calculate beta so a long short portfolio so if you're running a long short portfolio and by that I mean that you've bought us a basket of stocks and then you've sold short another basket of stock so you've essentially bought the stuff that you think will go up and you've sold the stocks that you think will go down you'll have to take the beta into account right because in in order to be market neutral or beta neutral and you'll see this term a lot in the hedge fund industry so if you bought $100 of a risky stock and sold $100 of a lesser ease risky stock you might say well under neutral in that I bought a hundred of one thing and I sold a hundred of another thing but we'll say if it's back to you know our water utility in our tech stock and if you bought $100 worth of the textile can sell $200 of the water utility the truth is that you're more long than short because you've bought more of the risky thing unless and you've sold short the same amount of the less risky thing so you're exposed to market risk through beta so usually within any sort of long short asset manager they will aim to neutralize or hedge the the portfolio for this beta risk this this market exposure that they are taking so our next slide then we're going to look at well how do we calculate beta and I sort of glossed oh I've run through the idea that's a regression analysis and it's the slope of the the regression analysis line but what do we get well the question is if you want it if I told you here's the name of a star calculate its beta what you do is you'd go out you'd get will say a few years worth of the stock price day and a few years worth of S&P 500 data and you you do this regression analysis and see what the slope of the line is and that would tell you how volatile this stock is in comparison to theirs and P but the the question is how much data would you use because in the example I have here we've used a bunch of different ones we've used five years of data one year of data three months of data one month of data you know you can calculate it however you want and there's even good arguments for each of the different ones you know you might say well you know that this company's changed a lot in the last year and so I really only want the last year's worth to date if I used five years of data four years of it are of almost a completely different type of company and that might be a reasonable argument but you you do get all of these different betas so in the example here we've got a beta of 0.75 point five eight point five or 0.38 we've got a bunch of different betas and they're all less than one so it's a low volatility stock we feel and so we'll decide in our example that we decide to hedge using the 3-month beta we just think that that's a reasonable one to use so we're going to use that and then in the real world what happens is that you've bought a hundred thousand dollars worth of ABC stock our company in question sold $50,000 worth of S&P futures short against it in order to hedge and your hope is that on a risk-adjusted basis that ABC is going to outperform the SP now what actually happens in our example instead ABC falls 7% and the sp500 Falls 9% and so you end up with a $2,500 loss so you were right that ABC stock outperformed the S&P but you were wrong about the the hedge ratio that you use based upon beta and the actual realized beta in our example was 0.97% and so we we hugely miss and lost money here so what's our take away which beta should we use well the the problem with this is it's kind of up to you to judge but one piece of advice I would give is that in the long run beta doesn't really hold up that well out-of-sample in all honesty I don't find beta to be a hugely useful calculation in all honesty it's worth looking at but it's not the most useful thing and I would argue or at least a statistical analysis would tell you that in the long run beta sort of seemed to revert to around one so we'll say if you calculated what would go here for different betas here my recommendation if I was doing this trade would be to pick the one that's closest to one and so if they were high Bader's if it was you know pages of two and three and you know 1.25 or whatever once again you'd pick the one that's closest to one because that tends to be what happens out-of-sample with with beta calculations so but in our example here actually no matter which one you used you would have been wrong because all of them were less than 0.97 which is what happened in the real world so that's just that's what beta is and something to be careful of with beta because you know sometimes the problem with a lot of calculations people do in finances you do a calculation and you have this huge faith that you know yes the mathematics of your calculation is right but that doesn't mean it'll work out for you and in the medium runner the long run even and so the truth is you're better off using these calculations than not using them but you always do have to take them with a pinch of salt and so and that's what most experienced market practitioners do you'll notice that often they're very experienced and knowledgeable about the numbers but they're also very experienced in how things can go wrong and that that's a good way to to think so the next thing we're going to talk about is correlation and how correlation might matter to a portfolio manager is investing money so I've got to the two slides here hopefully you can see them we've got positive correlation and negative correlation and some positive correlation just means that when one moves up there there moves up and when that wood moves down the other moves down so they move together to a certain extent negative correlation actually means that they move opposite to each other so when one is going up there there's going down and vice versa it's a bit of a seesaw like relationship okay so that's positive and negative correlation now why why might these appeal to you well the problem is if we take our two positively correlated assets and put them together in a portfolio the problem is that the we don't dampen out the volatility that much because if they're both moving together it's almost like we're exposed to the same risk factor while if one is going up and the other is going down and they still had you know we'll say if they each had the same expected return if we have these different assets all with the same expected returns but different correlations if we take the ones that are uncorrelated are negatively correlated to each other that still have a positive expected return we'll end up with this sort of dampening effect where when when market volatility gets sort of neutralized a little bit by the the randomness in the movement between the various components of your portfolio so let's work through an example because often to just a quick look at the mathematics of this explains it maybe a little bit better than any talk through I can give you so we've got here two stocks for our example ABC industries and XYZ Incorporated and of course I've got locals for both of them and they ABC is an expected return of 11% XYZ has an expected return of 25% ABC has a standard deviation of 15 percent and XYZ has a standard deviation of 20 percent so XYZ is both higher expected return and higher risk in terms of standard deviation now they have a correlation of 0.3 which means they are positively correlated but it's a fairly low correlation you know there's there's a lot of randomness in the movements but you because the correlation of one means they move exactly in lockstep with each other correlation of zero means that there's no relationship and a correlation of minus one means that when one is going up the other is going down exactly and so a correlation of 0.3 is a positive correlation in that they do move together but there's an awful lot around numbness in there so if you think about then creating portfolios of the two we know how to calculate the expected return so in our example here where we've got a hundred percent ABC and zero percent XYZ we've got an expected return of eleven percent and that's because that's the expected return of of ABC right and that's all we've got and that the other end where were a hundred percent in X Y Z we've got we've got the expected return of 25 percent which is the expected return of XYZ because that's all that's in the portfolio now these in-between ones we basically just get a weighted average so if you're 50/50 it'll be half of whatever 11 plus 25 divided by two will be your expected return and that's how you average the expected returns it's a pretty easy calculation now something happens though when we when we try and average our standard deviation because you don't just average standard deviation the way you average expected return we have fun with a different formula here which you can see here you can see it in your slides as well and and that is how we calculate the portfolio standard deviation it's a much more complicated formula and you'll notice that the weights are in there and then we've got covariance in there which which is coming from standard DVD is coming from correlation right so what we've got is if we look at our various portfolios here where we can have different holdings of the two different stocks and then we have an expected return of the any of these portfolios and then the standard deviation of any of the portfolios and you find down here that if you have a hundred percent of ABC your the deviation is 15% if you have 80% ABC and 20% XYZ you have a standard deviation of 13.7 percent and if you have 60% ABC and 40% XYZ you also have an expected standard deviation of 13.7 percent and so that's a little bit surprising right because you would have thought well hold on a minute is there shouldn't there be you know how can you have different expected returns with the same risk and the answer is that when we plot this whole thing we end up with a curve like that so there are lots of places where we have two different expected returns a low and a high one for the same level of volatility and so what that is telling us actually is that there is an optimal allocation between these two stocks so you don't just pick based on what you want you actually would pick the the highest expected return you can get for a given level of risk and then also because there might be a risk-free rate that we're able to invest in we're able to buy the risk-free bond we can also then just plot a line across to from the tangent of this curve to the expected return of the risk-free rate and then we choose the correct portfolio based on the the optimal risk return trade-off and and if we want less risk than that we allocate to the risk-free asset and equal if we want more more expected return than that we then leave her up we short or borrow money we short the risk-free asset and we we invested in in this levered portfolio so that's kind of how that's how correlation matters so if let's look at surely there's a better slide so here's our slide and hopefully you've probably seen this sort of thing a little bit as well this type of a diagram and so if if we had a correlation of one where XYZ and ABC moved exactly aligned with each other will then actually the way their standard deviations average would be the simple average and you'd have just a straight line there but the minute we move away from perfect correlation anything other than perfect positive correlation starts to bend this line out and so the lower correlation so line a is perfect correlation this curved one here B is correlation of zero point three C is correlation of minus zero point three so minus a negative correlation actually starts to give us even better risk return trade-off and if they were perfectly negatively correlated to each other it brings the line all the way over here because of course if we have something that's guaranteed that's definitely one one goes up and the other goes down and we're able to put them together into a portfolio we would just get the expected return of that portfolio with no risk right of course that's not gonna happen in the real world but that's said of the extreme of what could happen so this is why correlation matters is that if we can find uncorrelated assets and put them together in a portfolio we managed to get a lower a lower risk for a given level of return right and so that's why investors diversify you know when people say oh the first rule of investing is diversified but they don't really explain why and the reason is that when you've got all of these different assets in there they're going up and down for a variety of reasons if they're not all moving in lockstep with each other we end up with this diversification benefit which actually just means it's to do with correlation and how that feeds into that the averaging of standard deviations and and what it really means what it's telling you is that that you you can get with diversification you get the the same level of expected return but at a lower level of risk and that's attractive to all investors that makes sivadas correlation and standard deviation so diversification people this is just an idea then this slide is just an idea on diversification because an awful lot of people don't think about you know they might think about diversifying their stock portfolio but they don't necessarily think about their life risks as part of that portfolio so I'd the example I give here is that if you um if you worked in the oil industry or you know name and industry but I picked the oil industry for this example if you worked in the oil industry and we will say you lived in an oil city like you live in somewhere in the Middle East or you live in you know Calgary in Canada or Houston or Dallas in Texas or or you know in the Permian Basin isn't like that you own a house there and all sorts of things like that you actually have plenty of risk exposure to the oil industry right because if there's a downturn in the oil industry you might lose your job your house might fall in value because everyone else has lost their job in your town and there's all sorts of problems associated that so actually if you were investing your retirement account you should probably invest in all sorts of stocks other than oil stocks in order to be diversified because you're naturally exposed to the risk of oil through your career and through the town that you live in in the world and so it's always worth thinking about like what kind of natural exposures to risk does an individual have rather than just this pure portfolio approach hopefully that makes a little bit of sense to you and and then you can you know maybe come up with a better portfolio for an investor like that so what if we go diversification and I've got the footsie weightings here and this is sort of a thing I update every year when I teach this class and we've got you know the different types of company that make up the footsie and as you can see over time to change as nuts just do to some sectors doing well some sectors doing badly and then it changes the next year and so you know this slide here is showing footsie sector weightings in 1999 and then again in 2013 and so you can see here that you know there's been a lot of growth in what have we got here Telecom was huge in 99 quite small today financials were much bigger in 99 much smaller in 2013 basic materials much bigger in 2013 much smaller back in back in the late 1990s and so as you can see when you invest in a stock index like the foots here the S&P that that index is in is made up of a bunch of different companies and the waiting's do change over time and so at the next one we have appears to sp500 weightings and there's all the different sectors as you can see this is as of February 28th 2020 and almost a quarter of the S&P is in technology stocks and that's actually the highest it has been since 1999 with the Internet boom what else have we got we've got a very heavy weighting in healthcare a heavy weighting in financials in fact those three sectors alone are more than half of the S&P 500 now the idea of diversifying is that you're invested in a bunch of different types of business and when one does well and the other may not do well but overall it kind of smooths your return and so let's look at this this is this chart is basically showing the the rises and falls are those sector waiting's over time so that's 1995 through to 2012 and unfortunately I wasn't able to get an updated I just like the way this chart looks and wasn't able to get an updated one I think it came from JP Morgan but the the one here at the top is buying up to date I downloaded it today so that is sector weightings in the S&P and so as you can see over time this stuff all changes you know and it's due to how well or how badly a given sector has performed so more on diversification because I know you guys are loving this diversification material we've got here a chart that you often will see within the war to finance and what what it's showing here we've got at the bottom number of stocks and then on this axis here we've got risk a standard deviation and what you see is that once you reach around people often say 20 stocks it's actually 18 stocks but you know we can round to 20 you need to be invested in at least 18 stocks in order to be diversified so for each additional stock if you go from one stock to two stocks there's a huge drop-off in risk you have another stock another drop-off and risk and it really you stop getting an awful lot of additional benefit once you go beyond 20 stock so what that is telling you is that it's almost a free reduction in risk associated with buying a 20 stock or greater portfolio rather than being all in one stock so that's us stocks now you'll notice here that we've got another line that goes down an awful lot faster now once again it reaches the level of diversification at around 20 stocks but what we've got is international stocks so if you invest internationally you you tend to diversify faster and that should just make intuitive sense to you as well that if you imagine you know very you you've got foreign exchange risk in there which can work for or against you and you've just got the fact that certain countries can be doing well while others are doing badly and vice-versa and so you're essentially by investing internationally you are diversifying more because there is less correlation between international stocks than there are from single country stocks so wanted to take aways if this is that if you are investing you should be internationally investing you should be looking around the world rather than just locally and I grew up in Ireland and unfortunately an awful lot the people I know they only invested in Irish stocks and back in the credit crunch you know the biggest stocks in Ireland were the bank stocks and they kind of went to zero and and people lost an awful lot of money although global markets did very badly people who invested internationally would have done better than those who just invested in their local their local market and so that's the takeaway of this is that is that you should own at least 18 stocks and that you'll do better in terms of risk in return if if if you are looking at global stocks rather than just your local country stocks so what can we move to from here so we're able to create and plot what's called the efficient frontier the mark of its efficient frontier if we put together portfolios of all assets available for investment so the idea of the efficient frontier is that if we put all assets together and work out basically by throwing a lot of computer power at the optimal portfolio based on expected return and unexpected volatility we're able to come up with a set of portfolios with the highest return at each level of risk so that's what we see here this this curve and this is the mean variance efficient frontier that that can be created at the bottom with that standard deviation so risk and on this axis we've got expected return and so that is where the Markovitz efficient frontier comes from is this idea of correlation risk in return and that just tells us that you should only invest in a portfolio so a combination of all of these stocks that's on this efficient frontier and then if we add in the risk-free rate at the risk-free asset like a government bond we're then able to plot what's called the security market line which is just a tangent line to this curve that touches the the risk-free rate and that tells you how you should invest in a mix of either diversified stocks or or bonds in order to get the optimal risk return trade-off or whatever expected return or of whatever level of risk you're willing to and so that is the end of this class hopefully you found that useful we've looked at risk in return and a lot of the sort of financial mathematics that explains why we should be trying to do that I will put up another presentation tomorrow and hopefully you'll find all of these quite interesting see you then bye [Music]

Channel: Patrick Boyle

Views: 95,211

Rating: 4.9726925 out of 5

Keywords: finance, trading, trading and pricing financial derivatives, patrick boyle, on finance, cfa exam, level 1, level 2, level 3, kings college london, business school, queen mary university of london, quantitative finance, financial derivatives, portfolio management, applied portfolio management, risk & Return, asset management, university lectures

Id: PtDzY3-7ieE

Length: 74min 51sec (4491 seconds)

Published: Sat Mar 21 2020