Investment Science: Portfolio Optimization

hi I'm dr. Tucker bulge with the center research and in this video I'm going to tell you about portfolio optimization now this video is about the science of portfolio optimization there's another video that tells you how to use the portfolio optimizer that's part of a Lucinda's quant desk now portfolio optimization is a really important tool of a cornerstone of quantitative analysis and what is it well what it does is given a set of equities that you want to invest in and a target return that you want to achieve a portfolio optimizer will figure out the best allocation of cash to equities to give you the lowest risk for that portfolio now before I get too deep into this so we need to go through a couple of disclaimers listener research is not a registered investment advisor I'm not either you should definitely speak with a licensed financial advisor do not assume that the techniques we're going to show you here will be profitable and the stuff I'm going to show you is hypothetical it's based on historical of data and there's there's no guarantee that this kind of stuff will work in the future on real trading okay back to portfolio optimizer portfolio optimizers are a part of all serious investment techniques they're used by the largest hedge funds and investment banks and again what it what it does is it helps you figure out among a set of equities how much you should allocate to each one so that you can for given return have the lowest risk now what do we mean by risk list let's answer that by taking a look at two hypothetical stocks this stock XYZ had a pretty good historical performance that went up 10% note though that it's a kind of volatile goes up and down a lot let's compare that now to this other stock ABC that also gained ten percent over the same time period but it wasn't quite as volatile it's this volatility that is a measure of risk and that's what's traditionally used in the in the finance and industry to measure risk now there's other measures of risk that are also valid this one is convenient in the sense that it's easy to measure volatility how much the stock goes up and down is standard deviation of returns and it's a it's a calculation that's easy to do to do on a computer now we can consider equities stocks ETFs whatever in two dimensions one dimension is this risk that we are talking about or volatility and the other is return now ideally of course what we want is low risk high return stocks but as is usually the case you don't see return without without risk so the highest return stocks also tend to have the highest volatility or risk but you can you can view each of the equities that you might want to invest in in this in this sort of two dimensional view and when you build a portfolio by allocating a weighted amount of of cash to each one of these equities you get a portfolio that's sort of a weighted combination of each of these equities now the portfolio itself is somewhere on this graph it has a certain amount of risk and a certain amount of return or expected return and you would think that it would be sort of somewhere in the middle of all these of where all these equities are well it turns out that portfolio optimization allows us to do better than that we can we can find portfolios that for a given target return actually have lower risk than any of the individual equity and I'm going to show you how in this video how can we do it better well in the in the 60s and 70s a theory of finance evolved called Modern Portfolio theory this guy Harry Markowitz was one of the leaders and he discovered a way to combine equities into portfolios that actually have lower risk than any of the individual equities and he got the Nobel Prize for that in 1990 we use the that same algorithm as part of our court desk tool and I'm going to give you an example of that a little bit but let me introduce you now to the to the science behind what what Markowitz developed it's a little bit of math but it's it's not too bad I think you I think if you if you have an interest in this you'll find it interesting okay so what goes into a portfolio optimizer the inputs like we had talked about are for each equity a measure of return what are we expected to see has return for each equity also a measure of risk for each equity and we have you see there the each of our green dots there represents an equity on this on this map a target return so you can ask the optimizer look I want to get to I want to get this target return and you know fine for me the the lowest risk portfolio so that's the thing you got to give it there's this so there's this other piece of data that it takes called a covariance matrix and that's probably the most complicated of all this and I'll get into that in a moment but the you feed these inputs to the to the optimizer it does a lot of number crunching it's a really serious algorithm and it finds the weights for each equity to give you this portfolio and as you can as you can see as you can see here it's a lower risk than any of the other constituent equities and that's kind of the magic of portfolio optimization okay what is covariance and why does it matter what so let's take a look at that in the context of three example stocks ABC is the blue stock the EF is the green one GHI is the orange one sorry was it creative and naming there now notice how the blue stock and the green stock tend to move together they move closely together whereas this other stock GHI but it shows the same return but it it moves a sort of opposite those other two stocks another thing to notice is each of these equities has about the same volatility and they have about the same the same return and the magic of portfolio optimization is a way that you can combine them to get a much lower volatility portfolio for the same return okay now there's a important concept here about the relationship between two stocks and how they move from day to day and it's called covariance there's another measure that's very closely related I'm not going to go into the mathematical distinction but correlation we also use and the correlation between stock a b c and d EF in this case is is 0.9 a high number in fact the highest correlation you can have is 1.0 and the lowest you can have is negative 1 okay so they a high positive number means they move together very similarly a negative number means they move oppositely one almost the predicts which way the other one is going to go so in the same way that the relationship between the first two stocks is it is a positive number close to one relationship between the blue and the orange stock is a negative number because they move opposite one another okay let's look at a couple hypothetical portfolios built using these equities let's suppose we build a portfolio that's half ABC and half d EF now because these stocks move similarly we expect the resulting portfolio to move like they do and as you can see this just no red line represents the portfolio of combining those two stocks so it's got about the same amount of volatility the same return as as those two equities so we don't gain too much by combining those two equities into a portfolio now how about another portfolio what about a portfolio where we put 25% in the blue 25% in the green and 50% and the other one GHI so what that means now is we've got about half and the two equities that move together and the other half and the equity that moves opposite them now because um we've diversified now and stock that's anti-correlated that's the that's a fancy term for the that they move opposite one another we're going to get a much smoother performance and as you can see here of course I just drew this but as you can see when you combine these stocks that are anti-correlated you get a much smoother performance and these relationships are the relationships that are discovered automatically by a by an optimization tool like the one that we use that's part of quad desk at at Lucena okay so let's so let's go back to this this map with god of risk and return and the and each equity is a little green dot there that represents its particular risk and its particular return and as you recall there that that orange dot was a portfolio we were able to let discover well it turns out that for each of target return there is a unique portfolio that that is the minimum risk portfolio of for that amount of return and it defines a curve a line here so this line represents essentially an infinite number of different portfolios and each one is a different target return that one portfolio we discovered is just one of them but there's a continuum along that line there's three very important portfolios along that line that we provide access to in our desk one is the maximum return portfolio that's the one that gives you the highest return and and and unfortunately it's it's usually home oh it's often also the the highest risk portfolio and that's in the that's in the upper right corner of this chart you can also ask for the lowest risk portfolio and that's in the lower left there and and and that's essentially the portfolio that has the lowest volatility and you know you end up with a particular return it is usually lower for that there's this other interesting point along that line which is we call balance which is in between the two and that's the one that maximizes the ratio of reward or return to volatility that one maximizes the Sharpe ratio um okay so let's look at a couple examples with quant desk again there's another video that goes into much deeper specific examples on how to work with our portfolio optimizer let me just show you a couple simple ones that I've put together okay we we have this portfolio it's got the it's got four equities of there's a GG a bond fund GL d GL D which is of course a an ETF that represents gold SP why is an ETF that represents the S&P 500 and USO which is oil now I've built an example portfolio that's just a quarter of the portfolio is in each equity and you can you can see it's you can see it's a year-to-date performance here along the bottom we've got a few a few data points over here the volatility is 0.7 3% that means that on average it changes three quarters of a percent per day it's a sharp ratio is 0.15 which which is not not all that great okay so let's go to the optimized tab and we'll take a look at the how we can optimize this portfolio remember now there's four equities and to start with right now what we're comparing it to is a portfolio that's got a 1/4 of the 1/4 of the holdings in each of those 4 equities ok we'll we'll look back over 6 months to do our optimization and let's start with them with a maximum return optimization so what we should discover here is that it'll it'll select the single equity that has the highest return over that over that period ok so turns out that over this period of GLD gold has had the highest return and it's essentially puts 100% of the holdings into GLD and you can see this chart on the bottom the blue the blue line is what what we started with our original portfolio and the orange line is what we would have made if we had if we had and put all our eggs into gold and as you can see going forward there's a forecast volatility and a forecast return and as you can see the the volatility going forward is forecast to be more volatile than what we had been in all day ok let's let's let's we'll save that so our new portfolio now that we're working with essentially has everything in GLD alright let's try another optimization let's instead go for minimum risk and before before I have it started doing that take a look at the volatility of this portfolio that we're in right now it's a fairly volatile portfolio and going forward the forecast cone there diverges significantly because of the because of the forecast volatility right now we'll try and optimize from risk across these for equities okay now we've got got that back take a look at that um a very smooth return if you compare that the two returns we we don't get nearly as much as higher return with the with the original portfolio where we put to put all the put all the eggs into GLD but going forward we have a much lower much lower volatility okay now let's try a balanced optimization where we're asking it to to find a balance between maximum return and maximum volatility I'm sorry minimum volatility of course okay so this is the the balance portfolio and look it's a it is indeed much less volatile in our original portfolio not quite as high return looking back but looking forward also much lower volatility stepping forward again so that's that's the science behind portfolio optimization check out our other videos in particular the video about the details of you know all the all the cool things you can do with portfolio optimization with our tours look forward to seeing you again and thanks for thanks for checking out the center research and Watkins see you again

Channel: Tucker Balch

Views: 20,259

Rating: 4.8518519 out of 5

Keywords: investment, portfolio optimization, mvo, mean variance optimization, markowitz, lucena, finance, Trading, Market, Stock, quantitative, analysis

Id: 5qbMhXXq0vI

Length: 18min 9sec (1089 seconds)

Published: Wed Dec 19 2012