the following content is provided under a Creative Commons license your support will help MIT open courseware continue to offer highquality educational resources for free to make a donation or view additional materials from hundreds of MIT courses visit MIT opencourseware at ocw.mit.edu all right let's uh let's start so first of all um I hope uh youve been enjoying the class so far and uh thank you for filling out the survey so we got some very uh useful and interesting feedbacks one of the feedbacks it's my impression I haven't got a chance to talk to my uh uh co- um lecturers or colleagues yet but I read some comments uh you were saying that uh some of the problem sets are quite hard right the math part may be bit uh bit more difficult than the lecture so I'm thinking so this is this is really the application lecture and uh from now on after three more lectures by uh chumo that will be essentially the remainders of all applications uh the original point of having this class is really to show you how math is applied to show you those cases in different markets different strategies and in the real industry so I'm trying to think how do I give today's lecture with the right balance you know this is after all the math class should I give you more math or should I you have you had enough math I mean sound like from the survey you probably had enough math so I probably want to focus a bit more on the application side and from the survey also seems like most of you enjoyed uh or wanted to listen to more on the application side so uh anyway as uh you've already um uh learned from uh Peter's lecture uh the so-called modern portfolio Theory and it's actually not that modern anymore but we still call it modern portfolio Theory so you probably wonder in the real world how actually we use it do we follow those steps do we do those calculations and uh so today I like to share uh with you my uh my experience on that both in the past a different area and today probably more uh focused on the on the bu side oh come on in yeah actually these are my colleagues from Harvard management so so they will they will be able to ask me really tough questions um so anyway um so how how I'm going to start this class you wonder why I handed out each of you a page so does everyone have a blank page by now yeah actually uh yep so yeah could you also pass to yeah so I want everyone of you use that blank page to construct a portfolio Okay so you say wow I haven't done this before that's fine to do it totally from your intuition from your knowledge base as of now so what I want you to do is to write down to break down the 100% of what you want to have in your portfolio okay you said give me choices no I'm not going to give you choices you think about whatever you like to put on wide open right and uh and don't even ask me the goal or the criteria based on what you want to do and so uh totally free thinking and but I want to you do it in five minutes so don't overthink it and uh hand it back to me okay so that's really the first part I want to show intuitively how you can construct a portfolio Okay so what what does a portfolio mean okay that I have to explain to you let's say for undergraduates here so your parents give you some allowance you managed to save $1,000 on the side you decided to put into Investments buying stocks or whatever or you know gambling or buy lottery tickets whatever you can do just break down in percentage that could be a $1,000 or you could be a portfolio manager have hundred billions of dollars or whatever or then and save they raise some money start hedge fund they may have $10,000 to start with how do you want to use those money on day one right just think about and then so why are you filling out those pages so please hand it back to me it's your choice to put your name down or not and then I will start to assemble those ideas and put on blackboard and sometimes I may come back to ask to your question you know why do you put this so that's okay I don't feel uh embarrassed I we not going to put you on the spot but the the idea is uh I want to use those example right to to show you how we actually connect Theory with uh with practice I I remember when I was a college student I learned a lot of different stuff but I remember one lecture so well one teacher told me one thing I still remember vividly well so I want to pass it on to you so how do we learn something useful right you always start with observation so that's kind of the physics side you collect the data you ask a lot of questions try to find find out patterns then you what you do you build models you have theory try to explain what is work working what's repeatable what's not repeatable right so that that's where the mass comes in you solve equations sometimes but in economics a lot of times unlike physics the repeatable patterns are not so obvious so what you do after this so you you come back to observations again you confirm your Theory I verify your predictions and find your error then this feeds back to this R and A lot of times the verification process is really about understand understanding special cases that's why today I really want to illustrate the portfolio Theory use lot of special cases and uh so can you start to hand back your portfolio construction by now okay so just just hand back whatever uh you have one even have one thing on the paper that's fine or many things on the paper or you think as a portfolio manager or you think as a Trader or you think simply as a student as or as yourself all right so I'm getting things back I will start to write on the Blackboard and uh you can finish what you started by the way that's the only slide I'm going to use today I'm not because I realize if I show you a lot of SL slides you probably can't keep up with me so I'm going to write down everything just take my time and so hopefully you get a chance to think about questions as well is okay I think uh is is anyone finished anymore okay all right okay okay okay great you guys are awesome okay let me just have a quick look to see if I missed uh any okay wow very interesting so I have to say so some people have high conviction 100% in one of those uh I think I'm I'm going to I'm not going to reach your names so don't worry okay okay I just going to read the the assets people put on okay so small cap equities bonds real estate Commodities those were there uh quantitative strategies selection strategies deep value models Food Drug sector models energy consumer S&P index ETF fund government bonds top hedge funds so natural resources Timberland Farmland checking account stocks cash corporate bonds Rare Coins lotteries Collectibles that's that's very unique and Apple stock Google stock gold long-term saving annuities so Yahoo Morgan Stanley stocks I like that okay Family Trust okay I think that's that pretty much covered it okay so I would say that list is more or less here so after we youve done this when you when you were doing this what kind of questions came to your mind anyone wants to uh yeah please know was right but um to draw in my portfolio like whether it cash bills bonds like that yeah how do you do it right really what's the criteria and uh so before we answer that question how you do it how do you group assets or exposures or strategies or even people like Traders together I mean before we answer all those questions we have to ask ourself another question what is the goal what is the objective right so we understand what portfolio management is so here in this class we are not talking about how to come up with a specific winning strategy in trading or Investments but we are talking about how to put them together so this is what a portfolio management is about so before we answer how let's see why why we do it why do we want to have a portfolio right that's uh that's a very very good point so let's understand uh the goals of um portfolio management so before we understand goals of portfolio management let's understand your um your situations everyone's situation so let's so let's uh look at this chart so I'm going to plot your uh spending uh as a function of your age so when you are age zero to age of 100 so everyone's spending pattern is different so I'm not going to tell you this is the spending pattern so obviously when kids are young they probably don't have a lot of uh uh Hobbies or tuation but they have some basic needs so they they spend then the spending really goes up now your parents have to pay your tuition or you have to borrow loans scholarships and then you have that's College then you have you married you have kids you need to buy a house buy a car pay back student loans you have lot more spending then you you go on vacation you uh you buy Investments you you just have more spending coming up so but if goes to a certain point it will taper down right so you're not going to keep going forever so that's your spending curve and the other curve you think about is what's your income what's your earnings curve you don't you don't earn anything when you just you just born but use earning so this is spending so let's call this 50 you earn probably typically Peaks around age of 50 but really depends then you probably go down back up right so that's your earning and do they always match well they don't so how do you make up the difference right you hope to have a fund have a investment on the side which can generate those cash flows to balance your earning versus your spending okay so that's only one simple way to put it so you got to ask you about your situation what's your cash flow look like so then so you said my objective is I'm going to retire at age of 50 then after age of 50 I will live free I travel around the world then I calculate how much money I need so that's one situation the other situations I want to graduate I pay back all the student loan in one year right so that's probably another and typically people have to plan this out and or if I'm managing um a university endowment so I have to think about what the the University's operating budget is like how much money they need every year drawing from this fund and then by maintaining protecting the total fund for basically a Perpetual purpose right ongoing and keep growing it you you ask for more you know contributions but at the same time generate more return so that's man if you're a pension fund you have to think about at what time frame a lot of the people the workers will retire they will actually draw from the pension right and uh so every situation is very different I mean let me I even expanded so you think oh this is all about investment no no no this not this not just about investment so I was a a Trader for a long time at the Morgan Stanley and later on the trading manager so when I had many Traders working for me the the question I was facing is how much money I need to allocate to each Trader let them trade how much risk they take right so they all said I have this winning strategy I can make lots of money you why don't you give me more limits no you're not going to have all the limits you're not going to have all the capital we can give to you right so I mean I'm going to explain you have to diversify at the same time you have to compare the strategies with different parameters liquidity volatility and uh many other parameters and uh even you don't have you even you are not menine people let's say I was giv this so Dan safe Martin and Andrew so they start a hedge fund together so each of them had a you know great strategy and Dan has five Andrew has four so they all together have 30 strategies but so they raise certain amount of money or they just pull together the savings but how do you decide which strategy to put more money right so on day one so those questions are very practical so that's all so you understand your goals that's then you're really a lot clear on what how much risk you can take so let's come back to that so what is risk as Peter explained in his lecture right so risk is actually very not very well defined so in the modern portfolio Theory we typically talk about variance or standard deviation of return so today I'm going to start with that concept but then try to expand it beyond that so stay with that concept for now risk we use standard deviation for now so so what are we trying to do so this you're familiar with this chart right so return versus standard deviation standard deviation is not gonna go negative so we stop at zero but return can go to go below uh zero and I I'm I'm going to reveal one formula before I go into it I think it's useful to review what the uh previously you learned so you let's say you have I'm going to also clarify the notation as well so you don't get confused um so let's say um so Peter mentioned the here REM Mark with uh modern portfolio Theory which won him the Nobel Prize in 1990 right along with shop and uh and a few others so it's a very elegant piece of work and uh so but I today I was trying to give you some special cases to help you understand that uh so let's review one of the formulas here which is really the definition so let's say you have a portfolio let's call the expected Return of the portfolio is R of P equal to the sum of weighted the sum of all the return expected returns of each uh asset you basically I linearly I'll allocate them then the variance oh let's uh all yeah let's just look at the variance Sigma p² so these are vectors this is a matrix the the one in the sigma in the middle is a covariance matrix okay that's all you need to know about Mass uh at this point so I want us to go through the exercise on that piece of paper I just collected the back to put your choice of investment on this chart okay so let's start with one so what is cash cash cash is Cash has no standard deviation you hold cash so it's it's going to be on this access is positive return so that's here so let's call this cash where is uh let me think about another where's lottery so you buy um your power power barall right so what's lottery for you put let's assume you put everything in lottery so you're going to lose so your expected value is very close to lose 100% And your standard deviation is probably very close to zero so you'll be here so you somewh oh no no no it's not exactly zero so okay fine so maybe somewhere here okay so not 100% but you still have a pretty small deviation from getting losing all the money what is coin flipping so let's say you decide put all your money to gamble on the Fair coin flip Fair coin zero so expected return zero what is the standard deviation of that good so 100 100% so we we kind of got the three extreme cases covered okay so where's um where's US Government Bond so let's just call it fiveyear node or 10e Bond so should returns better than cash with some volatility let's call it here what is investing in startup Venture Capital fund like pretty up there right so you probably get F very high return but you can lose all your money so probably somewhere here VC uh buying stocks let's call it somewhere here uh last uh application lecture you heard about investing in Commodities right trading gold oil so that has higher volatility so sometimes higher returns so let's call this commodity and the ETFs is typically lower than single stock volatility so because it's un like just like index funds so here are there any other choices You' like to put on this map okay uh so let me just look at what you you came up with real estate okay real estate I would say probably somewhere around here private Equity probably somewhere here or invest in hedge funds right somewhere so I think that's you know example to cover so now let me turn the table around say um ask you a question how given this map how would you like to pick your uh Investments so you learned about the portfolio Theory as a so-called rational investor you try to maximize your return at the same time minimize your standard deviation right I I I hesitate to use the term risk okay because as as I said we we need to better Define it but let's just say you try to minimize this but maximize this uh the vertical axis okay so let's just say you trying to find the highest possible return for that portfolio with the lowest possible standard deviation so will you pick this one would you pick this one okay so then eliminate those two but for this that's actually all possible right so then that's where we learned about the efficient Frontier so what is efficient Frontier is really the the possible combination of those Investments you can push out to the boundary that you can no longer find another combination given the same standard ation you you no longer have you can find a higher return so you reach the boundary and same is true that for the same return you can no longer minimize your standard deviation by finding another combination okay so that's called efficient Frontier how do you find the efficient Frontier right that that's what uh essentially those work were done and uh got them Nobel Prize obviously it's more than that but uh but you get the flavor from uh the previous lectures um so what I'm going to do today is really reduce all these to the special case of two assets then we can really derive a lot of intuition from that so we have Sigma R we're going to ignore what's below this now right we don't want to be there and we want to stay on the upright so let's consider one special case um so again for that let's write out for the two assets so what is r of p is W1 R1 plus y - W1 or2 right very simple math and what is Sigma P so the standard deviation of the portfolio or the variance of that which is a square we know that's that's for the two AET class special case so let me give you um further uh restriction which let's consider if all1 equal to R2 again here meaning expected return I'm simplifying some of the notations and sigma 1 equal to zero and sigma 2 not equal to zero what is row what is the correlation zero right because you you have no volatility on okay so what is uh so undefined what say it's really undefined it's really undefined yes yeah yeah no there's no yeah that's right okay so let's look at this uh so you have Sigma 2 here Sigma 1 is zero and uh you have R1 equal to R2 what is r of P it's all right so because the weighting doesn't matter so it's going to you know it's going to be fall along this line so here is when Sig weight one equal to zero so you weigh everything on the second asset here you weigh way the first asset 100% so you have a possible combination along this line along this flat line so very simple right so I like to start with really simple case so what if what if Sigma one also is not zero but Sigma 1 equal to Sigma 2 and further I impose impose the Cor relation to be zero okay what is this line look at so I have Sigma 2 equal to Sigma 1 and R one still equal to R2 so r p still equal to R1 or R2 right what is this line look like so volatility is the same return is also the same of each of the asset class you have two strategies or two instruments they are zeroy correlated how would you how would you combine them so you take the derivative of this variance with regarding to the weight right and then you minimize that so that's you what you find is so at this point is R1 equal to zero or I I'm sorry W one or W1 equal to 1 you're at this point right agree so you choose either you will be ended up the portfolio exposure in terms of return and the variance will be right here but what if you choose so when you try to find the minimum variance you actually end up I'm not going to do the math you can do it afterwards you check by yourself okay you will find at this point that's when they are equally weighted half and a half so you get square root of that so you actually have a signif significant reduction of uh the variance of the portfolio by choosing half and half zero correlated portfolio so what's that called what's that benefit diversification right when you have less than perfectly correlated positively correlated assets you can actually achieve the same return but having a lower standard deviation or say okay that's fairly straightforward so so let's look at a few more special cases I want really uh to have you establish this intuition so let's think about what if in the same example what if row equals to one perfectly correlated then you can't right so you end up just at this one point you all agree okay what if it's totally negatively correlated perfectly negatively correlated what's this line look like right so if you weight everything to one side you're going to still at this point but if you wait half and half you can achieve basically zero variance I think we you showed that last time you learned that last time okay and so let's look Beyond those cases so what now let's look at so all1 does not not equal to R2 anymore Sigma 1 equal to zero there's no volatility of the first asset so that's cash okay so that's riskless asset in the first one so that so let's even call it R1 is less than all two so that's the right you have the cash asset then you have a non-cash asset row equal to zero zero correlation so let's look at what this line looks like so R1 R2 Sigma 2 here when you when you weigh asset two 100% you're going to get this point right when you weigh asset one 100% you're going to get this point right so what's in the middle of your uh return as a function of variance can can someone guess try again yeah I know I know thank you are there any other other answers okay this actually I let me just uh derive very quickly for you right Sigma one equal Z row equal to zero what's Sigma p right and uh Sigma p is essentially it's proportional to Sigma 2 with the weighting okay and what's r r is a com linear combination of R1 and R2 so it's still um so it's linear okay so because in these cases you actually you essentially um you uh return is a linear function uh and the slope what is what is the slope of this 's let's let's wait on the slope so we can we can come back to this because this actually relates back to the so-called uh uh Capital Market line or Capital uh allocation line okay because last time we talk about efficient Frontier that's when we have no riskless assets in in the portfolio right because when you add on cash then you actually you can select you can combine the cash into the portfolio by having a higher higher boundary higher efficient Frontier and essentially higher return with the same uh exposure so let's look at a couple more case then I will uh tell you um so I think let's look at so R1 is less than R2 and uh volatilities are not zero also Sigma 1 is less than Sigma 2 uh but it has it has a negative correlation of one so you have asset One S at two and as we know when you pick half and half this goes to zero so this is a quadratic function you you can uh verify and prove it later and uh what if when row equal to zero and uh I actually I what I so Sigma one should be here okay so when row uh equal to zero this no longer goes to the variance can no longer be minimized to zero so this is your efficient fronti here this part I think that's uh enough examples of two assets for the efficient Frontier so you get the idea so then what if we have three assets right so let me just touch upon that very quickly if you have one more asset here essentially you can you can solve the same equations and uh you when the stream uh special case I want I can you can verify afterwards you all the volatilities are equal and the zero correlation among the assets you're going to be able to minimize Sigma P equal to 1/ theare < TK of 3 of Sigma 1 okay so seems pretty neat right the math is uh not hard and straightforward but uh it gives you the idea how answer your question how to select them when you have you start with two right so why two assets are so important what's what's the implication in practice it's actually it's very uh popular combination lot of uh the asset managers they simply Benchmark to U bonds versus equity and one famous combination is really 6040 they call it 6040 combination 60% in equity 40 in bonds and even nowadays any fund manager you have that people still ask you to compare your performance with that combination so the two asset examples seem to be quite easy and simple but actually it's a uh it's a very um uh important one to uh uh to compare and that will lead me to get into the uh risk parity uh discussion but before I get to risk parity discussion I want to reveal the concept of beta and Shar ratio h so that's a so your portfolio return uh you this is your benchmark uh return off ofm expected return this the RF is the risk free uh return so essentially your cash return and Alpha is what you can generate addition uh additionally so let's even not to worry about this uh small other terms or not necessarily small but uh for the Simplicity I let just reveal that so that's your beta what is your sharp ratio okay and uh and you can uh you can so sometimes Shar ratio is also called risk weighted uh uh risk weighted return or risk adjusted return okay and how many of you have heard the Kelly's formula so Kelly's formula basically uh gives you that when you have let's say in the in the gambling example you know your winning probability is p so how this basically tells you how much to size up how much you want to bet on so it's very simple formula so if you have a winning uh probability of 50/50 how much you bet on nothing so if you have P equal to 100% you you you bet 100% of your position if you have winning probability of negative 100% % so that what does it mean that means your 100% probability of losing it what do you do you bet the other way around right you bet the other side so when P equal to negative uh I'm sorry actually I said when P equal to zero your losing probability becomes 100% right so you bet 100% the other way okay so that uh I leave to you to think about you know that's when you have discrete outcome case and uh but when you construct a portfolio this leads to the next question is in addition to the efficient Frontier discussion is that really all about asset allocation is that how we calculate our weights of each asset or strategy to choose from the the answer is no right so let's look at the 6040 uh portfolio example so again two assets stock stock has let's say 60% 40% bonds so on this so typically you SC I mean stock volatility is higher than the bonds and the return is expected return is also higher so your 60 40 combination is likely fall on this uh on the higher return and the higher uh standard deviation uh part of the of the efficient Frontier so the question was so that's typically people do before 2000 you know a real asset manager uh the easiest way or the passive way just to allocate 60/40 but after 2000 what happened was you know when after the equity Market peaked and the bond had a huge rally right as uh you know first you know Greenspan cut interest rate and uh um before the Y2K uh in the year 2000 you think it's kind of funny at that time everybody worried about the year 2000 coming up or the computers going to stop working because old software were not prepared for crossing this uh Millennium event so they had to cut the interest rate for this event but actually nothing happened so everything was okay but then left the market was plenty of cash and also after the tech bubble uh bursted so that was a good Port portfolio but then obviously in 2008 when the equity Market crashed the bond market the Government Bond highgrade Market Market had a huge rally and uh so that made people question that uh is this 6040 allocation of asset simply by the market value the mo the optimal way of doing it even though you're falling on the efficient Frontier but how do you compare different points is that simple choice of your objectives your situation or there's actually another ways to other ways to uh optimize it so that's where the risk parity concept was really the concept has been around but the term was really coined uh in 2005 so quite recently by by a guy named Edwood Chen uh he basically said okay instead of allocating 6040 based on market value why why shouldn't we consider allocating risk instead of a targeting return targeting asset amount let's target let's think think about a case where we can have equal waiting of risk between the two assets so risk parody really means equal risk waiting rather than equal uh Market exposure and uh then the further step uh he took was he said okay so this actually okay it's equal risk so you have lower return and the lower uh risk a lower standard deviation but sometimes people really want a higher return right how do you how do you satisfy both you know higher return and uh lower risk is there a free lunch so he was thinking right so there is actually it's not not quite free but it's the closest thing you probably heard this phrase many times the closest thing in investment of of free lunch is diversification okay and so he's he's using a leverage here as well so but let me talk about a bit more about diversification give you a couple of more examples okay that that phrase about the the free lunch and the diversification was actually from uh is that from uh Mars or people gave him that term okay but anyway so um so let me give you another simple example okay so let's consider uh uh two asset A and B in year one a goes up to basically doubles and year two goes down 50% so where does it end up so start with 100% it goes up to 200% then you you go down 50% on the new base so returns nothing right it comes back so asset B in year one loses 50% then doubles up 100% in the year two so asset B it basically goes down to 50% and it goes back up to 100% so that's when you look at them independently but if what if you had a 5050 weight of the two assets so someone is quick on mass can tell me what what does it change so a goes up like that b goes down like that now you have a 5050 A and B so let's look at Magic so in in year one a you have only 50% so goes up 100% so that's up 50% on the total basis B you also weit 50% but it goes down 50% so you you have lost 25% so at the end of the year one you actually so this is a combined 5050 portfolio year one and year two so you start with 100 you're up uh to 1.25 at this point okay so at the end of year one you rebalance right so you you have to come back to 50/50 so what do you do so this becomes 75 right so you no longer have the 5050 weight equal so you have to sell a to come back to 50 and buy use the money to buy B so you have new 50 50% uh uh weight uh asset again you can figure out the mass but what what it happens in the following year when you have this move this comp comes back 50% this goes up 100% you return another 25% positively without volatility so you have a straight line you can keep so you this twoyear is a so that's so-called diversification benefit and in the 6040 bond market that's really the idea people think about uh how to you know combine them and uh so let me talk a little bit about risk parody and how you actually achieve them I I try to leave uh plenty of time for for questions um so that's the return and so let's let's forget about these so let's leave cach here okay so the previous example I gave you when you have two assets one is cache all one the other is not the other has a volatility Sigma 2 you have this point right so and I said what's in between is a straight line that's your side allocation different combination did it occur to you why can't we go beyond this point so this point is when we weigh W2 equal to one W1 equal to zero right that's when you weight everything into this asset two but what if you go beyond that what does that mean so okay so let's say can we have W1 = to minus1 W2 = to +2 so they still add up to 100% but what's negative one mean borrow borrow right so you you went short cash 100% you borrow money you borrowed 100% of cash then put into to buy Equity or whatever risky assets here so have plus 2 minus one what is the return look like when you when you do this so RP equal to W1 r1+ W2 R2 so minus R1 plus 2 R2 that's your return is is this point here what's your uh uh variance look like or standard deviation look like as as we did before right so Sigma P simply equal to W2 Sigma 2 so in this case is 2 Sigma 2 so you're two times more risky two times as risky as the uh asset to so this introduces the concept of Leverage whenever you go short you introduce leverage you actually on your balance sheet you have you have two times of S2 you also sh one of the other instrument right so that's your that's your liability so your net is still one um so what this uh risk parity says is okay so we can Target on the equal risk uh waiting which will give you somewhere around let's call it 25 25% bonds 75% 25% Equity 75% of fixed income so or in other words 25% of stocks 75% of bonds so you have lower return but if you leverage it up you actually have higher return higher expected return given the same amount of uh uh standard deviation you achieve by leveraging up obviously you leverage up right uh there other implication of that we haven't talked about the liquidity risk but that's a that's a different topic so um what's your Shar ratio look like for for risk parity uh portfolio so you you essentially maximized the sharp Ratio or risk adjusted return by achieving the risk parody portfolio so 6040 is here you actually maximize that and U this is a does leverage matter does when you leverage up the sh ratio change or not so let's look at that uh that uh straight line This example okay so we we said sharp ratio equal to right so r p what is Sigma p 2 Sigma 2 right when you leverage up so this equals to R2 minus R1 IDE by Sigma two so that's the same as you at this point so that's essentially the slope of the the whole line it doesn't change okay so now you can see the connection right between the slope of this curve and the sharp ratio and how that links back to Beta so let me ask you another question when a when a portfolio is uh when the portfolio has higher standard deviation of Sigma P will beta to specific asset increase or decrease so how what's the relationship intuitively between beta so let's say look at the 6040 example okay your portfolio you have stocks you have Bonds in it so I'm asking you what is really the beta of this 6040 portfolio to the equity Market when Equity Market becomes when the portfolio becomes more volatile is your beta increas increasing or decreasing so you can derive that um I'm going to tell you the result but uh I'm not going to do the math here so beta equals to you can in this special case is Sigma p over Sig Sigma 2 okay I all right so so much for for all these I mean sounds like everything is uh nicely solved and uh so coming back to the real world and let me bring you back okay so are we all set for for portfolio management you know we can program make a robot to do this why do we need all these guys work on the portfolio management right so or why do we need any anybody to uh you know uh to to uh to manage a hedge fund you can just give money right so why do you need somebody anybody to put together so before I answer this question let me show you a video now all okay um anyone heard about the the London millennian uh Bridge so it was Bridge built around that time and thought it uh it had the latest technology and uh uh would really perfectly absorb you know you heard about soldiers marching across bridge and uh crush the bridge when everybody's walking in syn your Force gets you know synchronized then the bridge was not designed to take that synchronized the force so the bridge collaps collapsed in the past so they when they designed this they took all that into fall into account but what they haven't taken to what they hadn't taken into account was the the support of that is actually so they allowed the horizontal move to take take uh take that uh tension away but the problem is when everybody sees more people walking in syn then the whole Bridge start to swell right then the only way to keep a balance for you standing on the bridge is to walk in sync with other people so that's that's a survival Instinct and so I got this I mean that's actually my friend the Fidelity ranchan Dr Ranch CH brought this up to me he said oh you're doing uh how do you how do you think about the portfolio risk right this is what happened in the financial Market in 2008 when you think you got everything figured out you have the optimal strategy when everybody start to implement the same optimal strategy for your own as individual the whole system is actually not optimized it's actually in danger let me show you another one okay these are metronomes right so you you start anywhere you [Music] like are they in syn not yet what what is he doing you just have to listen you only have to listen to it you don't have to see it so what's going on here this is not that met metronomes don't have brains right they don't really follow the her why why are they synchronizing okay if you if you're expecting that getting out of sync it's not going to happen Okay so I'm going to stop right here okay you can try as many uh how do I get out of this okay so you can try you can look at I mean this I mean there's actually book uh uh written on this as well so but um uh the phenomena here is not nothing new but what when he did this what did he what's that what's that mean when he actually raised that thing on the plate and put on the cens what happened why why why is is that is so significant connected they are connected right so they are interconnected before they are individuals now they are connected and uh why did I show you the London Bridge and and this at the same time what's what this to do with portfolio management what's this to do with portfolio management like people who are traing like have the same they going to affect each other become connected in that way right like if as an individual you're doing a different strategy if everybody is doing something different you can maximize right very well said so uh so if you're looking for this stationary best way of optimizing your portfolio chances are everybody else is going to figure out the same thing and eventually you end up in this situation that you actually get killed okay so um that's the that's the that's the thing the last thing what you learn today what you walk away with this okay today is not what I want to know that all the problems are solved right so you say oh the problem solved Nobel Prize were given so let's just U program them no you actually it's a dynamic situation you you have to so that makes the problem interesting right as a younger generation you coming to the field the excitement is there are still a lot of interesting problems out there unsolved you can you can you can beat the others already in the field and uh and so that's one takeaway and what other takeaways you think by uh by listening to all these diversification ISE lunch diversification is a free lunch yeah so not so free free right in the end it's free to a certain extent but uh but it's something you know it's better than not Diversified right you it depends on how you do it but there is way you can optimize and so it's I want to leave with you I actually want to finish a few minutes earlier so that uh you can ask me questions uh you can ask you know probably better to have this uh open discussion and so I want you walk away to to to Really keep in mind is in the field of finance and uh particularly in the quantitative Finance um it's not mechanical it's not like solving physics problems it's not like you get everything's fig out it becomes predictable right so the the level of predictability is actually very much linked to a lot of other things physics you solve Newton's equations you have a controlled environment and you know what you're getting in the outcome but here you when you participate in the market you are changing the market you you're adding on other factors into it so think more from a broader scope point of view rather than uh just solve the mathematics that's why I come back to the original if you walk away from this lecture you remember what I said at the very beginning solving problems is about observe collecting data building models then verify and observe again okay so then with that I end right here so questions yeah yeah just the question so does that does this have anything to do with like it kind of sounds like Game Theory I'm not exactly too sure because you have like a huge population and you have no stable really like no stable equilibrium does it have anything to do with Game Theory by any chance it has a lot to do with Game Theory but not only to Game Theory right so Game Theory you have pretty well defined set of rules then two people play chess against each other that's where computer actually can become smarter right so in this uh Market situation you have so many people participating with not without clearly defined rules there are some rules but not not always clearly defined and uh so it's much more complex uh game the and but uh but it's part of it y Dan yeah can you talk maybe about why some of the risk parody portfolios did so poorly in May and June when our rat started to rise and what about their portfolio them to do that good question right so uh as you can see here what the risk parity uh approach does is essentially to wait more on the lower volatility asset in this case the question is how do you know which asset has low volatility right so you look at historical data which you conclude bonds have the lower volatility so you overweight bonds that's the essence of them right so then when bonds start to sell off after banki fed chairman banki said he's going to taper uh quantitative easing so bond from a very low high yield a very low yield uh level the yield went much higher interest rate when higher bonds got sold off so so this get uh this portfolio did poorly so now the question is so does that prove uh risk parity approach wrong or does it prove right does the financial crisis of 2008 prove the risk parody approach a superior approach or does the June May experience prove this as a uh you know Les uh less favored approach what what does it tell us I mean think about it right so it it really is inconclusive so you You observe you extrapolate from your historical data but what you really what you are really doing is you try to forecast volatility forecast return forecast correlation all based on historical data it's like a lot of people use that example it's like driving by looking at the the the rear view mirror that's what the only thing you look at you don't know what's going to happen in front of you yeah you have other question given like all this new information like do you find that people are still playing similar game stry with portfolio management very much very much true BEC why right so said people should be smaller than that it's very difficult to discover new asset classes it's also very difficult to discover to invent new strategies and which you have a better winning probability the other risk the other very interesting phenomena is most of the Traders and the portfolio managers the investors they are career uh investors meaning just like I'm if I'm the baseball coach I'm hired uh to coach a baseball team um my performance is really measured against the other teams when I win or lose right a portfolio manager or investor uh is also measured against the peers so this the safest way for them to do is to to Benchmark to index to to the herd so there's very little incentive for them to get out of the the crowd because if they WR they get killed first they lose their jobs so the tendency is to stay with the crowd it's for survival in think is again not the other example it's actually the optimal strategy for individual uh portfolio manager is really to do the same thing as other people are doing because you you stay with the force so you said even we have all these tools in the end it's not just that we could leave it to the computers we need managers so I mean what different are the managers doing can can you can you try to answer that question yourself what's what's the difference between human and the computer that's really right what can human add value to what computer can do factors the market factors and then news and what's going on so taking more information processing information make a judgment on more holistic approach so it's interesting question I had to say that uh computers are beating human humans in many different ways can computer ever get to the to the to the point actually beating human in investment I can't say confidently tell you uh that it's not going to happen it may happen so I don't know yeah uh any other questions yeah just add to that I think there's more to management than just um investing I think um managers also have like key roles in human um in their HR key roles in just like managing people and ensuring that they're maximizing their talents not just like not just oh how much money did you make but I mean are you moving forward in your career while you're there so I think management has a role to play in that as well not just investment yep I think that's a that's a good point Y all right so oh sure Jesse what is your portfolio breakdown is my personal portfolio well I I'm actually very conservative at this point because um if you look at my curve of those uh uh spending and earning curve uh I'm basically I'm trying to protect uh principles rather than try to maximize return at this point so I would I would be sliding down more towards this this this part rather than try to go to this corner yeah so I haven't really talked much about risk um what is risk right so I talk about volatility or standard deviation but as we all know that uh as uh Peter mentioned last time as well there are many other ways to look at risk value at risk or half distribution or truncated distribution or simply maximum loss you can afford to take right and uh on so but looking at a standard deviation or volatility is an elegant way you can see we can we can I can really show you in a very simple math about the how the concept actually plays out but in the end actually volatility is really not the best measure in my view of risk why let me give you uh another simple example before we we leave so so you let's say you have a this is overtime this is your accumul accumulative um return or your dollar amount so you start from uh here if you go flat then does anyone like to have this kind kind of a performance right of course right this very nice you keep going up you never go down but what's the volatility of that of that the volatility is probably not low right and U then on the other hand you could have you know what I'm trying to say when you look at expected return matchine expected return and the volatility uh you you can still really not selecting the the best uh combination because what you really should care about is not just your volatility and uh again bear in mind all the discussion about the modern portfolio theory is based on one key assumption here is about gaussian distribution okay normal distribution you the two parameters mean and the standard deviation categorize the distribution but in reality you have you know many other sets of distributions and uh so it's a it's a it's a concept still for a lot of uh discussion and the debate but uh but I want to leave that with you as well yeah just going back to the same question about these guys were asking about management and how do that they add value I think the people who added value in two there were some people who added a tremendous amount of value in the financial crisis and they were doing the same mathematics but the difference was that their expected return of various assets was different from the entire the broad market so if you can just know what expected return is that probably that is the only answer to the whole portfolio management theory yes you if you can forecast expected return uh then that's yeah then you know the game you solved it yeah you solve the big part of the P puzzle yeah and what management does is how good it can do the expected return full stop a thing yeah uh I I disagree on that that's the only thing because given two managers they have the same expected return but you can still further differentiate them right so that's yeah and that's where what this discussion is about yeah but yes expected return will drive a lot of these decisions if you know one manager is good you expect a return three years later he's going to make uh 150% you don't really care what's in between right you're just going to write it write it through but if you the the problem is you don't know for sure yeah you you will never be sure yeah i' like that comment on that the last problems I've looked at in simplified settings estimating returns and volatilities and the problem uh uh the conclusion from the problem was you basically cannot estimate returns very well even with more data over an historical period but you can estimate volatility much better with more data so there's really an issue of perhaps luck in getting the return estimates right with different managers which are you know hard to prove that there was really uh expertise behind that although with volatility uh you really can have have improved estimates and I think possibly with the risk parity portfolio uh those portfolios are focusing not on return expectations but saying we're going to consider different choices based just on how much risk they have and equalize that risk and the expected return you know we should be comparable across those perhaps so yeah so that's yeah so that highlights the difficulty of forecasting return forecasting volatility forecasting correlation so risk parody appears to be another elegant way of proposing a optimal strategy but it has the same problems yeah actually I also wanted to highlight that you mentioned the Kelly Criterion yeah which uh we haven't covered the theory for that okay previously but I encourage people to look into that it deals with issues of sort of multi-period investment ments as opposed to single period Investments and most all this classical Theory we've been discussing or that I discussed uh covers just a single period analysis which is an oversimplification of of investment and when you are investing over multiple periods uh I the Kelly Criterion tells you how to optimally basically bet with your bank role and uh the actually there was there's an excellent uh book at least I like it called Fortune's formula that talks about uh way said the origins of options Theory and finance but it does get into the Kelly Criterion and and there was a a rather major uh discussion between Shannon a mathematician at MIT who advocated applying of the Kelly Criterion and Paul Samuelson one of the major economists also also from MIT and uh there was great dispute about uh how you should do port F your optimization and uh that's a great book and uh there a lot of characters in that book actually are from MIT and at Thorp for example and it's really about I mean people try to find the holy Grill magic formula but not really to that extent but finding some you know something other people haven't figured out but uh it's very interesting history you know big names like uh you know Shannon very successful in other fields in his later part of uh his career and life really devoted most of his time studying this problem yeah you know Shannon right so the cloud Shannon he's the he's the father of information Theory yeah and has a lot to do with the later you know Information Age invention of computers and very successful yeah so anyway anyway so we'll end the class right here no homework for today okay so you just need to yeah okay all right thank you