The following content isprovided under a Creative Commons license. Your support will helpMIT OpenCourseWare continue to offer high qualityeducational resources for free. To make a donation orview added information from hundreds of MIT routes, inspect MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: Allright, let’s start. So first of all, I hope you’vebeen experiencing the class so far. And thank you forfilling out the survey. So we got some very usefuland interesting feedbacks. One of the feedbacks–this is my impression, I haven’t gotten a chanceto talk to my co-lecturers or colleagues hitherto, butI read some comments. You were saying that some ofthe problem sets are quite hard.The math part may be a bit moredifficult than the lecture. So I’m thinking. So “its certainly true it is” theapplication teach. And from now, after threemore lecturings by Choongbum, it will be essentially theremainder is all applications. The original pointof having this class is really to show youhow math is applied, to show you those casesin different sells, different strategies, and in the real industry. So I’m trying to think, howdo I give today’s chide with the right balance? This is, afterall, a math class. Should I give you more math, or should I– you’ve had enough math. I intend, it soundedlike from the survey you probably had enough math. So I would probablywant to focus a bit more on the work side. And from the survey alsoit seems like most of you enjoyed or wanted to listen tomore on the lotion side.So anyway, as you’ve alreadylearned from Peter’s teach, the so-called ModernPortfolio Theory. And it’s actuallynot that modern anymore, but we still callit 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 computations? And so today, I’d like to sharewith you my experience on that, both in the past, a different area, and today probably morefocused on the buy side.Oh, come on in. Yeah. Actually, theseare my colleagues from Harvard Management. So–[ CHUCKLES] –they will be able to askme really tough questions. So regardless, so how I’mgoing to start this class. You wondered why I handedout to each of you a page. So does everyone havea blank page by now? Yeah, actually. Yeah. Could likewise pass to–? Yeah. So I miss every one ofyou to use that blank sheet to erect a portfolio, OK? So you’re saying, well, Ihaven’t done this before. That’s fine. Do it absolutely fromyour insight, from your knowledgebase as of now. So what I want you todo is to write down, to break down the1 00% of what do you want to have in your portfolio. OK, you said, gives people preferences. No, I’m not goingto give you choices. You think about whateveryou like to put down.Wide open, OK? And don’t even ask methe goal or the criteria. Base it on what you want to do. And so totally freethinking, but I want you to do it in five minutes. So don’t overthink it. And side it back to me, OK? So that’s really the first part. I want you to showintuitively how you can construct a portfolio, OK? So what does a portfolio convey? That I have to explain to you. Let’s say forundergraduates here, so your mothers giveyou some permit. You manage to save a $1,000 on the side.You decided to put intoinvestments, buying assets or whatever, or gambling, buy raffle tickets, whatever you can do. Just break down your percentage. That could be $ 1,000, or youcould be a portfolio manager and have hundreds of billionsof dollars, or whatever. Or then and say if they raisesome money, start a hedge fund, they may have $10,000 merely begins with. How do you want to usethose money on day 1? Just think about it. And then so while you’refilling out those sheets, please entrust it back to me.It’s your hand-picked to putyour reputation down or not. And then I will startto assemble those ideas and gave them on the blackboard. And sometimes I may come backto ask you a question– you know, why did you leant this? That’s OK. Don’t feel humiliated. We’re not going toput you on the spot. But the idea is I want to usethose patterns to show you how we actually connecttheory with practise. I remember when I was acollege student I learned a lot of different stuff. But I retain onelecture so well, one teacher told me one thing. I still retain vividly well, so I want to pass it on to you. So how do we learnsomething beneficial, right? You always startwith watching. So that’s kind ofthe physics back. You muster the data. You ask a lot of questions. You try to find the patterns. Then what you do, you build sits. You have a theory. You try to explain what isworking, what’s repeatable, what’s not repeatable. So that’s wherethe math comes in. You solve the equations. Sometimes in financials, bunch of periods, unlike physics, the repeatablepatterns are not so obvious. So what the hell are you do after this, soyou come back to observations again. You demonstrate your philosophy, substantiate your projections, and find your correct. Then this feedsback to this rule. And a great deal of time, theverification process is really aboutunderstanding special cases. That’s why today I actually wantto illustrate the portfolio ideology working a lotof special cases. So can you start to hand backyour portfolio construction by now? OK, so precisely hand backwhatever you have. If you have one thing onthe paper, that’s fine. Or many things onthe paper, or you think as a portfolio overseer, or you think as a speculator, or you think simply asa student, as yourself. All privilege, so I’mgetting these back. I will start to writeon the blackboard. And you can finishwhat you started. By the style, that’s the onlyslide I’m going to use today. I’m not concerned– you realizeif I demo you a good deal of slithers, you probably can’tkeep up with me. So I’m going to write downeverything, just take my meter. And so hopefully you get achance to think about questions as well. OK, I think– isanyone finished? Any more? OK. All claim, OK. OK, immense. You guys are awesome. OK, so let me justhave a quick look to see if I missed any, OK? Wow, quite interesting. So I have to say, somepeople have high-pitched conviction. 100% of you, one of those. I conclude I’m not going to readyour refers, so don’t worry, OK? OK I’m just going to read theanswers that beings put down, OK? So small cap equities, attachments, real estate properties, stocks. Those were there. Qualitative approaches, selection policies, deep price prototypes. Food/ treat area mannequins, exertion, buyer, S& P index, ETF fund, government bonds, top hedge fund. So national resources, timber district, farmland, chequing account, stocks, currency, corporate ligaments, rare coppers, lotteries, collectibles. That’s very unique. And Apple’s broth, Googlestock, golden, long term saving annuities. So Yahoo, Morgan Stanley assets. I like that.[ LAUGHTER] OK. Family trust. OK, I think thatpretty much plastered it. OK, so I would say thatlist is more or less now. So after you’vedone this, when you were doing this, what kind ofquestions came to your knowledge? Anyone wants to– yeah, please. Public:[ Inaudible] how do Iknow what’s the right balance to draw in my portfolio? Whether it would be cash, invoices, or stuff like that? PROFESSOR: How doyou do it, actually? What’s the criteria? And so before weanswer the question how you do, how do you groupassets or revelations or strategies or even beings, merchants, together– before we ask all those questions, we have to ask ourselves another question.What is the goal? What is the purpose, right? So we understand whatportfolio management is. So here in this class, we’re not talking about how to come up witha specific winning strategy in trading or investments. But we are talking abouthow to throw them together. So this is what portfoliomanagement is about. So before we answerhow, let’s see why. Why do we make love? Why do we want to havea portfolio, right? That’s a highly, very good point. So let’s understand the goalsof portfolio management. So before we are aware of goalsof portfolio administration, let’s understandyour situations, everyone’s situation. So let’s look at this chart.So I’m going toplot your spending as a function of your age. So when you areage 0 to senility 100, so everyone’s spendingpattern is different. So I’m not going to tell youthis is the spending structure. So certainly whenkids are young, they probably don’t have alot of hobbies or tuition, but they have some basic needs. So they expend. And then the spendingreally goes up. Now your mothers haveto pay your tuition, or you have to borrow–loans, grants. And then you have college. Now you have– you’re married. You have kids. You need to buy a live, buya auto, pay back student lends. You have a lot more spending. Then you go on vacation. You buy investments. You really have morespending come through here. So but it goes toa certain point.You will decrease down, right? So you’re not goingto keep going forever. So that’s your spend veer. And with the other curve, you think about it. It’s what’s your income, what’s your earnings veer. You don’t earn anythingwhere you are just born. I use giving. So this is spending. So let’s call this 50. Your earning probablytypically peaks around age 50, but it truly depends. Then you probablygo down, back up. Right, so that’s your earning. And do they ever join well? They don’t. So how do you makeup the difference? You hope to have a fund, an investment on the side, which can generate those cashflows to poise your earning versus your spend. OK, so that’s only onesimple road to throw it. So you’ve got to askabout your place. What’s your cash flow look like? So my objective is, I’mgoing to retire at senility of 50. Then after the age of5 0, I will live free. I’ll travel around the world.Now I’ll calculatehow much coin I need. So that’s one situation. The other place is, I wantto postgraduate and pay back all the student lends in one year. So that’s another. And generally peoplehave to plan these out. And if I’m succeeding auniversity endowment, so I have to think about whatthe university’s operating budget is like, how much moneythey need every year drawing from this fund. And then bymaintaining, protecting the total fund for basicallya unending purpose, right? Ongoing and retain growing it.You ask for more contributions, but at the same time generating more return. If you have a pensionfund, you have to think about what time framelot of the people, the workers, will retire and will actuallydraw from the pension. And so every situationis very different. Let me even expand it. So you think, oh, thisis all about investment. No , no, this is notjust about investment. So I was a trader for along time at Morgan Stanley, and later on a trading manager.So when I had manytraders working for me, the question I wasfacing is how much coin I need to allocate to eachtrader to let them transactions. How much risk dothey make, right? So they said, oh, I havethis triumphing approach. I can offset lots of money. Why don’t you giveme more limits? No, you’re not goingto have all the limits.You’re not going to have allthe capital we can give to you. Right, so I’m going to explain. You have to diversify. At the same time, you haveto compare the strategies with parameters–liquidity, volatility, and many other constants. And even if you arenot managing beings, let’s say– I was going todo this, so Dan,[ INAUDIBLE ], Martin and Andrew. So they start ahedge fund together. So each of them hada great strategy. Dan has five, Andrew hasfour, so they altogether have 30 strategies. So they create anamount of money, or they just pooltogether their savings. But how do youdecide which policy to articulate more fund on day 1? So those questionsare very practical. So that’s all. So you understandyour goals, that’s then you’re really clear onhow much risk you can take. So let’s come back to that. So what is risk? As Peter explainedin his lecturing, gamble is actually notvery well defined. So in the ModernPortfolio Theory, we commonly talk aboutvariance or standard deviation of return.So today I’m going tostart with that concept, but then try toexpand it beyond that. So stay with thatconcept for now. Risk, we use standarddeviation for now. So what are we trying to do? So this, you are familiarwith this chart, right? So return versusstandard deviation. Standard deviation isnot going to go negative. So we stop at zero. But the returncan go below zero. And I’m going to review oneformula before I go into it. I think it’s useful to reviewwhat previously “youve learned”. So you let’s say youhave– I will likewise clarify the notation as wellso you don’t get confounded. So let’s say– so Petermentioned the Harry Markowitz Modern Portfolio Theorywhich acquired him the Nobel prize winner in 1990, right? Along with Sharpeand a few others. So it’s a veryelegant piece of work. But today, I will try togive you some special cases to help you understand that. So let’s reviewone of the formulas now, which is reallythe definition.So let’s say youhave a portfolio. Let’s call the expectedreturn of the portfolio is R of P, equal to thesum, a weighted sum, of all the expectedreturns of each asset. You’ll basicallylinearly allocate them. Then the variance– oh, let’sjust look at the variance, sigma_P squared. So these are vectors. This is a matrix. The sigma in the middleis a covariance matrix. OK that’s all you need toknow about math at this point. So I want us to go through anexercise on that piece of paper I simply compiled back to putyour select of the investment on the following chart. OK, so let’s start with one. So what is cash? Cash has no standard deviation. You braced cash– so it’sgoing to be on this axis.It’s a positive return. So that’s here. So let’s call this cash. Where is– and let’s me justthink about another example. Where’s gamble? Say you buy Powerball, right? So where’s raffle descending? Let’s assume you puteverything in raffle. So you’re going to lose. So your expected value isvery close to lose 100%. And your standard deviationis probably very close to 0. So you will be here. So some of you say, oh , no , no. It’s not exactly zero. So OK, penalize. So maybe it’ssomewhere now, OK? So not 100%, but you stillhave a reasonably small-minded difference from losing all the money. What is coin throwing? So let’s say you decide toput all your money to gamble on a bazaar silver throw, fair coin. So expected return is zero. What is the standarddeviation of that? AUDIENCE: 100%? PROFESSOR: Good. So 100%. So we got the threeextreme cases plowed. OK, so where is USgovernment bond? So let’s just call it five-yearnote or ten-year bond. So the return is better thancash with some volatility. Let’s call it now. What is investing in a startup venture capital fund like? Pretty up there, right? So you’ll probably geta very high return, by you can lose all your money.So probably somewherehere, you accompany. Buying stocks, let’scall it somewhere now. Our last applicationlecture, you heard about investingin commodities, right? Trading gold, lubricant. So that has higher volatility, so sometimes high returns. So let’s call this commodity. And the ETF is typically lowerthan single broth volatility, because it’s justlike indicator funds. So now. Are there any other choicesyou’d like to put on this planned? OK. So let me really look atwhat you came up with. Real estate, OK. Real estate, I would sayprobably somewhere around here. Private equity probablysomewhere here.Or investing in hedgefunds somewhere. So I think that’s enoughexamples to cover. So now let me turn the tablearound and ask you a question. Given this planned, how would youlike to pick your investments? So you learned aboutthe portfolio theory. As a so-calledrational investor, you try to maximize your return. At the same time, minimizeyour standard deviation, right? I hesitate to usethe term “risk, ” OK? Because as I said, weneed to better define it. But let’s just say youtry to minimize this but maximize this, the horizontal axis. OK, so let’s just say youtry to find the highest possible returnfor that portfolio with the lowest possiblestandard deviation. So would you pick this one? Would you pick this one? OK, so eliminate those two. But for this, that’sactually every possible, right? So then that’s where we learnabout the efficient territory? So what is theefficient frontier? It’s really thepossible combinations of those investments youcan push out to the boundary that you can no longer findanother combination– given the same standarddeviation, you can no longer find a higher return.So you reached the boundary. And the same is truethat for the same return, you can no longer minimizeyour standard deviation by detect another compounding. OK, so that’s calledefficient frontier. How do you find theefficient frontier? That’s what essentiallythose act were done and it got them theNobel Prize, patently. It’s more than that, but you get the flavor from the previous lecturings. So what I’m going to dotoday is really increase all of these to thespecial case of two assets. Now we can really derive alot of feeling from that. So we have sigma, R.We’re going to ignore what’s below that is something that, right? We don’t want to be there. And we want to stayon the up-right. So let’s considerone special case.So again for that, let’swrite out for the two resources. So what is R of P? It’s w_1 R_1 plus 1minus w_1 R_2, right? Very simple math. And what is sigma_P? So the standard deviation ofthe portfolio– or the variability of that, which is asquare– we know that’s for the two assetclass special case. So let me give you a furtherrestriction– which, let’s consider if R_1 equal to R_2. Again, now meaningexpected return. I’m simplifying someof the notations. And sigma_1 equalto 0, and sigma_2 not equal to 0, so what is rho? What is the correlation? Zero, right? Because you have novolatility on it. OK, so what is– what’s that? AUDIENCE: It’s really undefined. PROFESSOR: It’sreally undefined, yes.Yeah. Audience:[ Inaudible] no covariance. PROFESSOR: There’s no–yeah, that’s right. OK, so let’s look at this. So you have sigma_2 here. Sigma_1 is 0. And you have R_1 equal to R_2. What is all R of P? It’s R, right? Because the weightingdoesn’t matter. So you know it’s goingto fall along this strand. So here is whenweight one equal to 0. So you weight everythingon the second asset. Here you weight thefirst resource 100%. So you have a possiblecombination along this front, along this flat strand. Very simple, right? I like to start with areally a simple case.So what if sigma_1 also isnot 0, but sigma_1 equal to sigma_2. And further, I impose– impose–the correlation to be 0, OK? What is this line look like? So I have sigma_2equal to sigma_1. And R_1 is still equalto R_2, so R_P is still equal to R_1 or R_2, right? What does this line look like? So volatility is the same. Return is those are the sameof each of the resource class. You have two strategiesor two instruments. They are zero-ly correlated. How would you blend them? So you make the derivativeof this variance with regarding tothe heavines, right? And then you minimise that. So what the hell are you find is thatthis point is R_1 equivalent to 0, or– I’m sorry, w_1, or w_1 equivalent to 1. You’re at this level, right? Agreed? So you choose either, you willbe ending up– the portfolio revelation in terms of return andvariance will be right here.But what if youchoose– so when you try to find the minimumvariance, you actually end up– I’m not going to do the math. You can do it afterwards. You check by yourself, OK? You knows where to find atthis target, that’s when they are equallyweighted, half and half. So you get square beginning of that. So you actually have asignificant reduction of the variability of the portfolioby choosing half and half, zero-ly correlated portfolio. So what’s that called? What’s that benefit? Diversification, right? When you have less thanperfectly correlated, positively correlatedassets, you can actually achieve the samereturn but having a lower standard deviation.I’ll say, OK, that’sfairly straightforward. So let’s look at a fewmore special cases. I demand truly to have youestablish this intuition. So let’s think about whatif in the same example, what if rho equals to1, perfectly correlated? Then you can’t, right? So you be brought to an end atjust this one point. You agree? OK. What if it’s totallynegatively correlated? Perfectly negatively correlated. What’s this row was like? Right? So you if you weighteverything to one side, you’re going tostill get this top. But if you weighthalf and half, you’re going to achievebasically zero variance. I think we showedthat last time, you learned that last time.OK, so let’s lookbeyond those cases. So what now? Let’s look at– so R_1 doesnot equal to R_2 anymore. Sigma_1 equal to 0. There’s no volatilityof the first asset. So that’s currency, OK? So that’s a risklessasset in the firstly one. So let’s even call thatR_1 is less than R_2. So that’s the– right? You have the money resource, andthen you have a non-cash asset. Rho equal to 0, zero equivalence. So let’s look at whatthis line looks like. So R_1, R_2, sigma_2 here. When you weight assettwo 100%, you’re going to get this point, right? When you weight assetone 100%, you’re going to get this degree, right? So what’s in themiddle of your return as government functions of variance? Can someone guess? AUDIENCE: A parabola? Should it be a parabola? PROFESSOR: Try again. Public: A parabola. PROFESSOR: Yeah, I know, I know.Thank you. Are there any other rebuttals? OK, this is actuallyI– let me really derive very quickly for you. Sigma_1 equal to0, rho equivalent to 0. What’s sigma_P? Right? And sigma_P is essentiallyproportional to sigma_2 with the weighting. OK, and what’s R? R is a linear combinationof R_1 and R_2. So it’s still– so it’s linear. OK, so because in thesecases, you actually– you essentially– your returnis a linear function. And the ascent, whatis the slope of this? Oh, let’s wait on the downgrade. So we can come back to this. This actually pertains back tothe so-called capital market line or capitalallocation argument, OK? Because last-place age we talkedabout the efficient territory. That’s when we have no risklessassets in the portfolio, right? When you add on cash, thenyou actually can select. You can mix thecash into the portfolio by having a higher boundary, higher Efficient Frontier, and essentially a higherreturn with the same exposure. So let’s look at acouple more bags, then I will tell you– so Ithink let’s look at– so R_1 is less than R_2. And volatilities are not 0. Also, sigma_1 isless than sigma_2, but it has a negativecorrelation of 1. So you’ll have assetone, asset two. And as we are familiar, where you pickhalf and half, this goes to 0. So this is a quadratic function. You can support andprove it last-minute. And what if whenrho is equal to 0– and actually, I want to– sosigma_1 should be here, OK? So when rho is equalto zero, this no longer goes to– the difference canno longer be minimise to 0. So this is your efficientfrontier, this part. I think that’s enoughexamples of two assets for the efficient frontier. So you get the idea. So then what if wehave three assets? So let me merely touchupon that very quickly. If you have one moreasset here, virtually you can solve thesame equations. And when the– special case: you can verify afterwards, if all thevolatilities are equal, and zero correlationamong the resources. You’re going to be able tominimize sigma_P equal to 1 over the square rootof three of sigma_1. OK. So it seems pretty neat, right? The math is not hardand straightforward. But it gives you the ideahow to answer your question, how to select them whenyou start with two. So why are twoassets so important? What’s the implicationin practice? It’s actually a verypopular combination. Lot of the assetmanagers, they simply benchmark to bondsversus equity. And then one famouscombination is really 60/40. They call it a6 0/40 combination. 60% in equity, 40% in ligaments. And even nowadays, any fundmanager, you have that. Beings will still ask youto compare your performance with that combination. So the two-asset examples seemto be quite easy and simple, but actually it’s a veryimportant one to liken. And that will lead me toget into the risk parity discussion. But before I get torisk parity discussion, I want to review the conceptof beta and the Sharpe ratio. So your portfolio return, this is your benchmark return, R of m, expected return. R_f is the risk-free return, so essentially a money return. And alpha is what you cangenerate additionally.So let’s even not to worryabout these tiny other terms– or not necessarily tiny, but for the purity, I’ll precisely reveal that. So that’s your beta. Now what is your Sharpe ratio? OK. And you can– sosometimes Sharpe ratio is also calledrisk-weighted return, or risk-adjusted return. And how many of you haveheard of Kelly’s formula? So Kelly’s formulabasically gives you that when you have– let’ssay in the gambling speciman, you know your winningprobability is p. So this basically tellsyou how much to size up, how much you want to bet on. So it’s a very simple formula. So you have a winningprobability of 50/50, how much you bet on? Nothing. So if you have p equivalent to 100%, you bet 100% of your position.If you have a winningprobability of negative 100%, so what does it represent? That means you have a 100% probability of losing it. What do you do? You gambled the otherway around, right? You gambled the other side, so thatwhen p is equal to negative– I’m sorry, actuallywhat I should say is when p equal to 0, yourlosing probability becomes 100%, right? So you bet 100% the other way, OK? So that I leave toyou to think about. That’s when you havediscrete upshot event. But when youconstruct a portfolio, this leads to the next question. It’s in addition to theefficient frontier discussion, is that really allabout asset grant? Is that how we calculateour weights of each asset or policy make their own choices? The ask is no, right? So let’s look at a6 0/40 portfolio pattern. So again, two asset asset. Stock is, let’s say, 60% percentage, 40% alliances. So on this– so typicallyyour capital volatility is higher than the bonds, andthe return, expected return, is also higher.So your 60/40 combinationslikely fall on the higher return and the higherstandard deviation part of the efficient territory. So the question was–so that’s typically what parties do before 2000. A real asset director, theeasiest mode or the passive style is just to apportion 60/40. But after 2000 , what happenedwas when after the equity sell peaked and the bond hada huge rally as first Greenspan cut interest rates beforethe Y2K in its first year 2000. You think it’s kind of funny, but at that time everybody worried about its first year 2000. All the computersare going to stop working because aged softwarewere not prepared for crossing this millennium episode. So they had to cut interestrates for this event. But actually good-for-nothing happened, so everything was OK. But that left the marketwith plenty of cash, and also after thetech bubble abound. So that was a goodportfolio, but then obviously in 2008 when theequity sell crashed, the alliance marketplace, thegovernment ligament hybrid market, had a huge rally. And so that madepeople question that. Is this 60/40 distribution ofasset simply by the market value the optimalway of doing it, even though you are fallingon the Efficient Frontier? But how do you comparedifferent points? Is that simple select of yourobjectives, your statu, or there’s actually otherways to optimize it. So that’s where the riskparity perception was really– the concept has beenaround, but the term was really coined in2005, so quite recently, by a person worded Edward Qian.He mostly said, OK, instead of allocating 60/40 based on market value, why shouldn’t we consider allocating risk? Instead of targeting a return, targeting asset amount– let’s think abouta case where we can have equal weighting ofrisk between the two assets. So gamble parity genuinely meansequal jeopardy weighting rather than equal marketplace exposure. And then the further stephe took was he said, OK. So this actually, OK, is equal risk. So “youve had” lower returnand a lower threat, a lower standard deviation. But sometimes you will reallywant a higher return, right? How do you satisfy both? Higher return and lower risk.Is there a free lunch? So he was thinking, right? Here i am, actually. It’s not quite free, butit’s the closest thing. You’ve probably heardthis term many times. The closest thing ininvestment to a free lunch is diversification. OK, and so he’s using aleverage here as well. let me talk about it a bitmore, about diversification, give you a couplemore illustrations, OK? That quotation about the freelunch and diversification was actually from– wasthat from Markowitz? Or beings establish him that term.OK, but regardless. So let me give you anothersimple example, OK? So let’s consider twoassets, A and B. In year one, A goes up to– itbasically redoubles. And in year two, it goes down 50%. So where does it be brought to an end? So it begins with 100%. It goes up to 200%. Then it goes down5 0% on the new cornerstone, it is therefore returns nothing, right? It comes back. So resource B in time one loses5 0 %, then redoubles, up 100% in time two.So resource B basicallygoes down to 50% and it goes back up to 100%. So that’s when you lookat them independently. But what if you had a 50/50 load of the two assets? So if someone who isquick on math is also known, what does it reform? So A goes up like that, B goes down like that. Now you have a 50/50 A andB. So let’s look at magic. So in time one, A, you have only 50%. So it goes up 100%. So that’s up 50% on the total basis. B, you’ll also weight5 0 %, but it goes down 50%. So “youve lost” 25%. So at the end ofyear one, you’re actually– so this is a combined5 0/50 portfolio, year one and time two. So you started with 100. You’re up to 1.25 at this site, OK? So at the end of yearone, you rebalance, right? So you have tocome back to 50/50. So what do you do? So this becomes 75, right? So you no longer havethe 50/50 value equal. So you have to sellA to come back to 50 and use the money to buy B.So you have a brand-new 50/50 percentage load asset. Again, you canfigure out the math. But what happens inthe following year when you have this move, this comes back 50%, this goes up 100%. You return another 25% positively without volatility. So you have a straight line. You can keep– sothis two year is a– so that’s so-calleddiversification benefit. And in the 60/40 bail market, that’s really the relevant recommendations beings think abouthow to combine them.And so let me talk a littlebit about gamble parity and how you actuallyachieve them. I’ll try to leave plentyof age for questions. So that’s the return, andso let’s forget about these. So let’s leave cash now, OK? So the previous lesson I gaveyou, when you have two assets, one is cash, R_1, the other is not. The other has avolatility of sigma_2. You have this place, right? So and I said, what’s in between? It’s a straight line. That’s your asset rationing, different combining. Did it occur to you, whycan’t we go beyond this point? So this point is when we weightw_2 equal to 1, w_1 equal to 0. That’s when you weighteverything into the asset two. What if you go beyond that? What does that mean? OK. So let’s say, can we have w_1equal to minus 1, w_2 equal to plus 2? So they still add up to 100%. But what’s negative 1 mean? Borrow, right? So you led short-lived cash1 00%, you borrow money. You acquire 100% of money, then put into to buy equity or whatever, risky resources, here. So you have plus 2 minus 1. What does the return lookslike when you do this? So R_P equal to w_1R_ 1 plus w_2 R_2. So minus R_1 plus 2R_2. That’s your return. It’s this degree now. What’s your variability looklike, or standard deviation look like? As we done before, right? So sigma_P simplyequal to w_2 sigma_2. So in such cases, it’s 2sigma_2. So you’re two times morerisky, two times as risky as the asset two. So this introduces theconcept of leveraging. Whenever you go short, you interpose leveraging. You actually– onyour balance sheet, you have two times of resource two. You’re also short-lived one ofthe other instrument, right? OK so that’s your liability. So your net is still one. So what this riskparity says is, OK, so we can target on theequal threat weighting, which will give you somewherearound– let’s called it 25.25% alliances, 75% — 25% equity, 75% of fixed income. Or in other words, 25% of stocks, 75% of ligaments. So you have lower return. But if you leverageit up, you actually have higher return, higher expected return, given the same amountof standard deviation. You was carried out by leveraging up. Patently, youleverage up, right? That’s the otherimplication of that. We haven’t talked aboutthe liquidity risk, but that’s a different topic. So what’s your Sharpe ratio looklike for likelihood parity portfolio? So you essentiallymaximized the Sharpe ratio, or risk-adjusted return, byachieving the risk parity portfolio.So 60/40 is here. You actually maximize that, andthis is– does leveraging interest? When you leverage up, doesSharpe ratio alteration, or not? AUDIENCE: It divides in half. So you’ve got twice the [? deviation ?][ INAUDIBLE ]. PROFESSOR: So let’s look at thatstraight line, this example, OK? So we said Sharperatio equal to– right? So R_P, what is sigma_P? It’s 2sigma_2, right, when you leverage up. So this equals to R_2 minusR_1, partition by sigma_2. So that’s the sameas at this moment. So that’s essentially theslope of the whole line. It doesn’t modify. OK, so now you cansee the connection between the downgrade of thiscurve and the Sharpe ratio and how that tie-ups back to beta.So let me ask youanother question. When the portfolio has higherstandard origin of sigma_P, will beta to a specificasset increase or lessen? So what’s therelationship instinctively between beta– so let’s takea look at the 60/40 illustration. Your portfolio, you havestocks, “youve had” attachments in it. So I’m asking you, what isreally the beta of this 60/40 portfolio to the equity market? When equity grocery, itbecomes– when the portfolio becomes more volatile. Is your beta increasingor declining? So you are in a position to derive that. I’m going to tellyou the research results, but I’m not goingto do the math now. So beta equals to–[ INAUDIBLE] in this special case, is sigma_P over sigma_2. OK. All right, so somuch for all these. I represent, it sounds likeeverything is nicely solved. And so coming backto the real world, and let me bring you back, OK? So are we all set forportfolio management? We can program, makea robot to do this. Why do we need allthese guys working on portfolio management? Or why do we need anybodyto manage a hedge fund? You can time impart coin, right? So why do you need somebody, anybody, to articulate it together? So before I answerthis question, let me show you a video.[ VIDEO PLAYBACK][ HORN BLARING][ END VIDEO PLAYBACK] OK. Anyone heard about theLondon Millennium Bridge? So it was a bridgebuilt around that time and thought it hadthe latest technology. And it would reallyperfectly absorb– you heard about soldiers justmarching across a bridge, and they’ll crush the aqueduct. When everybody’swalking in sync, your troop comes synced. Then the aqueduct wasnot designed to take that synced force-out, so thebridge collapsed in the past.So when they designed this, they made all that into account. But what they hadn’ttaken into account was the support ofthat is actually– so they grant the horizontalmove to take that antagonism away. But their own problems iswhen everybody’s sees more parties walking insync, then the whole bridge starts to swell, right? Then the only wayto keep a balance for you standingon the aqueduct is to walk in syncwith other beings. So that’s a survival instinct. And so I got this–I mean, that’s actually my friend atFidelity, Ren Cheng. Dr. Ren Cheng broughtthis up to me. He said, oh, you’redoing– how do you think about theportfolio risk, right? This is what happened in thefinancial market in 2008. When you think you goteverything figured out, “youve had” the optimal approach. When everybodystarts to implement the same optimal strategyfor your own as individual, the entire system isactually not optimized. It’s actually in danger. Let me demo you another one.[ VIDEO PLAYBACK][ CLACKING] OK. These are metronomes, right? So can start anywhere you like. Are they in sync? Not more. What is he doing? You exclusively have to listen to it. You don’t have to see it. So what’s going on here? This is not– metronomesdon’t have brains, right? They don’t reallyfollow the herd. Why are they synchronizing? OK, if you’re expecting theyare getting out of sync, it’s not is happening. OK, so I’m goingto stop right here. OK.[ Death VIDEO PLAYBACK] You can try as many–how do I get out of this? OK, so you can try it.You can look at– there’sactually a record written on this as well, so. But the phenomenahere is nothing new. But what when he didthis, what’s that aim? When he actually raisedthat thing on the plate and gave it on the Coke cans? What happened? Why is that is so significant? AUDIENCE: Because nowthey’re connected. PROFESSOR: They’re connected. Right. So they are interconnected. Before, they were individuals. Now they’re connected. And why did I demo youthe London Bridge and this at the same time? What’s this to do withportfolio management? What’s this to do withportfolio management? AUDIENCE:[ Inaudible] people who are trading, if they have the same strategy ,[ INAUDIBLE] affect each other, they become connectedin that way– PROFESSOR: Right.AUDIENCE: If asan individual, you are doing a differentstrategy, if everybody has been doingsomething different, you can maximize [? in the opening. ?] PROFESSOR: Very well said. So if you’re lookingfor this stationary best mode of optimizingyour portfolio, chances are everybodyelse is going to figure out the same thing. And eventually, youend up in developments in the situation and you actually get killed. OK, so that’s the thing. What you learned today, what you walk away was this. OK, today is not what Iwant you to know that all the problems are solved. Right? So “youre telling”, oh, theproblem’s solved. The Nobel prize winner was given. So let’s just planned them. No, you actually– it’sa dynamic situation. You “re going to have to”. So that constitutes the probleminteresting, right? As a younger generation, you’re coming to the field. The agitation isthere are still a lot of interestingproblems out there unsolved. You can beat the othersalready in the field. And so that’s one takeaway.And what are thetakeaways you think by listening to all these? AUDIENCE: Diversificationis a free lunch.[ Laughters] PROFESSOR: Diversificationis a free lunch, yes. Not so free, right, in the end. It’s free to some extent. But it’s something–you know, it’s better than not diversified, right? It depends on how you make love. But there is a wayyou can optimize. And so it’s– I wantto leave with you, I actually want to finish a fewminutes earlier so that you can ask me questions. You can invite. It’s probably better tohave this open discussion. And so I want you towalk away, to really keep in mind is in thefield of finance, and particularly in thequantitative finance, it’s not mechanical. It’s not like solvingphysics questions. It’s not like you can geteverything figured so it becomes predictable, right? So the level of predictabilityis actually very much linked to a lot of other things.Physics, you solveNewton’s equations. You have a controlledenvironment and you know what you’regetting in the outcome. But here, when youparticipate in the market, you are changing the market. You are adding onother factors into it. So guess more from abroader scope kind of view rather than justsolve the mathematics. That’s why I comeback to the original– if you walk awayfrom this teach, you’ll remember what Isaid at the very beginning. Solving problemsis about observe, collecting data, house examples, then verify and detect again. OK, so I’ll culminate righthere, so questions. AUDIENCE: Yeah, simply[ INAUDIBLE] question. Does this have anything todo with– it kind of sounds like game theory, butI’m not exactly sure there is. Because you havea huge population and no stable equilibrium.Does it have anything to dowith game theory, by any chance? PROFESSOR: It has a lotto do with game theory, but not only to game theory. So game theory, you havea pretty well-defined gave of rules. Two parties toy chessagainst each other. That’s where personal computers actuallycan become smarter, right? So in this market situation, you have so many beings participating withoutclearly defined rules. There are some rules, butnot ever clearly defined. And so it’s much morecomplex than game theory. But it’s part of it, yeah. Dan, yeah? AUDIENCE: Can you talk a littlebit about why some of the risk parity portfolios that didso poorly in May and June when frequencies started to riseand what about their portfolio allows countries do that? PROFESSOR: Good question, right.So as you can see here, whatthe risk parity coming does is essentially to weight moreon the lower volatility asset. In this case, the questionis, how do you know which asset has low-pitched volatility? So you look athistorical data, which you conclude attachments havethe lower volatility. So you overweight alliances. That’s the essenceof them, right? So then when bondsto start to sell off after Bernanke, Fedchairman Bernanke, said he’s going to taperquantitative easing.So attachments from a very low highyield, a very low yield level, the crop proceeded far higher, the interest rate departed higher. Bonds get sold off. So this portfolio did poorly. So now the questionis, does that prove the risk parity approachwrong, or does it prove right? Does the financialcrisis of 2008 prove the risk parityapproach a superior coming, or does the June/ Mayexperience prove this as the less-favored approach? What does it tell us? Think about it. So it really is inconclusive. So you find, you extrapolatefrom your historic data. But what you arereally doing is you’re trying to forecast volatility, projection return, foreshadow correlation, all basedon historical data.It’s like– a good deal ofpeople consume that precedent. It’s like driving by lookingat the backside examine reflect. That’s the only thingyou look at, right? You don’t know what’s goingon, happening in front of you. You have another question? AUDIENCE: Given allthis new information, do you find thatpeople are still playing same[ INAUDIBLE] strategy with portfolio handling? PROFESSOR: Very much true-life. Why? Right, so you said, peopleshould be smarter than that. It’s very difficult todiscover brand-new asset castes. It’s also verydifficult to invent brand-new programmes in which you havea better earning likelihood. The other peril, the othervery interesting phenomenon, is most of the speculators andthe portfolio administrators, the investors, theyare profession investors– meaning just like ifI’m a baseball instruct, I’m hired to coacha baseball team. My performance isreally measured against the other teamswhen I earn or lose, right? A portfolio manageror investor is also measured against their peers. So the safest direction for them todo is to benchmark to an indicator, to the herd. So there’s very littleincentive for them to get out of the crowd, becauseif they are wrong, they get killed first.They lose their jobs. So the tendency is tostay with the crowd. It’s for survival tendency. It’s, again, the other example. It’s actually theoptimal strategy for individual portfolio manageris really to do the same thing as other parties aredoing because you stay with the force. AUDIENCE: So you said giventhat we have all these groups, in the end, it’s not justthat we could leave it to the computers.We need administrators. So what differentare the managers doing, other than[ INAUDIBLE ]? PROFESSOR: Can you try toanswer that question yourself? What’s the difference betweena human and a computer? That’s really– whatcan human add value to what a computer can do? AUDIENCE: Consider the factors, world markets ingredients and news and what’s going on. PROFESSOR: So making moreinformation, processing info, make a judgmenton a more holistic approaching. So it’s an interesting question. I have to say thatcomputers are pulsating humans in many different ways. Can a computer ever get tothe point actually overpowering a human in investment? I can’t confidently tell youthat it’s not is happening. It may happen. So I don’t know. Any other questions? Yeah? AUDIENCE: Just to add to that. I think there is some more tomanagement than really investing. I conceive managers too have keyroles in their HR, key roles in just like finagling peopleand ensuring that they’re maximizing theirtalents , not just like, oh, how much fund did you stimulate? But I imply, are you movingforward in your profession while you’re there? So I study control has arole to play in that as well , not just speculation. PROFESSOR: Yeah, I thinkthat’s a good point. Yeah. All claim, so– oh, sure. Jesse? AUDIENCE: What is yourportfolio breakdown? PROFESSOR: Mypersonal portfolio? Well, I am actually veryconservative at this station, because if you look at my curveof those spending and earning curve, I’m basically tryingto protect deans rather than try to maximizereturn at this degree. So I would be slithering downmore towards this part rather than try to goto this corner, yeah. So I haven’t reallytalked much about likelihood. What is risk, right? So I talk about volatilityor standard deviation. But as we all know that, asPeter mentioned last day as well, there are many other waysto look at risk– value at risk or half delivery ortruncated spread, or simply maximum loss youcan afford to take, right? But looking at standarddeviation or volatility is an elegant way.You can be found in. I can really evidence you invery simple math about how the concept actually plays out. But in the end, actually volatility is still not the bestmeasure, in my opinion, of hazard. Why? Let me give you another simpleexample before “were leaving”. So let’s say this is over time. This is your cumulativereturn or you dollar extent. So you start from here. If you go flat, then– does anyone like to have thiskind of a recital? Right? Of route, right? This is very nice. You keep going up.You never was down. But what’s thevolatility of that? The volatility isprobably not low-grade, right? And then on theother side, you could have– what I’mtrying to say, when you look at expectedreturn parallelling expected return and the volatility, you can still really not selecting the best combination. Because what you reallyshould care about is not just your volatility. And again, bear in mind allthe discussion about the Modern Portfolio Theory is basedon one key premise now. It’s about Gaussiandistribution, OK? Normal distribution. The two constants, meanand standard deviation, categorize the rationing. But in reality, you have manyother sets of disseminations. And so it’s a conceptstill up for a lot of discussion and debate. But I want to leavethat with you as well. Yeah? AUDIENCE: Just going back tothe same question about what these chaps were askingabout management and how do they addvalue, I picture the people who added value– therewere some people who contributed a tremendous amount ofvalue in the financial crisis.And they were doingthe same mathematics. But a difference was intheir expected return of various resources wasdifferent from the entire– the broad market. So if you can just know whatexpected return is that, probably that is the onlyanswer to the whole portfolio management debate. PROFESSOR: Yes. If you can forecast expectedreturn, then that’s– yeah , now you know the game. You answered it. You solved the bigpart of the riddle. Yeah? AUDIENCE: Whatmanagement does is how good it can do[ INAUDIBLE] expected return, full stop. Nothing more. PROFESSOR: I disagree on that. That’s the only thing. Because given two administrators, theyhave the same expected return, but you can still furtherdifferentiate them, right? So that’s– yeah. And that’s what all thisdiscussion is about. But yes, expected return willdrive pile of these decisions. If you know one manager’s goodexpected return, three years later, he’s going to make 150%. You don’t really carewhat’s in between, right? You’re just goingto go it through.But the problem is youdon’t know for sure. You will never be sure. Public: I’d liketo comment on that. PROFESSOR: Sure. Audience: What[ INAUDIBLE] looked at in simplifiedsettings, approximating returns and volatilities. And the problem, theconclusion for their own problems, was basically cannotestimate returns are you all right, even with more data, over a historical period. But you can estimate volatilitymuch better with more data. So there’s really anissue of perhaps luck in getting the return estimatesright with different overseers, which are hard to provethat there was really an expertise behind that. Although with volatility, youcan improved the quality of guesses. And I make possibly witha risk parity portfolio, those portfolios are focusingnot on return expectations, but saying if we’re going toconsider different preferences based on just howmuch risk they have and equalize that risk, thenthe expected return should be comparable acrossthose, perhaps.PROFESSOR: Yeah. So that highlightsthe difficulty of forecasting return, foreshadowing volatility, forecasting equivalence. So risk parity appearsto be another elegant way of proposing theoptimal strategy but it has the same questions. Yeah? AUDIENCE: Actually, Ialso wanted to highlight. You mentioned theKelly criterion, which we haven’t crossed thetheory for that previously. But I encourage peopleto look into that. It deals with issues ofmulti-period speculations as opposed tosingle-period speculations. And most– all this classicaltheory we’ve been discussing, or that I discuss, coversjust a single date analysis, which is an oversimplificationof major investments. And when you are investingover multiple ages, the Kelly criterion tells youhow to optimally mostly bet with your bank roll.And actually there’s anexcellent diary, at least I like it, calledFortune’s Formula that talks about– [? we already ?] said the origins ofoptions presumption in finance. But it does get intothe Kelly criterion. And there was a preferably majordiscussion between Shannon, a mathematician at MIT, whoadvocated addressing the Kelly criterion, and Paul Samuelson, one of the major economists. PROFESSOR: Also from MIT. AUDIENCE: Also from MIT. And there was a greatdispute about how you should do portfolio optimization. PROFESSOR: That’s a great bible. And a good deal ofcharacters in that journal actually are from MIT–and Ed Thorp, for example.And it’s really about peopletrying to find the Holy Grail magic formula– notreally to that extent, but witnessing something otherpeople haven’t figured out. But it’s veryinteresting autobiography. Big reputation like Shannon, verysuccessful in other environments. In his later part of hiscareer and living certainly focussed most of his time tostudying this question. You know Shannon, right? Claude Shannon? He’s the papa ofinformation theory and “ve got a lot” to do withthe later information age invention of computersand very successful, yeah. So anyway, so we’ll endthe class right here. No homework for today, OK? So you time need to– yeah, OK.All freedom, thank you.
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