All right, well, we talked about the hard way to accomplish mean variance optimization. And I promised you an easier way and here's the easier way, it actually really couldn't be easier. The easy way to accomplish mean variance optimization is to just take the value-weighted market index to be an efficient portfolio, okay? So take the value-weighted market index such as the S&P 500, that's pretty much a value-weighted market index here in the US, to be an efficient portfolio. Okay, now this might sound like just throwing up your hands like, okay, forget it. I'm not going to try to optimize. But actually there are some good economic reasons to believe that a value-weighted market index, the broader the index, the better is going to be at least reasonably efficient, okay. And so let me just sort of sketch what those reasons are. Once again if you want to see more math, it's easy to look it up. I'm just going to sketch it for you here. Here's one reason to believe that. And this is that there's a long academic literature on this point. Reason number one is, if you have two efficient portfolios, right? So there's two portfolios, each of which has this nice property that it's got the minimum risk for its expected return. And then you combine those portfolios, the combined portfolio Is also inefficient portfolio. Mathematically that works out, okay? So, if and I know it's a big if here, but if everybody in the world holds an efficient portfolio, then everybody's portfolio put together is an efficient portfolio, okay? Well, everybody's portfolio put together is essentially the value-weighted market index, right? That's sort of what it is. It's just all of the assets put together according to their sizes, right? So you put all that together. Well, that is everyone's portfolio put together. And so if everyone has a mean variance efficient portfolio, then their sum is going to be mean variance efficient. I think that's sort of the idealized way that economists talk. We know that in fact, none of us, probably, really have a truly mean variance efficient portfolio. So that's a bit of a stretch, but as a thought experiment, it certainly works out. And then, another point they make, and this is often how it's presented in a finance class here at Wharton. Which is that if, now here's another if, that's not as big an if as the previous one. If everybody can borrow, or lend, at the risk-free rate, all right? Everybody can borrow or lend at the risk-free rate, more or less. Then you can show that, ultimately, It's optimal for everybody to hold risky assets in the same proportional weights and then just lever up or down depending on how risk averse they are using the risk-free rate, right? So if you're very risk averse then you'd put a little bit in the risky assets and a lot in the risk-free rate. If you really want risk, then you're going to borrow a lot at the risk-free rate, you're going to lever up. Borrow money at the risk-free rate and then lever way up and put a huge amount of money in the risky assets. But the point is that you can see that it's optimal in fact for everyone to hold the same portfolio of risky assets in the same proportional weights and then just lever up or down. Okay, once again, this is something you can look up. I'm not going to try to prove that now, it will take way too long. But for our purposes the point is that, okay, if everyone's holding the same assets in the same weights, then everyone's holding once again by that same logic, the value-weighted market index. They're all holding the value-weighted market index, just sort of in different amounts, but it's always the same relative weights. Okay, so the point is when I say take the valuated market index, being an efficient portfolio, this is a position that's defensible. Both of the arguments I gave obviously are approximate, because we know that they're not exactly true statements about people and how they invest. But they're approximate, and economists learn to live with close enough, okay? So we're not saying that the value-weighted market index is going to be exactly mean variance efficient, but you can argue that it could easily be in the neighborhood of it, okay? So that's one reason to take the value-weighted market index to be an efficient portfolio. Another reason, which is very different reason, is that an index is generally going to be much cheaper to trade, cheaper to trade then individual assets. Okay, now when I see this I'm thinking of the work of another famous economist, his name is George Ackerlof, and he is professor at Berkeley. And he wrote a very famous paper, the 1970, for which he also won the Nobel Prize. And this is a paper he called The Market for Lemons. So take a look at, it's one of the most famous papers in all of economic, and it's written very clearly. And what he's saying very clearly in that paper is that when you and I want to trade and you know that I have private information about the thing that we're trading, that is going to make you nervous, all right? And what he shows in the paper is that, he tells this in the context of used cars, right? I've got a car, I drive it around. I know things about it, you don't. You know that I know things that you don't know, right? And he shows how the market could completely evaporate all due to the fact that you worry about whatever price you might offer the car. You worry about what would it mean, if I were to accept the price that you offered? What would that mean about what I really know about the car, okay? So he's writing about cars, but people appreciated that this point applies anywhere. It applies in any context where we're trading something where one of us might have private information, okay? So just take Dr. Ackerlof's point and think about it in the context now, of putting on a portfolio that the robo-advisor has proposed, right? If the portfolio of individual stocks, then every time you go to buy one of those individual stocks, the person on the other side of the trade is going to wonder why are you buying the stock. Might you know something that I don't know. Maybe, maybe not, right? The person on the other side has to defend against the possibility that you are trading due to some private information. And therefore is going to charge you a transactions cost. He's going to charge you what we call in the profession, a bid ask spread, right? If you're buying, he's going to charge you a price higher than you would get if you sold, right? That's the bid ask spread, okay? So the point is that individual assets, especially the more obscure it gets, like the smaller the company it is, the more the other side is going to charge you just to trade the asset. Okay, so that's what it's like to try to put on a position in individual assets. But what if you're trading the whole index? What if you're trading the whole index at once, okay? I'm not buying each of the 500 stocks in the S&P, I'm just buying the S&P index from somebody else. Well, now that worry is going to be far smaller. Okay, when I'm buying the S&P 500 index from you, you're probably worrying a lot less. What do I know about the whole index that you don't know? I might know something, right? I might know something, I might be the chair of the Federal Reserve, and maybe I do know something that you don't know the way the market's going. And actually here's a fun fact, who is George Ackerlof married to? Janet Yellen, who was the chair of the Federal Reserve, right? How's that for a power couple there, right? So what George Ackerlof is telling us about trading is try to trade in a way that the other side can see that you're probably not trading on private information. And you're going to get better transactions costs, okay? So trade of the index versus the individual assets is going to be cheaper in the long run. You're not going to have money going out the window from your portfolio in transactions cost if you're trading the index versus trade individual stocks, like not nearly as much, okay? So you can have an optimizer that optimizes over individual assets. Or you could just take the value-weighted index to be your optimal portfolio. You can also take a middle road here, kind of a hybrid approach, where your optimizer is optimizing over individual assets. But the assets themselves that it's optimizing over are index portfolios, okay? So the S&P could be one of those indices that goes into the optimizer. There could be the indices for other countries, right? One for Canadian stocks, one for Mexican stocks, one for Chinese stocks. And you could have different asset classes. One for Internet stocks, one for energy, one for cars, and so on. So you have indexes that you're optimizing over so that way maybe you can get what you feel is a little more diversification benefit than you're getting from just buying the value-weighted index of everything. But still when you're putting on the actual trades that the robo-advisor is telling you to make, you are trading at kind of reduced transactions costs that you get from trading the index versus the individual assets, okay? So in the next lesson, we'll talk about how it is you can actually go about trading these indices.
