So, what I want to do now is calculate the efficient portfolio of frontier which expresses the standard deviation of the portfolio in terms of r the expected return on the portfolio instead of X-1. So here is an example of the efficient portfolio frontier, I calculated for two investments, U.S. stocks and U.S. bonds using their historical expected returns, standard deviations, and covariances, variances and covariances. So what we have on this axis is the standard deviation of return and we have on this axis the expected annual return. So, and these are the possibilities we calculate with a formula. Let's consider a couple of special cases I have shown here. I can put all my assets in the stocks and then I would get an expected return equal to the return on stocks or I can invest entirely in bonds and I would be at this point here on the diagram. Bonds, these are long term bonds, they're risky because they're long term. Here, Professor Shiller mentions bonds are risky because they're a long term. I wouldn't fixate too much on the use of the term bonds here. We're analyzing the efficient portfolio frontier with any two risky assets. In this case he chose the example of stocks and bonds to emphasize that there are two separate types of assets. You could easily replace the word stocks and bonds with Microsoft stock and Tesla stock and the argument still works. Have historically, had a lower standard deviation of annual return but also a lower expected return. So I could achieve that by putting all of my money in bonds and I can achieve this by putting all of my money in stocks. What if I put half my money in stocks and half in bonds that puts me right here. So what we see is that there's an infinite number of possibilities. Oh, by the way, I could go more than 100% stocks if you like, I can go out here. So that looks like it's something like 120% in stocks and -20% in bonds. So to do that I'd have to short the bond market and buy the stock market. I can do that, I can do anything. It's just those two formulas that I just showed or the single formula for this curve. So what do you like? If you are investing your money and I showed you this, what would you pick? If Suppose you picked here then another adviser would come up and say, "you idiot, you could have picked up here and then you would have gotten more return". And note, no difference in risk, shorting the stock market is risky. If it has a negative expected return you don't want to do that. So what that means is that the hope curve here, below the minimum variance point is dominated, it's called the dominated. You don't ever want to be there. Well, what David Swensen says, "you know who is there before he arrived? Yale University was there." They had some fuddy duddy investment advisors who would say, "you know we've advised endowments of portfolios over the years and we find that for institutions like the Yale University they would do well to put their money in sound safe government bonds." And so, actually it wasn't David Swensen who first pointed out the foolishness of it. It was starting to come in with the whole capital asset pricing model. I think there was a Ford Foundation study of university endowments in the 60s that pointed out that universities are just stupidly putting their money in bonds. It used to be considered just smart, you know it was almost like religion, you had to do things the right way. In Europe, a lot of... a lot of foundations have put all their money in bonds because that was supposed to be safe. And then in Germany, in the 1920s, there was a hyperinflation in 1923. Every foundation in Germany was completely wiped out by the hyperinflation, they should have thought of this. It wasn't safe and they were undiversified and they were doing the under-performing under diversified asset. So, but it still takes a while you know you have university corporations or boards tend to be filled with various old fashioned educators. They can't imagine putting money in the stock market but David Swensen change that. So you don't ever want to be down here but you want to pick some point up here depending on your risk and it's a matter of taste where along this frontier you choose to go. So, here now I have the same curve that I showed you before for stocks and bonds and now let's add a third asset called oil. Okay? I did this with actual variances and covariances when I did this diagram. Forget this diagonal line for the moment, now I have three assets: stock, bonds, and oil. And so what is the minimum varian- minimum standard deviation I can get for any given expected return? And you can see there it gets more complicated now. The minimum variance portfolio... the minimum standard deviation portfolio would be 9% oil, 27% stocks and 64% bonds. Up here, this is 21% oil, 79% stocks, 0% bonds and here is 28% oil, 115% stocks, -44% bonds. All those things are possible and so, now you might say I should take the minimum standard deviation, shouldn't I? Or is that right? Well, not generally, right, because you're sacrificing some return for that. You have to pick a point that reflects your tastes. So, now that we've added oil, you should not own a portfolio with just stocks and bonds in it, it's because the new portfolio frontier dominates. In other words, you can get the same return with a lower standard deviation. So putting our oil as a risky asset as you know recently. I've did this chart some years ago, so this is not updated but what we're seeing lately confirms oil is risky. It has... it was up to $150 a barrel or over that in 2008 and now it's under $30 a barrel, it's jumping around wildly. So you might say, "I'm going to stay away from oil." The answer is, "no you shouldn't, you should have if you want everything in your portfolio." But maybe you want something like this point. So you're only 21% exposed to oil, 79 % stock, that sounds like a reasonable point. There are various possibilities here but the point is you don't want to... you don't want to just invest in stocks and bonds. Once you add oil there's more... there's more opportunity to achieve expected return without risk. Today's economy, there's so much uncertainty and many potential investors I think are fear- fearful of getting involved in the market. Is there a message that you think you would share with potential investors about what's going on today with fluctuating markets and how to kind of continue to stimulate our economy. Well it's going to be a mixed message. There is something inherently unsatisfying about investing in the stock market because you are putting yourself on the line for risks in so many different ways. And you can't possibly assess them all. Risks of financial crisis, risks of, I would say psychologically induced panics and so many people around the world have concluded-- I'm just going to stay out of stocks for example, because it's just a quagmire. I know that... I know that I can't figure out these investments and people are trying to sell me on this. I don't trust them. So that creates an atmosphere that inhibits business and business is ultimately the source of our prosperity. So I think, you know, the free market system that we have just kind of looks bad to a lot of people and you see people being taken advantage of sometimes and you think , "there should be a pure system that let a lot of people towards various forms of socialism." But on the other hand, it just seems like all the fun stuff is happening in capitalist countries, I don't know if it's a capitalist but countries that have markets and prices. Let people do things for themselves on their own initiative and suffer the consequences. So, the world has come in this direction. You can't really escape the fundamental problem that business involves intuitive judgment, risk taking, you'll never know all of the risks, you know, that you have to be at some point, just think, "hey, I'm just going to try it." And you might get a bad outcome but I think... I think what we've learn about human society is that as funny as this system looks, it's a good system.
