The Marginal Risk Contribution
A very important question is “How much are you willing to pay to have, say, one more yellow egg in your basket?” If you believe blue eggs offer the highest expected rates of return, would you even bring any yellow eggs? Yes! Even if you do not believe that yellow is likely to sell tomorrow, a yellow egg will likely sell precisely when most of your blue eggs won’t sell. Yellow provides you with the equivalent of “insurance”—it pays off when the rest of your portfolio is losing. Therefore, you may very well be willing to bring some yellow eggs, and even though you expect to make a loss on them—of course, within reasonable bounds. You may be prepared to lose 5 cents on each yellow egg you bring, but you would not be prepared to lose $100. In sum, yellow eggs are valuable to you because they are different from the rest of your portfolio. What matters is the insurance that yellow pay off when your blue investments do not. Perhaps the most important aspect is that you realize that it is not the own risk of each egg color itself that is important, but the overall basket risk and each color’s contribution thereto. In fact, you already know that you may even expect to lose money on yellow eggs (just as you may expect to lose money on your homeowner’s insurance). This again emphasizes that having yellow eggs as insurance is useful only because most of your eggs are not yellow. The risk contribution of yellow thus inevitably must depend on all the other eggs in your portfolios. Of course, it would make no sense to bring only yellow eggs—in this case, you would not only expect to lose 5 cents per egg, you would also most likely always lose these 5 cents and on all your eggs. In the financial market, the degree to which one stock investment is similar to others in your portfolio will be measured by the aforementioned beta—and if your portfolio is the market portfolio, then it is called the market beta. You will be willing to hold some stocks in the market portfolio that have a low expected rate of return because they are different from the rest of your portfolio—but only some, and only if their expected rate of return is not too low.
In sum, when you look at your final basket, you should consider each egg along two dimensions— how does it contribute to your overall expected rate of return (what is its own expected rate of return?), and how does it contribute to your overall portfolio risk (how does its return covary with that of your overall basket?). In a good portfolio, you will try to earn a high expected rate of return with low risk, which you accomplish by having a balanced mix of all kinds of eggs—a balance that evaluates each egg by its expected rate of return versus its uniqueness in your basket.