Fortunately, the expected value is all that we need to learn about statistics until we will get to Part III (investments). This is because we are assuming—only for learning purposes—that everyone is risk-neutral. Essentially, this means that investors are willing to write or take any fair bet. For example, you would be indifferent between getting $1 for sure, and getting either $0 or $2 with 50% probability. And you would be indifferent between earning 10% from a risk-free bond, and earning either 0% or 20% from a risky bond. You have no preference between investments with equal expected values, no matter how safe or uncertain they may be. If, instead, you were risk-averse—which you probably are in the real world—you would not want to invest in the more risky alternative if both the risky and safe alternative offered the same expected rate of return. You would prefer the safe $1 to the unsafe $0 or $2 investment. You would prefer the 10% risk-free Treasury bond to the unsafe corporate bond that would pay either 0% or 20%. In this case, if I wanted to sell you a risky project or bond, I would have to offer you a higher rate of return as risk compensation. I might have to pay you, say, 5 cents to get you to be willing to accept the project that pays off $0 or $2 if you can instead earn $1. Or, I would have to lower the price of my corporate bond, so that it offers you a higher expected rate of return, say, 1% and 21% instead of 0% and 20%. Would you really worry about a bet for either +$1 or −$1? Probably not. For small bets, you

are probably close to risk-neutral—I may not have to offer even one cent to take this bet. But what about a bet for plus or minus $100? Or for plus and minus $10,000? My guess is that you would be fairly reluctant to accept the latter bet without getting extra compensation. For large bets, you are probably fairly risk-averse—I would have to offer you several hundred dollars to take this bet. However, your own personal risk aversion is not what matters in financial markets. Instead, it is an aggregate risk aversion. For example, if you could share the $10,000 bet with 100 other students in your class, the bet would be only $100 for you. And some of your colleagues may be willing to accept even more risk for less extra money—they may have healthier bank accounts or wealthier parents. If you could lay bets across many investors, the effective risk aversion would therefore be less. And this is exactly how financial markets work: the aggregate risk absorption capability is considerably higher than that of any individual. In effect, financial markets are less risk averse than individuals. 

We will study risk aversion in the investments part of the blog. There, we will also need to define good measures of risk, a subject we can avoid here. But, as always, all tools we learn under the simpler scenario (risk-neutrality) will remain applicable under the more complex scenario (risk-aversion).