Just when you thought that you were safely immersed in the middle of a finance chapter, you find yourself caught up in a time warp, and you are a contestant on the television game show Let's Make a Deal. The host, Monty Hall, explains that you get to keep whatever you find behind either door #1 or door #2. He tells you that behind one door is $10,000 in cash, but behind the other door is a "zonk," a used tire with a current market value of zero. You choose to open door #1 and claim your prize. But before you can make a move, Monty says that he will offer you a sum of money to call off the whole deal.
(Before reading any further, decide for yourself what dollar amount would make you indifferent between taking what is behind the door or taking the money. That is, determine an amount such that one dollar more would prompt you to take the money; one dollar less and you would keep the door. Write this number down on a sheet of paper. In a moment, we will predict what that number will look like.)
Let's assume that you decide that if Monty offers you $2,999 or less, you will keep the door. At 53,000 you can't quite make up your mind. But at $3,001, or more, you would take the cash offered and give up the door. Monty offers you $3,500, so you take the cash and give up the door. (By the way, the $10,000 was behind door #1, so you blew it.) What does any of this have to do with this chapter on risk and return? Everything. We have just illustrated the fact that the average investor is averse to risk. Let's see why. You had a 50/50 chance of getting $10,000 or nothing by keeping a door. The expected value of keeping a door is $5,000 (0.50 x $10,000 plus 0.50 x SO). In our example, you found your-self indifferent between a risky (uncertain) $5,000 expected return and a certain return of $3,000. In other words, this certain or riskless amount, your certainty equivalent (CE) to the risky gamble, provided you with the same utility or satisfaction as the riskv expected value of $5,000.
It would be amazing if your actual certainty equivalent in this situation was exactly $3,000. the number that we used in the example. But take a look at the number that we asked you to write down. It is probably less than $5,000. Studies have shown that the vast majority of individuals, if placed in a similar situation, would have a certainty equivalent less than the expected value (i.e., less than $5,000). We can, in fact, use the relationship of an individual's certainty equivalent to the expected monetary value of a risky investment (or opportunity) to define their attitude toward risk. In general, if the
• Certainty equivalent < expected value, risk aversion is present.
• Certainty equivalent = expected value, risk indifference is present.
• Certainty equivalent > expected value, risk preference is present.
Thus, in our Let's Make a Deal example, any certainty equivalent less than $5,000 indicates risk aversion. For risk-averse individuals, the difference between the certainty equivalent and the expected value of an investment constitutes a risk premium; this is additional expected return that the risky investment must offer to the investor for this individual to accept the risky investment. Notice that in our example the risky investment's expected value had to exceed the sure-thing offer of $3,000 by $2,000 or more for you to be willing to accept it.
In this book we will take the generally accepted view that investors are, by and large, risk averse. This implies that risky investments must offer higher expected returns than less risky investments in order for people to buy and hold them. (Keep in mind, however, that we are talking about expected returns; the actual return on a risky investment could be much less than the actual return on a less risky alternative.) And, to have low risk, you must be willing to accept investments having lower expected returns. In short, there is no free lunch when it comes to investments. Any claims for high returns produced by low-risk investments should be viewed skeptically.