In this article we are beginning with a TV game as an illustration for a proper explanation of the topic covered by the title.
At the time you thought that you were safely immersed in the middle of a finance operation, you find yourself caught up in a time warp, and you are a contestant on the television game “Let’s Make a Deal�?. The host explains that you get to keep whatever you find behind either door #1 or door #2. He tells you that behind one door is $10,000in cash, but behind the other door is ‘Junk’ 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, the host says that he will offer you a sum of money to call off the whole deal.
Decide for yourself what dollar amount would make you indifferent, between taking what is behind the door and taking the money offered. 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 the host Monty offers you $2,999 or less, you will keep the door. At $3,000 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.)
Certainty equivalent (CE):
The amount of cash someone would require with certainty at a point in time to make the individual indifferent between that certain amount and an amount expected to be received with risk at the same point in time.
What does any of this have to do with this on risk and return?
Everything; we have just illustrated the fact that the average investor is averse to risk. Let us 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$0). In our example, you found yourself indifferent between a risky (uncertain) $5,000 expected return and a certain return of $3,000. In other words, this certain or risk less amount, your certainty equivalent (CE) to the risky gamble, provided you with the same utility or satisfaction as the risky expected value of $5,000.
It would be amazing if actual certainly 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 towards risk. In general, if the
Ø Certainty equivalent < expected value, risk aversion is present.
Ø Certainty equivalent = expected value, risk indifference is present.
Ø Certainty equivalent > expected value, risk preference is present.
Thus, in our 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.
Risk-averse term applied to an investor who demands a higher expected return, the higher the risk.
We will take the generally accepted view that investors are, by and large averse. This implies that risky investments must offer higher expected returns than less risky investments in order for people to buy and hold them.
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.