# Risk Aversion and Required Returns

You are lucky to be invited by the host of a television game show. After the usual introduction the host shows two boxes to you. He tells you that one box contains Rs 5,000 and the other box is empty. He does not tell you which one is which.

The host asks you to open any one of two boxes and keep whatever you find in it. You are not sure which box you should open. Sensing your vacillation, he says he will offer you a certain Rs 3,000 if you forfeit the option to open a box. You don’t accept his offer. He raises his offer to Rs 3,500. Now you feel indifferent a certain return of Rs 3,500 and a risky (uncertain) expected return of Rs 5,000.This means that a certain amount of Rs 3,500 provides you with the same satisfaction as a risky expected value of Rs 5,000 . Thus your certainty equivalent (Rs 3,500) is less than the risky expected value (Rs 5,000).

Empirical evidence suggests that most individuals, if placed in a similar situation would have a certainty equivalent which is less than risky expected value.

The relationship of a person’s certainty equivalent to the expected monetary value of a risky investment defines his attitude toward risk. If the certainly equivalent is less that the expected value, the person is risk averse if the certainty equivalent is equal to the expected value, the person is risk-neutral finally if the certainty equivalent is more that the expected value, the person is risk loving.

In general, investors are risk averse. This mans that risky investments must offer higher expected returns that less risky investments to induce people to invest in them. Remember, however, that we are talking about expected returns; the actual return on a risky investment may well turn out to be less than the actual return on a less risky investment.

Put differently, risk and return go hand to hand. This indeed is a well established empirical fact, particularly over long periods of time. For example the average annual rates and annual standard deviations for Treasury bills, bonds and common stocks in the US over a 75 year period (1926-2000) as calculated by Ibbotson Associates have been shown below.

Return and Risk Performance of Different Categories of financial assets in the US over 75 years (1926-2000)

Portfolio Average Annual Rate of return(%)

Treasury bills 3.9
Government bonds 5.7
Corporate bonds 6.0
Common stocks (S&P 500) 13.0
Small firm common stock 17.3

From the above it is clear that: (1) Treasury bills, the least risky of financial assets, earned the lowest average annual rate of return; (2) Common stocks the most risky of financial assets, earned the highest average annual rate of return, (3) Bonds which occupy a middling position on the risk dimension, earned a middling average annual return.

Investors assume risk so that they are rewarded in the form of higher. Hence risk premium may be defined as the additional return investors expect get, or investors earned in the past, for assuming additional risk. Risk premium may be calculated between two classes of securities that differ in their risk level. There are three well known as risk premiums.

Equity Risk Premium: This is the difference between the return on equity stocks as a class and the risk free rate represented commonly by the return on Treasury bills.

Bond Horizon Premium: This is the difference between the return on long term government bonds and the return on Treasury bills.

Bond Default Premium: This is difference between the return on long term corporate bonds (which have some probability of default) and the return on long term government bonds (which are free from default risk).

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