Question

Consider another situation involving the SML. Suppose that the risk-free interest rate stays the same, but that investors’ dislike of risk grows more intense. Given this change, will average expected rates of return rise or fall? Next, compare what will happen to the rates of return on low-risk and high-risk investments. Which will have a larger increase in average expected rates of return, investments with high betas or investments with low betas? And will high-beta or low-beta investments show larger percentage changes in their prices?

Short answer

Suppose the investor’s dislike of risk grows more intense, the average expected rate of return will increase, provided the risk-free interest rate remains the same.

The rates of return on low-risk will be lower than the rates of return on high-risk. Thus, the high beta investments will have a larger increase in the expected rate of return.

High-beta investments will show a larger increase in their prices.

Step-by-step solution

Step 1. Impact risk aversion on the average expected rate of return

The average expected rate of return is the sum of the risk premium and the risk-free interest rate, which is the compensation for time preference.

As the dislike of risk grows more intense, the rate that compensates for the risk, the risk premium, will increase. Hence, the average expected rate of returns will increase. As the risk premium will be lesser for low-risk, the rate of returns on low risk will be lower.

Step 2. Relation between risk measure and expected rate of return

The beta value measures the level of risk. A beta value greater than 1 will show a higher risk, and less than 1 shows less risk. The investments with a higher beta have a higher risk. The higher risk means a higher risk premium and a larger increase in the average expected rate of return as the average rate of return comprises the risk premium.

Thus, investments with higher beta values will have a larger increase in the average expected rate of return and vice versa.

Step 3. Impact of risk level in investment on the price of investment

The investment with higher betas will have a larger increase in average expected rates of return than the investment with lower beta. A higher expected rate of return will increase the investment demand. Higher demand will drive the prices up.

Therefore, the investments with a high beta will show a larger change in the prices than the low beta investments.