Question

If rRF = 5%, rM = 11%, and b = 1.3 for Stock X,

a. what is rX, the required rate of return for Stock X?
b. What would rX be if investors expected the inflation rate to increase by 2 percentage points?
c. What would rX be if an increase in investors’ risk aversion caused the market risk premium to increase by 3 percentage points? rRF remains at 5 percent.
d. What would kX be if investors expected the inflation rate to increase by 2 percentage points and their risk aversion increased by 3 percentage points?

Answer 1

Answer(a): From CAPM:

rX = rF + b (rM - rF)

Where:

• rX = Required rate of return from a stock
• rF = Risk free rate of return
• b = Beta (Measure of systematic risk)
• rM = Market return.

Given values: rF = 5%, rM = 11%, b = 1.3, rX = ?

Putting all the given values in the formula, we get:

rX = .05 + 1.3 (.11-.05)

rX = 12.8%

Answer(b): If inflation goes up 2% then risk fee rate will come down by 2%.

So the risk free rate is 5-2 = 3%

Now calculating required rate of return rX-

rX = .03 + 1.3 (.11-.03)

rX = 13.4

Answer(c): If market risk premium (rpm) increases by 3% then the required rate of return is:

Market risk premium = Market return - Risk free return,

when Market return was 11% and Risk free rate was 5%, Market risk premium was 6% now market risk premium is increased by 3% so new market risk premium is 9%

Putting it in the formula to know the require return-

rX = 5% + 1.3 (9%)

rX = 16.7%

Answer(4): If inflation increased by 2% then rF will decrease by 2% so the rF is 3% and Risk premium is 9%

Putting the new values in the formula, we get rX-

rx = 3% + 1.3 (9%)

rX = 14.7%