Question

Calculate the required return for a stock after market returns have changed:
Initial conditions: risk-free rate is 4%, the required return on the market is 10%, and the beta is 1.20.
Risk aversion increases such that the market risk premium increases by 1 percentage point, with no change in the risk-free rate.
Calculate the new required return. (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).

Answer 1

Required return is calculated as:
Required return=Risk-free rate+Beta*(Required return on the market-Risk free rate)
Market risk premium=Required return on the market-Risk free rate
Given that:
Risk free rate=4%
Required return on the market=10%
Beta =1.20
Required return=4%+1.20*(10%-4%)=4%+1.20*(10%-4%)=0.04+1.20*0.06=0.112 or 11.20%

Now, market risk premium=Required return on the market-Risk free rate
Required return on the market-Risk free rate=10%-4%=6%
So, market risk premium=6%
Now, market risk premium increases by 1 percentage point. It means, the new market risk premium will be 6%+1%=7%

New required return=Risk free rate+Beta*(New market risk premium)
Now, after substituting the values, we get:
New required return=4%+1.20*(7%)=0.04+1.20*0.07=0.124 or 12.40%