In: Finance
a) Given a risk-free rate of 3%, an expected return of the market of 9%. What is the risk premium for an asset with b = 1?
b) What is the required return of an asset with b = 1.6?
c) What is the reward to risk ratio?
d) What is the expected return on a portfolio of 30% of the asset in b) and the remainder in an asset with an average amount of systematic risk?
1. Calculation of Risk Premium
The Risk Premium is the return on an Investment less the return that would be earned on Investment without any risk.
Therefore the formula of risk premium is as below:
Risk Premium = Rm - Rf
Risk Premium = 9% - 3
Risk Premium = 6%
WhereRm - Expected Return
Rf - Return on Risk Free Investment
2. Calculation of Required Return
Using Capital Asset Pricing Model (CAPM) Required Rate of Return (RRR) is calculated as below:
RRR = b x (Rm - Rf)
Note : It is assumed that Rm and Rf is unchanged and Beta is given as 1.60
RRR = 1.60 X (9% - 3%)
RRR = 1.60 X 6%
RRR = 9.60%
3. Calculation of Reward to Risk Ratio
Reward to Risk Ratio = (Expected Return - Risk free return) / Beta
It is assumed that :
Expected Return (Rm) - 9%
Risk Free Return (Rf) - 3%
Beta (b) - 1.60
Reward to Risk Ratio = (0.09 - 0.03)/ 1.60
Reward to Risk Ratio = 0.06 / 1.60
Reward to Risk Ratio = 0.0375
4. Calculation of Expected Return
a) Required Rate of Return when Beta = 1.60 is 9.60%
b) Required Rate of Return when Beta = 1.00 is 6.00%
Required Rate of Return when 30% is invested in a) and balance in b)
Required Rate of Return = (0.30 x 9.60%) + (0.70 x 6%)
Required Rate of Return = 7.08%