In: Finance
A portfolio consists of four assets in equal weights. Asset 1 has a beta of 0.95. Asset 2 has a beta of 1.00. Asset 3 has a beta of 1.45. Asset 4 has a beta of 1.15. If the portfolio's required return is 7.75% and the risk-free rate is 3.70%, what is Asset 2's required return?
Asset 2's required return is 7.25%
| Step-1:Calculation of weighted beta of portfolio | ||||||||
| Weight | Beta | |||||||
| a | b | c=a*b | ||||||
| Asset 1 | 0.25 | 0.95 | 0.24 | |||||
| Asset 2 | 0.25 | 1.00 | 0.25 | |||||
| Asset 3 | 0.25 | 1.45 | 0.36 | |||||
| Asset 4 | 0.25 | 1.15 | 0.29 | |||||
| Portfolio Beta | 1.14 | |||||||
| Step-2:Calculation of market risk premium | ||||||||
| Portfolio required return | = | Risk free rate + Beta * Market Risk Premium | ||||||
| 0.0775 | = | 0.037+1.14*Market Risk Premium | ||||||
| 0.0405 | = | 1.14*Market Risk Premium | ||||||
| Market Risk Premium | = | 3.55% | ||||||
| Step-3:Calculation of Asset 2's required return | ||||||||
| Required return | = | Risk free rate | + | Beta | * | Market Risk Premium | ||
| = | 3.70% | + | 1.00 | * | 3.55% | |||
| = | 7.25% |