Question

Use the data in the scenario analysis from Problem 13 and consider a portfolio with weights of .60 in stocks and .40 in bonds. (LO11-3) a. What is the rate of return on the portfolio in each scenario? b. What are the expected rate of return and standard deviation of the portfolio? c. Would you prefer to invest in the portfolio, in stocks only, or in bonds only? Explain the benefit of diversification.

Answer 1

Answer:

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Explanation:

a. The rate of return in each scenario is gotten by multiplying the weight of each asset in the portfolio by the rate of return

Recession = 0.6(-5%)+0.4(14%)=2.6%

Normal economy = 0.6(15%)+0.4(8%)=12.2%

Boom = 0.6(25%)+0.4(4%)=16.6%

b. The expected rate of return for each asset (stock or bond) is obtained calculating the weighted average return and multiplying this by their respective weight in the portfolio.

The weighted average return on stock is -5%(0.2)+15%(0.6)+25%(0.2)=13%

The weighted average return on bond is 14%(0.2)+8%(0.6)+4%(0.2)=8.4%

The expected return of the portfolio is 0.6(13%)+0.4(8.4%)=11.16%

The standard deviation of stock is obtained by calculating the standard deviation of -5%,15% and 25% = 12.47%

The standard deviation of bond is obtained by calculating the standard deviation of 14%,8% and 4% = 4.1%

The formula for calculating the standard deviation of the population = $\sqrt{w_{a} ^{2}A^{2} +w_{b}^{2} B^{2} +2w_{a}w_{b}ABR_{ab} }$

where

${w_{a}$ is weight of stock

${w_{b}$ is weight of stock bond

A is the standard deviation of stock

B is the standard deviation of bond

$R_{ab} }$ is the correlation between returns on stock and bond

The correlation coefficient measure the interdependence of the two assets = - 0.99

The standard deviation of the population is 0.34%

c. Yes, one should invest in the portfolio because it helps minimizes the risk of investing in only one asset. Diversification is a risk management strategy that helps to lower volatility and increases the risk-adjusted return