Question

Use the following information for the next three questions: You have $20,000 available to invest in the market portfolio, which has an expected return of 9% and the risk-free asset, which returns 3%: 18. How would you use your available funds to invest in the market portfolio and the risk-free asset to achieve a beta of 0.9? How much money would you invest in the market? A) $18,000 B) $2,000 C) $4,300 D) $2,180 19. What is the expected return of the portfolio constructed in part a? A) 8.4% B) 6.0% C) 9.0% D) 8.2% 20. If the volatility of the market portfolio is 35%, what is the volatility of the portfolio constructed in part a.? A) 9.9% B) 9.0% C) 28.9% D) 31.5%

Answer 1

Beta of a portfolio is sum product of asset’s beta and asset’s weight in the portfolio:

Where,

β = beta

P = Portfolio

m = market

w = weight

f = risk free assets.

Beta is measure of price sensitivity of stock with change in market. Thus, beta of market is always 1. Risk-free asset is not related to market thus beta of risk-free assets always 0

Provided,

Beta of Portfolio = 0.9

We can compute the weight of market in portfolio by putting values in Portfolio beta equation:

Thus, weight of market in portfolio = 0.9 and weight of risk-free asset = 1-0.9 = 0.1

18)

Total Amount invested in Portfolio = $20,000

Thus,

Amount invested in market = 20,000*0.9 = $18,000

19)

Expected Return of Portfolio = Market Return*weight-market + Risk-free return*weight-risk-free

Provided,

Market return = 9%

Risk-free return = 3%

Thus,

Expected Return of Portfolio = 0.09*0.9+0.03*0.1

Expected Return of Portfolio = 0.084 = 8.4%

20)

Volatility of Portfolio having one risky asset and one risk free assets:

Volatility of Portfolio = weight of market*volatility of market

Provided,

Market volatility = 35%

Thus,

Volatility of Portfolio = 0.9*0.35

Volatility of Portfolio = 0.315 = 31.5%