A stock has a beta of 1.1 and an expected return of 8 percent. A risk-free asset

Question

A stock has a beta of 1.1 and an expected return of 8 percent. A risk-free asset currently earns 3.2 percent. a. What is the expected return on a portfolio that is equally invested in the two assets? (Do not round intermediate calculations. En your answer as a percent rounded to 2 decimal places.) Expected return b. If a portfolio of the two assets has a beta of 0.38, what are the portfolio weights? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.) Portfolio Weight Stock Risk-free asset

Explanation / Answer

a.

Expected Return = (50% × 8%) + (50% × 3.20%)

= 4% + 1.60%

= 5.60%

Expected return is 5.60%.

b.

Beta of stock = 1.10

Beta of risk free assets = 0

Beta of portfolio = 0.38

Let X% invested in stock and (1 - X) invested in risk free security.

So, 0.38 = (1.10 × X) + 0 × (1 - X)

X = 0.38 / 1.1

X = 34.55%

Investment in stock is 34.55%.

Investment in risk free assets = 1 - 34.55%

= 65.45%.

Investment in risk free assets is 65.45%.

c.

Expected return of portfolio = 11%

let X% invested in stock and (1 - X%) invested in risk free assets.

11% = 8% × X + (1 - X) × 3.20%

11% = 4.80 × X + 3.20%

X = (11% - 3.20%) / 4.80%

= 162.50%

So, 162.5% invested in stock and -62.50% in risk free assets. it mean investor borrow 62.50% from risk free assets and invest in stpcl.

Beta of portfolio = 1.10 × 162.50%

= 1.7875.

Beta of portfolio would be 1.7875.

d.

Beta of stock = 1.10

Beta of risk free assets = 0

Beta of portfolio = 1.15

Let X% invested in stock and (1 - X) invested in risk free security.

So, 1.15 = (1.10 × X) + 0 × (1 - X)

X = 1.15 / 1.1

X = 104.55%

Investment in stock is 104.55%.

Investment in risk free assets = 1 - 104.55%

= -4.45%.

Investment in risk free assets is -4.45%. it mean investor borrow 4.45% of portfolio at risk free rate and invest in stock.

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