Question

You have estimated that the annual expected return on Apple stock is 15% and that Apple’s standard deviation is 20%. The Treasury bill rate is 1%. You are considering an asset allocation between T-bills and Apple stock and given your risk preferences and investment objectives, you seek to establish a portfolio with an expected return of 8%.

27. In relation to the problem above, what proportion of your portfolio should you allocate to Apple stock (rounding to the nearest whole percent)?

a. 20%

b. 40%

c. 50%

d. none of the above.

28. In relation to the problem above, what will be the variance on your portfolio?

(a) 0.01

(b) 0.04

(c) 0.08

(d) 0.1

(e) 0.15

Answer 1

Question 27

Apple

Return on Apple stock = R_A = 15%, Standard deviation of Apple =  σ_A = 20%

Treasury Bill

Return on Treasury bill = R_T = 1%, Standard deviation of Treasury Bills = σ_T = 0 (Treasury Bills are risk-free, so, the standard deviation of Treasury bill is 0)

Portfolio

The portfolio consists of Apple stock and Treasury Bills

weight of Apple in the portfolio = w_A,

weight of Treasury bills in the portfolio = w_T

Expected Return on the portfolio = E[R_P] = 8%

Expected return on the portfolio is calculated using the formula:

E[R_P] = w_A*R_A + w_T*R_T

8% = w_A*15% + w_T*1%

w_A + w_T = 1

Using w_T = 1 - w_A

8% = w_A*15% + (1 - w_A)*1%

8% = w_A*15% + 1% - w_A*1%

7% = w_A*14%

w_A = 7%/14% = 0.5

w_T = 1 - w_A = 0.5

proportion of your portfolio allocated to Apple stock = w_A = 0.5 = 50%

Answer -> 50%

Question 28

Variance of the portfolio is calculated using the formula

Variance of the portfolio = σ_P² = w_A²σ_A² + w_T²*σ_T² + 2*ρ*w_A*w_T*σ_A*σ_T

where ρ is the correlation between the return of the Apple stock and the Treasury Bill

w_A = 50%, w_T = 50%

Standard deviation of Apple = σ_A = 20%, Standard Deviation of Treasury Bill = σ_T = 0 (Traesury Bills are risk-free)

σ_P² = w_A²σ_A² + w_T²*σ_T² + 2*ρ*w_A*w_T*σ_A*σ_T = (50%)²*(20%)² + 0 + 0 = 0.01

Answer -> Variance of the portfolio = 0.01