Question

The stock of a restaurant franchise enterprise has a standard deviation of return of 10 percent, while the stock of a grocery store chain has a standard deviation of return of 20 percent. The correlation coefficient between the two stocks is 0.5. If you invest 60 percent of your funds in the restaurant chain stock and 40 percent in the grocery store stock, what is the standard deviation of your portfolio? A) 10.3 percent B) 21.0 percent C) 12.2 percent D) 14.8 percent

Answer 1

Answer: Correct option is option C, i.e. 12.2 Percent.

Explanation:

Standard deviation of portfolio(σ_p ​​​​​​)

=[w_{​​​​​​1}²σ₁²+w_​2² σ_{​​​​​2}²+2w₁w₂ρσ₁σ₂]^1/2

Where,

w_{​​​​​​1}= proportion of security 1 in portfolio=0.6

w_{​​​​​​2}= proportion of security 2 in portfolio=0.4

σ_{​​​​​​1=} standard deviation of return on security 1=10

σ_{​​​​​​2}= standard deviation of return on security 2=20

ρ= coefficient of correlation between the returns on securities 1&2= 0.5.

Calculating standard deviation of portfolio using above formula, we get

standard deviation of return on portfolio=

=[(0.6)²×(10)²+(0.4)²×(20)²+2×0.6×0.4×0.5×10×20]^1/2

=[0.36×100+0.16×400+48]^1/2

=[36+64+48]^1/2=[148]^1/2= 12.2 percent.