Question

1. Pepsi’s mean return over the last 5 years is 19% while McDonald’s is 14%. Their respective standard deviations are 21% and 18%. The two stocks correlation coefficient is -.20.

1. Calculate the portfolio mean return for the minimum variance portfolio.
2. Calculate the portfolio risk for the minimum variance portfolio.
3. Discuss the benefits of diversification for Pepsi and McDonald’s.

Answer 1

(a).The formula to calculate Mean/ expected return of minimum variance porfolio is

.................(1)

where,

E(r_P)=Mean return of Pepsi, w_p=weight of pepsi

E(r_M)=Mean return of McDonald's, w_M=weight of McDolanld

Here we have to calculate w_P & w_A

We know that for only two asset the weight w_P+w_M=1 or, w_P=1-w_M

Now from the variance formula,

.........................(2)

differentiating with respect to w_P,,we get

Putting these values in 1

E(r)=16.31%

Therefore ,portfolio mean return =16.31% answer.

(b) here volatility is same as risk

so we calculate volatility

from euation (2)

Hence, portfolio risk =11.815% answer.

(c).Of these two portfolio pepsi has a higher return than Mcdonald.also these are negatively co related to each other.

Adding the riskier stock to the porfolio can actually lower the portfolio risk.

Here the portfolio risk is 11.815%,so adding Pepsi to the porfolio is the great idea because,it can increase the expected return to 14%to 16% and portfolio standard deviation from 18% to 12%.