Question

11. Suppose Foxgo is an ISO app development company with its stock expected return of 23% and its stock volatility of 53%. Cowump is a global paper company with its stock expcected return of 8% and its stock volatility is 17%. If the correlation between Foxgo and Cowump is zero. The risk-free rate is 2% per year.

11.1 Your uncle is interested in constructing a portfolio by using thse two stocks however he prefers having the same volatility as Cowump. If short selling is not feasible, then what is the weight of each stock respectively? (Choose the closest answer)

A) 21.3 of Foxgo, 78.6% of Cowump.

B) 50% of Foxgo, 50% of Cowump

C) 18.7% of Foxgo, 81.3 of Cowupm

D) 32.4% of Foxgo, 67.6 of Cowump.

11.2 If your uncle wants to optimize the volatility of his portfolio and short selling is not feasible, what is the weight of each stock respectively? (Choose the clocest answer)

A) 8.8% of Foxgo, 91.2% of Cowump

B) 17.3 % of Foxgo, 82.7% of Cowump

C) 32.4 % of Foxgo, 67.6% of Cowump

D) 5.2% of Foxgo, 94.8% of Cowump

Answer 1

Portfolio Variance (volatility²) = w²A*σ²(R_A) + w²B*σ²(R_B) + 2*(w_A)*(w_B)*Cov(R_A, R_B), where:

• A = Foxgo stock, B = Cowump stock
• w_A and w_B are portfolio weights,
• σ²(R_A) and σ²(R_B) are variances = volatility squared and
• Cov(R_A, R_B) is the covariance between both stocks

11.1: C) 18.7% of Foxgo, 81.3 of Cowupm

Required Volatility of portfolio = 17% and covariance = 0.

Using the above formula, we get

(17^{^2}) = w²A*(53^{^2}) + w²B*(17^{^2}) + 0

Since W_A + W_B = 1, we get, W_B = 1-W_A : Substituting this in the above equation we get:

(289) = w²A*(2809) + (1-W_A)²*(289)

Solving for W_A, we get W_A = 18.7%. Thus, W_B = 1-0.187 = 81.3%

11.2: A) 8.8% of Foxgo, 91.2% of Cowump

An optimized portfolio is the portfolio with lowest variance (i.e.a minimum variance portfolio). Using the following formula for calculating the weights:

W_A = [σ²(R_B) - Cov(R_A, R_B)] / [σ²(R_A) +σ²(R_B) -2Cov(R_A, R_B)]

W_A = [17² - 0] / [53² +17² -0] = 9.33%

W_B = 1- 9.33% = 90.67%

Thus, the closest answer is option A.

Cross check 11.2:

Options	Weights		Standard deviation		Variance
	Foxgo	Cowump	Foxgo	Cowump
A	8.8%	91.2%	53.00	17.00	262.13
B	17.3%	82.7%	53.00	17.00	281.73
C	32.4%	67.6%	53.00	17.00	426.94
D	5.2%	94.8%	53.00	17.00	267.32

For option A, the variance is minimum.