Question

We would like to invest $10,000 into shares of companies XX and YY.

Answer 1

Answer:

c. $5,000 into each company

Explanation:

Let X be the actual (random) return from each share of XX, and  Y be the actual return from each share of YY. Computing the returns from each option:

A) Investing $10,000 into XX

Given that variance = (standard deviation)²

Since XX cost $20 per share, only 500 shares can be bought.

Expected value = 500 * E(x) = 500 * 1 = 500

Variance = 500² * Var(x) = 500² * 0.5² = 62500

B) Investing $10,000 into YY

Since YY cost $50 per share, only 200 shares can be bought.

Expected value = 200 * E(y) = 200 * 2.5 = 500

Variance = 200² * Var(y) = 200² * 1² = 40000

C) Investing $5,000 into each company

Since XX cost $20 per share and YY cost $50 per share, only 250 shares of XX and 100 shares of YY can be bought.

Expected value = 250 * E(x) + 100 * E(y) = 250 * 1 + 100 * 2.5 = 500

Variance = 250² * Var(x) + 100² * Var(y) = 250² * 0.5² + 100² * 1 = 25625

Since all options have the same expected return, but option C has the lowest variance hence it is the least riskiest. So the best option is C