We would like to invest $10,000 into shares of companies XX and YY. Shares of XX cost $20 per share. The market analysis shows that their expected return is $1 per share with a standard deviation of $0.5.
Shares of YY cost $50 per share, with an expected return of $2.50 and a standard deviation of $1 per share.

Returns from the two companies are independent. In order to maximize the expected return and minimize the risk (standard deviation or variance), is it better to invest

a. All $10,000 into XX
b. All $10,000 into YY
c. $5,000 into each company

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

a manufacturer of printed circuit boards uses exponential smoothing with trend to forecast monthly demand of its product. at the end of december, the company wishes to forecast sales for january. the estimate of trend through november has been 200 additional boards sold per month. average sales have been around 1000 units per month. the demand for december was 1100 units. the company uses α = 0.20 and β = 0.10. make a forecast including trend for the month of january.