Denote Xi and X2 the rate of returns of the stock of company 1 and company 2, re

Question

Denote Xi and X2 the rate of returns of the stock of company 1 and company 2, respectively. Assume that the performance of the 2 companies is independent from one another, and that E(Xi)-E(X2) and Var(Xi)- Var(X2). If you have 6000 usd and want to invest in the stock market, please answer the following questions 1. You have two options: 1) Use 3000 usd to buy stocks of company 1 and 3000 usd to buy stocks of company 2; and 2) use 6000 usd to buy stocks of company 1. Which option would you choose? Why? 2. How would you allocate 6000 usd between stocks of the two companies so that you get smallest variance? 3. Would you change your answer for question 2 above if the two companies are no longer independent from one another but correlated

Explanation / Answer

1)

Option 1) will be better.

This is because variance will reduce

2)

When variance are equal and variables are uncorrelated

Then for minimum variance

Equal weightage to both

Hence 3000 in each stock

3) yes, it would change

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