Suppose that you have received an inheritance of $10,000 (!) and wish to invest

Question

Suppose that you have received an inheritance of $10,000 (!) and wish to invest it one or more of 5 different companies. The stock price of each company is the same - $1,000 – and have the same variance. Suppose that we know these each company has the same expected return and the same variance in return. Furthermore, these returns are independent of each other. (a) If you want to minimize the risk (variance) in the expected return from your stock portfolio, how would you invest your $10,000? Explain carefully your answer. (b) How, if at all, would your answer change if the stock returns were NOT independent?

Explanation / Answer

a) If the returns and the variances of all the stocks are same and they are not related to each other (Correlation coefficient =0) , then it does not matter how much amount is invested in which stock because the returns, stock price and variance are same for all the companies. The investor can invest all his amount (10,000 $ ) in one single company or invest 2000$ each in all 5 companies , or any combination in between. The Return of the portfolio and variance will be same for all combinations.

b) In case the stock returns are not same but rest of the factors remain same as above, the investor should maximize his portfolio return by investing all his money in the stock with highest returns.

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