Question

Pete has a six-stock portfolio that has a market value equal to $500,000. The portfolio’s beta is 1.2. Pete is considering selling a particular stock from his portfolio to help pay some expenses. The stock is valued at $150,000, and if he sells it, the portfolio’s beta will increase to 1.4. (i) What is the beta of the stock Pete is considering selling? (ii) Explain the implications of your results for Pete's decision to sell a particular stock. (Marks 1 + 2 = 3) (c) Craig has bought a house for $600,000 with 30% cash down payment. The remaining balance is financed by a 30-year mortgage at 6% per annum. The mortgage installments are paid monthly and the first installment is due now. (i) How much is Craig’s monthly mortgage repayment? (ii) What are the implications of having the payment due at the beginning of the month as opposed to the end of the month? (iii) Re-calculate the monthly mortage repayment if the first installment is due at the end of the month.

Answer 1

(i) The portfolio beta is sum of the products of the individual beta * weight of the stock in the portfolio.

Weight of the stock in the portfolio = Market Value of Stock / Market Value of Portfolio.

Therefore, weight of the selling stock = 150000/500000 = 30%

which means that remaining stocks have a weight of 70%. Therefore we can say that

1.2 = average beta of remaining stock + 30% * beta of selling stock

1.4 = average beta of remaining stock.

1.2 = 1.4 + 0.3X

X = -0.2/0.3 = -0.67

(ii) The stock Pete sold moved at odds with the rest of the portfolio. It provided a diversification to the rest of the portfolio (5 stocks) which had a high Beta, i.e. they are sensitive to market movements. Selling the stock would increase the risk of the portfolio but also, it had the probability to offer higher return in case of market upturn.