Question

You and your Team have to brief the head of a hedge fund, Mr. Moneypockets, who is thinking about creating a portfolio investing just in these three stocks, for a major client of his that is willing to invest $100M in this particular portfolio. However, since this is a very large amount of money, relatively speaking, he wants your team to advise him on his idea. The volatility of his proposed market portfolio is 10% and it has an expected return of 8%, The risk free rate is 3%, and is based on appropriate U.S. government securities ("Treasuries"). The portfolio weights, volatility and correlation with the market portfolio of his three stocks are given in the table below:

Portfolio weight Volatility Correlation with the market portfolio

Yahoo 0.25 12% 0.4

Microsoft 0.35 25% 0.6

Google 0.40 13% 0.5 1.

1.If you (and his client) expect to receive a rate of return 9% on this portfolio , would your Team recommend investing in this portfolio? Explain your team rationale to Mr. Moneypockets.

2. Assume the CAPM correctly prices risk, does your Team think the market portfolio is efficient? Explain why or why not to Mr. Moneypockets.

Answer 1

1. In order to make a decision regarding whether to invest in this portfolio, we need to find out the return on this portfolio. This can be calculated as follows:

E(R_p) = w_yE(R_y) + w_mE(R_m) + w_gE(R_g)

where: E(R_p) = Expected return on portfolio

w = weights of each of the stocks in the portfolio

E(R_Y/m/g) = Expected returns on the stock.

Since we do not know the expected returns on each of the individual stock so we will calculate the expected return of a stock using Capital Asset Pricing Model (CAPM):

Expected Return = Risk-free Rate + (Market rate - Risk-free rate) x Beta

To calculate Beta, we use the following formula:

? = Correlation of stock with the market portfolio x ( ? _stock / ? _market)

From the information given below we shall calculate beta for all the three stocks using the above-mentioned formula:

Name of Stocks	Portfolio weight (w)	Volatility (?)	Corre (ra, rm)	Beta (?)
Yahoo	0.25	12%	0.4	0.4 x (0.12/0.10) = 0.48
Microsoft	0.35	25%	0.6	0.6 x (0.25/0.10) = 1.5
Google	0.4	13%	0.1	0.1 x (0.13/0.10) = 0.13

Expected return on Yahoo = Risk-free Rate + (Market rate - Risk-free rate) x Beta of yahoo

= 3 + (8 - 3) x 0.48 = 5.4%

Expected return on Microsoft = Risk-free Rate + (Market rate - Risk-free rate) x Beta of Microsoft

= 3 + (8 - 3) x 1.5 = 10.5%

Expected return on Google = Risk-free Rate + (Market rate - Risk-free rate) x Beta of Google

= 3 + (8 - 3) x 0.13 = 3.65%

Now, expected return on portfolio can be calculated as:

E(R_p) = w_yE(R_y) + w_mE(R_m) + w_gE(R_g)

= (0.25 x 0.054) + (0.35 x 0.105) + (0.40 x 0.0365) = 0.06485 or 6.5% (approx.)

Since the expected return on this portfolio is less than what you expect so the team would recommend not to invest in the portfolio.

2) An efficient portfolio is the one which gives maximum return for a given level of risk or which has the minimum risk with the given level of return. The team does think of market portfolio to be efficient that is why the above portfolio failed to give a return equivalent to the market portfolio's return.