You are the money manager of a $2 million dollar portfolio. The portfolio consis

Question

You are the money manager of a $2 million dollar portfolio. The portfolio consists of 4 stocks with an equal investment in each one. The betas of the 4 stocks are 1.25, -1.75, 1.00 and 0.75. The market’s required return is 12% and the risk-free rate of return is 4%. Calculate this portfolio's beta.

You are the money manager of a $2 million dollar portfolio. The portfolio consists of 4 stocks with an equal investment in each one. The betas of the 4 stocks are 1.25, -1.75, 1.00 and 0.75. The market’s required return is 12% and the risk-free rate of return is 4%. Calculate this portfolio's required return.

Explanation / Answer

Stock A - A 1.25, wA 0.25 ($0.5m/$2m)

Stock B- B -1.75, wB 0.25 ($0.5m/$2m)

Stock C- C 1.00, wC 0.25 ($0.5m/$2m)

Stock D- D 0.75, wD 0.25 ($0.5m/$2m)

Rm - 12%

Rf - 4%

PORTFOLIO's BETA -

The beta of a portfolio is the weighted sum of the individual asset betas, According to the proportions of the investments in the portfolio. E.g., if 50% of the money is in stock A with a beta of 2.00, and 50% of the money is in stock B with a beta of 1.00, the portfolio beta is 1.50. Portfolio beta describes relative volatility of an individual securities portfolio, taken as a whole, as measured by the individual stock betas of the securities making it up. A beta of 1.05 relative to the S&P 500 implies that if the S&P's excess return increases by 10% the portfolio is expected to increase by 10.5%.

So then,

PORTFOLIO's Beta,

= (A*wA) + (B*wB) + (C*wC) + (D*wD)

= (1.25*0.25) + (-1.75*0.25) + (1.00*0.25) + (0.75*0.25)

= >0.3125

PORTFOLIO REQUIRED RATE OF RETURN-

Identifying the return on risky securities, we use "CAPITAL ASSET PRICING MODEL - CAPM"

The CAPM says that the expected return of a security or a portfolio equals the rate on a risk-free security plus a risk premium. If this expected return does not meet or beat the required return, then the investment should not be undertaken. The security market line plots the results of the CAPM for all different risks (betas).

Using the CAPM model and the following assumptions, we can compute the expected return of a stock in this CAPM example: if the risk-free rate is 5%, the beta (risk measure) of the stock is 3 and the expected market return over the period is 10%, the stock is expected to return 12% (5%+3(10%-5%)).

Required rate of return for stock A = Rf+A*(Rm-Rf) = 4%+1.25*(12%-4%) = 14%

Required rate of return for stock B = Rf+B*(Rm-Rf) = 4%+(-1.75)*(12%-4%) = -10%

Required rate of return for stock C = Rf+C*(Rm-Rf) = 4%+1.00*(12%-4%) = 12%

Required rate of return for stock D = Rf+D*(Rm-Rf) = 4%+0.75*(12%-4%) = 10%

So, then

PORTFOLIO'S required rate of return = wA*A + wB*B + wC*C + wD*D

= (0.25*14%) + (0.25*-10%) + (0.25*12%) + (0.25*10%)

= 3.50% + (-)2.50% + 3.00% + 2.50%

=> 6.50%

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