You own a portfolio that has $8,000 invested Stock A and $6000 invested in each

Question

You own a portfolio that has $8,000 invested Stock A and $6000 invested in each of Stocks B and C (for a portfolio total of $20,000). The Probabilities of the State of Economy and stocks' returns in each state as well as stock betas are given in table 13.1 below:

a)Compute (show work) the expected return on each stock and the portfolio.

b) The yield on a 10-year Treasury bond the expected return on the market is also provided below.   Given the betas for each stock and the portfolio:

(i) Use the CAPM model (the SML approach) to compute expected return for each stock and the portfolio.

(ii) Compare your results to those in part (a). Are they similar or significantly different? Comment.

Table 13.1 State of the Probability of Return on Stock   Economy State of Economy A B C   Boom 0.2 0.36 0.46 0.26   Good 0.55 0.2 0.22 0.11   Poor 0.2 -0.18 -0.2 -0.15   Bust 0.05 -0.4 -0.7 -0.3 Stock Betas 1.5 1.6 0.8 Yield on 10-Year treasury note 5% Expected return on the market 9%

Explanation / Answer

Ans: Expected Retuns on Stocks

Expected Returns for Stock A

Expected Retunrs for Stock B

Expected Retuns for Stock C

2.025

Expected Return on Portfolio = Expected Retunrs on StockA + Expected Retunrs on StockB +Expected Retunrs on StockC

= 5.04+4.14+2.025 = 11.025

Using CAPM model the Expected Retunrs on stocks are =

Rm + B(Rm-Rf) ; Rm is Expected return on the market ; Rf is Yield on 10-Year treasury note & B is Beta of each stock

Stock A=

5+1.5(9-5.04) = 10.94%

Stock B =

5 + 1.6(9-4.14) = 12.76%

Stock C =

5 + 0.8(9-2.025) = 10.58%

Expected Returns for Portfolio is 10.94 + 12.76 + 10.58 = 34.28%

The results with that of the (a) is significantly different. Reason is becasue, while using CAPM model the Risk free rate of retunrs & the Beta is also taken care of the impact of which is substantial depending upon the volatality of the stocks.

Stock A 8000 / 20000 40% Economy Proportion Return on stock Gross Probability Expected Rate of Return Boom 40 0.36 14.4 0.2 2.88 Good 40 0.2 8 0.55 4.4 Poor 40 -0.18 -7.2 0.2 -1.44 Bust 40 -0.4 -16 0.05 -0.8 5.04

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