Assignment
I. The Capital Asset Pricing Model
1. Write down the formula for the Capital Asset Pricing Model (CAPM) and explain every variable in the model.
2. The betas for each of the assets are given in the table below. The risk-free rate of return is 4% and the market rate of return is 12% (or the market risk premium is 8%). Please fill out the blanks in the table. Note that the betas for the market portfolio and the riskfree security are intentionally left blank.
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Security
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Beta
(β)
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Expected Return, based on the Capital Asset Pricing Model (CAPM)
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Reward-to-risk Ratio
(R - Rf )/β
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Stock A
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0.50
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Stock B
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0.75
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Stock C
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1.50
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Stock D
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2.0
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Market Portfolio
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Risk-free asset
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3. Present draw the Security Market Line (SML) and mark the six securities in the above table.
4. If you believe that the return on Security D is 22%, should you buy the security or not? Please explain.
II. Portfolio Risk and Return
Consider a portfolio that is composed of the following two securities
Security A Security B
Expected return 10% 12%
Standard deviation 8% 14%
Correlation coefficient, ρ = -0.5
1. Please fill out the blanks in the table (you can use the Excel for the calculations):
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Weight of Security A
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Weight of Security B
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Portfolio Return
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Portfolio Risk
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0%
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10%
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20%
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30%
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40%
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50%
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60%
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70%
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80%
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90%
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100%
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2. Present the results in the above table on a return-standard deviation diagram.
3. Please explain the benefit of diversification, using the above diagram to illustrate.
III. Bond Valuation General Motors (GM) has just issued a new bond with a 10-year maturity, 10% coupon rate, and $1,000 face value. The GM bond carries a credit rating of AA by the Standard & Poor's. Assume that bond investors' required rate of return is 12%. Please answer the following questions:
1. Please explain the purposes of bond credit ratings.
2. Please calculate the price of the bond, assuming annual coupon payments.
3.Suppose Standard and Poor's downgrades GM's credit rating from AA to BBB, how will this change affect the price of the bond? Please explain.
4. Suppose the Federal Reserve suddenly cut interest rates. What is the immediate impact on the price of the bond? Please explain.
IV. Bond Duration
Consider a five-year bond with a 8 percent coupon paid annually. The yield of the bond is currently 9%.
1. Please calculate the duration of the bond.
2. Suppose the yield increases by 50 basis points from 9% to 9.50%. What is the impact on bond price? Please calculate the percentage change in bond price, using the duration concept.