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发表于 201242 18:00
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Sandy Wilson is a research analyst for WWW Equities Investments. She has just finished collecting the information on Table 1 to answer questions posed by her supervisor, Jackie Lewis. For example, using the Capital Market Line (CML), Lewis wants to know the market price of risk. Also, given all the attention paid to index funds in recent years, Lewis asked Wilson to see if any one of the securities would prove a better investment than the S&P 500. If not, can she compose a portfolio from stocks A, B, and C that is more efficient than the S&P 500?
Lewis wants Wilson to explore whether the results on Table 1 are congruent with the Capital Asset Pricing Model (CAPM). Using a regression analysis where the S&P 500 represents the market portfolio, she computes the beta of Stock A, and finds that it equals one. Using this, she will derive the betas of the other stocks and compare them to betas estimated with other techniques. As she performs her calculations, she reviews reasons why her results might not be congruent with the CAPM. Lewis asserts that the S&P 500 may not be a good proxy for “the market portfolio” needed for CAPM calculations. Table 1
Expected Return and Risk for Selected Investments  Investment  Expected Return  Standard Deviation 
Stock A  12%  30% 
Stock B  15%  35% 
Stock C  11%  40% 
S&P 500  12%  22% 
Treasury Bills  3%  0% 
Correlation Coefficient for Stocks A and B equals 0.4.
Correlation Coefficient for Stocks A and C equals 0.5.
Correlation Coefficient for Stocks B and C equals 0.1. 
Assuming that the S&P 500 is the market portfolio and her estimates are accurate, what is the price of risk based on the slope of the Capital Market Line (CML)?
The market price of risk, or return per unit of standard deviation risk, is determined as follows: (0.12 − 0.03) / 0.22 = (0.09 / 0.22) = 0.409. (Study Session 18, LOS 60.d)
What is the expected return and standard deviation of a portfolio that consists of 40% of stock A and 60% of stock B? A)
 Expected Return: 13.8%, Standard Deviation: 29.5%. 
 B)
 Expected Return: 13.8%, Standard Deviation: 28.0%. 
 C)
 Expected Return: 13.8%, Standard Deviation: 33.0%. 

E(RP) = 0.4(0.12) + 0.6(0.15) = 0.048 + 0.09 = 0.138 or 13.8%The portfolio standard deviation is:
[(0.4)2(0.3)2 + (0.6)2(0.35)2 + 2(0.4)(0.6)(0.3)(0.35)(0.4)]0.5 = [0.0144 + 0.0441 + 0.02016]0.5 = 0.2805
(Study Session 18, LOS 60.a)
Wilson uses the computed beta of stock A, the covariance of stock A and B, and their standard deviations to compute stock B’s beta. Given stock B’s expected return, the results are: A)
 not congruent with the CAPM, which does not support Lewis’ assertion concerning the S&P 500 as a proxy for the market. 
 B)
 congruent with the CAPM, which does not support Lewis’ assertion concerning the S&P 500 as a proxy for the market. 
 C)
 not congruent with the CAPM, which supports Lewis’ assertion concerning the S&P 500 as a proxy for the market. 

The provided standard deviations and covariance and the beta of stock A can be entered into the following relationship:
covariance(A,B)=(beta of A) × (beta of B) × (Variance of market) gives us
(0.3 × 0.35 × 0.40) = 0.042 = 1 × (beta of B) × (0.22 × 0.22)
beta of B = 0.042 / 0.0484 = 0.868.
expected return of B = risk free rate + (beta of B) × (Market risk premium),
expected return of B = 0.03 + (0.868) × (0.12 − 0.03) = 0.108 < 0.15, which is the expected return she computed from her analysis. One explanation for this is that the S&P 500 is not a good proxy for the market portfolio. (Study Session 18, LOS 60.a,g)
Based upon the given information, can Wilson compose a portfolio with any one of the three stocks and Treasury bills that is more efficient than the S&P 500? A)
 No, the S&P 500 is more efficient than any of the individual stocks. 
  
To investigate this, Wilson can first rule out stocks A and C. Both of them have an expected return that is less than or equal to the S&P 500, but their standard deviations are higher. Wilson must perform some calculations to see if stock B is more efficient than the S&P 500. Wilson would first determine the portfolio weights that can make the expected return of the stock B and Tbill portfolio equal to the S&P 500 portfolio. By setting up 0.12 = w × 0.15 + (1 − w) × 0.03 and solving for w, Wilson finds that a (0.75 / 0.25) stock B/Tbill portfolio has the same expected return of 0.12. The standard deviation of that portfolio is (0.75 × 35%) = 26.25% > 24% which is the standard deviation of the S&P 500. Thus, the portfolio using Stock B and Treasury bills is not more efficient than the S&P 500. (Study Session 18, LOS 60.b)
With regard to the capital allocation line (CAL), moving along the CAL above the point of the tangency portfolio represents: A)
 borrowing at the riskfree rate to be invested in more than 100% of the tangency portfolio. 
 B)
 buying Tbills to reduce risk yet still maximize efficiency by being on the CAL. 
 C)
 increasing risk exposure by being above the efficient frontier. 

Moving along the CAL above the tangency portfolio represents borrowing at the risk free rate (shorting Tbills) to invest in more than your original capital in the tangency portfolio. The CAL becomes the efficient frontier when the risk free asset is available to invest in. (Study Session 18, LOS 60.d)
Which of the following is least likely an assumption of the Capital Asset Pricing Model (CAPM)? A)
 Capital markets are perfectly competitive and all assets are marketable. 
 B)
 The distribution of investors' forecasts of a given asset’s return is normal. 
 C)
 Investors can borrow and lend at the riskfree rate. 

The CAPM assumes that investors have the same forecast of a given asset’s return. Thus, according to the required assumption, the distribution will not be normal because the variance of the forecasts is zero. (Study Session 18, LOS 60.e) 
