Question 1

Testing the CAPM is difficult,as empirical tests have to rely on __________ data,whereas the CAPM is an __________ model.

A) ex-ante; ex-ante
B) ex-ante; ex-post
C) ex-post; ex-ante
D) ex-post; ex-post

Accepted Answer

One problem with testing the CAPM is the requirement that an ex-ante model be tested using ex-post information.The CAPM is ex-ante in the sense that it assumes investors price assets according to their beliefs about future returns.The tests are ex-post in the sense that they rely on historical data.The assumption generally made in testing is that past information will reflect expectations given a sufficiently long time period.

Question 2

An asset has a standard deviation of 15% and a correlation with the market portfolio of 0.46.If the market has a standard deviation of 25%,what is the beta of the asset?

A) $ 0.25 $
B) $ 0.31 $
C) $ 0.27 $
D) $ 0.28 $

Accepted Answer

Using equation 8.2,the beta of an asset is calculated as the covariance of the asset divided by the market variance.However,the equation can also be rewritten as follows;F1F1F1S1F1F1F10_i = F1F1F1S1F1F1F10_imF1F1F1S1F1F1F10_i/F1F1F1S1F1F1F10_m.Given that F1F1F1S1F1F1F10_im= 0.46,F1F1F1S1F1F1F10_i= 0.15 and F1F1F1S1F1F1F10_m= 0.25,then the beta of the asset is equal to 0.28.

Question 3

Assume the CAPM is the correct asset pricing model,and the risk-free rate of return is 6% and the market portfolio has an expected return and a standard deviation of 16% and 0.10%,respectively.An investor has a portfolio consisting of asset A,which has a beta of 1.6,and asset B,which has a beta of 0.6.If the investor wishes to earn a return identical to that of the market portfolio,what weight should the investor place in assets A and B?

A) $ 33 \% $ in asset $ \mathrm{A} $ and $ 67 \% $ in asset $ \mathrm{B} $
B) $ 40 \% $ in asset $ A $ and $ 60 \% $ in asset $ B $
C) $ 50 \% $ in asset $ A $ and $ 50 \% $ in asset $ B $
D) $ 60 \% $ in asset A and $ 40 \% $ in asset $ B $

Accepted Answer

To earn a return equal to the market portfolio,the portfolio must have the same risk as the market portfolio.In terms of the CAPM,that means the beta of the portfolio must be equal to 1.Using equation 8.4,and defining the weight in asset A as w_A,we know 1 = w_A(1.6)+ (1 - w_A)(0.6),which can be solved to obtain w_A = 0.40.Hence,w_B = 0.6.

Question 4

Assume the CAPM is the correct asset pricing model,the risk-free rate of return is 6%,and the market portfolio has an expected return and a standard deviation of 16% and 0.10%,respectively.An investor has a portfolio consisting of asset A,which has a beta of 0.6,and asset B,which has a beta of 0.8.If the investor wishes to earn a return identical to that of the market portfolio,what weight should the investor place in assets A and B?

A) $ -200 \% $ in asset $ A $ and $ 300 \% $ in asset $ B $
B) $ -100 \% $ in asset $ A $ and $ 200 \% $ in asset $ B $
C) $ 20 \% $ in asset A and $ 80 \% $ in asset B
D) $ 40 \% $ in asset $ A $ and $ 60 \% $ in asset B

Accepted Answer

To earn a return equal to the market portfolio,the portfolio must have the same risk as the market portfolio.In terms of the CAPM,that means the beta of the portfolio must be equal to 1.Using equation 8.4,and defining the weight in asset A as w_A,we know 1 = w_A(0.6)+ (1 - w_A)(0.8),which can be solved to obtain w_A = -1 or -100%,and therefore w_B= 2 or 200%.

Question 5

Assume the CAPM is the correct asset pricing model.An asset has a standard deviation of 30% and the market has a standard deviation of 20%.What would the correlation of the asset with the market need to be if the asset were to have the same expected return as the risk-free asset?

A) $ -0.200 $
B) $ 0.000 $
C) $ 0.200 $
D) $ 0.300 $

Accepted Answer

According to the CAPM,the risk of an asset is measured by beta,where the beta of the market is 1.Similarly,the beta of the risk-free asset must be zero (by definition it must have zero risk,and hence zero beta).Therefore,if an asset is to have the same return as that of the risk-free,then it must also have a beta of 0.Using equation 8.2,page 240,the beta of an asset is calculated as follows: F1F1F1S1F1F1F10_i = F1F1F1S1F1F1F10_imF1F1F1S1F1F1F10_i/F1F1F1S1F1F1F10_m.Given that F1F1F1S1F1F1F10_i= 0.30 and F1F1F1S1F1F1F10_m= 0.20,and F1F1F1S1F1F1F10_i = 1,then solving for F1F1F1S1F1F1F10_im gives a required correlation of 0.000.Intuitively this makes sense,as the risk-free asset should be constant regardless of the state of the world,and hence uncorrelated with the risky asset.

Question 6

Expected returns are also called:

A) ex-post returns
B) ex-ante returns
C) cost of capital
D) required rate of return

Accepted Answer

Ex-ante returns are expected returns,whereas ex-post returns are realised returns.The CAPM is an ex-ante model,and it provides estimates of expected returns adjusted for risk.Thus,any application of the CAPM will require an estimate of the ex-ante or expected risk premium.

Question 7

Assume the CAPM is the correct asset pricing model,the risk-free rate of return is 6%,and the market portfolio has an expected return and a standard deviation of 16% and 0.10%,respectively.An investor has a portfolio consisting of asset A,which has a beta of 1.6,and asset B,which has a beta of 0.6.If the investor wishes to earn a return identical to that of the risk-free asset,what weight should the investor place in assets A and B?

A) $ -60 \% $ in asset $ \mathrm{A} $ and $ 160 \% $ in asset $ \mathrm{B} $
B) $ 0 \% $ in asset $ A $ and $ 100 \% $ in asset $ B $
C) $ 20 \% $ in asset $ A $ and $ 800 \% $ in asset $ B $
D) $ 60 \% $ in asset A and $ 40 \% $ in asset B

Accepted Answer

To earn a return equal to the market portfolio,the portfolio must have the same risk as the risk-free rate ,which can be solved to obtain w_A = -0.6.Hence,w_B = 1.6.

Question 8

Which of the following is a testable proposition in empirical regression tests of the CAPM of average excess returns against beta?

A) The intercept is zero.
B) The beta coefficient is the market risk premium.
C) The market risk premium is greater than the risk-free rate
D) all of the aboye

Accepted Answer

The testable propositions of the CAPM are that the intercept is zero,the beta is the linear,and is equal to the market risk premium,and that over longer periods the market risk premium is greater than the risk-free rate.Hence,the only statement which is not a testable proposition is 'The relationship between beta and return is non-linear'.

Question 9

If the distribution of returns is non-normal and positively skewed,the investor has a greater probability of earning __________ returns rather than __________ returns.

A) extreme positive; extreme negative
B) extreme negative; extreme positive
C) none of theses choices

Accepted Answer

As investors prefer positive returns to negative returns,a positively skewed return distribution would be favoured over a symmetric distribution or a negatively skewed distribution.Where the distribution is positively skewed,the investor has a greater probability of earning extreme positive returns than of earning extreme negative returns.

Question 10

The SML is valid for _______________,and the CML is valid for ______________.
A)only individual assets;well-diversified portfolios only
B)only well-diversified portfolios;only individual assets
C)both well-diversified portfolios and individual assets;both well-diversified portfolios and individual assets
D)both well-diversified portfolios and individual assets;well-diversified portfolios only

Accepted Answer

The SML is based on the principle that a security's expected return is linearly related to its systematic risk (beta). This relationship holds true for both individual assets and well-diversified portfolios. On the other hand, the CML is based on the concept of efficient portfolios and assumes that all investors hold well-diversified portfolios. Therefore, it is only valid for well-diversified portfolios.

Question 11

An asset has a standard deviation of 30% and a correlation with the market portfolio of 0.60.If the market has a standard deviation of 30%,how much lower is the beta of the asset relative to the market?

A) $ 0.05 $
B) $ 0.10 $
C) $ 0.18 $
D) $ 0.40 $

Accepted Answer

Using equation 8.2,the beta of an asset is calculated as the covariance of the asset divided by the market variance.However,the equation can also be rewritten as follows: F1F1F1S1F1F1F10_i =F1F1F1S1F1F1F10_imF1F1F1S1F1F1F10_i/F1F1F1S1F1F1F10_m.Given that F1F1F1S1F1F1F10_im= 0.60,F1F1F1S1F1F1F10_i= 0.30 and F1F1F1S1F1F1F10_m= 0.30,then the beta of the asset is equal to 0.60.Therefore,since the market has a beta of 1,the asset's beta is 0.40 lower than the beta of the market.

Question 12

Assume the CAPM is the correct asset pricing model,the risk-free rate of return is 6%,and the market portfolio has an expected return and a standard deviation of 16% and 0.10%,respectively.An investor has a portfolio consisting of asset A,which has a beta of 0.75,and asset B,which has a beta of 1.25.If the investor wishes to earn a return identical to that of the risk-free asset,what weight should the investor place in assets A and B?

A) $ -60 \% $ in asset $ \mathrm{A} $ and $ 160 \% $ in asset $ \mathrm{B} $
B) $ 0 \% $ in asset $ A $ and $ 100 \% $ in asset $ B $
C) $ 200 \% $ in asset $ A $ and $ -100 \% $ in asset $ B $
D) $ 250 \% $ in asset $ A $ and $ -150 \% $ in asset $ B $

Accepted Answer

To earn a return equal to the market portfolio,the portfolio must have the same risk as the risk-free rate ,which can be solved to obtain w_A = 2.5 or 250%.Hence,w_B = -1.5 or -150%.

Question 13

The issue that realised returns only relate to actual returns in the long-term is relevant to use of the CAPM because:

A) beta is often measured with error
B) of issues raised in Roll's critique
C) no risk-free asset exists
D) the CAPM is an ex-ante model

Accepted Answer

Ex-ante returns are expected returns,whereas ex-post returns are realised returns.The CAPM is an ex-ante model,and it provides estimates of expected returns adjusted for risk.Thus,any application of the CAPM will require an estimate of the ex-ante or expected risk premium.However,in practice,the ex-ante value is often estimated using ex-post returns,or realised returns.

Question 14

Where thin trading is present in a market index used for the approximation of a beta,the beta will be __________ for a thinly traded company,and __________ for a frequently traded stock.

A) understated; overstated
B) overstated; understated
C) understated; understated
D) overstated; overstated

Accepted Answer

Thin trading has an important impact on beta estimation,as it affects both equity return estimation and market return estimation.In general,where thin trading is present,beta estimates for thinly traded stocks are underestimated (downward biased)and the beta estimates for heavily traded stocks are overstated (upward biased).

Question 15

Beta stability tends to:

A) increase with an increase in portfolio size
B) decrease with an increase in market size
C) decrease over time
D) apply better the smaller the company

Accepted Answer

One important result is the finding that although beta estimates for individual shares or small portfolios are not particularly stable over time,beta stability tends to increase with increases in portfolio size (Sharpe and Cooper 1974;Brooks,Faff and Lee 1995).

Question 16

In empirical tests of the CAPM in excess return form,the intercept in a regression of average returns against beta should be:

A) Zero
B) one
C) the risk-free rate
D) none of the above

Accepted Answer

The intercept should be zero.That is,the CAPM should completely explain the expected returns of the portfolio.

Question 17

Assume the CAPM is the correct asset pricing model.An asset has a standard deviation of 40% and the market has a standard deviation of 15%.What would the correlation of the asset with the market need to be if the asset were to have the same expected return as the market?

A) $ 0.150 $
B) $ 0.375 $
C) $ 0.600 $
D) $ 0.667 $

Accepted Answer

According to the CAPM,the risk of an asset is measured by beta,where the beta of the market is 1.Therefore,if an asset is to have the same beta as that of the market,then it must also have a beta of 1.Using equation 8.2,page 240,the beta of an asset is the calculated as follows: F1F1F1S1F1F1F10_i = F1F1F1S1F1F1F10_imF1F1F1S1F1F1F10_i/F1F1F1S1F1F1F10_m.Given that F1F1F1S1F1F1F10_i= 0.40 and F1F1F1S1F1F1F10_m= 0.15,and F1F1F1S1F1F1F10_i = 1,then solving for F1F1F1S1F1F1F10_im gives a required correlation of 0.375.

Question 18

Assume the CAPM is the correct asset pricing model,and the risk-free rate of return is 6% and the market has an expected return and a standard deviation of 16% and 0.10%,respectively.An investor has a portfolio consisting of equal amounts in assets A and B.Asset A has an expected return of 8%.If the portfolio has an expected return of 10%,what is the covariance between asset B and the market portfolio?

A) $ 2.000 $
B) $ 3.000 $
C) $ 6.000 $
D)$ 7.000 $

Accepted Answer

Given that the portfolio has a 10% return and is composed of 50% in asset A and 50% in asset B,then we know that (0.5)(8%)+ (0.5)E(R_b)= 10%,where E(R_b)is the expected return of asset B.Solving this equation gives a value for E(R_b)of 12%.We can now use the CAPM to determine what beta is required to give an asset an expected return of 12%;that is,0.12 = 0.06 + F1F1F1S1F1F1F10(0.16 - 0.06),which can be solved to obtain a F1F1F1S1F1F1F10 value of 0.6.Using equation 8.2,page 240,we know that F1F1F1S1F1F1F10_i = cov_im/F1F1F1S1F1F1F10_m,or 0.6 = cov_im/0.10,which can be solved to obtain a cov_im value of 6.00.

Question 19

In his famous critique of the CAPM,Roll argued that the CAPM ______________.
A)is not testable because the true market portfolio can never be observed
B)is of limited use because systematic risk can never be entirely eliminated
C)should be replaced by the APT
D)should be replaced by the Fama-French three-factor model

Accepted Answer

The major contribution of Roll's critique is the suggestion that the only test of the CAPM is a test of the efficiency of the market portfolio.

Question 20

An asset has a standard deviation of 5% and a correlation with the market portfolio of 0.70.If the market has a standard deviation of 28%,what is the beta of the asset?

A) $ 0.13 $
B) $ 0.31 $
C) $ 0.60 $
D) $ 0.68 $

Accepted Answer

Using equation 8.2,the beta of an asset is calculated as the covariance of the asset divided by the market variance.However,the equation can also be rewritten as follows: F1F1F1S1F1F1F10_i = F1F1F1S1F1F1F10_imF1F1F1S1F1F1F10_i/F1F1F1S1F1F1F10_m.Given that F1F1F1S1F1F1F10_im= 0.70,F1F1F1S1F1F1F10_i= 0.05 and F1F1F1S1F1F1F10_m= 0.28,then the beta of the asset is equal to 0.13.

Quiz 8: Risky Asset Pricing Models and the Capm

Testing the CAPM is difficult,as empirical tests have to rely on data,whereas the CAPM is an model.