Question 1

The international capital asset pricing model (ICAPM)assumes:

Accepted Answer

The international capital asset pricing model (ICAPM)prices assets as if there are no national or political boundaries.This model assumes a completely integrated global financial market in which there are no barriers to capital flows and no investment restrictions.

Question 2

Marion and Birkan (i.e.M and B)are aspiring young investment students.During the lecture on asset pricing,both were inspired by the beauty of the models presented.M found the CAPM model overly simplistic and favoured the Fama-French model,while B disagreed,and instead believed that the CAPM,being more theoretical,was the better model.As part of a class assignment,they were each given the tabled information regarding an asset and asked to recommend a trading strategy based upon their preferred asset pricing model.If the asset is observed in the market trading with an expected return of 28%,and the risk-free rate is 8%,what are the relative trading strategy recommendations of each investor?

Accepted Answer

Birkan (B)favours the CAPM: The CAPM (see the case study CCAPM Estimate for BHP Billiton)can be expressed as E(R_i)= R_f + F1F1F1S1F1F1F10_i[(R_m)- R_f],and hence the expected return for the asset can be calculated as E(R)= 0.08 + 1.75(0.12)= 0.29 or 29.0%.If the asset were observed in the market to be trading with a return of 28%,then the market is out of equilibrium.Therefore,B's recommendation,based on the CAPM,is that the asset's return is too low,and hence the asset should be short-sold.

Question 3

If the All-Ordinaries has a beta with respect to the world market of 1.2,and the world market return and risk-free rate are 12% and 6% respectively,then the expected return predicted by the ICAPM for Australia is:

Accepted Answer

Using equation 9.10,we can compute the expected return for Australia as follows,0.06 + 1.2 (0.12 - 0.06)= 0.132 or 13.2%.

Question 4

Using Solnik's (1974)ICAPM,what is the expected return on an Australian security with a world market beta of 0.78 if the Australian risk-free rate is 5.37%,the world risk-free rate is 1.7% and the expected return on the world market portfolio is 13.19%?

Accepted Answer

Using equation 9.10,we can calculate the expected return on an Australian security in the following way: E(R_i)= 0.0537 + 0.78(0.1319 - 0.017)= 0.1433 or 14.33%.

Question 5

Which of the following is NOT a factor used by Chen,Roll and Ross (1986)in their empirical test of the APT?

Accepted Answer

Chen, Roll, and Ross (1986) in their empirical test of the Arbitrage Pricing Theory (APT) did not include oil prices as one of the factors. They focused on factors like industrial production, expected inflation, and unanticipated changes in the term structure, among others, to explain asset returns.

Question 6

$\begin{array}{|l|l|l|l|}
\hline \text { Factor } & {\left[\mathrm{E}\left(\mathrm{R}_{\mathrm{M}}\right)-\mathrm{R}_{\mathrm{F}}\right)} & \mathrm{SMB} & \mathrm{HML} \
\hline \text { Sensitivity } & \mathrm{b}_{\mathrm{i}}=1.75 & \mathrm{~s}_{\mathrm{i}}=-0.80 & \mathrm{~h}_{\mathrm{i}}=0.60 \
\hline \text { Risk premium } & 18.5 \% & 5.25 \% & 0.50 \% \
\hline
\end{array}$
-Suppose the above asset is observed in the market trading with an expected return of 18%.What strategy would you suggest to profit from this situation,assuming the CAPM was the correct pricing model and the risk-free rate was 8%?

Accepted Answer

The CAPM (see the case study on page 277)can be expressed as E(R_i)= R_f + F1F1F1S1F1F1F10_i[(R_m)- R_f],and hence the expected return for the asset can be calculated as E(R)= 0.08 + 1.75(0.12)= 0.29 or 29.0%.If the asset was observed in the market to be trading with a return of 28%,then the market is out of equilibrium.The correct strategy would be to short-sell the asset,as it has a return lower than expected by the CAPM model.That is,the price of the asset is too high (i.e.the return is to low),and hence the investor can then profit from the expected future fall in price as the market moves back into equilibrium.

Question 7

$\begin{array}{|l|l|l|l|}
\hline \text { Factor } & {\left[\mathrm{E}\left(\mathrm{R}_{\mathrm{M}}\right)-\mathrm{R}_{\mathrm{F}}\right)} & \mathrm{SMB} & \mathrm{HML} \
\hline \text { Sensitivity } & \mathrm{b}_{\mathrm{i}}=0.60 & \mathrm{~s}_{\mathrm{i}}=-0.44 & \mathrm{~h}_{\mathrm{i}}=0.28 \
\hline \text { Risk premium } & 12.7 \% & -2.17 \% & 3.25 \% \
\hline
\end{array}$
-Consider the single factor APT.Portfolio A has a beta of 0.2 and an expected return of 13%.Portfolio B has a beta of 0.4 and an expected return of 15%.The risk-free rate of return is 10%.If you wanted to take advantage of an arbitrage opportunity,you should take a short position in portfolio __________ and a long position in portfolio _________.

Accepted Answer

$\frac{13-10}{.2}>\frac{15-10}{.4} \text { Short B; Buy } A$
$  \quad $$A$ $  \quad $$  \quad $$B$

Question 8

An arbitrage portfolio exists,including an asset A with a total market value of $60 000 and 100 other assets with a combined market value of $850 000.Assume that asset A is mispriced,with a pricing error of 17%,while the remainder of the assets are priced correctly according to the factor structure.What is the arbitrage portfolio pricing error?

Accepted Answer

Following example 9.5,the arbitrage pricing error can be found according to: (60000/910000)0.17 + (850000/910000)0.00 = 0.011 or 1.1%.

Question 9

The ICAPM has been extended to a two-factor version by Adler and Dumas (1983)that incorporates what additional type of risk?

Accepted Answer

Adler and Dumas (1983)provide a framework for the international pricing of securities incorporating the different consumption preferences of individuals across national markets.The model consists of two sources of risk.The first is the world market risk,akin to that in Solnik's model,while the second is for exchange rate risk.

Question 10

If the ICAPM beta is 0.8,and the world market return and risk-free rate are 12% and 5% respectively,then the expected return predicted by the ICAPM is:

Accepted Answer

Using equation 9.10,and the inputs provided,we can compute the expected return as follows: 0.05 + 0.8 (0.12 - 0.05)= 0.106 or 10.6%.

Question 11

Calculate the consumption beta for an asset with a standard deviation of 10%,where the variance of consumption growth is 10% and the covariance between the growth rate in consumption and the asset is 0.015.

Accepted Answer

The consumption beta is defined as the covariance of the asset with the growth rate of consumption divided by the variance of the growth rate in consumption.That is;0.015/(0.1)² = 0.015/0.01 = 1.50.

Question 12

A major difference between the application of the ICAPM compared with the domestic CAPM is:

Accepted Answer

A number of complications arise when attempting to model in an international context.First,no uniform risk-free rate exists for all markets.Second,the existence of exchange rates results in an additional risk for investors,the effect of which needs to be included in the model.Exchange rate risk means that investors in different countries will perceive the risk and return characteristics of foreign investments differently.

Question 13

$\begin{array}{|l|l|l|l|}
\hline \text { Factor } & {\left[\mathrm{E}\left(\mathrm{R}_{\mathrm{M}}\right)-\mathrm{R}_{\mathrm{F}}\right)} & \mathrm{SMB} & \mathrm{HML} \
\hline \text { Sensitivity } & \mathrm{b}_{\mathrm{i}}=0.60 & \mathrm{~s}_{\mathrm{i}}=-0.44 & \mathrm{~h}_{\mathrm{i}}=0.28 \
\hline \text { Risk premium } & 12.7 \% & -2.17 \% & 3.25 \% \
\hline
\end{array}$
-Assume the Fama-French model is the correct model to price assets.If an asset has the above sensitivities and the risk-free rate is 5%,what is the asset's expected return?

Accepted Answer

Using equation 9.8,which can be expressed as E(R_i)= R_f + F1F1F1S1F1F1F10_i[(R_m)- R_f] + s_iE(SMB)+ h_iE(HML),the expected return can be calculated as E(R)= 0.05 +0.60(0.127)- 0.44(-0.0217)+ 0.28(0.0325)= 0.1448 or 14.5%.

Question 14

An asset in the Australian market has a consumption beta of 0.5.If the variance of the asset is 0.024 and the variance of the growth rate in consumption is 0.035,what is the asset's covariance with the growth rate in consumption?

Accepted Answer

The consumption beta is defined as the covariance of the asset with the growth rate of consumption divided by the variance of the growth rate in consumption.In this case,we can solve for the covariance by multiplying the consumption beta (0.5)by the variance of the growth rate in consumption (0.035)to give an answer of 0.0175.

Question 15

Consider the multifactor APT with two factors.Portfolio A has a beta of .5 on factor 1 and a beta of 1.25 on factor 2.The risk premiums on the factor 1 and 2 portfolios are 1% and 7%,respectively.The risk-free rate of return is 7%.The expected return on portfolio A is __________ if no arbitrage opportunities exist.

Accepted Answer

Using the equation 9.4 the basic pricing relationship of the APT

Question 16

$\begin{array}{|l|l|l|l|}
\hline \text { Factor } & {\left[\mathrm{E}\left(\mathrm{R}_{\mathrm{M}}\right)-\mathrm{R}_{\mathrm{F}}\right)} & \mathrm{SMB} & \mathrm{HML} \
\hline \text { Sensitivity } & \mathrm{b}_{\mathrm{i}}=1.75 & \mathrm{~s}_{\mathrm{i}}=-0.80 & \mathrm{~h}_{\mathrm{i}}=0.60 \
\hline \text { Risk premium } & 18.5 \% & 5.25 \% & 0.50 \% \
\hline
\end{array}$
-Suppose the above asset is observed in the market trading with an expected return of 28%.What strategy would you suggest to profit from this situation,assuming the Fama-French model was the correct pricing model and the risk-free rate was 8%?

Accepted Answer

Using equation 9.8,which can be expressed as E(R_i)= R_f + F1F1F1S1F1F1F10_i[(R_m)- R_f] + s_iE(SMB)+ h_iE(HML),the expected return can be calculated as E(R)= 0.08 + 1.75(0.185)- 0.80(0.0525)+ 0.60(0.005)= 0.251 or 25.1%.If the asset is observed in the market to be trading with a return of 28%,then the market is out of equilibrium.The correct strategy would be to buy the asset,as it has a return that is higher than expected by the Fama-French model.That is,the price of the asset is too low (i.e.the return is too high),and hence the investor can then profit from the expected future rise in price as the market moves back into equilibrium.

Question 17

Which of the following is NOT a risk premium incorporated in the Fama and French (1992)three-factor model of expected returns?

Accepted Answer

Fama and French (1993,1996)take a different approach to that followed by Chen,Roll and Ross (1986).They use variables 'that have no special standing in asset-pricing theory [but that] show reliable power to explain the cross-section of average returns'.That is,they rely upon prior research,which has shown there are some variables that for whatever reason appear relevant.The variables chosen in the analysis include size and book-to-market value for equities and term premium and default premium for bonds.

Question 18

Using Solnik's (1974)ICAPM,what is the expected return on an Australian security with a world market beta of 1.2 if the Australian risk-free rate is 7%,the world risk-free rate is 3.5% and the expected return on the world market portfolio is 22%?

Accepted Answer

Using equation 9.10,the expected return from the ICAPM is E(R_i)= 0.07 + 1.2(0.22 - 0.035)= 0.292 or 29.2%.

Question 19

Considering the CAPM in an international context leads to further complications on top of those associated with the local CAPM.These include:

Accepted Answer

A number of complications arise when attempting to model in an international context.First,no uniform risk-free rate exists for all markets.Second,the existence of exchange rates results in an additional risk for investors,the effect of which needs to be included in the model.Exchange rate risk means that investors in different countries will perceive the risk and return characteristics of foreign investments differently.

Question 20

$\begin{array}{|l|l|l|l|}
\hline \text { Factor } & {\left[\mathrm{E}\left(\mathrm{R}_{\mathrm{M}}\right)-\mathrm{R}_{\mathrm{F}}\right)} & \mathrm{SMB} & \mathrm{HML} \
\hline \text { Sensitivity } & \mathrm{b}_{\mathrm{i}}=0.60 & \mathrm{~s}_{\mathrm{i}}=-0.44 & \mathrm{~h}_{\mathrm{i}}=0.28 \
\hline \text { Risk premium } & 12.7 \% & -2.17 \% & 3.25 \% \
\hline
\end{array}$
-An asset has the above sensitivity to the market portfolio and the risk-free rate is 6%.If an investor uses the CAPM model,but the Fama-French model is the correct model,by how much is the asset's expected return differ?

Accepted Answer

Using equation 9.8,which can be expressed as E(R_i)= R_f + F1F1F1S1F1F1F10_i[(R_m)- R_f] + s_iE(SMB)+ h_iE(HML),the expected return can be calculated as E(R)= 0.06 + 0.60(0.127)- 0.44(-0.0217)+ 0.28(0.0325)= 0.1448 or 14.5%.Hence,the Fama-French expected return is 14.5%.Using the CAPM (see the case study on page 283),which can be expressed as E(R_i)= R_f + F1F1F1S1F1F1F10_i[(R_m)- R_f],the expected return can be calculated as E(R)= 0.06 +0.60(0.127)= 0.136 or 13.6%.Therefore,the CAPM understates the true expected return by 0.145 - 0.136 = 0.009 or 0.9%.

Quiz 9: Alternative Risky Asset Pricing Models

The international capital asset pricing model (ICAPM) assumes:

If the All-Ordinaries has a beta with respect to the world market of 1.2,and the world market return and risk-free rate are 12% and 6% respectively,then the expected return predicted by the ICAPM for Australia is:

Using Solnik's (1974) ICAPM,what is the expected return on an Australian security with a world market beta of 0.78 if the Australian risk-free rate is 5.37%,the world risk-free rate is 1.7% and the expected return on the world market portfolio is 13.19%?

Which of the following is NOT a factor used by Chen,Roll and Ross (1986) in their empirical test of the APT?

The ICAPM has been extended to a two-factor version by Adler and Dumas (1983) that incorporates what additional type of risk?

If the ICAPM beta is 0.8,and the world market return and risk-free rate are 12% and 5% respectively,then the expected return predicted by the ICAPM is:

Calculate the consumption beta for an asset with a standard deviation of 10%,where the variance of consumption growth is 10% and the covariance between the growth rate in consumption and the asset is 0.015.

A major difference between the application of the ICAPM compared with the domestic CAPM is:

An asset in the Australian market has a consumption beta of 0.5.If the variance of the asset is 0.024 and the variance of the growth rate in consumption is 0.035,what is the asset's covariance with the growth rate in consumption?

Which of the following is NOT a risk premium incorporated in the Fama and French (1992) three-factor model of expected returns?

Using Solnik's (1974) ICAPM,what is the expected return on an Australian security with a world market beta of 1.2 if the Australian risk-free rate is 7%,the world risk-free rate is 3.5% and the expected return on the world market portfolio is 22%?

Considering the CAPM in an international context leads to further complications on top of those associated with the local CAPM.These include: