Question

2. APT For this question, you want to round up to two digits for the final answer. If the final answer is in percentage form, round up to the nearest basis point. Suppose all assets follow a two-factor model, where factor 1 is the market, and factor 2 is inflation. Risk premium on the market is $E[R^M] = 8\%$, while risk premium on inflation is $E[R^\pi] = -3\%$. (a) Well-diversified portfolio A has betas $\beta_{A,M} = 0.6$, $\beta_{A,\pi} = 0.2$. What is its risk premium, $E[R^A]$, under APT? (b) Well-diversified portfolio B has betas $\beta_{B,M} = 1$, $\beta_{B,\pi} = 0.2$. Its expected return is $E[r^B] = 8\%$. What must risk free rate, $r^f$, be, under APT? (c) Assuming that risk-free rate is given by the value in part (b). Well-diversified portfolio C has betas $\beta_{C,M} = 0.5$, $\beta_{C,\pi} = 1.5$. Its expected return is $E[r^C] = 2\%$. Is asset C mispriced? If so, what is its alpha with respect to the two factors? (d) Suppose an investor believes that CAPM holds, with $R^M$ specified in this question as the market. Is asset B in part (b) mispriced in the eyes of this investor? If so, what is its alpha?

          2. APT
For this question, you want to round up to two digits for the final answer. If the final answer is in
percentage form, round up to the nearest basis point.
Suppose all assets follow a two-factor model, where factor 1 is the market, and factor 2 is inflation.
Risk premium on the market is $E[R^M] = 8\%$, while risk premium on inflation is $E[R^\pi] = -3\%$.
(a) Well-diversified portfolio A has betas $\beta_{A,M} = 0.6$, $\beta_{A,\pi} = 0.2$. What is its risk premium, $E[R^A]$,
under APT?
(b) Well-diversified portfolio B has betas $\beta_{B,M} = 1$, $\beta_{B,\pi} = 0.2$. Its expected return is $E[r^B] = 8\%$.
What must risk free rate, $r^f$, be, under APT?
(c) Assuming that risk-free rate is given by the value in part (b). Well-diversified portfolio C has
betas $\beta_{C,M} = 0.5$, $\beta_{C,\pi} = 1.5$. Its expected return is $E[r^C] = 2\%$. Is asset C mispriced? If so,
what is its alpha with respect to the two factors?
(d) Suppose an investor believes that CAPM holds, with $R^M$ specified in this question as the market.
Is asset B in part (b) mispriced in the eyes of this investor? If so, what is its alpha?

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2. APT
For this question, you want to round up to two digits for the final answer. If the final answer is in
percentage form, round up to the nearest basis point.
Suppose all assets follow a two-factor model, where factor 1 is the market, and factor 2 is inflation.
Risk premium on the market is E[R^M] = 8%, while risk premium on inflation is E[R^π] = -3%.
(a) Well-diversified portfolio A has betas βA,M = 0.6, βA,π = 0.2. What is its risk premium, E[R^A],
under APT?
(b) Well-diversified portfolio B has betas βB,M = 1, βB,π = 0.2. Its expected return is E[r^B] = 8%.
What must risk free rate, r^f, be, under APT?
(c) Assuming that risk-free rate is given by the value in part (b). Well-diversified portfolio C has
betas βC,M = 0.5, βC,π = 1.5. Its expected return is E[r^C] = 2%. Is asset C mispriced? If so,
what is its alpha with respect to the two factors?
(d) Suppose an investor believes that CAPM holds, with R^M specified in this question as the market.
Is asset B in part (b) mispriced in the eyes of this investor? If so, what is its alpha?

Added by Anthony J.

Horngren’s Cost Accounting

Srikant M. Datar, Madhav V. Rajan 16th Edition

Instant Answer

Solved by Expert Sri K

06/13/2023

Step 1

6$, $\beta_{A,\pi} = 0.2$, $E[R^M] = 8\% = 0.08$, and $E[R^\pi] = -3\% = -0.03$. We need to find $r^f$ first. Show more…

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2. APT For this question, you want to round up to two digits for the final answer. If the final answer is in percentage form, round up to the nearest basis point. Suppose all assets follow a two-factor model, where factor 1 is the market, and factor 2 is inflation. Risk premium on the market is $E[R^M] = 8\%$, while risk premium on inflation is $E[R^\pi] = -3\%$. (a) Well-diversified portfolio A has betas $\beta_{A,M} = 0.6$, $\beta_{A,\pi} = 0.2$. What is its risk premium, $E[R^A]$, under APT? (b) Well-diversified portfolio B has betas $\beta_{B,M} = 1$, $\beta_{B,\pi} = 0.2$. Its expected return is $E[r^B] = 8\%$. What must risk free rate, $r^f$, be, under APT? (c) Assuming that risk-free rate is given by the value in part (b). Well-diversified portfolio C has betas $\beta_{C,M} = 0.5$, $\beta_{C,\pi} = 1.5$. Its expected return is $E[r^C] = 2\%$. Is asset C mispriced? If so, what is its alpha with respect to the two factors? (d) Suppose an investor believes that CAPM holds, with $R^M$ specified in this question as the market. Is asset B in part (b) mispriced in the eyes of this investor? If so, what is its alpha?

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Transcript

00:01 Hello, let's look at the question.

00:02 In the definition, eri is the expected return on a security, our lambda0 is the expected return on asset with zero systematic risk, our lambdaj is the risk premium related to the jth factor, our betaij is the pricing relationship between risk and premium.

01:01 Thus, the expression conveys the return on a security can be estimated or model using the linear relationship between the security expected return and the number of macroeconomic factors that affect the security risk, where sensitivity to the changes in each factor represented by beta.

01:19 This was the answer for the first term where we had been given eri is equals to lambda0 plus bij lambda1 plus bij lambda2 up to bin lambda n.

01:38 We have defined all terms for part a.

01:41 Now for part b, we will see in the context of apt, our risk -free portfolio will be one such asset or portfolio whose return is independent of macroeconomic parameters or factors.

02:36 One such portfolio will be non -sensitive to any factors apt model, thus it will have all the betas as zero.

02:44 Hence, the expected return for risk -free portfolio of using apt expression will be lambda0.

02:53 Now for c part, we will see when our lambda0 is 0 .02, using the apt equation, we can straight away get to the two equations for p1 will have 0 .18 is equals to 0 .02 plus 0 .2 lambda1 plus 0 .7 lambda2 or 0 .2 lambda1 plus 0 .7 lambda2 is equals to 0 .16 as equation a and our p2 will be 0 .05 equals to 0 .02 plus 0 .1 lambda1 plus 0 .3 lambda2 or 0 .1 lambda1 plus 0 .3 lambda2 is equals to 0 .03 as our equation b.

03:44 Equation a minus 2 multiplied by equation b results into 0 .1 lambda2 is equals to 0 .10...

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