Question 1

Exhibit 8.3
Use the Information Below for the Following Problem(S)
 $$\begin{array} { c c c c } 
\text { Periad } & \begin{array} { c } 
\text { Return } \
\text { of Radtran } \
\text { (Percent) }
\end{array} & \begin{array} { c } 
\text { Praxy } \
\text { Epecific Index } \
\text { (Percent) }
\end{array} & \begin{array} { c } 
\text { True } \
\text { Ceneral Index } \
\text { (Percent) }
\end{array} \
\hline 1 & 10 & 12 & 15 \
2 & 12 & 10 & 13 \
3 & - 10 & - 8 & - 8 \
4 & - 4 & - 10 & 0
\end{array}$$
-Refer to Exhibit 8.3.The average true return is

Accepted Answer

R (True)= (15 + 13 - 8 + 0)/4 = 20/4 = 5%

Question 2

The variance of returns for a risky asset is 25%.The variance of the error term,Var(e),is 8%.What portion of the total risk of the asset,as measured by variance,is systematic?

Accepted Answer

8%/25% = 0.32.1 - 0.32 = 68% systematic.

Question 3

Exhibit 8.3
Use the Information Below for the Following Problem(S)
 $$\begin{array} { c c c c } 
\text { Periad } & \begin{array} { c } 
\text { Return } \
\text { of Radtran } \
\text { (Percent) }
\end{array} & \begin{array} { c } 
\text { Praxy } \
\text { Epecific Index } \
\text { (Percent) }
\end{array} & \begin{array} { c } 
\text { True } \
\text { Ceneral Index } \
\text { (Percent) }
\end{array} \
\hline 1 & 10 & 12 & 15 \
2 & 12 & 10 & 13 \
3 & - 10 & - 8 & - 8 \
4 & - 4 & - 10 & 0
\end{array}$$
-Refer to Exhibit 8.3.The average return for Radtron is

Accepted Answer

R (Proxy)= (12 + 10 - 8 - 10)/4 = 4/4 = 1%

Question 4

Assume that as a portfolio manager the beta of your portfolio is 1.3 and that your performance is exactly on target with the SML data under condition 1.If the true SML data is given by condition 2,how much does your performance differ from the true SML?
$\begin{array}{c}
\begin{array}{c}
(1)\
(2)
\end{array}
\begin{array}{l}
\mathrm{RFR}=.08 \
\mathrm{R}_{\mathrm{K}}=.07
\end{array}
\begin{array}{l}
\mathrm{R}_{\mathrm{m}}(\text { proxy })=0.11 \
\mathrm{R}_{\mathrm{m}}(\text { true })=0.14
\end{array}
\end{array}$

Accepted Answer

The expected return using condition 1 is $0.08 + 1.3(0.11 - 0.08) = 0.118$. Using condition 2, it is $0.07 + 1.3(0.14 - 0.07) = 0.161$. The difference is $0.161 - 0.118 = 0.043$ or 4.3% lower, which rounds to 4.2% lower.

Question 5

Consider an asset that has a beta of 1.5.The return on the risk-free asset is 6.5% and the expected return on the stock index is 15%.The estimated return on the asset is 20%.Calculate the alpha for the asset.

Accepted Answer

6.5 + 1.5(15 - 6.5)= 19.25%
alpha = 20 - 19.25 = 0.75%

Question 6

An investor wishes to construct a portfolio consisting of a 70% allocation to a stock index and a 30% allocation to a risk free asset.The return on the risk-free asset is 4.5% and the expected return on the stock index is 12%.The standard deviation of returns on the stock index is 6%.Calculate the expected standard deviation of the portfolio.

Accepted Answer

0.7(6)= 4.2%

Question 7

A friend has some reliable information that the stock of Puddles Company is going to rise from $43.00 to $50.00 per share over the next year.You know that the annual return on the S&P 500 has been 11% and the 90-day T-bill rate has been yielding 5% per year over the past 10 years.If beta for Puddles is 1.5,will you purchase the stock?

Accepted Answer

Expected Return = 5 + (1.5)(11 - 5)= 14.0%
Estimated Return = (50 - 43)¸ 43 = 16.28%
Estimated Return > Expected Return
$ \therefore $  Stock is undervalued and should be purchased.

Question 8

Assume that as a portfolio manager the beta of your portfolio is 1.2 and that your performance is exactly on target with the SML data under condition 1.If the true SML data is given by condition 2,how much does your performance differ from the true SML?
$\begin{array}{c}
\begin{array}{lll}
(1)\
(2)
\end{array}
\begin{array}{lll}
\mathrm{RFR}=.09 \
\mathrm{R}_{\mathrm{K}}=.10
\end{array}
\begin{array}{lll}
\mathrm{R}_{\mathrm{m}}(\mathrm{proxy})=.12 \
\left.\mathrm{R}_{\mathrm{m}} \text { (true }\right)=.13
\end{array}
\end{array}$

Accepted Answer

The expected return using the proxy SML is 0.09 + 1.2*(0.12 - 0.09) = 0.126. The expected return using the true SML is 0.09 + 1.2*(0.13 - 0.09) = 0.138. The difference is 0.138 - 0.126 = 0.012 or 1.2% lower, rounded to 1% lower.

Question 9

Assume that as a portfolio manager the beta of your portfolio is 1.15 and that your performance is exactly on target with the SML data under condition 1.If the true SML data is given by condition 2,how much does your performance differ from the true SML?
$\begin{array}{c}
\begin{array}{c}
(1)\
(2)
\end{array}
\begin{array}{l}
\mathrm{RFR}=0.0625 \
\mathrm{R}_{\mathrm{K}}=0.078
\end{array}
\begin{array}{l}
\mathrm{R}_{\mathrm{m}}(\text { proxy })=0.12 \
\mathrm{R}_{\mathrm{m}}(\text { true })=0.10
\end{array}
\end{array}$

Accepted Answer

The answer of Assume that as a portfolio manager the...

Question 10

Assume that as a portfolio manager the beta of your portfolio is 1.1 and that your performance is exactly on target with the SML data under condition 1.If the true SML data is given by condition 2,how much does your performance differ from the true SML?
$\begin{array}{c}
\begin{array}{lll}
(1)\
(2)
\end{array}
\begin{array}{lll}
\mathrm{RFR}=.07 \
\mathrm{R}_{\mathrm{K}}=.06
\end{array}
\begin{array}{lll}
\mathrm{R}_{\mathrm{m}}(\mathrm{proxy})=.15 \
\left.\mathrm{R}_{\mathrm{m}} \text { (true }\right)=.12
\end{array}
\end{array}$

Accepted Answer

The answer of Assume that as a portfolio manager the...

Question 11

Recently you have received a tip that the stock of Buttercup Industries is going to rise from $76.00 to $85.00 per share over the next year.You know that the annual return on the S&P 500 has been 13% and the 90-day T-bill rate has been yielding 3% per year over the past 10 years.If beta for Buttercup is 1.0,will you purchase the stock?

Accepted Answer

Expected Return = 3 + (1.0)(13 - 3)= 13.0%
Estimated Return = (85 - 76)¸ 76 = 11.84%
Estimated Return < Expected Return
$ \therefore $  Stock is overvalued and should not be purchased.

Question 12

Exhibit 8.3
Use the Information Below for the Following Problem(S)
 $$\begin{array} { c c c c } 
\text { Periad } & \begin{array} { c } 
\text { Return } \
\text { of Radtran } \
\text { (Percent) }
\end{array} & \begin{array} { c } 
\text { Praxy } \
\text { Epecific Index } \
\text { (Percent) }
\end{array} & \begin{array} { c } 
\text { True } \
\text { Ceneral Index } \
\text { (Percent) }
\end{array} \
\hline 1 & 10 & 12 & 15 \
2 & 12 & 10 & 13 \
3 & - 10 & - 8 & - 8 \
4 & - 4 & - 10 & 0
\end{array}$$
-Refer to Exhibit 8.3.What is the beta for Radtron using the proxy index?

Accepted Answer

$$\begin{array} { l c l c } 
( 12 - 1 ) ^ { 2 } = & 121 & ( 15 - 5 ) ^ { 2 } = & 100 \
( 10 - 1 ) ^ { 2 } = & 81 & ( 13 - 5 ) ^ { 2 } = & 64 \
( - 8 - 1 ) ^ { 2 } = & 81 & ( - 8 - 5 ) ^ { 2 } = & 169 \
( - 10 - 1 ) ^ { 2 } = & \frac { 121 } { 4 [ 1 / 4 } = 101 & ( 0 - 5 ) ^ { 2 } = & \frac { 25 } { 350 / 4 } = 89.50
\end{array}$$ 88 ¸ 101 = 0.87

Question 13

Exhibit 8.3
Use the Information Below for the Following Problem(S)
 $$\begin{array} { c c c c } 
\text { Periad } & \begin{array} { c } 
\text { Return } \
\text { of Radtran } \
\text { (Percent) }
\end{array} & \begin{array} { c } 
\text { Praxy } \
\text { Epecific Index } \
\text { (Percent) }
\end{array} & \begin{array} { c } 
\text { True } \
\text { Ceneral Index } \
\text { (Percent) }
\end{array} \
\hline 1 & 10 & 12 & 15 \
2 & 12 & 10 & 13 \
3 & - 10 & - 8 & - 8 \
4 & - 4 & - 10 & 0
\end{array}$$
-Refer to Exhibit 8.3.The covariance between Radtron and the true index is

Accepted Answer

$$\begin{array} { l c } 
( 10 - 2 ) ( 15 - 5 ) = & 80 \
( 12 - 2 ) ( 13 - 5 ) = & 80 \
( - 10 - 2 ) ( - 8 - 5 ) = & 156 \
( - 4 - 2 ) ( 0 - 5 ) = & &\frac { 30 } { 346 / 4 } = 86.50
\end{array}$$

Question 14

Recently your broker has advised you that he believes that the stock of Casey Incorporated is going to rise from $55.00 to $70.00 per share over the next year.You know that the annual return on the S&P 500 has been 12.5% and the 90-day T-bill rate has been yielding 6% per year over the past 10 years.If beta for Casey is 1.3,will you purchase the stock?

Accepted Answer

Expected Return = 6 + (1.3)(12.5 - 6)= 14.45%
Estimated Return = (70 - 55)¸ 55 = 27.27%
Estimated Return > Expected Return
$ \therefore $  Stock is undervalued and should be purchased.

Question 15

Assume that as a portfolio manager the beta of your portfolio is 1.4 and that your performance is exactly on target with the SML data under condition 1.If the true SML data is given by condition 2,how much does your performance differ from the true SML?
$\begin{array}{c}
\begin{array}{lll}
(1)\
(2)
\end{array}
\begin{array}{lll}
\mathrm{RFR}=.06 \
\mathrm{R}_{\mathrm{K}}=.05
\end{array}
\begin{array}{lll}
\mathrm{R}_{\mathrm{m}}(\mathrm{proxy})=.12 \
\left.\mathrm{R}_{\mathrm{m}} \text { (true }\right)=.11
\end{array}
\end{array}$

Accepted Answer

The answer of Assume that as a portfolio manager the...

Question 16

Exhibit 8.3
Use the Information Below for the Following Problem(S)
 $$\begin{array} { c c c c } 
\text { Periad } & \begin{array} { c } 
\text { Return } \
\text { of Radtran } \
\text { (Percent) }
\end{array} & \begin{array} { c } 
\text { Praxy } \
\text { Epecific Index } \
\text { (Percent) }
\end{array} & \begin{array} { c } 
\text { True } \
\text { Ceneral Index } \
\text { (Percent) }
\end{array} \
\hline 1 & 10 & 12 & 15 \
2 & 12 & 10 & 13 \
3 & - 10 & - 8 & - 8 \
4 & - 4 & - 10 & 0
\end{array}$$
-Refer to Exhibit 8.3.The average proxy return is

Accepted Answer

R (Radtron)= (10 + 12 - 10 - 4)/4 = 8/4 = 2%

Question 17

Exhibit 8.3
Use the Information Below for the Following Problem(S)
 $$\begin{array} { c c c c } 
\text { Periad } & \begin{array} { c } 
\text { Return } \
\text { of Radtran } \
\text { (Percent) }
\end{array} & \begin{array} { c } 
\text { Praxy } \
\text { Epecific Index } \
\text { (Percent) }
\end{array} & \begin{array} { c } 
\text { True } \
\text { Ceneral Index } \
\text { (Percent) }
\end{array} \
\hline 1 & 10 & 12 & 15 \
2 & 12 & 10 & 13 \
3 & - 10 & - 8 & - 8 \
4 & - 4 & - 10 & 0
\end{array}$$
-Refer to Exhibit 8.3.What is the beta for Radtron using the true index?

Accepted Answer

$$\begin{array} { l c l c } 
( 12 - 1 ) ^ { 2 } = & 121 & ( 15 - 5 ) ^ { 2 } = & 100 \
( 10 - 1 ) ^ { 2 } = & 81 & ( 13 - 5 ) ^ { 2 } = & 64 \
( - 8 - 1 ) ^ { 2 } = & 81 & ( - 8 - 5 ) ^ { 2 } = & 169 \
( - 10 - 1 ) ^ { 2 } = & \frac { 121 } { 4 [ 1 / 4 } = 101 & ( 0 - 5 ) ^ { 2 } = & \frac { 25 } { 350 / 4 } = 89.50
\end{array}$$ 86.5 ¸ 89.5 = 0.97

Question 18

Assume that as a portfolio manager the beta of your portfolio is 0.85 and that your performance is exactly on target with the SML data under condition 1.If the true SML data is given by condition 2,how much does your performance differ from the true SML?
$$\begin{array} { l l l } 
\text { (1) } & R F R = 0.0475 & R _ { m } ( 0 r a x y ) = 0 .0975 \
\text { (2) } & R _ { R } = 0.0325 & R _ { m } ( t u e ) = 0 .0845
\end{array}$$

Accepted Answer

(proxy)k = 0.0475 + 0.85 (0.0975 - 0.0475)= 0.09
According to the True SML it should be:
(True)K = 0.0325 + 0.85 (0.0845 - 0.0325)= 0.0767
You have been overperforming by 1.33%.

Question 19

Exhibit 8.3
Use the Information Below for the Following Problem(S)
 $$\begin{array} { c c c c } 
\text { Periad } & \begin{array} { c } 
\text { Return } \
\text { of Radtran } \
\text { (Percent) }
\end{array} & \begin{array} { c } 
\text { Praxy } \
\text { Epecific Index } \
\text { (Percent) }
\end{array} & \begin{array} { c } 
\text { True } \
\text { Ceneral Index } \
\text { (Percent) }
\end{array} \
\hline 1 & 10 & 12 & 15 \
2 & 12 & 10 & 13 \
3 & - 10 & - 8 & - 8 \
4 & - 4 & - 10 & 0
\end{array}$$
-Refer to Exhibit 8.3.The covariance between Radtron and the proxy index is

Accepted Answer

$$\begin{array} { l c } 
( 10 - 2 ) ( 12 - 1 ) = & 88 \
( 12 - 2 ) ( 10 - 1 ) = & 90 \
( - 10 - 2 ) ( - 8 - 1 ) = & 108 \
( - 4 - 2 ) ( - 10 - 1 ) = & 66 \&\underline{ { 352 / 4 }} = 88.00
\end{array}$$

Question 20

A friend has information that the stock of Zip Incorporated is going to rise from $62.00 to $65.00 per share over the next year.You know that the annual return on the S&P 500 has been 10% and the 90-day T-bill rate has been yielding 6% per year over the past 10 years.If beta for Zip is 0.9,will you purchase the stock?

Accepted Answer

Expected Return = 6 + (0.9)(10 - 6)= 9.6%
Estimated Return = (65 - 62)¸ 62 = 4.80%
Estimated Return < Expected Return
$ \therefore $ Stock is overvalued and should not be purchased.

Quiz 8: An Introduction to Asset Pricing Models

The variance of returns for a risky asset is 25%.The variance of the error term,Var(e) ,is 8%.What portion of the total risk of the asset,as measured by variance,is systematic?

Consider an asset that has a beta of 1.5.The return on the risk-free asset is 6.5% and the expected return on the stock index is 15%.The estimated return on the asset is 20%.Calculate the alpha for the asset.