Question 1

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 2

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%. Calculate the expected return on the portfolio.

Accepted Answer

E(R)= 0.3(4.5)+ 0.7(12)= 9.75%

Question 3

Exhibit 8.3
USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) $$\begin{array} { c c c c } 
\text { Period } & \begin{array} { c } 
\text { Return } \
\text { of Radtron } \
\text { (Percent) }
\end{array} & \begin{array} { c } 
\text { Proxy } \
\text { Specific Index } \
\text { (Percent) }
\end{array} & \begin{array} { c } 
\text { True } \
\text { General Index } \
\text { (Percent) }
\end{array} \
\hline 1 & 10 & 12 & 15 \
2 & 12 & 10 & 13 \
3 & - 10 & - 8 & - 8 \
4 & - 4 & - 10 & 0
\end{array}$$
-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 4

Exhibit 8.3
USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) $$\begin{array} { c c c c } 
\text { Period } & \begin{array} { c } 
\text { Return } \
\text { of Radtron } \
\text { (Percent) }
\end{array} & \begin{array} { c } 
\text { Proxy } \
\text { Specific Index } \
\text { (Percent) }
\end{array} & \begin{array} { c } 
\text { True } \
\text { General Index } \
\text { (Percent) }
\end{array} \
\hline 1 & 10 & 12 & 15 \
2 & 12 & 10 & 13 \
3 & - 10 & - 8 & - 8 \
4 & - 4 & - 10 & 0
\end{array}$$
-Refer to Exhibit 8.3. The average return for Radtron is

Accepted Answer

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

Question 5

Exhibit 8.3
USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) $$\begin{array} { c c c c } 
\text { Period } & \begin{array} { c } 
\text { Return } \
\text { of Radtron } \
\text { (Percent) }
\end{array} & \begin{array} { c } 
\text { Proxy } \
\text { Specific Index } \
\text { (Percent) }
\end{array} & \begin{array} { c } 
\text { True } \
\text { General Index } \
\text { (Percent) }
\end{array} \
\hline 1 & 10 & 12 & 15 \
2 & 12 & 10 & 13 \
3 & - 10 & - 8 & - 8 \
4 & - 4 & - 10 & 0
\end{array}$$
-Refer to Exhibit 8.3. The covariance between Radtron and the true index is

Accepted Answer

The answer of Exhibit 8.3
USE THE INFORMATION BELOW FOR THE...

Question 6

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? (1) $ \mathrm{RFR}=0.0625 \quad \mathrm{R}_{\mathrm{m}}( $ proxy) $ =0.12 $
(2) $ \mathrm{R}_{\mathrm{K}}=0.078 \quad \mathrm{R}_{\mathrm{m}}( $ true $ )=0.10 $

Accepted Answer

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

Question 7

Exhibit 8.3
USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) $$\begin{array} { c c c c } 
\text { Period } & \begin{array} { c } 
\text { Return } \
\text { of Radtron } \
\text { (Percent) }
\end{array} & \begin{array} { c } 
\text { Proxy } \
\text { Specific Index } \
\text { (Percent) }
\end{array} & \begin{array} { c } 
\text { True } \
\text { General Index } \
\text { (Percent) }
\end{array} \
\hline 1 & 10 & 12 & 15 \
2 & 12 & 10 & 13 \
3 & - 10 & - 8 & - 8 \
4 & - 4 & - 10 & 0
\end{array}$$
-Refer to Exhibit 8.3. The average proxy return is

Accepted Answer

The answer of Exhibit 8.3
USE THE INFORMATION BELOW FOR THE...

Question 8

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? (1) $ \mathrm{RFR}=0.0475 \quad \mathrm{R}_{\mathrm{m}}( $ proxy) $ =0.0975 $
(2) $ \mathrm{R}_{\mathrm{K}}=0.0325 \quad \mathrm{R}_{\mathrm{m}}( $ true $ )=0.0845 $

Accepted Answer

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

Question 9

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.

Question 10

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

According to the information given in the question, Casey Inc. is expected to have a 27.27% increase in its stock price from $55 to $70 per share. As the beta for the stock is 1.3, which is higher than the market average of 1, it indicates that it is a relatively risky stock. However, an investor expects higher returns for higher risk investments. Thus, it can be assumed that the expected return of Casey is higher than the index return of 12.5%.

To calculate the expected return, we use the Capital Asset Pricing Model (CAPM):
Expected Return = Risk-Free Rate + Beta*(Expected Market Return - Risk-Free Rate)
Risk-Free Rate = 6%
Expected Market Return = 12.5%
Beta = 1.3

Expected Return = 6% + 1.3*(12.5% - 6%)
Expected Return = 15.45%

Comparing the expected return of Casey (15.45%) with the estimated return (27.27%), the stock seems undervalued as the expected return is lower than the estimated return. Therefore, it is advisable to purchase the stock as it can give higher returns than the market average.

Question 11

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? (1(1) $ \mathrm{RFR}=.08 $$\quad\quad R_{m}(\text { proxy })=.11$
(2) $ \mathrm{RK}_{\mathrm{K}}=.07 $$\quad\quad\mathrm{R}_{\mathrm{m}}(\text { true })=.14
$

Accepted Answer

The correct answer is A.The difference in performance is calculated as follows:(True SML return - Proxy SML return) * Beta= (0.14 - 0.11) * 1.3= 0.039= 3.9%Therefore, the performance is 3.9% lower than the true SML.

Question 12

An investor wishes to construct a portfolio by borrowing 35% of his original wealth and investing all the money in a stock index. The return on the risk-free asset is 4.0% and the expected return on the stock index is 15%. Calculate the expected return on the portfolio.

Accepted Answer

Let W be the wealth of the investor, then the amount of money invested in the stock index is 0.65W (since the investor is borrowing 35%). The expected return on the portfolio is:

0.65(15%) + 0.35(4%) = 0.0975 + 0.014 = 0.1115 or 11.15%

Therefore, the expected return on the portfolio is 11.15%, or approximately 18.85% if we consider the return on the portfolio as if it were invested with no borrowing.

Question 13

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 14

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

Alpha is calculated as the difference between the actual return and the expected return based on the Capital Asset Pricing Model (CAPM). The expected return using CAPM is: 6.5% + 1.5 * (15% - 6.5%) = 19.25%. The alpha is 20% - 19.25% = 0.75%.

Question 15

Exhibit 8.3
USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) $$\begin{array} { c c c c } 
\text { Period } & \begin{array} { c } 
\text { Return } \
\text { of Radtron } \
\text { (Percent) }
\end{array} & \begin{array} { c } 
\text { Proxy } \
\text { Specific Index } \
\text { (Percent) }
\end{array} & \begin{array} { c } 
\text { True } \
\text { General Index } \
\text { (Percent) }
\end{array} \
\hline 1 & 10 & 12 & 15 \
2 & 12 & 10 & 13 \
3 & - 10 & - 8 & - 8 \
4 & - 4 & - 10 & 0
\end{array}$$
-Refer to Exhibit 8.3. The average true return is

Accepted Answer

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

Question 16

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? (1) $ \mathrm{RFR}=.06 $$\quad\quad\quad R_{m}(\text { proxy })=.12
$
(2) $ \mathrm{RK}_{\mathrm{K}}=.05 $$ \quad\quad\quad R_{m}( $ true $ )=.11 $

Accepted Answer

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

Question 17

Exhibit 8.3
USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) $$\begin{array} { c c c c } 
\text { Period } & \begin{array} { c } 
\text { Return } \
\text { of Radtron } \
\text { (Percent) }
\end{array} & \begin{array} { c } 
\text { Proxy } \
\text { Specific Index } \
\text { (Percent) }
\end{array} & \begin{array} { c } 
\text { True } \
\text { General Index } \
\text { (Percent) }
\end{array} \
\hline 1 & 10 & 12 & 15 \
2 & 12 & 10 & 13 \
3 & - 10 & - 8 & - 8 \
4 & - 4 & - 10 & 0
\end{array}$$
-Refer to Exhibit 8.3. The covariance between Radtron and the proxy index is

Accepted Answer

The answer of Exhibit 8.3
USE THE INFORMATION BELOW FOR THE...

Question 18

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? (1) $ \mathrm{RFR}=.07 $$\quad\quad\quad R_{m}(\text { proxy })=.15
$
(2) $ \mathrm{RK}_{\mathrm{K}}=.06 $$\quad\quad\quad R_{m}( $ true $ )=.12 $

Accepted Answer

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

Question 19

Exhibit 8.3
USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) $$\begin{array} { c c c c } 
\text { Period } & \begin{array} { c } 
\text { Return } \
\text { of Radtron } \
\text { (Percent) }
\end{array} & \begin{array} { c } 
\text { Proxy } \
\text { Specific Index } \
\text { (Percent) }
\end{array} & \begin{array} { c } 
\text { True } \
\text { General Index } \
\text { (Percent) }
\end{array} \
\hline 1 & 10 & 12 & 15 \
2 & 12 & 10 & 13 \
3 & - 10 & - 8 & - 8 \
4 & - 4 & - 10 & 0
\end{array}$$
-Refer to Exhibit 8.3. What is the beta for Radtron using the true index?

Accepted Answer

The answer of Exhibit 8.3
USE THE INFORMATION BELOW FOR THE...

Question 20

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? (1) $ \mathrm{RFR}=.09 $$\quad\quad R_{m}(\text { proxy })=.12
$
(2) $ \quad \mathrm{R}_{\mathrm{K}}=.10 $$\quad\quad R_{m}( $ true $ )=.13 $

Accepted Answer

The expected return based on condition 1 is $0.09 + 1.2 \times (0.12 - 0.09) = 0.126$. The expected return based on condition 2 is $0.10 + 1.2 \times (0.13 - 0.10) = 0.136$. The performance is 1% lower under condition 1 compared to condition 2.

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?

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%. Calculate the expected return on the portfolio.

An investor wishes to construct a portfolio by borrowing 35% of his original wealth and investing all the money in a stock index. The return on the risk-free asset is 4.0% and the expected return on the stock index is 15%. Calculate the expected return on the portfolio.

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.