ESSENTIALS CORPORATE FINANCE + CNCT A.
ESSENTIALS CORPORATE FINANCE + CNCT A.
9th Edition
ISBN: 9781259968723
Author: Ross
Publisher: MCG CUSTOM
Question
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Chapter 10, Problem 8QP

a)

Summary Introduction

To determine: The arithmetic average for large-company stocks and Treasury bills.

Introduction:

Arithmetic average return refers to the returns that an investment earns in an average year over different periods.

a)

Expert Solution
Check Mark

Answer to Problem 8QP

Answer:

The arithmetic average of large-company stocks is 3.24%, and the arithmetic average of Treasury bills is 6.55%.

Explanation of Solution

Explanation:

Given information:

Refer to Table 10.1 in the chapter. Extract the data for large-company stocks and Treasury bills from 1973 to 1978 as follows:

Year

Large co.

stock

return

T-bill return

Risk

premium

1973–14.69%7.29%–21.98%
1974–26.47%7.99%–34.46%
197537.23%5.87%31.36%
197623.93%5.07%18.86%
1977–7.16%5.45%–12.61%
19786.57%7.64%–1.07%
Total19.41% 39.31%–19.90%

The formula to calculate the arithmetic average return:

Arithmetic average(X¯)=i=1NXiN

Where,

“∑Xi” refers to the total of observations,

“Xi” refers to each of the observations from X1 to XN (as “i” goes from 1 to “N”),

“N” refers to the number of observations.

Compute the arithmetic average for large-company stocks:

The total of the observations is 19.41%. There are 6 observations.

Arithmetic average(X¯)=i=1NXiN=19.41%6=3.24%

Hence, the arithmetic average of large-company stocks is 3.24%.

Compute the arithmetic average for Treasury bill return:

The total of the observations is -39.31%. There are 6 observations.

Arithmetic average(X¯)=i=1NXiN=39.31%6=6.55%

Hence, the arithmetic average of Treasury bills is 6.55%.

b)

Summary Introduction

To determine: The standard deviation of large-company stocks and Treasury bills.

Introduction:

Variance refers to the average difference of squared deviations of the actual data from the mean or average.

Standard deviation refers to the deviation of the observations from the mean.

b)

Expert Solution
Check Mark

Answer to Problem 8QP

Answer:

The standard deviation of large-company stocks is 24.11%, and the standard deviation of Treasury bills is 1.24%.

Explanation of Solution

Explanation:

Given information:

Refer to Table 10.1 in the chapter. The arithmetic average of Treasury bills is 6.55%. Extract the data for large-company stocks and Treasury bills from 1973 to 1978 as follows:

Year

Large co. Stock

return

T-bill return

Risk

premium

1973–14.69%7.29%–21.98%
1974–26.47%7.99%–34.46%
197537.23%5.87%31.36%
197623.93%5.07%18.86%
1977–7.16%5.45%–12.61%
19786.57%7.64%–1.07%
Total19.41%39.31%–19.90%

The formula to calculate the standard deviation of the returns:

SD(R)=σ=i=1N(XiX¯)2N1

“SD(R)” refers to the standard deviation of the return,

“X̅” refers to the arithmetic average,

“Xi” refers to each of the observations from X1 to XN (as “i” goes from 1 to “N”),

“N” refers to the number of observations.

Compute the squared deviations of large-company stocks:

Large-company stocks

Actual

return

Average

return(B)

Deviation

(A)–(B)=(C)

Squared

Deviation

(C)2

(A)
−0.14690.0324−0.17930.0321485
−0.26470.0324−0.29710.0882684
0.37230.03240.33990.115532
0.23930.03240.20690.0428076
−0.07160.0324−0.1040.010816
0.06570.03240.03330.0011089
Total of squared deviation0.05813
i=1N(XiX¯)2N1
 

Compute the standard deviation of the return:

SD(R)=σ=i=1N(XiX¯)2N1=0.290681461=0.24111 or 24.111%

Hence, the standard deviation of large-company stocks is 24.111%.

Compute the squared deviations of Treasury bill:

 Treasury bill

Actual

return

Average

Return

(B)

Deviation

(A)–(B)=(C)

Squared

Deviation

(C)2

(A)
0.07290.06550.00740.00005
0.07990.06550.01440.00020736
0.05870.0655-0.00680.00004624
0.05070.0655-0.01480.00021904
0.05450.0655-0.0110.000121
0.07640.06550.01090.00011881
i=1N(XiX¯)2N10.000154

Compute the standard deviation:

SD(R)=σ=i=1N(XiX¯)2N1=0.0007761=0.0124 or 1.24%

Hence, the standard deviation of Treasury bills is 1.24%.

c)

Summary Introduction

To determine: The arithmetic average and the standard deviation of observed risk premium.

Introduction:

Arithmetic average return refers to the returns that an investment earns in an average year over different periods.

Standard deviation refers to the deviation of the observations from the mean.

c)

Expert Solution
Check Mark

Answer to Problem 8QP

Answer:

The arithmetic average is −3.32%, and the standard deviation is 24.92%.

Explanation of Solution

Explanation:

Given information:

Refer to Table 10.1 in the chapter. Extract the data for large-company stocks and Treasury bills from 1973 to 1978 as follows:

Year

Large co. stock

return

T-bill return

Risk

premium

1973–14.69%7.29%–21.98%
1974–26.47%7.99%–34.46%
197537.23%5.87%31.36%
197623.93%5.07%18.86%
1977–7.16%5.45%–12.61%
19786.57%7.64%–1.07%
Total19.41%39.31%–19.90%

The formula to calculate the arithmetic average return:

Arithmetic average(X¯)=i=1NXiN

Where,

“∑Xi” refers to the total of observations,

“Xi” refers to each of the observations from X1 to XN (as “i” goes from 1 to “N”),

“N” refers to the number of observations.

The formula to calculate the standard deviation:

SD(R)=σ=i=1N(XiX¯)2N1

“SD (R)” refers to the standard deviation of the return,

“X̅” refers to the arithmetic average,

“Xi” refers to each of the observations from X1 to XN (as “i” goes from 1 to “N”),

“N” refers to the number of observations.

Compute the arithmetic average for risk premium:

The total of the observations is (-19.90%). There are 6 observations.

Arithmetic average(X¯)=i=1NXiN=0.19906=0.032or 3.32

Hence, the arithmetic average of risk premium is −3.32%.

Compute the squared deviations of risk premium:

Risk premium

Actual return

(A)

Average

Return

(B)

Deviation

(A)–(B)=(C)

Squared

deviation

(C)2
-0.2198-0.0332-0.18660.034820
-0.3446-0.0332-0.31140.096970
0.3136-0.03320.34680.120270
0.1886-0.03320.22180.049195
-0.1261-0.0332-0.09290.008630
-0.0107-0.03320.02250.000506
i=1N(XiX¯)2N10.062078

Compute the standard deviation:

SD(R)=σ=i=1N(XiX¯)2N1=0.3103961=0.2492 or 24.92%

Hence, the standard deviation of risk premium is 24.92%.

d)

Summary Introduction

To determine: Whether the risk premium can be negative before and after the investment.

Introduction:

Arithmetic average return refers to the returns that an investment earns in an average year over different periods.

Variance refers to the average difference of squared deviations of the actual data from the mean or average.

Standard deviation refers to the deviation of the observations from the mean.

d)

Expert Solution
Check Mark

Explanation of Solution

Explanation:

The risk premium cannot be negative before the investment because the investors require compensation for assuming the risk. They will invest when the stock compensates for the risk. The risk premium can be negative after the investment, if the nominal returns are very low compared to the risk-free returns.

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Chapter 10 Solutions

ESSENTIALS CORPORATE FINANCE + CNCT A.

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