Investments
Investments
11th Edition
ISBN: 9781259277177
Author: Zvi Bodie Professor, Alex Kane, Alan J. Marcus Professor
Publisher: McGraw-Hill Education
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Chapter 6, Problem 20PS

a

Summary Introduction

Adequate information:

U.S. market is risky portfolio

Risk-aversion coefficient A=4

Period representing the future expected performance = 1926 to 2015

     Average Annual ReturnsS&P 500 Portfolio
    PeriodS&P 500 Portfolio1-month T-billsRisk premiumStandard deviationSharpe RatioProbability
    1926-2015 11.673.588.10 20.48 0.40 -- 
    1992-201511.103.527.5918.220.420.94
    1970-199110.917.483.4416.710.210.50
    1949-196915.352.2813.0817.660.740.24
    1926 -19489.401.048.3627.950.300.71

To compute: The fraction of portfolio to be allocated to T-bills and Equity.

Introduction:

Risk aversion coefficient: In today’s world, every aspect has a risk factor along with the benefits. When it comes to financial product, then it is obvious to have a risk. To measure such risk relative with its performance, we make use of standard deviation of returns. These are also known as volatility of returns. When a number from 1 (assuming to be lowest risk aversion) to 5 (assuming to be highest risk aversion) is attributed to an investor, this number is further assigned the letter A which is called the risk aversion coefficient.

a

Expert Solution
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Explanation of Solution

Here, we have to calculate the proportion of Y of the total investment. It is clear that the optimal position y related to a risky asset will be proportional to the risk premium while there is an inverse proportional relationship with that of the variance and degree of risk aversion.

  y=E(rp)rfAσp2

When the entire period 1926-2015 is representing future expected performance, then A=4

  E(rm)rf=8.10%σm=20.48%y=E(rm)rfAσm2

By substituting the values, we get

  y=8.10%4×(20.48%)2

We need to convert the percentages to normal values. After that, we get the equation as :

  y=0.0810.167772y=0.482798

Or 48.28% when converted to percentages

So, 48.28% have to be allocated to equity

If 100 is assumed to be the total, then

  TBills=TotalAllocation to Equity=10048.28%=51.72%

Therefore, 51.72% is to be allocated to T-bills.

Conclusion

So, 48.28% have to be allocated to equity and 51.72% is to be allocated to T-bills.

b

Summary Introduction

Adequate information:

U.S. market is risky portfolio

Risk-aversion coefficient A=4

Period representing the future expected performance = 1970 to 1991

To compute: The circumstances if period is representing the future expected performance is 1970 to 1991.

Introduction:

Risk aversion coefficient: In today’s world, every aspect has a risk factor along with the benefits. When it comes to financial product, then it is obvious to have a risk. To measure such risk relative with its performance, we make use of standard deviation of returns. These are also known as volatility of returns. When a number from 1 (assuming to be lowest risk aversion) to 5 (assuming to be highest risk aversion) is attributed to an investor, this number is further assigned the letter A which is called the risk aversion coefficient.

b

Expert Solution
Check Mark

Explanation of Solution

When the entire period 1970-1991 is representing future expected performance, then A=4

E(rm)-rf=3.44%

sM=16.71%

  y=E(rm)rfAσm2

By substituting the values, we get

  y=3.44%4×(16.71%)2

We need to convert the percentages to normal values. After that, we get the equation as :

  y=0.3444× (0.1671)2y=0.03440.11169y=0.307995

or 30.80% when rounded off and converted to percentages

So, 30.80% have to be allocated to equity

If 100 is assumed to be the total, then

  TBills=TotalAllocation to Equity=10030.80%=69.20%

Therefore, 69.20% is to be allocated to T-bills.

Conclusion

So, 30.80% have to be allocated to equity and 69.20% is to be allocated to T-bills.

c

Summary Introduction

Adequate information:

U.S. market is risky portfolio

Risk-aversion coefficient A=4

Period representing the future expected performance = 1926 to 2015

Period representing the future expected performance = 1970 to 1991

To compute: The analysis of circumstances in both the given periods i.e, 1926-2015 and 1970-1991.

Introduction:

Risk aversion coefficient: In today’s world, every aspect has a risk factor along with the benefits. When it comes to financial product, then it is obvious to have a risk. To measure such risk relative with its performance, we make use of standard deviation of returns. These are also known as volatility of returns. When a number from 1 (assuming to be lowest risk aversion) to 5 (assuming to be highest risk aversion) is attributed to an investor, this number is further assigned the letter A which is called the risk aversion coefficient.

c

Expert Solution
Check Mark

Explanation of Solution

It is clear that the risk premium in the period 1926-2015 is 8.10 ; whereas for the period 1970-1991 it is 3.44. So, when we compare both values, we find that the risk premium for the period 1970-1991 is less than the risk premium of the period 1926-2015.

Secondly, the Sharpe ratio for the period 1970-1991 is less and it has higher proportion of T-bills.

Conclusion

The results got from the calculation states that as market risk premium is probable to be less for the period 1926-2015, the market risk is supposed to higher and secondly, since the proportion of T-bills is more for the period 1970-1991, its Sharpe ratio will be less when compared to the period 1926-2015.

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