Ch 7 OLC Two Security Model

Section 7.4 OLC Model

Chapter 7 Two-Security Portfolio

Asset Allocation Analysis: Risk and ReturnExpected Standard Corr.

Return Deviation Coeff s,b CovarianceSecurity 1 0.08 0.12 0.3 0.0072Security 2 0.13 0.2T-Bill 0.05 0

Weight Weight Expected Standard Reward toSecurity 1 Security 2 Return Deviation Variability

1 0 0.08000 0.12000 0.250000.9 0.1 0.08500 0.11559 0.302810.8 0.2 0.09000 0.11454 0.349220.7 0.3 0.09500 0.11696 0.384740.6 0.4 0.10000 0.12264 0.407710.5 0.5 0.10500 0.13115 0.419370.4 0.6 0.11000 0.14199 0.422580.3 0.7 0.11500 0.15466 0.420270.2 0.8 0.12000 0.16876 0.414790.1 0.9 0.12500 0.18396 0.40771

0 1 0.13000 0.20000 0.40000

Minimum Variance Portfolio Short Sales No Short Allowed Sales

Weight 1 0.82000 0.82000Weight 2 0.18000 0.18000Return 0.08900 0.08900Risk 0.11447 0.11447

Optimal Risky Portfolio Short Sales No Short Allowed Sales

Weight 1 0.40000 0.40000Weight 2 0.60000 0.60000Ex Ret 0.11000 0.11000St Dev. 0.14199 0.14199

Reward to Variability 0.42258 0.42258

Optimal Portfolio with a Risk Free AssetShort Sales No Short

Allowed SalesDesired rate of return: 0.12

Weight OP 1.16667 1.16667Weight RF -0.16667 -0.16667Ex Ret 0.12000 0.12000St Dev 0.16565 0.16565

Optimal Portfolio w/o a Risk Free Asset

Desired rate of return: 0.12

Weight 1 0.20000Weight 2 0.80000Ex. Return 0.12000St Dev 0.16876

CAL(MV)

CAL(OR)

A B C D E F123456789

10111213141516171819202122232425262728293031

32

33343536373839

40

4142434445464748495051525354555657585960616263

C1

This model is developed using the text example in Section 8.2. Security 1 would be debt while security 2 would be equity.

B7

Enter the return for Security 1 in decimal format.

C7

Enter the standard deviation for Security 1 in decimal format

D7

Enter the correlation coefficient for the returns of Security 1 with Security 2.

E7

The covariance is equal to the product of the individual securities standard deviation and the correlation coefficient

B8


C8


B9

Enter the return for the T-Bill in decimal format.

C28

Solution for the minimum risk portfolio using the minimum variance formula developed in Section 8.2. This solution allows short sales.

D28

Solution for the minimum risk portfolio using the minimum variance formula developed in Section 8.2. This solution is constrained to positive amounts and does not allow short sales.

C29

What is not invested in 1 is invested in 2.

D29


C36

Solution for the optimal weight of 1 using the formula 8.7 in Chapter 8. The solution allows for short selling.

D36

Solution for the optimal weight of 1 using the formula 8.7 in Chapter 8. The solution restrains investment to positive amounts and does not allow for short selling.

C37


D37


C48

Enter the target rate of return in decimal form.

C57

Enter the target return in decimal form. This solution is limited to some combination of risky assets. Note that the risk of this combination will exceed the risk with the optimal combination.

Solution to OLC Ques 1-4

Chapter 7 Two-Security Portfolio

Asset Allocation Analysis: Risk and ReturnExpected Standard Corr.

Return Deviation Coeff 1,2 CovarianceSecurity 1 0.09 0.18 0.3 0.01512Security 2 0.17 0.28T-Bill 0.035 0

Weight Weight Expected Standard Reward toSecurity 1 Security 2 Return Deviation Variability

1 0 0.09000 0.18000 0.305560.9 0.1 0.09800 0.17248 0.365260.8 0.2 0.10600 0.16944 0.419020.7 0.3 0.11400 0.17112 0.461660.6 0.4 0.12200 0.17739 0.490460.5 0.5 0.13000 0.18778 0.505920.4 0.6 0.13800 0.20166 0.510770.3 0.7 0.14600 0.21836 0.508330.2 0.8 0.15400 0.23730 0.501480.1 0.9 0.16200 0.25797 0.49230

0 1 0.17000 0.28000 0.48214

Minimum Variance PortShort Sales No Short Allowed Sales

Weight 1 0.78550 0.78550Weight 2 0.21450 0.21450Return 0.10716 0.10716Risk 0.16939 0.16939

Optimal Risky Portfoli Short Sales No Short Allowed Sales

Weight 1 0.39063 0.39063Weight 2 0.60937 0.60937Ex Ret 0.13875 0.13875St Dev. 0.20311 0.20311

Reward to Variability 0.51080 0.51080

Optimal Portfolio with a Risk Free AssetShort Sales No Short

Allowed SalesDesired rate of return: 0.12

Weight OP 0.81928 0.81928Weight RF 0.18072 0.18072Ex Ret 0.12000 0.12000St Dev 0.16641 0.16641

Optimal Portfolio w/o a Risk Free Asset

Desired rate of return: 0.12

Weight 1 0.62500Weight 2 0.37500Ex. Return 0.12000St Dev 0.17541

CAL(MV)

CAL(OR)

A B C D E F123456789

10111213141516171819202122232425262728293031

32

33343536373839

40

4142434445464748495051525354555657585960616263

C1

This model is developed using the text example in Section 8.2. Security 1 would be debt while security 2 would be equity.

B7


C7


D7

Enter the correlation coefficient for returns of Security 1 and Security 2 in decimal format

E7

The covariance is equal to the product of the individual securities standard deviation and the correlation coefficient

B8


C8

Enter the standard deviation for Security 2 in decimal format.

B9

Enter the return for the T-Bill in decimal format.

C28

Solution for the minimum risk portfolio using the minimum variance formula developed in Section 8.2. This solution allows short sales.

D28

Solution for the minimum risk portfolio using the minimum variance formula developed in Section 8.2. This solution is constrained to positive amounts and does not allow short sales.

C29


D29


C36

Solution for the optimal weight of 1 using the formula 8.7 in Chapter 8. The solution allows for short selling.

D36

Solution for the optimal weight of 1 using the formula 8.7 in Chapter 8. The solution restrains investment to positive amounts and does not allow for short selling.

C37


D37


C48

Enter the desired return in decimal format

C57

Enter the target return in decimal form. This solution is limited to some combination of risky assets. Note that the risk of this combination will exceed the risk with the optimal combination.

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Ch 7 OLC Two Security Model