《投资学》模型

P ORTFOLIO O PTIMIZATION

Two Risky Assets and a Riskfree Asset

Inputs

Display on the Graph

3

Expected Standard Exp Ret Return/Mon Deviation - Riskless E(r i )s i E i =E(r i )-r f

Riskfree Rate (r f )0.40%0.00%0.00%Risky Asset 1 1.50%10.00% 1.10%Risky Asset 20.80%

5.00%0.40%

Correlation (r)-0.30

Risk Aversion

2.7

4151008507

27

Outputs

Risky Asset Capital Utility Optimal Proportion Opp Set AllocationIndifference Complete

in Risky (x-axis)Curve Line Curve Portfolio Asset 1 or Standard Expected Expected Expected Expected Opt Risky

Deviation Ret / Mon Ret / Mon Ret / Mon Ret / Mon

Opp Set Curve -500.0%65.6%-2.7%Opp Set Curve

-150.0%

22.2%-0.3%

Opt Comp Port

Risky Asset 2

Risky Asset 1

Opt Risky Port Riskfree Rate

0.00%

0.50%

1.00%

1.50%

2.00%

0.00%

5.00%

10.00%

15.00%

E x p e c t e d R e t u r n / M o n t h

Standard Deviation (s)

Risky Opportunity Set, Capital Allocation

Line, and Indifference Curve

()()2

222121w w w w s s s ρs s =+-+-Risky Opportunity Set + Capital Allocation Line

+ Indifference Curve

Display on the Graph

Opp Set Curve-80.0%13.7%0.2%

Opp Set Curve-70.0%12.5%0.3%

Opp Set Curve-60.0%11.3%0.4%

Opp Set Curve-50.0%10.2%0.5%

Opp Set Curve-40.0%9.0%0.5%

Opp Set Curve-30.0%7.9%0.6%

Opp Set Curve-20.0% 6.9%0.7%

Opp Set Curve-10.0% 5.9%0.7%

Opp Set Curve0.0% 5.0%0.8%

Opp Set Curve10.0% 4.3%0.9%

Opp Set Curve20.0% 3.9%0.9%

Opp Set Curve30.0% 3.9% 1.0%

Opp Set Curve34.0% 4.0% 1.0%

Opp Set Curve40.0% 4.2% 1.1%

Opp Set Curve50.0% 4.9% 1.2%

Opp Set Curve60.0% 5.7% 1.2%

Opp Set Curve70.0% 6.7% 1.3%

Opp Set Curve80.0%7.8% 1.4%

Opp Set Curve90.0%8.9% 1.4%

Opp Set Curve100.0%10.0% 1.5%

Opp Set Curve110.0%11.2% 1.6%

Opp Set Curve120.0%12.3% 1.6%

Opp Set Curve250.0%28.2% 2.6%

Opp Set Curve750.0%90.2% 6.1%

Opt Risky Port37.2% 4.1% 1.1%

Cap Alloc Line0.0%0.0%0.4%

Cap Alloc Line1000.0%41%7.0% Indifference Curve0.0%0.64% Indifference Curve 1.0%0.67% Indifference Curve 2.0%0.75% Indifference Curve 3.0%0.88% Indifference Curve 4.0% 1.07%

()()

2

222

1212

121

w w w w

s s sρs s =+-+-

()()()()

12

1

E r wE r w E r

=+-

()

()

()

2

112212

22

12211212 /

w E E

E E E E

sρs s

s sρs s =-

+-+

Indifference Curve 5.0% 1.32% Indifference Curve 6.0% 1.61% Indifference Curve7.0% 1.96% Indifference Curve8.0% 2.37% Indifference Curve9.0% 2.83% Indifference Curve10.0% 3.34% Indifference Curve11.0% 3.91% Indifference Curve12.0% 4.53% Indifference Curve13.0% 5.20% Indifference Curve14.0% 5.93% Indifference Curve15.0% 6.72%

Opt Comp Port 3.0%0.9% Constant Utility Value0.0064

.