Lawrence Corporation is considering these three projects whose returns are normally distributed:
Project | Investment | Exp. Ret | Std. Dev. | Corr. Coeff. |
A | $20,000 | 12% | 20% | A, B = 0.4 |
B | $30,000 | 14% | 20% | A, C = 0.5 |
C | $50,000 | 16% | 30% | B, C = 0.6 |
Find the probability that the return on the portfolio is more than 20%
a | b=a/100000 | ||||||||||||||||
Investment | Weight | ||||||||||||||||
Project A | $20,000 | 0.20 | wa | ||||||||||||||
Project B | $30,000 | 0.30 | wb | ||||||||||||||
Project C | $50,000 | 0.50 | wc | ||||||||||||||
$100,000 | |||||||||||||||||
Ra=Return of Project A | 12% | ||||||||||||||||
Rb=Return of Project B | 14% | ||||||||||||||||
Rc=Return of Project C | 16% | ||||||||||||||||
Portfolio Return =wa*Ra+wb*Rb+wc*Rc | |||||||||||||||||
Portfolio Return =0.2*12+0.3*14+0.5*16= | 14.60% | ||||||||||||||||
Sa=Standard Deviation of Project A | 20% | ||||||||||||||||
Sb=Standard Deviation of Project B | 20% | ||||||||||||||||
Sc=Standard Deviation of Project C | 30% | ||||||||||||||||
Corr(a,b)=Correlation of Project A and B | 0.40 | ||||||||||||||||
Corr(a,c)=Correlation of Project A and C | 0.50 | ||||||||||||||||
Corr(b,c)=Correlation of Project B and C | 0.60 | ||||||||||||||||
Covariance (a,b)=Correlation(a,b)*Sa*Sb | 160.00 | %% | (0.4*20*20) | ||||||||||||||
Covariance (a,c)=Correlation(a,c)*Sa*Sc | 300.00 | %% | (0.5*20*30) | ||||||||||||||
Covariance (b,c)=Correlation(b,c)*Sb*Sc | 360.00 | %% | (0.6*20*30) | ||||||||||||||
Portfolio Variance =(wa^2)*(Sa^2)+(wb^2)*(Sb^2)+(wc^2)*(Sc^2)+2wa*wb*Cov(a,b)+2wa*wc*Cov(a,c)+2wb*wc*Cov(b,c) | |||||||||||||||||
Portfolio Variance | 464.2 | %% | (0.2^2)*(20^2)+(0.3^2)*(20^2)+(0.5^2)*(30^2)+2*0.2*0.3*160+2*0.2*0.5*300+2*0.3*0.5*360 | ||||||||||||||
Portfolio Standard Deviation =SQUARE ROOT (Variance) | |||||||||||||||||
Portfolio Standard Deviation | 21.5453 | % | SQRT(464.2) | ||||||||||||||
Portfolio Mean Return | 14.60% | ||||||||||||||||
Probability of return of the portfolio more than 20% | |||||||||||||||||
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Lawrence Corporation is considering these three projects whose returns are normally distributed: Project Investment Exp. Ret...
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