Question

Benefits of

diversification.

Sally Rogers has decided to invest her wealth equally across the following three​ assets:

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.

What are her expected returns and the risk from her investment in the three​ assets? How do they compare with investing in asset M​ alone?  

Hint​:

Find the standard deviations of asset M and of the portfolio equally invested in assets​ M, N, and O.

What is the standard deviation of the portfolio that invests equally in all three assets​ M, N, and​ O?

nothing​%​(Round to two decimal​ places.)

States   Probability   Asset M Return   Asset N Return   Asset O Return
Boom   25%   12%   23%   0%
Normal   53%   9%   14%   9%
Recession   22%   0%   3%   12%

Answer 1

Expected Return when invested equally in assets M, N, O
Expected Return in Boom =Weight of Asset M*Return of Asset M in Boom+Weight of Asset N*Return of Asset N in Boom+Weight of Asset O*Return of Asset O in Boom =1/3*(12%+23%+0%)=11.67%
Expected Return in Normal =Weight of Asset M*Return of Asset M in Normal+Weight of Asset N*Return of Asset N in Normal+Weight of Asset O*Return of Asset O in Normal =1/3*(9%+14%+9%)=10.67%
Expected Return in Recession =Weight of Asset M*Return of Asset M in Recession+Weight of Asset N*Return of Asset N in Recession+Weight of Asset O*Return of Asset O in Recession=1/3*(0%+3%+12%)=5%

Expected return of Portfolio =Probability of Boom*Expected Return in Boom+Probability of Normal*Expected Return in Normal+Probability of Recession*Expected Return in Recession =25%*11.67%+53%*10.67%+22%*5% =9.6726% or 9.67%
Standard Deviation of Portfolio =(25%*(11.67%-9.6726%)^2+53%*(10.67%-9.6726%)^2+22%*(5%-9.6726%)^2)^0.5 =2.51%

Expected Return in Asset M =Probability of Boom*Expected Return in Boom+Probability of Normal*Expected Return in Normal+Probability of Recession*Expected Return in Recession =25%*12%+53%*9%+22%*0% =7.77%
Standard Deviation of M =(25%*(12%-7.77%)^2+53%*(9%-7.77%)^2+22%*(0%-7.77%)^2) =4.31%

Investing in Portfolio is better than investing in Asset M as they have higher expected return with lower standard deviation than asset M