In Example 13.3, what are the standard deviations on the two portfolios?

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Accepted Answer

To answer, we first have to calculate the portfolio returns in the two states. We will work with the second portfolio, which has 50 percent in Stock A and 25 percent in each of Stocks B and C. The
relevant calculations can be summarized as follows:

Returns if State Occurs
Portfolio	Stock C	Stock B	Stock A	Probability of state of Economy	State of Economy
13.75%	20%	15%	10%	.40	Boom
5.00	0	4	8	.60	Bust

The portfolio return when the economy booms is calculated as:

.50×10%+.25×15%+.25×20%=13.75%

The return when the economy goes bust is calculated the same way. The expected return on the portfolio is 8.5 percent. The variance is thus:

[latex]σ^{2}=.40×(.1375-.085)^{2}+.60×(.05-.085)^{2}[/latex]

=.0018375

The standard deviation is thus about 4.3 percent. For our equally weighted portfolio, check to see that the standard deviation is about 5.4 percent.

Question 13.4: In Example 13.3, what are the standard deviations on the two...

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