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# Expected return of a portfolio; variance and standard deviation

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Problem 1

a. Your portfolio is invested 28 percent each in A and C, and 44 percent in B. The expected return of the portfolio is_______% (Input answer as a percent rounded to 2 decimal places).

b. The variance of this portfolio is________ (Round answer to 6 decimal places) and standard deviation is__________% (Input answer as a percent rounded to 2 decimal places).

Problem 2

a. Your portfolio is invested 16 percent each in A and C, and 68 percent in B. The expected return of the portfolio is________% (Input answer as a percent rounded to 2 decimal places).

b. The variance of this portfolio is________ (Round answer to 6 decimal places) and standard deviation is ________% (Input answer as a percent rounded to 2 decimal places).

#### Solution Preview

See attached file.

Problem 1
a. In order to find the expected return of the portfolio, we must first calculate the return of the portfolio in each of the possible states of the economy. The return of a portfolio is:

Ret of portfolio = wa*Ra + wb*Rb + wc*Rc where wa, wb, wc,... are the weights of each of the components of the portfolio (in this case: wa = 0.28, wb = 0.44, wc = 0.28) and Ra, Rb, Rc are the returns of each component. So, for example, if the state is "Boom", the return would ...

#### Solution Summary

The solution explains both problems in concise narrative as well as clear calculations.

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