Question

In: Finance

Suppose an economy has three states: boom, normal, and recession. Assume that the probability of a...

Suppose an economy has three states: boom, normal, and recession. Assume that the probability of a boom state is 0.2, a normal state is 0.5, and a recession state is 0.3. And there are three stocks in this economy, called Alpha, Beta, and Gamma respectively. The return performance of these stocks has been summarized by the following table:

Alpha

Beta

Gamma

boom

15%

28%

1%

normal

6%

12%

3%

recession

-12%

-30%

20%

(Please show your intermediate processes, instead of just a final number for your answers. Only round your final answers to two decimal places.)

(a) What is the expected return of Stock Alpha?

(b) What is the variance of Stock Beta?

(c) What is the standard deviation of Stock Gamma?

(d) Suppose you build a portfolio by including these three stocks. The weight of Stock Alpha in your portfolio is 0.2, the weight of Stock Beta is 0.3, and the weight of Stock Gamma is 0.5. What are the expected return, variance, and standard deviation of your portfolio?

(e) Based on what you observe from the calculations and what you learned from the class, could you specify what are the characteristics of portfolios?

Solutions

Expert Solution

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

Cell reference -

e. characteristics of portfolio:

  • Portfolio is combination two or more stocks
  • Expected return of portfolio is weighted average of stock's return in portfolio
  • Standard deviation of Portfolio is always below the weighted average of stock's standard deviation when stocks are not perfectly correlated.
  • A well diversified portfolio can diversify the unsystematic risk.

Formula:

jeff jeffy answered 1 year ago
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