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 2 years ago
Next > < Previous

Related Solutions

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...
4. Assume there are three possible future states for the economy (Boom, Stagnant, and Recession) with...
4. Assume there are three possible future states for the economy (Boom, Stagnant, and Recession) with associated probabilities of 20%, 45%, nd 35%. For each future stae of the economy, a security pays either $40.00 or $20.00 with equal probability (i.e., a 50% chance of either payoff occuring). a. What is the expected future cash flow for any given future state of the economy? b. What is the expected future cash flow for the security? c. Further assuming the future...
1. Assume the economy can either be booming or in recession. The probability of a boom...
1. Assume the economy can either be booming or in recession. The probability of a boom is 65%. If the economy is booming, a certain stock has an expected return of 20%. If the economy is in recession, the expected return of that same stock is 4%. What is the long term expected return of the stock? 2. Over the last year you observe that a certain company had a stock return of 24%, while the market had a return...
The probabilities of an economic boom, normal economy, and a recession are 2 percent, 93 percent,...
The probabilities of an economic boom, normal economy, and a recession are 2 percent, 93 percent, and 5 percent, respectively. For these economic states, Stock A has deviations from its expected returns of 0.04, 0.07, and −0.11 for the three economic states respectively. Stock B has deviations from its expected returns of 0.14, 0.08, and −0.22 for the three economic states, respectively. What is the covariance of the two stocks?
II. Arbitrage Suppose the economy can be in one of the following three states: (i) Boom...
II. Arbitrage Suppose the economy can be in one of the following three states: (i) Boom or “good” state, (ii) Neutral state, and (iii) Recession or “bad” state. Each state can occur with an equal probability. There are three securities available in the economy: A, B, C. The net payoffs of these securities are as follows: • Security A: at the end of the year, the security is expected to yield a net payoff of $30 in the good state,...
Consider 2 scenarios: Boom Economy and Normal Economy. The Boom economy has 30% chance of happening,...
Consider 2 scenarios: Boom Economy and Normal Economy. The Boom economy has 30% chance of happening, while Normal economy has 70% chance of happening. For each scenario (Boom and Normal), stock ABC has a return of 25%, and 4%, respectively; stock XYZ has a return of 10% and 6.5%, respectively; the market portfolio has a return of 12% and 5% respectively. 1) Calculate Expected return, Variance and Standard deviation for stock ABC and XYZ 2) Based on your results in...
Consider 2 scenarios: Boom Economy and Normal Economy. The Boom economy has 30% chance of happening,...
Consider 2 scenarios: Boom Economy and Normal Economy. The Boom economy has 30% chance of happening, while Normal economy has 70% chance of happening. For each scenario (Boom and Normal), stock ABC has a return of 25%, and 4%, respectively; stock XYZ has a return of 10% and 6.5%, respectively; the market portfolio has a return of 12% and 5% respectively. 1) Calculate Expected return, Variance and Standard deviation for stock ABC and XYZ 2) Based on your results in...
Consider 2 scenarios: Boom Economy and Normal Economy. The Boom economy has 30% chance of happening,...
Consider 2 scenarios: Boom Economy and Normal Economy. The Boom economy has 30% chance of happening, while Normal economy has 70% chance of happening. For each scenario (Boom and Normal), stock ABC has a return of 25%, and 4%, respectively; stock XYZ has a return of 10% and 6.5%, respectively; the market portfolio has a return of 12% and 5% respectively. 1) Calculate Expected return, Variance and Standard deviation for stock ABC and XYZ 2) Based on your results in...
Consider 2 scenarios: Boom Economy and Normal Economy. The Boom economy has 30% chance of happening,...
Consider 2 scenarios: Boom Economy and Normal Economy. The Boom economy has 30% chance of happening, while Normal economy has 70% chance of happening. For each scenario (Boom and Normal), stock ABC has a return of 25%, and 4%, respectively; stock XYZ has a return of 10% and 6.5%, respectively; the market portfolio has a return of 12% and 5% respectively. 1) Calculate Expected return, Variance and Standard deviation for stock ABC and XYZ 2) Based on your results in...
Consider 2 scenarios: Boom Economy and Normal Economy. The Boom economy has 30% chance of happening,...
Consider 2 scenarios: Boom Economy and Normal Economy. The Boom economy has 30% chance of happening, while Normal economy has 70% chance of happening. For each scenario (Boom and Normal), stock ABC has a return of 25%, and 4%, respectively; stock XYZ has a return of 10% and 6.5%, respectively; the market portfolio has a return of 12% and 5% respectively. 1) Calculate Expected return, Variance and Standard deviation for stock ABC and XYZ 2) Based on your results in...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT