In: Finance
A. A stock is expected to earn 29 percent in a boom economy and 14 percent in a normal economy. There is a 42 percent chance the economy will boom and a 58.0 percent chance the economy will be normal. What is the standard deviation of these returns?
B.
A portfolio consists of 35 percent Stock A, 54 percent Stock B, and 11 percent Stock C. What is the portfolio expected return given the following: |
State of Economy |
Probability of State of Economy |
Stock A Returns |
Stock B Returns |
Stock C Returns |
Normal |
.85 |
27% |
20% |
48% |
Recession |
.15 |
–2 |
41 |
–24 |
C.
A portfolio is comprised of the following stocks. What is the portfolio beta? |
Stock |
Market Value of Shares |
Beta |
||
A |
$ |
26,000 |
2.39 |
|
B |
$ |
23,500 |
1.22 |
|
C |
$ |
11,000 |
1.28 |
A. The correct answer is 7.40%
Notes:
Probability | Stock Return | Expected Return ( Probability * Expected Return) | |||
Normal | 0.58 | 0.14 | 0.0812 | ||
Boom | 0.42 | 0.29 | 0.1218 | ||
Expected Return | 0.20 | ||||
Expected Return % | 20.30 | ||||
Stock | Probability | Probable Return | Deviation ( Probable Return- Expected Return) | Deviation Squared | Product ( Deviation Squared* Probability) |
Normal | 0.58 | 14.00 | -6.30 | 39.69 | 23.02 |
Boom | 0.42 | 29.00 | 8.70 | 75.69 | 31.79 |
Variance | 54.81 | ||||
Standard Deviation (Square root of Variance) | 7.40 |
B. The correct answer is 24.52%
Stock A | Stock B | Stock C | Total | |||||
State of economy | Probability | Stock A | Probability* Return | Stock B | Probability* Return | Stock C | Probability* Return | |
Normal | 0.85 | 0.27 | 0.2295 | 0.2 | 0.17 | 0.48 | 0.408 | |
Recession | 0.15 | -0.02 | -0.003 | 0.41 | 0.0615 | -0.24 | -0.036 | |
Total Returns | 22.65 | 23.15 | 37.2 | |||||
Weights | 35% | 54% | 11% | |||||
expected return | 7.9275 | 12.501 | 4.092 | 24.5205 |
C. The correct answer is 1.73
Note :
Stock | Market Value of Shares | Weight ( Market value / Total Value) | Beta | Weight * Beta |
A | 26,000 | 0.429752066 | 2.39 | 1.027107438 |
B | 23,500 | 0.388429752 | 1.22 | 0.473884298 |
C | 11000 | 0.181818182 | 1.28 | 0.232727273 |
60500 | Portfolio Beta | 1.733719008 |