Questions and Solutions.
- The following information is available for Stock AB C
|
Return |
10% |
21% |
15% |
|
Probability |
30% |
40% |
25% |
Calculate the expected return for stock ABC
Suggested Solution
- Expected = Σ𝑬(𝑹)
- (E x R) +(E x R)
| 10 | 21 | 15 |
| 30 | 40 | 25 |
| (0.3×0.10) | (0.40×0.21) | (0.25×0.15) |
| 0.03 + | 0.084+ | 0.0375= 15.15% |
Question 2
- A financial asset has the following returns and probabilities of returns
|
Return |
3% |
1.2% |
2.3% |
|
Probability |
30% |
50% |
25% |
Calculate the expected return for the financial asset.
Suggested Solution
| Return | 3 | 1.2 | 2.3 |
| Probability | 30 | 50 | 25 |
| Expected Return Σ𝑬(𝑹) | (0.3×0.03) | (0.5×0.012) | (0.25×0.023) |
| 0.009 + | 0.006+ | 0.00575= 2.08% |
You are employed in the investment and portfolio management department. The head of the department gave you a task to select the ideal portfolios. In other words, portfolios likely to lie on EF( Efficient frontier).
| Portfolio | |||||
| A | B | C | D | E | |
| Expected Return | 15% | 17% | 23% | 14% | 10% |
| Standard Deviation | 18 | 10 | 15 | 32 | 3 |
List 3 portfolios that are likely to lie on the Efficient frontier.
Suggested Solution
- Portfolio B, C and E
- Because they display high return and lowest risk on the available portfolios.
Question
- ABJ owns the following stocks.
|
Stock |
A |
B |
C |
|
Market Value |
ZAR5,000 |
ZAR2,500 |
ZAR4,000 |
|
Expected Return |
10% |
9% |
7% |
The portfolio expected return will be close to?
Suggested Solution
First calculate the weights attached to the 3 securities
- 5,000+2,500+4,000= ZAR11,500
- A=5000/11500 = 0.43
- B=2500/11500 =0.22
- C=4000/11500=0.35
- (0.43+0.22+0.35) =1
Insert the formula
- E(Rp) = WA(RA) +WB(RB) +WC(RC)
- =(0.43×10) +(0.22X9)+(0.35×7)
- = 8.73%
Question
A portfolio has two assets that are perfectly positively correlated. If 40% of an investor’s funds were allocated to an asset with a standard deviation of 0.5% and 60% were invested in an asset with a standard deviation of 0.4,% what is the standard deviation of the portfolio?
- What if the two assets are perfectly negatively (-1)
- Comment on the values from negative and positive correlations. ( 1 and -1).
Suggested Solution
Perfect positive correlation.
- =(0.4)^2(0.5)^2+(0.6)^2(0.4)^2+2(0.4)(0.6)[(1)(0.5)(0.4)]
- =0.04+0.0576+0.096
- =√0.1936
- =0.44%
Perfect negative correlation
- =(0.4)^2(0.5)^2+(0.6)^2(0.4)^2+2(0.4)(0.6)[(-1)(0.5)(0.4)]
- =0.04+0.0576+(-0.096)
- =0.0016
- =√(0.0016 )
- =0.04%
Perfect positive correlation is not necessarily ideal because we failed to reduce the standard deviation of the asset with lowest standard deviation (0.4) i.e. (0.5≤𝝈≥0.4). With perfect negative correlation standard deviation has fallen to 0.04.
Question
Consider the expected returns and standard deviations for the following portfolios:
Portfolio 1 Portfolio 2 Portfolio 3 Portfolio 4
Expected Return 10% 12% 11% 14%
Standard Deviation 15% 13% 12% 18%
Relative to the other portfolios, the portfolio that is not mean variance efficient is:
Suggested Solution
Portfolio 1 is not efficient because it has a lower expected return and higher risk than both Portfolios 2 and 3.