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a small entity in the mining industry is involved in operations that result in the company having stocks of cash resource
a small entity in the mining industry is involved in operations that result in the company having stocks of cash resource. The company has thus decided to create a portfolio of investments comprising of agriculture notes, a debt instrument, and ordinary shares of a company that is into telecommunications. The intended investment in Agriculture Notes is sixty percent and the remainder in ordinary shares. Forecasts have shown the following possibilities in as far as scenarios and their chances of occurring as well as annual returns are concerned.
|
Scenarios |
Probability |
Return on Agric Notes ($) |
Return on Ordinary Shares ($) |
|
Booming Economy |
0.3 |
25 000 |
10 000 |
|
Normal Economy |
04 |
20 000 |
11 000 |
|
Depressed Economy |
0.2 |
18 000 |
22 000 |
|
Recession |
0.1 |
10 000 |
28 000 |
Required
- Determine the annual expected return for each scenario for this portfolio. (8 marks)
- If the target of the company is to get at least $16 800/ annum from funds invested, does this portfolio presents such prospect overally? Support your answer with workings (5 marks)
- Compute the risk of each investment in the portfolio if it were to stand alone and which one has greater risk. Use the standard deviation. (5 marks)
- Calculate the covariance of returns for the above investment and interpret. (7 marks)
- Determine the correlation coefficient of investment returns in the portfolio and comment on their potential to reduce diversifiable risk. (6 marks)
- Determine the portfolio risk as measured by standard deviation and comment on whether the portfolio has been constructed using correct investments. (5 marks)
- If the objective of the portfolio manager is not to have expected returns fluctuating by more than $1 500/annum. Can it be concluded that this portfolio is ideal for the company and why?
Expert Solution
The information given in this case is various probabilistic scenarios and their corresponding returns .
In such a case , we apply the following formulas for Expected return and Expected Standard Deviation
where pi represents the individual probabilities in different scenarios
Ri represents the corresponding returns in different scenarios and
represents the expected return calculated as above.
a) The Expected return on a portfolio which is 60% invested in Agricultural Notes and 40% in Ordinary shares for each Scenario is presented in the table below (Expected return is the weighted average return of individual securities)
| Scenarios | Probability | Return on Agric Notes ($) | Return on Ordinary Shares ($) | Expected Return on Portfolio |
| Booming Economy | 0.3 | 25000 | 10000 | 19000 |
| Normal Economy | 0.4 | 20000 | 11000 | 16400 |
| Depressed Economy | 0.2 | 18000 | 22000 | 19600 |
| Recession | 0.1 | 10000 | 28000 | 17200 |
b) Achieving a return of at least $16800/annum is fulfilled in each scenario except in Normal economy (probability 40%) when the return is $16400/annum . So, the prospect of achieving this target is 60%
c) Expected Return from Agriculture Notes = 0.3*25000+ 0.4*20000+0.2*18000+0.1*10000 =$20100
Standard deviation of Agriculture Notes
= (0.3*(25000-20100)^2+0.4*(20000-20100)^2+0.2*(18000-20100)^2+0.1*(10000-20100)^2)^0.5
=$4276.68
Expected Return from Ordinary Shares = 0.3*10000+ 0.4*11000+0.2*22000+0.1*28000 =$14600
Standard deviation of Ordiinary Shares
= (0.3*(10000-14600)^2+0.4*(11000-14600)^2+0.2*(22000-14600)^2+0.1*(28000-14600)^2)^0.5
=$6359.25
So, Ordinary Shares are more risky as compared to Agriculture Notes on stand alone basis as their standard deviation is higher. Also, the standard deviation per unit return (Coefficient of variation) is also higher
d) Covariance between returns of security A and security M is given by
Where RAi are the individual return of the security A for probability pi and
· RMi are the individual return of the security M for probability pi and 
and 
are the expected returns of security A and security M respectively
So, covariance between returns of Agri Notes and Ordinary Shares
=0.3*(25000-20100)*(10000-14600) +0.4*(20000-20100)*(11000-14600)+0.2*(18000-20100)*(22000-14600)+0.1*(10000-20100)*(28000-14600)
= - 23260000
Covariance is negative and large implying that there is huge negative correlation between the two securities.
please see the attached file.
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