Question

Question 1
M & M (Pvt) Ltd, 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
a) Determine the annual expected return for each scenario for this portfolio. (8
marks)
b) 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
c) 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.
d) Calculate the covariance of returns for the above investment and interpret. (7
marks)
e) Determine the correlation coefficient of investment returns in the portfolio and
comment on their potential to reduce diversifiable risk.
f) Determine the portfolio risk as measured by standard deviation and comment on
whether the portfolio has been constructed using correct investments. (5
marks)
g) 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?

Answer 1

a)CALCULATIONOF ANNUAL EXPECTED RETRUN FOR EACH SCENARIO

KDJFDSKHFFV	BOOMING ECONOMY	NORMAL	DEPRESSED	RECESSION	Total expected retrun of individual asset
type of security agric notes ordinary shares Total under each scenario	prob. return expected return .3 25000 7500 .3 10000 3000 10500	prob. return expected return .4 20000 8000 .4 11000 4400 12400	prob return expected return .2 18000 3600 .2 22000 4400 8000	prob return expected return .1 10000 1000 .1 28000 2800 3800	20100 14600

So, annual expected retrun under scenario is

BOOMING ECONOMYV= 10500

NORMAL ECONOMY= 12400

DEPRESSED ECONOMY= 8000

RECESSION ECONOMY= 3800

B) Overall profolio expected return:

expected retrun from portfolio = proportion invested in agric notes * expexted return in agric notes

+ proportion invested in ordinary shares * expected return in ordinary shares

Expected return in agric notes = 7500+8000+3600+1000= 20100

Expected retrun in ordinary shares=3000+4400+4400+2800= 14600

Expected retrun in portfolio = .60 * 20100 + .40 * 14600 = 12600+5840= 18440

As the expected retruns from the portfolio are more than $ 16800, so this protfolio represent this prospects.

c) computing risk of each investment using standard deviation:

Standard deviation of agric notes

scenario	retrun	average return	deviation	deviation square	prob.	prob.* deviaiton square
Booming	25000	20100	4900	24010000	.3	7203000
normal	20000	20100	-100	10000	.4	4000
depressed	18000	20100	-2100	4410000	.2	882000
recession	10000	20100	-10100	102010000	.1	10201000

Total of last column = 18290000

Standard deviation =(18290000)^1/2 = 4276.68

So, the value of expected return of agric notes can be 20100+4276.68 or 20100-4276.68

Coefficient of variationv= 4276.68 /20100 =21.277 %

Standard deviation of ordinary shares

scenario	retrun	average return	deviation	deviation square	prob.	prob.* deviaiton square
Booming	10000	14600	-4600	21160000	.3	6348000
normal	11000	14600	-3600	12960000	.4	5184000
depressed	22000	14600	7400	54760000	.2	10952000
recession	28000	14600	13400	179560000	.1	17956000

=

Total of last column = 40440000=

Standard deviation =(40440000)^1/2 = 6359.245

So, the value of expected return of agric notes can be14600 + 6359.245 or 14600-6359.245

Coefficient of variation= 6359.245/14600= 43.556 %

So, on the basis of coefficient of variaton we can say ordinary shares are more risky.

d) calculating covariance of above returns

	deviation agric notes (i)	deviation ordianry share (ii)	(i)*(ii)	prob.	prob. *(iii)
booming	25000-20100=4900	10000-14600=-4600	-22540000	.3	-6762000
	20000-20100=-100	11000-14600=-3600	360000	.4	144000
	18000-20100=-2100	22000-14600=7400	-15540000	.2	-3108000
	10000-20100=-10100	28000-14600=13400	-134340000	.1	-13434000
Total
Covariance					-23160000

securities move in opposite direction.