Question

STATE OF WEATHER	PROBABILITY OF STATE OF WEATHER	INVESTMENT AND LIKELY RETURNS
		Pig Farming	Crop Farming	Floriculture
BAD	20%	2%	-3%	-5%
GOOD	50%	10%	7%	11%
EXCELLENT	30%	20%	15%	25%
INVESTMENT N$		300, 000	250, 000	450, 000

Required:

a. Calculate the farmer’s Expected return on the floriculture investment.

b. What is the Standard Deviation of the pig farming project?

c. What is the farmer's Expected combined return if he invests in the three farming activities as shown in the table?

d. What is the Standard Deviation on the farmer’s portfolio?

Answer 1

STATE OF WEATHER	PROB.	Pig Farming	Crop Farming	Floriculture
BAD	20%	2%	-3%	-5%
GOOD	50%	10%	7%	11%
EXCELLENT	30%	20%	15%	25%
INVESTMENT N$		300000	250000	450000	1000000
Weight to Total		30%	25%	45%	100.00%

a.The farmer’s Expected return on the floriculture investment:

ER(FL)=Sum of(Prob.*Returns)

ie.(20%*-5%)+(50%*11%)+(30%*25%)=

12.00%

b. Standard Deviation of the pig farming project

We need to find expected return for pig-farming project

ER(PF)=Sum of(Prob.*Returns)

ie.(20%*2%)+(50%*10%)+(30%*20%)=

11.40%

Std. deviation =Sq. rt. Of(sum of (r,PF-ER,PF)^2)

((20%*(2%-11.40%)^2)+(50%*(10%-11.40%)^2)+(30%*(20%-11.40%)^2))^(1/2)=

0.06391

6.39%

c.First we will find the expected returns of the portfolio under the 3 states of weather(without applying probability) as follows:

for which we need weights of each in the investment -portfolio--which we have calculated as 30%,25% & 45% --in the table above---

ER,p(Bad)=(30%*2%)+(25%*-3%)+(45%*-5%)= -0.024

ER,p(Good)=(30%*10%)+(25%*7%)+(45%*11%)=0.097

ER,p(Excellent)=(30%*20%)+(25%*15%)+(45%*25%)=-0.21

Now, applying the given probabilities of the 3 weather,to the respective expected returns, calculated above,

(20%*-0.024)+(50%*0.097)+(30%*0.21)=

we get the portfolio expected return as ,

10.67%

Portfolio Variance =

(0.20*(-0.024-0.1067)^2)+(0.50*(0.097-0.1067)^2)+(0.30*(0.21-0.1067)^2)=

0.00666481

d. Portfolio standard deviation=

Sq. rt. Of variance

ie. (0.006665)^(1/2)=

8.16%