NB:

KINDLY ASSIST TO TACKLE THE OTHER QUESTIONS THAT I AM NOT ABLE TO WORK ON THEM

Assume that you recently graduated with a major in finance, and you just landed a job in the trust department of a large regional bank. Your first assignment is to invest KES 10 Million from an estate for which the bank is a trustee. Because the estate is expected to be distributed to the heirs in about one year, you have been instructed to plan for a one-year holding period. Further, your boss has restricted you to the following investment alternatives, shown with their probabilities and associated outcomes.

		Returns on alternatives investments
		Estimated rate of return
State of economy	Prob.	T-Bills	High-Tech Corporation	Excel collections Ltd	Ribbon manufacturing	Market portfolio
Recession	0.1	8%	-22%	28%	10%	-13%
Below average	0.2	8%	-2%	14.7%	-10%	1%
Average	0.4	8%	20%	15%	7%	15%
Above average	0.2	8%	35%	-10%	45%	29%
Boom	0.1	8%	50%	-20%	30%	43%

High-Tech Corporation is an electronics firm; Excel Collections Ltd. Collects past-due debts; and Ribbon Manufacturing Ltd. manufactures tyres and other rubber and plastics products. The bank also maintains an Index fund which owns a market weighted fraction of all publicly traded stocks; you can invest in that fund and thus obtain average stock market results.

a) Calculate the expected rate of return on each alternative.

Expected Rate of Return of T - Bills

{(0.1*8%)+(0.2*8%)+(0.4*8%)+(0.2*8%)+(0.1*8%)} = 8.00%

Expected Rate of Return of High - Tech Corporation

{(0.1*-22%)+(0.2*-2%)+(0.4*20%)+(0.2*35%)+(0.1*50%)} = 17.40%

Expected Rate of Return of Excel Collections Ltd

{(0.1*28%)+(0.2*14.7%)+(0.4*15%)+(0.2*-10%)+(0.1*-20%)} = 7.74%

Expected Rate of Return of Ribbon Manufacturing

{(0.1*10%)+(0.2*-10%)+(0.4*7%)+(0.2*45%)+(0.1*30%)} = 13.80%

Expected Rate of Return of Market Portfolio

{(0.1*-13%)+(0.2*1%)+(0.4*15%)+(0.2*29%)+(0.1*43%)} = 15.00%

b) Basing a decision solely on expected returns is only appropriate for risk neutral individuals. Because the beneficiaries of the trust, like most people are risk averse, and the riskiness of each alternative is an important aspect of the decision. Calculate the standard deviation for each alternative.

Standard Deviation is square root of {(Pr*(Rr-ERR)2)+(Pba*(Rba-ERR)2)+(Pa*(Ra-ERR)2)+(Pav*(Rav-ERR)2)+(Pb*(Rb-ERR)2)}

Standard Deviation of T - Bills

(0.1*(8%-8%) )+(0.2*(8%-8%) )+(0.4*(8%-8%) )+(0.2*(8%-8%) )+(0.1*(8%-8%) )

= 0+0+0+0+0

= 0.00%

Standard Deviation of High - Tech Corporation

(0.1*(-22%-17.4%) )+(0.2*(-2%-17.4%) )+(0.4*(20%-17.4%) )+(0.2*(35%-17.4%) )+(0.1*(50%-17.4%) )

= 155.236+75.272+2.704+61.952+106.276 = 401.44

= 20.04%

Standard Deviation of Excel Collections Ltd

(0.1*(28%-7.74%) )+(0.2*(14.7%-7.74%) )+(0.4*(15%-7.74%) )+(0.2*(-10%-7.74%) )+(0.1*(-20%-7.74%) )

= 41.04676+9.68832+21.08304+62.94152+76.95076 = 211.7104

= 14.55%

Standard Deviation of Ribbon Manufacturing

(0.1*(10%-13.8%) )+(0.2*(-10%-13.8%) )+(0.4*(7%-13.8*%) )+(0.2*(45%-13.8%) )+(0.1*(30%-13.8%) )

= 1.444+113.288+18.496+194.688+26.244 = 354.16

= 18.82%

Standard Deviation of Market Portfolio

(0.1*(-13%-15%) )+(0.2*(1%-15%) )+(0.4*(15%-15%) )+(0.2*(29%-15%) )+(0.1*(43%-15%) )

= 78.4+39.2+0+39.2+78.4 = 235.2

= 15.34%

c) Calculate the coefficient of variation (CV) for the different securities. Does the CV produce the same rankings as the standard deviation?

d) Suppose you create a two-stock portfolio by investing KES 4 million in High-Tech Corporation and KES 6 million in Excel Collections Ltd.

i. Calculate the expected return, the standard deviation and the coefficient of variation for this

portfolio.

ii. How does the riskiness of this two-stock portfolio compare to the riskiness of the individual stocks if they are held in isolation?