Question

 

Assume that you recently graduated and you just landed a job as a financial planner with the Cleveland Clinic. Your first assignment is to invest $100,000. Because the funds are to be invested at the end of 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.

State of Economy	Probability	T-Bills	Alta Inds.	Repo Men	American Foam	Market Port.
Recession	0.1	8.00%	-22.0%	28.0%	10.0%	-13.0%
Below Average	0.2	8.00%	-2.0%	14.7%	-10.0%	1.0%
Average	0.4	8.00%	20.0%	0.0%	7.0%	15.0%
Above Average	0.2	8.00%	35.0%	-10.0%	45.0%	29.0%
Boom	0.1	8.00%	50.0%	-20.0%	30.0%	43.0%

Barney Smith Investment Advisors recently issued estimates for the state of the economy and the rate of return on each state of the economy. Alta Industries, Inc. is an electronics firm; Repo Men Inc. collects past due debts; and American Foam manufactures mattresses and various other foam products. Barney Smith 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. Given the situation as described, answer the following questions.

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

b. Calculate the standard deviation of returns on each alternative.

c. Calculate the coefficient of variation on each alternative.

d. Calculate the beta on each alternative.

 

Answer 1

Solution :

Here is the tabular column calculated all the requirements :

State of Economy	Probability	T bills	Alta Inds	Repo Men	American Foam	Market Port
			Stock A	Stock B	Stock C	Stock D
Recession	0,1	0,08	-0,22	0,28	0,10	-0,13
Below average	0,2	0,08	-0,02	0,15	-0,10	0,10
Average	0,4	0,08	0,20	0,00	0,07	0,15
Above Average	0,2	0,08	0,35	-0,10	0,45	0,29
Boom	0,1	0,08	0,50	-0,20	0,30	0,43
	Expected value	0,08	0,17	0,01	0,07	0,07
	Standard deviation	0,00	0,20	0,13	0,20	0,17
	Coeff of Variation = SD/Mean	0,00	1,15	13,17	3,07	2,57

The explanation is stated below :

a) The expected rate of return from each stock and t bills would be calculated by multiplying the rate of return from each state of the economy with the probability and it will have arrived.

ex fro stock A ie Alta Inds = -,22 *,1 + -,02*,2 + ,2*,4 + ,35*,2 + ,5*,1

= .17 =17% as shown below for others as well :

b) The standard deviation of returns on each alternative would be :

SQRT ((sum product of the Stock A return of each state economy - the expected rate of return; probability ))

hence for stock A = 20%

c) Coeff of variation = Standard deviation / Mean = lesser the Coeff of variation less the risk would be in terms of investing in that stock

hence for stock A = 20/17 = 1,15

d) To compute Beta formula is = Covariance of stock with t bills / Variance of the t bills