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. e. Do the SD, CV, and beta produce the same risk ranking? Why or why not? f. Suppose you create a two-stock portfolio by investing $50,000 in Alta Industries and $50,000 in Repo Men. Calculate the expected return, standard deviation, coefficient of variation, and beta for this portfolio. How does the risk of this two-stock portfolio compare with the risk of the individual stocks if they were held in isolation?

Answer 1

Sr. No.	State of Economy		Probability (P)	T-Bill	Alta Inds.	Repo Men	American Foam	Market Port.
1	Recession		0.1	8%	-22%	28%	10%	-13%
2	Below Average		0.2	8%	-2%	14.7%	-10%	1%
3	Average		0.4	8%	20%	0%	7%	15%
4	Above Average		0.2	8%	35%	-10%	45%	29%
5	Boom		0.1	8%	50%	-20%	30%	43%
a.	Expected Return (Mean)= (P1*R1) + (P2*R2)+...+(P5*R5)			8%	17.4%	1.74%	13.8%	15%
b.	Standard Deviation= [ P1*(X1-Mean)2 + P2*(X2-Mean)2+...+P5*(X5-Mean)2]1/2			0%	20%	13.4%	18.8%	15.3%
c.	Coefficient of Variation (CV)= [Standard Deviation/Mean]*100			0	114.94	770	136.23	102
d.	Beta= Cov (X,Y) / Variance of X i.e Market			0	0.49	3.27	0.58	0.43
	Co variance (X,Y)= Sum of P*[(X-mean)*(Y-Mean)] X= Market Port. Y= Alternative			0	84.56	-56.5	55.44
e.	Ranks as per SD CV Beta			1 1 1	5 3 3	2 5 5	4 4 4	3 2 2

Ranking as per SD,CV and Beta id not same because the dimensions of the three are different

SD measures upside and downside risk of a security where as CV measures the risk per unit of return of a security on the other hand beta measure the change in return of the security due to 1% change in market return. All the three are better when lower in value.