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.

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? **Please show all calculations and formulas used to derive the answers**

Answer 1

State of Economy	Probability	Market Port.	Px	P(R-X)^2
	P	X	a * b
Recession	0.1	-13.00%	-1.30%	92.42	-13
Below Average	0.2	1.00%	0.20%	53.79	1
Average	0.4	15.00%	6.00%	2.30	15
Above Average	0.2	29.00%	5.80%	26.91	29
Boom	0.1	43.00%	4.30%	65.54	43
		Expected return (R)	15.00%	240.96
		Standard deviation		16%
Investment in Repo Man (Wx)	50,000.00
Investment in Alta Inds. (Wy)	50,000.00
	100,000.00
Compution of weight of investment
Wx	0.50	50000/100000
Wy	0.50	50000/100000
State of Economy	Probability	Repo Men			Alta Inds.			Cov(xy)
	P	X	PX	P(X-ERx)^2	Y	PY	P(Y-ERy)^2	P(X-ERx)(Y-ERy)
Recession	0.1	28.00%	2.80%	11.24	-22.00%	-2.20%	155.24	-103.46
Below Average	0.2	14.70%	2.94%	1.46	-2.00%	-0.40%	75.27	-50.28
Average	0.4	0.00%	0.00%	121.10	20.00%	8.00%	2.70	-1.81
Above Average	0.2	-10.00%	-2.00%	150.15	35.00%	7.00%	61.95	-41.32
Boom	0.1	-20.00%	-2.00%	139.88	50.00%	5.00%	106.28	-70.87
Avarege return		ERx	1.74%	423.83	ERy	17.40%	401.44	-267.74
		SDx		20.59%	SDy		20.04%
Coefficient of r	Cov(xy) / SDxSDy =
SD of portfolio	8.52	Wx2SDx2 + Wy2SDy2 + 2* Wy* Wx*Cov(xy)
Return of portfolio	9.57	(1.74*50000)+(17.40*50000)/100000
Coefficient of variation	0.89	Sd of portfolio / Return of portfolio
Beta of stock =	Return of stock/Market return
B_Repo Men	0.12	1.74/15
B_Alta Inds.	1.16	17.4/15
B_portfolio	0.64	(0.12*50000)+(1.16*50000)/100000

Portfolio	ER	SD	Coeff of variation (SD/ER*100)
Two Stock portfolio	9.57	8.52	89%
Alta Inds.	17.40%	20.04%	115%
Repo Men	1.74%	20.59%	1183%

Since Coeff of variation is lowest in two stock portfolio hence two stock portfolio is efficient as compared to stocks held in isolation.