Question

Assume that you recently graduated from ADU’s MHA program and landed a job as an assistant financial officer with the Cleveland Clinic. The clinic has $100,000 sitting in a checking account. The funds were designated by the board for the construction of a proton therapy facility. Construction of the facility will start one year from now. Your first assignment is to invest the $100,000 with the understanding that you need to plan for a one-year holding period because the funds must be available when construction begins in one year. 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.

g. 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

So to solve this questions the following steps need to be taken:

For each alternative we calculate the Expecter return by multiplying the probabilty with the return and then we calculate the variance as shown in the below screen shot and take an under root to find the standard deviation.

Coefficient of variation is calculated by dividing the standard deviation with the expected return

Beta is calculated using the capm equatio. Tbills are risk free so they have 0 beta and market portfolio has 1 beta. for all others beta is used by backcalculating using the capm equation:

Er=Rf+b(Rm-Rf)

Where Rf is the expected return of the t bills, and Rm is that on the market portfolio. Er is the ecpected return of that alternative as calculatied in the screen shot below

Coming to the calculations of the two asset portfolio:

We first need to find the covariance of the two alternatives and dividing the covariance by the standard deviation of both the alternatives, we calculate the coefficient of correlation

Using this correlation and the equation of portfolio standard deviation we calculate the standard deviation for this portfolio:

here the rho sign is the correlation

So as shown in the above screenshot, the standard deviation and the expected retun of the portfolio have been calculated as 1.423% and 9.57% respectively variance is the square of standard devaition which is 0.020%

Two asset portfolio has a much lower standard deviation as compared to the assets individually therefore it has a lower risk. this is so because Alta inds does well when the economy is doing well and rapomen does well when the economy is doing bad so together the portfolio does better in all conditions as compared to the individual alternatives.