Question

You are to invest $100,000 for a client. Because the funds are to be invested in business(es) 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.

                                   Returns On Alternative Investments              

                                                  Estimated Rate Of Return                   

    State of            ??     T-         Alta      Repo          Am.         Market            2-Stock

     Economy              Prob.      Bills      Inds Men       Foam       Portfolio           Portfolio

Recession                 0.1        8.0%    -22.0%    28.0%    10.0%      -13.0%         3.0%

Below Avg                0.2         8.0          -2.0        14.7       -10.0             1.0             6.4

Average                    0.4         8.0         20.0          0.0          7.0           15.0           10.0

Above Avg               0.2         8.0         35.0       -10.0        45.0           29.0           12.5

Boom                        0.1         8.0         50.0       -20.0        30.0           43.0           15.0

Expected Return ()             8.0         17.4%   1.7% 13.8%       15.0%       9.58%

Std Dev (?)                           0.0         20.0       13.4 18.8          15.3           3.34

Beta (?) 0          1.29 -0.86 0.68 1           0.215

The estimated returns of Am.Foam(American Foam) do not always move in the same direction as the overall economy. For example, when the economy is below average, consumers purchase fewer mattresses than they would if the economy was stronger. However, if the economy is in a flat-out recession, a large number of consumers who were planning to purchase a more expensive inner spring mattress may purchase, instead, a cheaper foam mattress. Under these circumstances, we would expect American Foam’s stock price to be higher if there is a recession than if the economy was just below average.

Alta Inds(Alta Industries) is an electronics firm; Repo Men collects past-due debts; and American Foam manufactures mattresses and other foam products.

Sungkyunkwan Investment’s economic forecasting staff has developed probability estimates for the state of the economy, and its security analysts have estimated the rate of return on each alternative under each state of the economy.

Sungkyunkwan Investment 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.

Disregard for now the items at the bottom of the data; you will fill in the blanks later.

Given the situation as described, answer the following questions:

1) Why is T-Bill's return independent of economic conditions? Can T-Bill promise completely risk free rates? (5 points)

2) Calculate the expected return on Alta Inds. (5 points)

3) You should be aware that making investment decisions based solely on expected returns is possible only if it is risk neutral. Your customers are risk takers and recognize that the level of risk of each investment alternative is a very important part of investment decisions. The standard deviation of returns is presented as an estimate of risk.

(a) Alta Ind. Present an equation to calculate the standard deviation of returns and do the actual calculation. (5 points)

(b) What type of risk is measured by the standard deviation?

4) Assume that you invested $ 50,000 each in Alta Inds and Repo Men.

(a) Calculate expected returns and standard deviations for this portfolio. (5 points)

(b) What is the risk level of this 2-stock portfolio compared to the risk level of each individual stock before forming the portfolio? Is it higher or lower? (5 points)

5) How is market risk measured for individual stocks? What does beta (?) mean? (10 points)

6) Sungkyunkwan Investment Inc. (Sungkyunkwan Investment Company) presents statistically estimated expected rates of return and beta coefficients for individual investments as follows. (Summarized in the table above)

Security                      Return ()                  Risk (?)

                                 Alta Inds                       17.4%                         1.29

                                 Market 15.0 1.00

                                 Am. Foam                    13.8 0.68

                                 T-Bills                           8.0 0.00

                                 Repo Men                     1.7 (0.86)

(a) Calculate the required rate of return for each investment alternative using the stock market linear equations. (10 points)

(b) Compare each of the investment alternatives with the expected rates of return and the required rates of return (CAPM-theorized expected return) to give an overvaluation or undervaluation . (10 points)

(c) Calculate the market risk and demand rate of a portfolio consisting of 50% each of Alta Ind and Repo Men. (10 points)

Answer 1

	State of Economy	Probability	Treasury Bills	Alta Industries	Repo men	Am foam	Market Potpolio	2-stock portpolio
	Recession	10.00%	8.00%	-22.00%	28.00%	10.00%	-13.00%	3.00%
	Below Avg	20.00%	8.00%	-2.00%	14.70%	-10.00%	1.00%	6.40%
	Average	40.00%	8.00%	20.00%	0.00%	7.00%	15.00%	10.00%
	Above Average	20.00%	8.00%	35.00%	-10.00%	45.00%	29.00%	12.50%
	Boom	10.00%	8.00%	50.00%	-20.00%	30.00%	43.00%	15.00%
	Expected Return		8.00%	17.40%	1.70%	13.80%	15.00%	9.58%
	Std Deviation		0.00%	20.00%	13.40%	18.80%	15.30%	3.34%
	Beta		0	1.29	-0.86	0.68	1	0.215
Solution 1)
	T-bill is risk free stock .It is risk neutral i.e.whether market moves up or down but return on t-bill remains constant so T-bill return is independent of state of economy
	Yes,t-bill promised totally risk free rates consequently it's S.d and Beta is always 0.
Solution 2)	Calculation of expected return on Alta inds. :
	(sum of returns at various probablity under state of economy)
	i.e.(-22*10%)+(-2*20%)+(20*40%)+(35*20%)+(50*10%)
	17.4
	i.e. 17.4%
Solution 3(a)
	Calculation of statndard deviation on Altd indus :
		N	N-mean(n)	(N-mean(n))^2	Prob.
		(A)	(B)	©	(D)	©*(D)
	Recession	-22	-39.4	1552.36	10.00%	155.24
	Below Avg	-2	-19.4	376.36	20.00%	75.27
	Average	20	2.6	6.76	40.00%	2.70
	Above Average	35	17.6	309.76	20.00%	61.95
	Boom	50	32.6	1062.76	10.00%	106.28
	Total					401.44
	mean (n) i.e expected return	17.4
	Std.Dev
	Square root (N-mean(n)^2)*Prob)
	i.e.square root of 401.44
	i.e.20%
Solution 3(b)
	Std deviation measures deviation from mean and than take average of deviations i.e average of deviations.
	It involves both both systematic risk(affected by market factors) as well as unsystematic risk (due to factors specific to co.)
Solution 4(a)
	Expected Return:
	we invested 50000 each in both stocks;so weight is equal.
	return =(E.R.(Alta inds)*weight in portpolio)+(E.R.(Repo men)*weight in portpolio)					E.R. expected Return
	(17.4%*0.5)+(1.7%*0.50)
	9.55%
	Standard Deviation:
	Calculation Of Covariance	Beta(alta)*beta(repo)*(s.d. of market)^2
		1.29*-0.86*((15.3)^2)
		Approx -259.70%
	Calculation of correlation Coefficeinti.e r	cov/(s.d(alta)*s.d(repo))
		(-259.7)/(20%*13.4%)
		-0.97
	S.d.	Squrae root((S.d(Alta)*0.5)^2 (+) (S.D.(Repo)*0.5)^2 (+) 2*(S.d(Alta)*0.5)*(S.D.(Repo)*0.5)*Covariance)							(0.5 is weight in portpolio here)
		(20*50%)^2+(13.4*50%)^2+2*(20*50%)*(13.4*50%)*-0.97				14.91%
		3.86
		i.e 3.86%
Solution 4 (b)
		Alta Industries	Repo men	Am foam	Market Potpolio	2-stock portpolio
	Risk level (s.d.)	20.00%	13.40%	18.80%	15.30%	3.34%
	Expected Return	17.40%	1.70%	13.80%	15.00%	9.58%
	Coefficient of varaiation(C.V) (S.d/E.R.)	1.15	7.88	1.36	1.02	0.35
	By computing C.v we can say that 2stock portpolio have less risk level as per unit of return only 0.35 % is risk as compare to others.
	i.e. lower risk level