Question

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1.

You decide to invest in a portfolio consisting of 24 percent Stock A, 44 percent Stock B, and the remainder in Stock C. Based on the following information, what is the variance of your portfolio? Probability of State of Economy Return if State Occurs State of Stock A Economy Stock B Stock C - 4.70% -13.70% Recession .126 -11.30% 18.10% Normal .689 10.60% 10.90% .185 21.79% 25.59% 30.29% Boom Multiple Choice .00874 .01062 .00940 .01269 .00987

2. Maud'Dib Intergalactic has a new project available on Arrakis. The cost of the project is $38,000 and it will provide cash flows of $21,400, $27,300, and $27,000 over each of the next three years, respectively. Any cash earned in Arrakis is "blocked" and must be reinvested in the country for one year at an interest of 3.1 percent. The project has a required return of 8.9 percent. What is the project's NPV？
A）33,076.52
B）25,577.58
C）37,075.00
D）22,191.45
F）40,445.46

Answer 1

1)

in order to calculate variance first we have to calculate expected return,standard deviation,co-variance and correlation coefficient of all stocks

Formulas:

Expected return = $\sum probability* return$

Standard deviation = $\sqrt{P(X-X')^2}$

Where P = Probability

X = return with respect to particular probability

X' = Expected return

Co-variance between two stocks = $\sum P(X-X')(Y-Y')$

Where P = Probability

X = return with respect to particular probability of stock 1

X' = Expected return of stock 1

Y = return with respect to particular probability of stock 2

Y' = Expected return of stock 2

correlation coefficient between two stocks = Co-variance of xy / standard deviation of x * Standard deviation of y

Using the above formulas:

Expected return of A P(A-A')^2 Probability Stock A P(A-A')(B-B') -1.4238 0.126 -11.3 56.68688536 43.70174481 0.327320173 -0.357143469 0.689 10.6 7.3034 4.0312 30.63089262 0.185 21.79 26.1065674 73.9755 Total 9.9108 83.1208 Expected return of B P(B-B')^2 P(B-B')(C-C') Stock B Probability -4.7 0.126 -0.5922 33.69108194 61.91036732 0.389684071 -0.907639256 0.689 10.9 7.5101 25.59 35.93929329 0.185 4.73415 35.94883381 Total 96.9516 70.0201 11.6521 P(A-A')(C-C') Probability Expected return of C P(C-C')^2 -1.7262 Stock C 0.126 -13.7 113.7658206 80.30585301 12.4709 0.689 18.1 2.114043351 0.831846761 30.63902397 5.60365 0.185 30.29 35.95837687 Total 16.3484 151.8382 111.7767

Standard deviation A		9.12
Standard deviation B		8.37
Standard deviation C		12.32

CORab	0.9696653
CORbc	0.9402709
CORac	0.9949609

(COR = correlation)

first lets calculate standard deviation of portfolio

Standard deviation of portfolio

= [(Wa*stand.devA)^2+(Wb*stand. devB)^2+(Wc*stand.devC)^2+2*Wa*Wb*stand.devA*stand.devB*CORab+2*Wb*Wc*stand.devB*stand.devC*CORbc+2*Wa*Wc*stand.devA*stand.devC*CORac]^1/2

Wa,Wb,Wc = weights of stocks A,B,C respectively

=[(0.24*9.12)^2+(0.44*8.37)^2+(0.32*12.32)^2+2*0.24*0.44*9.12*8.37*0.9696653+2*8.37*12.32*0.44*0.32*0.9402709+2*0.24*0.32*9.12*12.32*0.9949609]^1/2

standard deviation of portfolio = 9.6955741% or 0.096955741

variance = square of standard deviation

= (0.096955741)^2

= 0.00940

2)

here it is given we have to invest cash flows for one year at 3.1%

so year 1 cash inflow = 0

Year 2 cash inflow = year 1 cash flow(1+3.1%) = 21400(1+3.1%) = 22,063.4

same formula for subsequent years

discount rate given = 8.9%

cash flows PV [email protected]% Present value Year 0.9182736455 18604.4433 22063.4 0.8432264881 21794.03646 3 28146.3 0.7743126613 27837 0.7110309102 4 19792.96745 60191,4472 Total 2.

NPV = present value of cash flows - initial cash outflow

= 60,191.4472 - 38000 = 22,191.45(rounded to two decimals)

Answer 2

For number 2, the answer is D.