Question

7) You are considering investing in the following stock X. State of the Economy Recession Below Average Average Above Average Boom Probability 10% 16% 51% 14% 9% Stock x Return - 75% -10% 15% 33% 82% a) Calculate the expected return of the stock. b) Calculate the standard deviation (riskiness) of returns for this stock. c) You are also looking into Stock Y which has the same expected return as Stock X, but a higher standard deviation. Which stock would you invest in and why?

Answer 1

A. Expected return is 10.55%

B. Standard deviation is 0.37

C. I would prefer to invest in Stock X as the Stock y has a higher standard deviation.

Please find the solution

Expected Return =R1*P1+R2*P2+R3*P3+R4*P4+R5*P5 = 10.55% (refer to the below table)

Where R is Return on Stock X and P is Probability.

Standard deviation= Square root of Variance, Variance is Summation of P* (Return on Stock X-Expected Return)^2 =0.37 (refer to the below table)

State of the economy	Probability (P)	Stock X Return (R)	Expected Return= P* R	(R-E(R))^2	Standard Deviation=SQUARE ROOT OF (R-E(R))^2*P
Recession	10%	-75%	-7.50%	0.73	0.07
Below AVG	16%	-10%	-1.60%	0.04	0.01
Average	51%	15%	7.65%	0.002	0.001
Above Average	14%	33%	4.62%	0.05	0.01
Boom	9%	82%	7.38%	0.51	0.05
			10.55%		0.13
					0.37	SD