Question

1. A stock ABC can be in one of the four economic states in 2020. The return for each state is shown below. The probability of each state is the same = 25%:

   • Good state of the economy will cause the stock to return 35%
   • Normal state of the economy will cause the stock to return 15%
   • A bad state of the economy will cause the stock to be flat, return 0%
   • In case of a severe crash in the economy, the stock will lose 20%

   What is the stock’s average return and standard deviation?

   	A.	E(R) = 7.5%; SD 20.2%
   	B.	E(R) = 15.5%; SD 16.0%
   	C.	E(R) = 5.5%; SD 19.1%
   	D.	E(R) = 17.5%; SD 15.4%

Answer 1

Given Data :

R(G) = 35%

R(N) = 15%

R (B) = 0%

R (C) = -20%

= 35%*25% + 15*25% + 0*15% -20*25%

= 8.75% + 3.75% + 0 - 5%

= 7.50%

Hence the Expected return = 7.50%

State	Probability	Return	Expected return	Deviation	D2	P x D2
Good	0.25	35	8.75	27.50	756.25	189.0625
Normal	0.25	15	3.75	7.50	56.25	14.0625
Bad	0.25	0	0	-7.50	56.25	14.0625
Severe	0.25	-20	-5	-27.50	756.25	189.0625

Total 7.50% 406.25

Standard Deviation = Square root of 406.25

= 20.20

Hence the correct option is A.