Question

Expected Returns: Discrete Distribution

The market and Stock J have the following probability distributions:

Probability	rM	rJ
0.3	14%	18%
0.4	9	7
0.3	19	12

1. Calculate the expected rate of return for the market. Round your answer to two decimal places.
   %
   
   Calculate the expected rate of return for Stock J. Round your answer to two decimal places.
   %
   
2. Calculate the standard deviation for the market. Do not round intermediate calculations. Round your answer to two decimal places.
   %
   
   Calculate the standard deviation for Stock J. Do not round intermediate calculations. Round your answer to two decimal places.
   %

Answer 1

We need to calculate all the required numbers in the table below:

Probability	rM	PxRm	(rM-Er)2	rJ	PxRj	(rj-Er)2
0.3	14.000%	0.3 x 14= 4.200%	0.000025	18.000%	0.3 x 18 = 5.400%	0.003844
0.4	9.000%	0.4 x 9= 3.600%	0.002025	7.000%	0.4 x 7 = 2.800%	0.002304
0.3	19.000%	0.3 x 19=5.700%	0.003025	12.000%	0.3 x 12=3.600%	4E-06
Er		4.2+3.6+5.7=13.500%	0.005075		5.4+2.8+3.6 = 11.800%	0.006152
Variance			0.005075/2=0.002538			0.006152/2=0.003076
Standard deviation = Square root of variance			5.0%			5.5%

• We multiply the returns to their corresponding probability and add these probability weighted values to calculate expected returns
• To find the standard deviation, we follow the following steps:
  • First we calculate the difference of each return value with the expected return value
  • Second we square these differences
  • Third we sum these squared differences
  • Fourth we divide the sum by (n-1) so in this case as there are 3 probable cases, we divide the sum of squared difference by 2. This value we receive is the variance
  • We take a square root of the variance to calculate the standard deviation

1. So Expected return for market is 13.5%
2. So Expected return for stock j is 11.8%
3. So Standard deviation for market is 5%
4. So Standard deviation for stock J is 5.5%