Question

Expected Return: Discrete Distribution

A stock's return has the following distribution:

Demand for the Company's Products	Probability of This Demand Occurring			Rate of Return if This Demand Occurs (%)
Weak		0.1		-35	%
Below average		0.2		-8
Average		0.4		10
Above average		0.2		35
Strong		0.1		50
		1.0

Calculate the stock's expected return. Round your answer to two decimal places.

  %

Calculate the standard deviation. Do not round intermediate calculations. Round your answer to two decimal places.

  %

Answer 1

Stock’s Expected Return = ∑ R_i*P_i

where, R_i is expected return at given demand

                P_i is probability of return achieved in given demand

                i is demand for the Company's Products

In the given problem,

Probability of This Demand Occurring P(i)	Rate of Return if This Demand Occurs (%) R(i)	P(i) * R(i)
0.1	-35%	-0.035
0.2	-8%	-0.016
0.4	10%	0.04
0.2	35%	0.07
0.1	50%	0.05

Hence Expected return of stock = (-0.035-0.016+0.04+0.07+0.05) = 0.109 i.e. 10.90%

Expected return of stock is 10.90%.

Considering the given distribution as population:

Stock’s Standard Deviation = √{1/(n)*∑(R_i-R_mean)²}

where, R_i is expected return at given demand

                R_mean is arithmetic mean of return achieved in given demand

                i is demand for the Company's Products

                n is number of observation

Rate of Return if This Demand Occurs (%) R(i)	R(mean)	R(i)-R(mean)	{R(i)-R(mean)}2
-0.35	0.104	-0.45	0.206116
-0.08	0.104	-0.18	0.033856
0.10	0.104	0.00	0.000016
0.35	0.104	0.25	0.060516
0.50	0.104	0.40	0.156816

Stock’s Standard Deviation = Square root {(0.206116+0.033856+0.000016+0.060516+0.156816)/5}

= Square root {0.4573/5}

= Square root {0.091}

= 0.3024 i.e. 30.24%

Stock’s Standard Deviation is 30.24%