Question

A stock has the following probability distribution:

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      Demand for the                 Probability of this                   Rate of return if this

      Company’s products         demand occurring                   demand occurs                       

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      Weak                                 0.10                                         -50%

      Below Average                 0.20                                         -5%

      Average                             0.40                                         16%

      Above Average                 0.20                                         25%

      Strong                               0.10                                         60%

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      Calculate the stock’s expected return, variance of returns, and standard deviation of returns.

Answer 1

a.	Expected return	11.40%
	Working:
	Demand for the Company’s products	Probability of this demand occurring	Rate of return if this demand occurs
		a	b	a*b
	Weak	0.10	-50%	-5.00%
	Below Average	0.20	-5%	-1.00%
	Average	0.40	16%	6.40%
	Above Average	0.20	25%	5.00%
	Strong	0.10	60%	6.00%
	Total			11.40%
b.	Variance of the return	0.0712
	Working:
	Demand for the Company’s products	Probability of this demand occurring	Rate of return if this demand occurs	Expected return
		a	b	c	d=((b-c)^2)*a
	Weak	0.10	-50%	11.40%	0.0377
	Below Average	0.20	-5%	11.40%	0.0054
	Average	0.40	16%	11.40%	0.0008
	Above Average	0.20	25%	11.40%	0.0037
	Strong	0.10	60%	11.40%	0.0236
	Total				0.0712
c.	Standard deviation of return	26.69%
	Working:
	Standard deviation of return	=	Variance ^ (1/2)
		=	0.0712	^ (1/2)
		=	26.69%