Question

Suppose that you have invested a large sum of Investopedia $ into natural gas, which is used by a large percentage of homes for heating.

The returns on your position will depend upon the weather as given in the following table:

State Severe cold 0.075 Normal weather 0.7 Severe heat Probability Return 00.5 0.3 0.3 0.225

a.What is the expected return on your natural gas position?

b.What is the volatility of the natural gas returns?

Answer 1

Scenario	Probability	Retrun	Retrun* Probability	Deviation=Return-Expected return	Deviation^2	Probability*Deviation^2
Severe Cold	7.50%	0.90	6.750%	69.000%	47.610%	3.57075%
Normal	70.00%	0.30	21.000%	9.000%	0.810%	0.56700%
Severe Hot	22.50%	(0.30)	-6.750%	-51.000%	26.010%	5.85225%
		Total	21.000%		Total	9.99000%
So expected return is 21%
Stock variance	9.9900%
Stock Standard deviation	'9.99%^(0.5)
Stock Standard deviation	31.61%