Question

Following are three economic states, their likelihoods, and the potential returns: Economic State Probability Return Fast growth 0.26 60% Slow growth 0.37 27 Recession 0.37 -39 Determine the standard deviation of the expected return.(Do not round intermediate calculations and round your answers to 2 decimal places)

Answer 1

We first need to calculate expected standard deviation for this question:

Expected return is weighted (by probability) average of returns expected in different scenarios.

E[R] = (0.26 * 60%) + (0.37 * 27%) + (0.37 * -39%) = 15.6% + 9.99% + (-14.43%) =11.16%

Now, in order to calculate the standard deviation, we first need to calculate the sum squared deviations of individual returns from the expected return. (It sounds complicated, but in simple terms, calculation is shown as below in table):

Scenario	Probability	Return	Squared Deviation from Expected Return
1	0.26	60%	= (0.6 - 0.1116)^2 = 0.238535
2	0.37	27%	= (0.27 - 0.1116)^2 = 0.025091
3	0.37	-39%	= (-0.39 - 0.1116)^2 = 0.251603

Variance = (0.238535 * 0.26) + (0.025091 * 0.37) + (0.251603 * 0.37) = 0.062019 + 0.009284 + 0.093093 = 0.1644

Standard deviation = square root of variance = square root of 0.1644 = 40.55% --> Answer