Question

If there is a 30% chance of a 14% return, a 20% chance of an 18% return. a 25% chance of an 19.5% return and a 25% chance of a 12% return, then what is the standard deviation of returns?

1.

8.95

2.

3.07

3.

2.91

4.

2.99

5.

3.47

Answer 1

Answer :

Expected return = Respective return * Respective probability

= ( 0.3 * 14 ) + ( 0.2 * 18 ) + ( 0.25 * 19.5 ) + ( 0.25 * 12 )

= 15.675%

Probability	Return	Probability * ( Return - Expected return )^2
0.3	14	0.3 * ( 14 - 15.675 ) = 0.84
0.2	18	0.2 * ( 18 - 15.675 ) = 1.08
0.25	19.5	0.25 * ( 19.5 - 15.675 ) = 3.66
0.25	12	0.25 * ( 12 - 15.675 ) = 3.38
		Total = 8.96%

Standard deviation = [ Total probability * ( Return - Expected return )^2 / Total probability ]^(1/2)

= ( 8.96 / 1 )^(1/2)

= 2.99 ( Approx. )

The answer is option (4) i.e., 2.99.