Question

For 5 years (from 1962-1966), the Dow Jones Industrial Average had returns of -7.6%, 20.6%, 18.7%, 14.2%, and

-15.6%. What is the standard deviation of these returns?

A. 14.79

B. 38.45

C. 24.62

D. 16.53

E. 40.66

Answer 1

The correct Answer is D

Let us understand Step by Step Working of the Same

Step 1 - We need to Calculate the mean

Step 2:- We then need to calculate the Deviation of Each Return from its mean

Step 3:- We then need to take a square of the deviation

Step 4:- We then need to do a summataion of Such Squared Deviation

Step 5:- We then need to use the formula mentioned below:-

Standard Deviation = {(X-Mean)^2 / N-1} ^(1/2)

We have used N-1 as this is a sample and not the entire population of returns.

Therefore accordingly we have the below:-

Years	Retruns of Dow Johns (D)	Mean ('E)	Deviation (F= D-E)	Squared Deviation (G= |F|^2)
1992	-0.0760	0.0606	-0.1366	0.0187
1993	0.2060	0.0606	0.1454	0.0211
1994	0.1870	0.0606	0.1264	0.0160
1995	0.1420	0.0606	0.0814	0.0066
1996	-0.1560	0.0606	-0.2166	0.0469
Total (A)	30.30%			0.1093
No. of Years (B)	5.00
Mean ('C)	6.06%

Now a Total Squared Deviation = 0.1093192

Standard Deviation = (0.1093192/ 5-1)^(1/2)

Standard Deviation = 0.0273298/^(1/2) = 16.531%

We can also calculate the same using the equation approach