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# Standard Deviation and BA II Calculator

#### WoodsFRM

##### New Member
I have come across this question and cannot seem to do the calculation in the BA II calculator. The question is:

Use the probability distribution to calculate the standard deviation for the portfolio

State of economy Prob Return
Boom 0.30 15%
Bust 0.70 3%

a) 6.0%
b) 7.0%
c) 6.5%
d) 5.5%

I use to use the following formula

(0.3 x 0.15) + (0.7 x 0.03) = 0.0660

0.3 x (0.15 - 0.0660)2 = 0.0021 +
0.7 x (0.03 - 0.0660)2 = 0.0009

The issue is I get 0.0028 everytime. What am I doing wrong? is there an easier way to calculate this?

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @WoodsFRM See below, my simple XLS is here https://www.dropbox.com/s/72ux3k27hwlu4in/120920-2st-variance.xlsx?dl=0

looks like the exact variance is about 0.003024 such that the volatility is sqrt(0.003024) = 5.4991%, or about 5.5%. Re easier way, I tend to prefer σ^2(R) = E(R^2) - [E(R)]^2; see https://en.wikipedia.org/wiki/Variance

In this case, σ^2(R) = E(R^2) - [E(R)]^2 = 0.007380 - 0.0660^2 = 0.003024 where 0.007380 = (0.30*15%^2) + (0.70* 3.0%^2), although maybe that's not easier. Hope that's helpful, 