Proability Rate of Return (Quants) return, standard, following, developed

hardwork24

An analyst developed the following probability distribution of the rate of return for a common stock
Scenario Probability Rate of Return
1 0.25 0.08
2 0.50 0.12
3 0.25 0.16
The standard deviation of the rate of return is closest to
A. 0.0200
B. 0.0267
C. 0.0283
D. 0.0400

Answer:C
Expected value=0.12
Variance=0.0008
Standard deviation=0.028

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Anyone know why the ans is C.

thisisbrianly

Thanks! This was taken off the net from kaplan-financial for CFA 2008 hence they still have it in 4 choices I guess.

My exam is in June 2010.

mnieman

0.25 * 0.08 = 0.02
0.5 * 0.12 - 0.06
0.25 * 0.16 = 0.04

Now add all those three to get the Expected return of the portfolio.

0.02 + 0.06 + 0.04 = 0.12

The variance formula is as follows:

Variance = 0.25 * (0.08-0.12)^2 + 0.5 * (0.12-0.12)^2 + 0.25 * (0.16-0.12)^2
Variance = 0.0004 + 0 + 0.0004
Variance = 0.0008

Standard Deviation = Variance^0.5

Therefore:
Standard Deviation = Variance^0.5 = 0.0008^0.5 = 0.0283

Hope it helps.

Good luck

Kiakaha

BTW, why do you have four choices in your question?
The CFAI changed to three choices... fyi