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.

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

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.