CMA Intermediate · Financial Management and Business Data Analytics · Risk and Return
Security P has possible returns of 10%, 20% and 30% with probabilities 0.25, 0.50 and 0.25 respectively. What is its standard deviation (approximately)?
The standard deviation is about 7.07%. The expected return is 20%, deviations are ±10 for the outer outcomes, giving variance of 0.25×100 + 0.25×100 = 50. The square root of 50 is 7.07%. Reporting 50 would confuse variance with standard deviation.
- A7.07%Correct
- B50%
- C5.00%
- D10.00%
Explanation
Expected return = 2.5 + 10 + 7.5 = 20%. Variance = 0.25(10)^2 + 0.5(0) + 0.25(10)^2 = 25 + 25 = 50 (%²). Standard deviation = √50 = 7.07%. The option 50% mistakenly reports variance as standard deviation.
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