15. Consider an investment with the following payoffs and probabilities:
State of the Economy Probability Return
GDP grows slowly .70 1,000
GDP grow fast .30 2,000
Let the expected value in this example be 1,300. How do we find the standard deviation of the
investment?
a. = { (1000-1300)2 + (2000-1300)2 }
b. = { (1000-1300) + (2000-1300) }
c. = { (.5)(1000-1300)2 + (.5)(2000-1300)2 }
d. = { (.7)(1000-1300) + (.3)(2000-1300) }
e. = { (.7)(1000-1300)2 + (.3)(2000-1300)2 }
16. An investment advisor plans a portfolio your 85 year old risk-averse grandmother. Her portfolio
currently consists of 60% bonds and 40% blue chip stocks. This portfolio is estimated to have an ex-
pected return of 6% and with a standard deviation 12%. What is the probability that she makes less
than 0% in a year? [A portion of Appendix B1 is given below, where z = (x – ) with as the mean
and as the standard deviation.]
a. 2.28%
b. 6.68%
c. 15.87%
d. 30.85%
e. 50% Table B1 for Z
Z Prob.
-3 .0013
-2.5 .0062
-2. .0228
-1.5 .0668
-1 .1587
-.5 ..3085
0 .5000
17. Two investments have the following expected returns (net present values) and standard deviations:
PROJECT Expected Value Standard Deviation
Q $100,000 $20,000
X $50,000 $16,000
Based on the Coefficient of Variation, where the C.V. is the standard deviation dividend by the
expected value.
a. All coefficients of variation are always the same.
b. Project Q is riskier than Project X
c. Project X is riskier than Project Q
d. Both projects have the same relative risk profile
e. There is not enough information to find the coefficient of variation.