Question

You invest in a stock with the following probability distribution of returns:

A probability of .15 that the return will be 16%; a probability of .35 that the return will be 24%; a probability of .3 that the return will be -40%; and a probability of .2 that the return will be 45%.

Based on this data and assuming the stock returns are normally distributed, you can say with a probability of 68% that the actual return will be in the range of:

-24.82% to 40.42%

-57.44% to 73.04%

-90% to 105%

None of the above

Answer 1

Answer is “-24.82% to 40.42%”

Expected Return = 0.15 * 0.16 + 0.35 * 0.24 + 0.30 * (-0.40) + 0.20 * 0.45
Expected Return = 0.0780 or 7.80%

Variance = 0.15 * (0.16 - 0.078)^2 + 0.35 * (0.24 - 0.078)^2 + 0.30 * (-0.40 - 0.078)^2 + 0.20 * (0.45 - 0.078)^2
Variance = 0.106416

Standard Deviation = (0.106416)^(1/2)
Standard Deviation = 0.3262 or 32.62%

65% Range of Return = Expected Return - Standard Deviation, Expected Return + Standard Deviation
65% Range of Return = 7.80% - 32.62%, 7.80% + 32.62%
65% Range of Return = -24.82%, 40.42%