Question

# Your investment has a 9% chance of earning a 55% return, a 25% chance of earning...

Your investment has a 9% chance of earning a 55% return, a 25% chance of earning an 17% rate of return, a 31% chance of earning an 9.25% rate of return, a 20% chance of losing 16%,and a 15% chance of losing 50%. What is the standard deviation of this investment?

 probability return probability*return 0.09 55 4.95 0.25 17 4.25 0.31 9.25 2.8675 0.2 -16 -3.2 0.15 -50 -7.5 average return = sum of probability*return 1.3675 probability return return-average return square of (return-average return) probability*(square of return-average return) 0.09 55 53.6325 2876.445 258.8801 0.25 17 15.6325 244.3751 61.09376 0.31 9.25 7.8825 62.13381 19.26148 0.2 -16 -17.3675 301.6301 60.32601 0.15 -50 -51.3675 2638.62 395.793 average return = sum of probability*return 1.3675 Variance = sum of probability*(square of return-average return) 795.3543 standard deviation = square root of variance 28.20

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