Question

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?

Answer 1

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