Question

1. Given the following probability distributions, what are the standard deviations for the Market and for Security J? (rm is the return for the market, and rj is the return for security J)

State     PRj         rm        rj   

1            0.3         -20%     40%

2            0.4         10%       -20

3            0.3         20%       20

Answer 1

	STANDARD DEVIATIO
MARKET	11.5%
SECURITY J	18.32%

	market					security J
PROBABLITY	RETURN x	MEAN	return x - mean	(return-mean)^2*pr	PROBABLITY	RETURN x	MEAN	return x - mean	(return-mean)^2*pr
0.3	-20.0%	0.0333	-0.233	0.01633	0.3	40.0%	0.133333333	0.267	0.0213
0.4	10.0%	0.0333	0.067	0.00178	0.4	-20.0%	0.133333333	-0.333	0.0444
0.3	20.0%	0.0333	0.167	0.00833	0.3	20.0%	0.133333333	0.067	0.0013
average return	3.33%		sum	0.0264	average return	13.33%		sum	0.0671
variance			=sum/n-1	1.32%	variance			=sum/n-1	3.36%
std deviation			=(sum/n-1)^(1/2)	11.50%	std deviation			=(sum/n-1)^(1/2)	18.32%