Question

Given this table and that the weight of both High Tech (HT) and Collections (Coll) are both 50% how would you find the standard deviation of HT (σHT) and the standard deviation of Coll (σColl) separately?

Port -2.5% 0.5% Economy Recession Below avg Average Above avg Boom Prob 0.1 0.2 0.4 0.2 0.1 HT -29.5% -9.5% 12.5% 27.5% 42.5% Coll 24.5% 10.5% -1.0% -5.0% -20.0% 5.8% 11.3% 11.3%

Answer 1

Expected returns=Sum(probability*returns)

Standard deviation=Sqrt(Sum(probability*(returns-expected returns)^2))

Expected returns of HT=0.1*(-29.5%)+0.2*(-9.5%)+0.4*(12.5%)+0.2*(27.5%)+0.1*(42.5%)=9.90%

Standard deviation of HT=sqrt(0.1*(-29.5%-9.90%)^2+0.2*(-9.5%-9.90%)^2+0.4*(12.5%-9.90%)^2+0.2*(27.5%-9.90%)^2+0.1*(42.5%-9.90%)^2)=20.04%

Expected returns of Coll=0.1*(24.5%)+0.2*(10.5%)+0.4*(-1%)+0.2*(-5%)+0.1*(-20%)=1.15%

Standard deviation of Coll=sqrt(0.1*(24.5%-1.15%)^2+0.2*(10.5%-1.15%)^2+0.4*(-1%-1.15%)^2+0.2*(-5%-1.15%)^2+0.1*(-20%-1.15%)^2)=11.23%