How to compute the variance?

RM,e=10%+M(M)() - The risk-free rate is 0 . - Manager D1: R1=5%+2RM,e+1=25%+2M+1,1N(0,5%) i.i.d. - Manager D2: R2=5%+2RM,e+2=25%+2M+2,2N(0,5%) i.i.d. What is the strategy to max Sharp ratio? Short $1 market, invest $0.25 with D1 and $0.25 with D2, and $0.5 risk free. - Return on short position RM,e - Payoff on long position: 0.25(5%+2RM,e+2)+0.25(5%+2RM,e+2)+0.50= 0.55%+RM,e+0.25(1+2) - Normalized by initial investment: dividing by $1 to get return. Simple convention: return on a balanced long-short portfolio is the sum of the long position and the short position. Expected return: 0.55%; Variance: 1/1610%; Sharp ratio: 25% (about 0.316) RM,e=10%+M(M)() - The risk-free rate is 0 . - Manager D1: R1=5%+2RM,e+1=25%+2M+1,1N(0,5%) i.i.d. - Manager D2: R2=5%+2RM,e+2=25%+2M+2,2N(0,5%) i.i.d. What is the strategy to max Sharp ratio? Short $1 market, invest $0.25 with D1 and $0.25 with D2, and $0.5 risk free. - Return on short position RM,e - Payoff on long position: 0.25(5%+2RM,e+2)+0.25(5%+2RM,e+2)+0.50= 0.55%+RM,e+0.25(1+2) - Normalized by initial investment: dividing by $1 to get return. Simple convention: return on a balanced long-short portfolio is the sum of the long position and the short position. Expected return: 0.55%; Variance: 1/1610%; Sharp ratio: 25% (about 0.316)