4. Indicate whether the following statements are true or false (circle one). Use 1 or 2 sentences to discuss why it is so. (a) Let rt be continuously compounded (cc) 1-month return. If rt is negative for a certain month, then the gross simple return 1+Rt is also negative. True False Why? (b) Let rGS,t and rAIG,t be continuously compounded 1-month returns for Goldman Sachs Group (GS) and American International Group (AIG). If we construct a portfolio using the share [0,1] for GS, the variance of the portfolio cc return is p,t=2Var(rGS,t)+ (1)2Var(rAIG,t)+2(1)Cov(rGS,t,rAIG,t). True False Why? (c) Assume rt is continuously compounded (cc) 1-month returns with rt iid N(,2). Then the annualized cc return rA=r1+r2++r12. True False Why? (f) If RAIG,tN(0,AIG2) and RGS,tN(0,GS2) and they are correlated, the simple portfolio return Rp,t=xGSRGS,t+xAIGRAIG,t is distributed as N(0,xGS2GS2+xAIG2AIG2). True False Why? (g) In multi-factor asset pricing models, Rit=i+i1f1t++iKfKt+it=i+ift+it where - Rit is the return on asset i at t(i=1,,N), - fjt is the realization of the j-th factor at t(j=1,,K) it is the idiosyncratic disturbances the estimates for ij for j=1,,K are usually negligible, i.e., they are very close to zeros empirically