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=r for each month, then the annualized return is rA=(1+r)121. 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 portfolio cc return is rp,t=rGS,t+(1)rAIG,t. True False Why? (c) Assume rt is continuously compounded (cc) 1-month returns with rtiidN(,2). Then the sample mean ~=T1t=1Trt has a same distribution with rt hence ~N(,2), because of (i) the iid property of rt, and (ii) the property of the normal distribution. (d) Let ^=0.01 be the estimates of the population mean of Goldman Sachs ce returns and its estimated standard deviation ^=0.1. Then (asymptotic) 95%CI for is (0,0.02). True False Why? (e) If X and Y are uncorrelated (i.e., Corr (X,Y)=0 ), then they are statistically independent. True False Why? (f) If RAIG,tN(0,AIG2) and RGS,tN(0,GS2) and they are not independent, the simple portfolio return Rp,t=xGSRGS,t+xAIGRAIG,t is distributed as N(0,xGS2GS2+xAIG2AIG2)