a$)$ b$)$ c$)$ d$)$ e$)[10$ marks$]$ Consider two stocks that satisfy the CAPM. The returns of these two stocks are given by the equation ri$=$ rf $+$ bi$($rM $-$rf$)+$ei$,$ where i$=1,2.$ Idiosyncratic shocks ei are uncorrelated across assets and have volatility se $=30\%.$The stocks have betas b$1=1$ and b$2=1\mathrm{.}5,$ respectively. The expected annual return and the volatility of the market portfolio are given by E$[$rM$]=6\%$ and sM $=20\%,$ respectively. The riskless rate is rf $=2\%$ per year. Construct a portfolio of these two stocks that has expected annual return of $6\mathrm{.}5\%.$ What are the portfolio weights? What is the volatility of this portfolio? $[10$ marks$]$ Consider $10$ stocks with returns given by: ri$=!+$rf $+$ b$($rM $-$rf$)+$ei$,$ where i$=1,...,10.$ All stocks have the same $!"$#$$\%$& and b$=0\mathrm{.}7.$ Idiosyncratic shocks ei are uncorrelated across assets and with the market portfolio returns rM$,$ and have volatility se $=30\%.$ The expected annual return and the volatility of the market portfolio are given by E$[$rM$]=6\%$ and sM $=30\%,$ respectively. The riskless rate is rf $=2\%$ per year. Calculate the Sharpe ratio and return volatility for each individual stock. Then, calculate the Sharpe ratio and volatility of the equally weighted portfolio of these $10$ stocks. $[10$ marks$]$ Consider three portfolios A$,$ B$,$ and C that have the following annual volatilities and expected returns: $1)$ sA$=10\%,$ E$[$rA$]=6\%$; $2)$ sB$=15\%,$ E$[$rB$]=8\%$; $3)$ sC$=18\%,$ E$[$rC$]=7\%$; respectively. Two of these portfolios lie on the efficient frontier and one portfolio does not lie on the frontier. The frontier is constructed assuming that the riskless investment is possible, and hence, the frontier is a straight line. Which of the portfolios is inefficient $($that is$,$ does not lie on the efficient frontier$)?$ What is the volatility of a portfolio P that lies on the efficient frontier and has the same expected return as the inefficient portfolio that you have identified? $[10$ marks$]$ Explain, why implementation costs may prevent investors from eliminating arbitrage opportunities. Discuss the costs of short$-$selling stocks. $[10$ marks$]$ What is noise trader risk? How can noise traders create limits to arbitrage and prevent arbitrageurs from eliminating arbitrage opportunities?