Example of Arbitrage Suppose there are two well-diversified portfolios, A and B, in the economy; portfolio A has B,-1 and expected return of 10%, while the portfolio B has Bg= 0.5 and the expected return of 6%. The risk-free rate is 4%. First, let us determine which portfolio, if any, is mispriced. According to CAPM: E(re) - 0.04 +0.5*(0.1-0.04) = 0.07 = 7% - priced? Clearly, portfolio B is o Since portfolio B is below the SML, it means that its return is less than that necessary to compensate investor for bearing that level of risk; to put it differently, its return is too low: o Since prices and returns are inversely related, if the return is too low, it means that its price is too high, so price B is overpriced. o which means that we want to sell B. Does this strategy call arbitrage? Then we will combine the risk-free asset and portfolio A so that the new portfolio C, has the acer F11 Numlk Ven Mum F12 F8 F9 F10 F7 F6 F5 F4 F3 F2 z' 8. & 1/2 3. U 4 1 5 0 6 P T Y %23 10% ADMN3700 7 same beta as portfolio B What are the weights of the risk-free asset and portfolio A in the portfolio C? Bc = WABA +WrBr = BB %3D Since Br= Bc WA BA 0.5 0.5 W = 1- WA1 - 0.5 0.5 What is the expected return on portfolio C? E (rc) = WAE(rA) +wrT - So we want to sell and buy It follows that asset B and portfolio C provides the same risk exposure (since B B). but return of asset B is lower. We conclude that asset B is overpriced with respect to asset A and an investor can follow the following arbitrage strategy: Sell short asset B and use all the proceeds to buy portfolio C. The cost of this strategy is zero but the profit is positive and riskless. For example, if we short asset B worth SI. 000, 000 and invest this amount into portfolio C, then our return will be: 1.000, 000 (-0.06) Sell B -S600,000 WRW acer F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 Prsc Sya & 8. 3. 4 1CLE 8 1/2 Y U 4 I 50 6 P *