Just need help with Part IV! Other answers provided

83. Consider a market where two factors are sufficient to describe the returns on common stock. The following table gives the sensitivities of the stocks of ABC inc, and PQR inc, to the two factors, as well as the expected returns. Security | ABC | POR Riskless Bi 10.5 1.5 0.0 Bi 10.8 1.4 0.0 E[ri] 16.2 21.6 10.0 (i) Consider a portfolio, C, made up by selling short $.50 of security PQR and Purchasing $1.50 of ABC with the proceeded and with $1.00 of your own money in portfolio C. How sensitive will this portfolio be to each of the two factors? (1.50 Beta C = Sensitivity to B = - * 1.5 = 0 7 .50 Beta C2 = Sensitivity to B Beta (z = Sensitivity to B: = (1.59) +.8+(:59) 1.4 = 0.5 - *.8 +- * 1.4 = 0.5 1 17 Consider a portfolio, D, made up by borrowing $1.00 at the risk free rate and investing it with $1.00 of your own money in portfolio C. How sensitive will this portfolio be to each of the factors? This won't affect the sensitivities above. (-1* 0) + (1 * 0) = 0 (-1*0) + (1 * 0.5) = 0.5 (iii) What combination of securities ABC, PQR and the riskless security will move on a one-to-one basis with factor 1 and be insensitive to factor 2? W (ABC) * 0.5 + W (PQR) * 1.5 = 1 W(ABC) * 0.8 + W (POR) * 1.4 = 0 W(ABC) = -2.8, W(PQR) = 1.6 W(rf) = 1 1.6 + 2.8 = 2.2 (iv) You have discovered another portfolio P with the following characteristics: Portfolio BP Ba B 0 | Elter] 0.08 Design an arbitrage to earn your $1M (reference part (iii) above)