Part A. Short Answer. 75 marks 1. Consider a two Factor Model where the factors are the market return and interest rates. (5) a. Suppose an investor constructs a well diversified risky portfolio of stocks which we call P and tries to eliminate market risk via holding P and the market portfolio. So he holds P with weight w and the market with weight 1 - w. Are returns of this combined portfolio certain as with the identical portfolio constructed with the Index Model of Arbitrage Pricing Theory? (10) b. Suppose arbitrage is impossible, then what does this imply for non market returns op of portfolio P?|letting n - co in (1.12) and using these infinite sums we obtain a much sharper expression for p,, namely Pt = 1 + #( Pt - p*) 1tr (1.15) Price Effects of Noise Traders: notice _ 27of pushes the price down. this suggests any dividend yields will be higher than usual (the price is de- pressed but the same dividend raises the percentage return). this higher yield may be regarded as compensating fundamental traders for the extra risk noise traders impose. hence, this model may explain the equity pre- mium puzzle, validating the view noise traders are responsible for high stock yields. conventional wisdom might suggest speculation raises prices and cap- ital gains are responsible for the high returns. extra capital gains being the source of the equity premium was certainly the finding of Fama and French. while speculation may explain the equity premium here some of this rests on a depressed price and a resulting excessive dividend yield. however, the term " offers potential for noise traders to push prices up beyond what they would have been without speculators. so the model generates an equation that allows noise trading to generate excess capital gains for stock investors. this is compatible with the Fama-French finding that unexpected capital gains are responsible for the equity premium puzzle. this term may account for excess price volatility in response to news which is observed in Event Studies. so the Summers, Schliefer and Waldman present a model of noise traders that allows us to explain empirical findings in finance that are hard to justify with traditional theories. the original paper on noise traders that cited some facts supporting the noise trader hypothesis is Summers, L.: Does the stock market rationally reflect fundamental val- ues? Journal of Finance 41, 591-601 (1986).\f6. Portfolios . P - risky Portfolio: Portfolio of risky bond and stock - . risky assets . C - Combined Portfolio: Portfolio consisting of P and the risk-free asset Risky Portfolio (P) m TP Ewirit vig; i= 1 j=1 Wi =the weight on the i-th risky stock i = 1,...,n. Vi =the weight on the j-th risky bond j = 1, ...,m. n =the return on the i-th risky stock i = 1,...,n. gi =the return on the j-th risky bond j = 1,...,m. Combined portfolio (Risky portfolio + RF asset) - determine weight of P and weight of RF asset Erc = rf + y(Erp - rf ) 02 = 1zap > y =_s y =the fraction of capital invested in the risky portfolio. 1 - y =the fraction of capital invested in the risk-free asset. Erc= rf O TC E(rp - rf) o(TP) Sharpe ratio - reward-to-volatility ratio S = - E(rc) - TF OC
