Arbitrage pricing theory, Business Economics

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Question:

(a) Assume that a market is in equilibrium and all investors agree that the return on any diversified portfolio P is equal to

RP = ap + bp1 F1 + bp2F2 + · · · + bpLFL

What does the Arbitrage Pricing Theory says about the expected return of this portfolio?

(b)  Suppose that there are only 3 portfolios that are only available in the market and the following data are available.

297_Arbitrage Pricing Theory.png

Based on the APT, if there are only two factors that influence returns, then the expected returns on any diversified portfolio P should satisfy the equation E[RP] = λ0 + bp1λ1 + bp2λ2 in equilibrium. Find the values of the factor prices.

(c) Consider a three-period binomial tree for the stock price.  Let S0 = $210 and assume the stock price rises by 25% or falls by 20 at each time step.  Assume also  that the risk-free rate, r, is 5.12% per period.  A European call with strike price X =$70 expiring at time 3 is written on S.

(i) Find the probability measure which makes the discounted asset price a martingale?

(ii) Show that the price of the contingent claim is $60.371.

(iii) If the price movements for the asset were up-down-down, write down the trading strategy required to hedge the option.


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