Question 10 (1) Describe the arbitrage pricing theory (APT) assuming there are t
ID: 2615097 • Letter: Q
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Question 10 (1) Describe the arbitrage pricing theory (APT) assuming there are three are systematic risk factor (F1, F2, and F3) please clearly define the notation: a. Write down the factor model for any individual risky security. b. Write down the factor model for a well-diversified portfolio. c. Write down the three-factor Security Market Line (SML) under no- arbitrage constrain. Describe the CAPM as especial case of APT. Specifically, what is the shock or surprise to the systematic risk factor in the CAPM and what is the one-factor SML equation.Explanation / Answer
Answer (1) Arbitrage Pricing Theory - This theory was proposed by a great economist Stephen Ross in 1976. This theory is similiar to CAPM theory but there is only some modification in it such as in CAPM Theory we consider only the risk Factor of market but in the APT we consider many other factors also such as decline in profitability and economic conditions government regulations Etc.
(a) The Factor for any Indivadual Risky Security is Rf + Beta of security ( Rm - Rf )
(b) The Factor for well diversified Portfolio is is Rf + ( Beta * Risk Premium ) of each Factor
= E(rp) = Risk free rate + { ?F1 × R(F1) } + { ?F2 × R(F2) }
(c) SML equation reflects the relation between CAPM Returnn And Beta. It is the graphical representation of CAPM
equation is Y = a + b x i.e CAPM Return is Rf + (Rm - Rf)/Bm * Bs and Beta of market is always be 1
so equation is similiar to Capm i.e, Rf + ?F1(Rm-Rf) + ?F2(Rm-Rf) + ?F3(Rm-Rf)
Answer (2) CAPM in especial case of APT is that where there is a only one risk factor and the market premium is that risk factor of CAPM . The shock and surprise to systemmatic risk factor in CAPM is that it deals only and only with the market risk not at any other risk except to it
and the one factor SML equation is Rf + (Rm - Rf)/Bm * Bs or we can say Y = a + b X
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