Page 292 - DCOM504_SECURITY_ANALYSIS_AND_PORTFOLIO_MANAGEMENT

Unit 11: Capital Market Theory

Notes
Example: SCM provides the following data, compute beta of Security J:
= 12% = 9%
j m
Cor = + 0.72
jm
Solution:
i Cor 12 9 0.72 77.76
Calculation of beta of Security J = i 2 jm = 2 0.96
m 9 81
11.9 Arbitrage Pricing Theory (APT)

Arbitrage Pricing Theory (APT) in finance is a general theory of asset pricing, which has become
influential in the pricing of shares.
APT holds that the expected return of a financial asset can be modelled as a linear function of
various macro-economic factors or theoretical market indices, where sensitivity to changes in
each factor is represented by a factor specific beta coefficient. The model-derived rate of return
will then be used to price the asset correctly – the asset price should equal the expected end-of-
period-price discounted at the rate implied by model. If the price diverges, arbitrage should
bring it back into line. The theory was initiated by the economist Stephen Ross in 1976.
1. The APT Model: If APT holds, then a risky asset can be described as satisfying the following
relation:
E(r ) = r + b RP + b RP + ... + b RP
j j j1 1 j2 2 jn n
r = E(r) + b F + b F + ... + b F +
j j j1 1 j2 2 jn n j
where
E(r) is the risky asset’s expected return,
j
RP is the risk premium of the factor,
k
r is the Risk-free
f
F is the macroeconomic factor,
k
b is the sensitivity of the asset to factor k, also called factor loading,
jk
is the risky asset’s idiosyncratic random stock with mean zero.
j
Arbitrage and the APT: Arbitrage is the practice of taking advantage of a state of imbalance
between two (or possibly more) markets and thereby making a risk-free profit, rational
Pricing.

Arbitrage in Expectations: The APT describes the mechanism whereby arbitrage by
investors will bring an asset that is mispriced, according to the APT model, back into line
with its expected price. Note that under true arbitrage, the investor locks-in a guaranteed
payoff, whereas under APT arbitrage as described below, the investor locks-in a positive
expected payoff. The APT, thus, assumes “arbitrage in expectations” – i.e. that arbitrage by
investors will bring asset prices back into line with the returns expected by the model
portfolio theory.
Arbitrage Mechanics: In the APT context, arbitrage consists of trading in two assets – with
at least one being mispriced. The arbitrageur sells the asset that is relatively too expensive
and uses the proceeds to buy one which is relatively too cheap.

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