Page 293 - DCOM504_SECURITY_ANALYSIS_AND_PORTFOLIO_MANAGEMENT

Security Analysis and Portfolio Management

Notes Under the APT, an asset is mispriced if its current price diverges from the price predicted
by the model. The asset price today should equal the sum of all future cash flows discounted
at the APT rate, where the expected return of the asset is a linear function of various
factors, and sensitivity to changes in each factor is represented by a factor-specific beta
coefficient.
A correctly priced asset here may be in fact a synthetic asset – a portfolio consisting of other
correctly priced assets. This portfolio has the same exposure to each of the macroeconomic
factors as the mispriced asset. The arbitrageur creates the portfolio by identifying x correctly
priced assets (one per factor plus one) and then weighting the assets such that portfolio
beta per factor is the same as for the mispriced asset.
When the investor is long the asset and short the portfolio (or vice versa) he has created a
position which has a positive expected return (the difference between asset return and
portfolio return) and which has a net-zero exposure to any macroeconomic factor and is,
therefore, risk free (other than for firm specific risk). The arbitrageur is thus in a position
to make a risk free profit:
2. Where today’s price is too low: The implication is that at the end of the period the portfolio
would have appreciated at the rate implied by the APT, whereas the mispriced asset
would have appreciated at more than this rate. The arbitrageur could therefore:
Today: (a) Short-sell the portfolio
(b) Buy the mispriced-asset with the proceeds.
(c) At the end of the period:

(i) Sell the mispriced asset
(ii) Use the proceeds to buy back the portfolio
(iii) Pocket the difference.

3. Where today’s price is too high: The implication is that at the end of the period the portfolio
would have appreciated at the rate implied by the APT, whereas the mispriced asset
would have appreciated at less than this rate. The arbitrageur could therefore:
Today: (a) Short sell the mispriced-asset

(b) Buy the portfolio with the proceeds
(c) At the end of the period:
(i) Sell the portfolio
(ii) Use the proceeds to buy back the mispriced-asset

(iii) Pocket the difference
4. Relationship with the Capital Asset Pricing Model: The APT along with the CAPM is one
of two influential theories on asset pricing. The APT differs from the CAPM in that it is less
restrictive in its assumptions. It allows for an explanatory (as opposed to statistical) model
of asset returns. It assumes that each investor will hold a unique portfolio with its own
particular array of betas, as opposed to the identical “market portfolio.” In some ways, the
CAPM can be considered a “special case” of the APT in that the securities market line
represents a single-factor model of the asset price, where Beta is exposure to changes in
value of the market.

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