The APT Model
Risky asset returns are said to follow a factor structure if they can be expressed as:
- where
- is a constant for asset
- is a systematic factor
- is the sensitivity of the th asset to factor, also called factor loading,
- and is the risky asset's idiosyncratic random shock with mean zero.
Idiosyncratic shocks are assumed to be uncorrelated across assets and uncorrelated with the factors.
The APT states that if asset returns follow a factor structure then the following relation exists between expected returns and the factor sensitivities:
- where
- is the risk premium of the factor,
- is the risk-free rate,
That is, the expected return of an asset j is a linear function of the assets sensitivities to the n factors.
Note that there are some assumptions and requirements that have to be fulfilled for the latter to be correct: There must be perfect competition in the market, and the total number of factors may never surpass the total number of assets (in order to avoid the problem of matrix singularity),
Read more about this topic: Arbitrage Pricing Theory
Famous quotes containing the words apt and/or model:
“It is natural to indulge in the illusions of hope. We are apt to shut our eyes to that siren until she “allures” us to our death.”
—Gertrude Stein (1874–1946)
“... if we look around us in social life and note down who are the faithful wives, the most patient and careful mothers, the most exemplary housekeepers, the model sisters, the wisest philanthropists, and the women of the most social influence, we will have to admit that most frequently they are women of cultivated minds, without which even warm hearts and good intentions are but partial influences.”
—Mrs. H. O. Ward (1824–1899)