TOPIC 7 - MULTIPLE RISK FACTORS Flashcards
What do multifactor models seek to do?
improve the explanatory power of single-factor models by explicitly accounting for the various components of systematic risk (use indicators to capture wide range of macroeconomic risk factors)
once we start allowing for multiple risk factors, we conclude that:
the SML ought to also be multidimensional, with exposure to each risk factor contributing to the total risk premium of the security
A risk-free arbitrage opportunity arises when 2 or more security prices enable investors to
construct a zero net investment portfolio that will yield a sure profit.
The presence of arbitrage opps will generate
a large volume of trades that puts pressure on security prices until prices reach levels that preclude such arbitrage.
When securities are priced so that there are no risk-free arbitrage opportunities, we say that they
satisfy the no-arbitrage condition (. A situation in which all relevant assets are priced appropriately and there is no way for one’s gains to outpace market gains without taking on more risk)
Assuming an arbitrage-free condition is important in financial models, thought its existence is mainly theoretical.
why are price relationships that satisfy the no risk-free arbitrage condition important?
bc we expect them to hold in real-world markets
well diversified portfolio =
large no securities with sufficiently small investment proportions
in a single factor security market, all well diversified portfolios have to satisfy
the expected return-beta relationship of the CAPM to satisfy the no-arbitrage condition
the arbitrage pricing theory doesn’t require
the restrictive assumptions of the CAPM and its unobservable market portfolio –> but consequence of this is that the APT can’t guarantee this relationship for all securities 100% of the time
A multifactor APT generalises
the single factor model to accommodate several sources of systematic risk.
- the multi-dimensional SML predicts that exposure to each risk factor contributes to
the security’s total risk premium by an amount = to the factor B x risk premium of the factor portfolio that tracks that source of risk
The multifactor extension of the single-factor CAPM, the ICAPM predicts
the same multidimensional security market line as the multifactor APT.
what is arbitrage?
the exploitation of security mispricing in such a way that risk free profits can be earned
what is the most basic principle of capital market theory?
that well-functioning security markets rule out arbitrage opportunities
why do we generalise the SML of the CAPM?
to get a richer insight into the risk-return relationship –> use arbitrage pricing theory
what do multifactor models posit?
that returns respond to several systematic (non diversifiable risk factors) + firm specific influences
3 propositions the APT relies on
1) security returns can be described by a factor mode (1 or as many as u like)
2) there are sufficient securities to diversify away idiosyncratic risk
3) well-functioning security markets don’t allow for the persistence of arbitrage opportunities
for the APT’s first proposition that 1) security returns can be described by a factor model, for every factor chosen it’s assumed that
all variance is captured by the security analysis)
–> if we don’t get factors right we could overlook substantial factors and the proposition will be defeated!!!
Arbitrage opportunity exists when an investor can
earn riskless profits without making a net investment
–> requires 0 investment outlay
The law of one price states that
in the absence of friction between global markets, the price for any asset will be the same.
The law of one price is achieved by
eliminating price differences through arbitrage opportunities between markets.
Market equilibrium forces would eventually converge the price of the asset.
A well-diversified portfolio is one with each weight
small enough that for practical purposes the non-systematic variance is negligible
does APT assume investors are mean variance optimisers?
NO
what can’t the APT rule out?
a violation of the expected return-beta relationship for any particular asset (to be relevant for pricing of individual assets, argues that if principles of arbitrage pricing apply to well-diversified portfolios are price such that they’re commensurate in a linear fashion to level of beta risk (sensitivity to systematic factor) on average all the assets in the portfolio have to observe that relationship too
APT uses what sort of index?
an observable market index
CAPM provides XXXX statement on expected return-beta relationship
Provides unequivocal statement on the expected return-beta relationship for all securities
(APT doesn’t state this but suggests certain pricing relationships ought to hold for well diversified portfolios and having established that it needs to on average hold for the individual assets within the well diversified portfolio and not necessarily for every individual asset)
CAPM achieves equilibrium from
individual investors
APT equilibrium can be
the actions of a few investors seizing arbitrage opportunities
the multifactor APT states that the overall risk premium on a portfolio should =
sum of the risk premiums required as compensation for each source of systematic risk
(aka get the risk premium for exposure to each source of risk)
ratio of risk premium to beta
E(r)/B
why do you look at the ratio of risk premium to beta
to compare with assets have the highest returns for their betas –> can make a portfolio out of this and create an arbitrage opp
if you’re calculating the expected excess return for a portfolio with investments in the rf asset, what’s the return on the rf asset?
it’s 0% bc the rf asset doesn’t have an excess return
E(Rp) =
expected excess return = E(rp) - rf
