5. Multifactor Models

Question 1

What is Arbitrage?

Answer 1

The exploitation of asset security mispricing in such a way that risk-free profits can be earned

Question 2

If the APT is to be a useful theory, the number of systematic factors in the economy must be small. Why?

Answer 2

Any pattern of returns can be explained if we are free to choose an indefinitely large number of explanatory factors. If a theory of asset pricing is to have value, it must explain returns using a reasonably limited number of explanatory variables (i.e., systematic factors such as unemployment levels, GDP, and oil prices).

Question 3

What are the three main assumptions behind APT?

Answer 3

Only 3 key assumptions:
* Security returns can be described by a factor model
* There are sufficient securities
* No arbitrage (very powerful argument

Question 4

What does APT not give guidance about?

Answer 4

• Number of factors
• Which factors
• Whether market portfolio is a factor

Question 5

How can we interpret the market reaction?

What is the the Campbell-Shiller decomposition?

Realized return =

Answer 5

Realized return = E[R] + CF news + DR news + “noise”

Noise was added later as market are not fully rational

Cash flow (CF) news, Discount rate (DR)

Question 6

Empirical tests of market efficiency

What are the two main types of tests used to test market efficiency?

Answer 6

1. Can we identify patterns in security returns that are
   inconsistent with the random walk hypothesis and/or
   rational asset pricing theories such as CAPM?
2. Is it possible to beat the market?

Question 7

Briefly explain how the Arbitrage Pricing Theory (APT) assumptions ensure that all assets lie on the arbitrage pricing line (or plane). How does this differ from the argumentation behind the Capital Asset Pricing Model (CAPM) prediction that all assets lie on the Security Market Line (SML)?

Answer 7

In the APT world, any security that is mispriced would immediately be exploited by arbitrageurs
that will take opposite positions in the mispriced asset and the replicating security with similar exposures to the APT factors. Therefore, these assets are pushed back to the arbitrage pricing line (or plane) immediately (no arbitrage). The key difference with the CAPM is that the CAPM requires all investors to invest in the same way (mean-variance optimization) and to update their portfolios continuously. The APT ‘just’ requires that there are sufficiently many (or wealthy) arbitrageurs out there that exploit mispricing fast enough.

Question 8

What is carharts model?

Answer 8

Carharts 4- factor model, adding the identify another stock characteristic (next to size and BE/ME) that explains the cross-section of stock returns: stocks with relatively strong 6-12 months past returns (“past winners”) continue to outperform stocks with poor past returns (“past losers”) over the next 6-12 months (the “momentum” effect)

Momentum is return spread of stocks between highest and lowest
quintiles of returns performance over the past year

Question 9

Why can factor risk premia be negative?

Answer 9

If in a bad state of the market, maybe the risk factor that captures that can be negative

Like unexpected inflation. Super interesting, if I think inflation will spike and I find an security, I will make money in bad times. Its a hedge and risk management tool. Risk premium might be negative as they are popular and have a high price, low expected return.

Question 10

What happen when a security scores high in a specific beta? Say “unexpected inflation”

Answer 10

High postive beta means -> high positive covariance -> the return on that security is going to be high when there is a lot of inflation

Link -> factor mimicking portfolio

Question 10

A factor mimicking portfolio (a.k.a. a factor portfolio or a tracking portfolio) is a well-diversified portfolio of securities constructed to have a beta of 1 on one of the factors and a beta of 0 on any other factor
What is the logic behind it?

Answer 10

If security returns can be described by a factor model, and if there are sufficient securities, it should be possible to construct such a portfolio for each (e.g., macroeconomic) factor
* This means that we can replicate any security with a
combination of factor mimicking portfolios
* This implies that we can use a no arbitrage argument

Question 10

What is the relationship between covariance and beta?

Answer 10

Beta effectively describes the activity of a security’s returns as it responds to swings in the market. A security’s beta is calculated by dividing the product of the covariance of the security’s returns and the market’s returns by the variance of the market’s returns over a specified period.

Beta = Cov(Ri,Rm)/Var(Rm)

Question 11

Briefly explain the two-stage Fama-MacBeth (1973) asset pricing test procedure, including how to compute the appropriate t-statistic for the coefficient on the variable of interest (in this case gross profitability).
.

Answer 11

Stage 1. Estimate the risk loadings betas of the individual stocks (or portfolios of stocks) using time series regressions for each stock (portfolio) on the relevant risk factors
Stage 2. Each period (month, year), run a cross-sectional regression of stock returns on (multiple) characteristics (or betas) [Assess the significance of the relation between returns and each characteristic using a time-series t-statistic based on the standard error of the time-series of coefficients]

Question 12

HML and BE/ME mean

Who invented?

Answer 12

HML is return spread between high and low BE/ME (book to market equity) stocks
* Tracking portfolio for “value effect” (Financial distress factor?)

Fama french

Question 13

SMB means

Who invented?

Answer 13

SMB is return spread between small-cap and large-cap stocks
* Tracking portfolio for “size effect” (Business cycle factor?)

Fama french

Question 14

Whether cross-sectional anomalies like the size, book-tomarket,
and momentum effects are driven by risk (beta) or
mispricing (alpha) remains one of the hottest issues in both
academic and applied finance

Why would you argue mispricing (alpha)?

Answer 14

• FF (1993) only perform time-series, no cross-sectional test
• Main result in DT (1997): when you do a cross-sectional
  horse race between size and BE/ME as characteristics vs.
  βSMB and βHML as risk measures (covariances/betas), it is the
  characteristics that matter, not the covariances
• Sheds doubt on the FF interpretation, and suggests the size
  and value effects are perhaps more behavioral (mispricing
  rather than risk), as in Lakonishok, Shleifer & Vishny (1994):
• “extrapolating past earnings growth too far into the future”
  (overreaction)

Question 15

The question of whether cross-sectional anomalies like the size, book-to-market, and momentum effects are driven by risk (beta) or mispricing (alpha) is a central debate in financial economics, particularly in the context of asset pricing.

explain the two sides

Answer 15

Risk (Beta):

Beta represents the systematic risk of a security or a portfolio in relation to the overall market. The Capital Asset Pricing Model (CAPM) posits that expected returns on assets are a function of their beta, with higher-beta assets requiring higher expected returns as compensation for higher risk.
Proponents of the risk explanation argue that anomalies are actually proxies for undetected risk factors. For example, smaller companies might have higher betas because they are more sensitive to economic downturns, thus investors require higher returns for holding these riskier assets. The same goes for high book-to-market (value) stocks, which might be more exposed to certain economic risks.
Mispricing (Alpha):

Alpha represents the portion of a security’s return that is not explained by the risk (beta) associated with the market as a whole. It is often seen as a measure of the asset’s intrinsic or unique value.
Those who argue for the mispricing explanation suggest that these anomalies reflect investors’ irrational behavior or market inefficiencies. For instance, if investors systematically overvalue or undervalue certain characteristics like company size or book-to-market ratios, this could lead to mispriced assets. These mispricings result in returns that deviate from what would be expected based on risk alone.

The paper by Daniel and Titman (1997) provided evidence that challenged the risk-based explanation. They suggested that it was the characteristics of firms themselves (like size or book-to-market ratios) that explained returns better than the covariances or betas associated with certain factors, like SMB (small minus big) or HML (high minus low book-to-market). This implies that the returns might be driven by mispricing (alpha) rather than risk (beta).

The debate is significant because it touches on whether markets are efficient at pricing assets (a core assumption of the CAPM and related models) or whether there are systematic deviations from efficiency that can be exploited for excess returns (alpha). This has implications for investment strategy, portfolio management, and the development of financial models. It remains a hot issue because it questions the fundamental mechanisms of financial markets and challenges the traditional view that higher returns are always a compensation for higher risk.