L9 - APT Flashcards
Brief description of the Single Factor Model?
- Returns on security come from two sources: common macro-economic factors and firm-specific events
- Possible common macro-economic factors:
- GDP Growth
- Interest Rate
- Inflation
- Exchange Rates
- Business Cycles
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How can a factor surprise affect total return under the single index model?
- If it was already predicted, the surprise would already be accounted for in the price and thus F = 0
What could a Multi-factor model look like?
- Models like these are good because we are directly modelling the factors (or uses a proxy that is closely linked to the factor but is released at a higher frequency)
- The problem is the frequency of which the data comes out (IR/GDP is monthly/ quarterly)
- What about in times of crisis
- OPEC now meet monthly to discuss oil reserves due to covid
What is the Arbitrage Pricing Theory?
- The APT predicts a security market line linking expected returns to risk, SML. It relies on three propositions:
- (1) Securities described with a Factor Model
- (2) There are enough securities to diversify away the idiosyncratic risk
- (3) Arbitrage will disappear quickly
- An arbitrage opportunity arises when a zero investment portfolio has a sure profit (risk arbitrage opportunities(
- No investment is required so investors can create large positions to obtain large profits (zero risk profits)
- Regardless of wealth or risk aversion, investors will want an infinitely large position in the risk-free arbitrage portfolio.
- In efficient markets, profitable arbitrage opportunities will quickly disappear.
- In CAPM the assumption that a large number of investors are mean-variance optimizers is critical. APT, the implication of a no-arbitrage condition is that a few investors who identify an arbitrage opportunity will mobilize large dollar amounts and quickly restore equilibrium.
How does APT apply to a well-diversified portfolio?
- For A - as well-diversified, it has only taken account for market risk and thus is a good predictor
- For B - still have elements of firm-specific risk as it has not been diversified away –> thus it does not fall of the excess return line generated by the equations above the graph
Example of a Zero-net-investment Arbitrage Portfolio?
- If you plotted A and B of a graph of returns v Factor, they would be parallel due to having the same beta
How do you calculate the arbitrage return in the zero-net-investment example?
Long A (return x amount invested) - your short in B (return x amount invested)
- Beta - Beta = 0 –> no risk in the portfolio
- Under the no-arbitrage assumption the alpha shouldn’t be persistent in the market for too long
What happens when securities don’t fall on the APT SML line?
- APT only applies to well-diversified portfolios (CAPM applied to all securities)
- IF security is below the SML –> Long portfolio of same beta up higher return, and short this security
- If security is above the SML —> Long portfolio , and short a portfolio that lies of the SML with the same beta
How does APT compare to CAPM?
APT:
- Equilibrium means no arbitrage opportunities.
- APT equilibrium is quickly restored upon arbitrage.
- Assumes a diversified portfolio, but the residual risk is still a factor.
- Does not assume investors are mean-variance optimizers.
- Reveals arbitrage opportunities.
CAPM:
- The model is based on an inherently unobservable “market” portfolio.–> have to use proxy
- Rests on mean-variance efficiency. The actions of many small investors restore
- CAPM equilibrium. CAPM describes equilibrium for all assets.
What does the Multi-Factor APT model look like?
- How can we model the factors:
- Directly (expected GDP growth from their data)
- Factor mimicking in the portfolio (uses a close proxy)
- Reason why beta = 1
- Expected return of that factor proxy = 1 * return of the factor (beta = 1)
- Thats why we can use a factor proxy as a factor mimicking portfolio - as it follows the true factor with an exact magnitude
- Expected return of that factor proxy = 1 * return of the factor (beta = 1)
What is the Fama-French three-factor model?
- The multifactor models that currently occupy center stage are the three-factor models introduced by Fama and French.
- The systematic factors in the FF model are firm size and book-to-market ratio (B/M) as well as the market index.
- These additional factors are empirically motivated by the observations.
What did researchers find out about the excess returns on stocks ordered by their market cap?
- Ordered them then grouped them into deciles
- Small firms tend to generate a higher return that larger firms (but have a high risk/beta)
- Small caps tend to have positive alpha, but have a large variance in its statistically significant excess returns
- Been a persistent arbitrage opportunities that have not been exploited to zero
Is market cap mimicking the business cycle risk factor? As smaller firms tend to do worse in a recession in comparison to those large, well-established ones –> need higher return to take into account this risk
What did researchers find out about the excess returns on stocks ordered by their book to the market ratio?
- High book to market (value) firms tend to outperform Low book to market (growth) stocks
- low book to market are usually new firms that don’t have many assets under management yet nor many future cashflows to predict the current worth
- High book to market ratio may included distressed companies too
high book to market ratios returns may come from the distressed companies –> low market value to book due to less demand for them, (so high B/M) –> to hold these you require a higher return to account for this risk
Analysts tend to extrapolate data out too far, thus ‘glamour firms’ that have been performing well recently tend to underperform (relative to expectations) value firms with high B/M ratio, thus they have higher prices but lower B/M ratio
What are the implications of the positive alpha trading strategies like under the Value/Growth and market cap research findings?
- The only way positive-alpha strategies can persist in a market is if some barrier to entry restricts competition.
- However, the existence of these trading strategies has been widely known for more than 15 years.
- Another possibility is that the market portfolio is not efficient, and therefore, a stock’s beta with the market is not an adequate measure of its systematic risk.
How do we select a portfolio under the Fama-French model?
- the empirical graphs demonstrate that, even when the model fails (positive alpha), portfolios with higher average returns do tend to have higher betas.
- Thus, the first portfolio in the collection is a self-financing (or zero-net investment size-factor) portfolio that consists of a long position in the market portfolio that is financed by a short position in the risk-free security
How are the SMB and HML portfolios generated under the Fama-French model?
What does the three-factor model look like?
MORE WIDER READING ON THIS
- CAPM tends to predict that all the portfolios have the same beta
- Not a very good predicting of actual return
- FF model seems to predict a return that is similar to reality
