Week 7 Factor Pricing Models

Question 1

What is a Factor?

Answer 1

• a variable which influences the returns of many assets
• exposure to a risk factor over a long-term yields a risk premium
• -> cannot be diversified away; compensation for bearing losses during bad times

Question 2

What is the CAPM?

Answer 2

• equilibrium model which specifies the risk-return tradeoffs of (1) an individual stock and (2) the market portfolio and risk

Question 3

CAPM Assumptions

Answer 3

1. Individual
   - Investors are rational, mean-variance optimizers; each investor holds securities in the investable universe with optimized weights
   - Their common planning horizon is a single-period
   - Homogenous expectations: all relevant public information
2. Market Structure
   - all assets are publicly held and trade on exchange; investors would calculate identical efficient frontiers of risky assets, they would then draw an identical CAL and would arrive at the same risky portfolio
   - investors can borrow and lend at risk-free
   - no taxes

Question 4

Do risk premiums compensate for idiosyncratic risk?

Answer 4

• Risk premiums will be proportional to exposure to systematic risk and independent of firm-specific risk

Question 5

CAL and CML

Answer 5

• the CAL based on each investor’s optimal risky portfolio will in fact also be the CML
• when we aggregate the portfolios of all individual investors, lending and borrowing will cancel out, and the value of the aggregated risky portfolio will equate the entire wealth of the economy. Tangent portfolio becomes equilibrium market portfolio

Question 6

Capital Market Line

Answer 6

• the CML graphs the risk premiums of efficient portfolios as a function of portfolio standard deviations
• standard deviation is a valid measure of risk for well-diversified portfolios

Question 7

Security Market Line

Answer 7

• the SML graphs individual asset risk premiums as a function of asset risk –> relevant risk measure is the contribution of the asset to the portfolio variance

Question 8

Multifactor Models

Answer 8

• financial model that employs multiple factors in its calculation to explain asset prices
• the market factor can be split up even further into different macroeconomic factors
• a factor can be defined as a variable which explains the expected return of an asset

Ri = E(Ri) + B1F1+B2F2…BkFk

• the macroeconomic factors are surprise factors, if there are no macroeconomic surprises - if everything goes as investors expects - all those terms go away

Question 9

What the Arbitrage Pricing Theory Says

Answer 9

APT Says:

• factors drive common complements of asset returns
• expected excess return for any asset is a weighted combination of the asset’s exposure to factors multiplied by the corresponding risk premium
• idiosyncratic not priced in

APT Does Not Say:
- what the factors are or what the weights are

Question 10

Value vs. Growth Stocks

Answer 10

• Value Stocks: stocks that are out of favour, selling at low P/E. Produce above average dividend income.
• Growth Stocks: companies with above average prospects for growth. High P/E
• value stocks have high expected returns because risky during bat times. Growth tend to payoff during bad times.

Question 11

CAPM –> CAL and CML

Answer 11

• the CAPM assumes that investors are single-period planners who agree on a common input list from security analysis and seek mean-variance optimal portfolios
• the CAPM assumes that security markets are ideal in the sense that…
  1. they are large and investors are price takers
  2. there are no taxes or transaction costs
  3. all risky assets are publicly traded
  4. investors can borrow and lend any amount at the Rf rate
• with these assumptions, all investors hold identical risky portfolios. The CAPM holds that in equilibrium the market portfolio is the unique MV efficient tangency portfolios. Thus a passive strategy is efficient.

Question 12

More explaining of mutlifactor models

Answer 12

• multifactor models seek to improve the explanatory power of single factor models by explicitly accounting for the various systematic components of security risk
• a multifactor APT generalizes the single factor model to accommodate several sources of systematic risk
• the multi-dimensional security market line predicts that exposure to each risk factor contributes to the security’s total risk premium by an amount equal to the factor beta times the risk premium

Question 13

The Law of One Price

Answer 13

Identical assets in different locations should be price identically in the different locations

Question 14

Hedging Exposure to Multiple Factors

Answer 14

• Consider a PM who manages a portfolio with the following factor betas: GDP Beta = 0.4, Consumer Sentiment beta = 0.2
• Assume that the investor wishes to hedge away GDP factor risk, yet maintain the 0.2 exposure to consumer sentiment
  –> how would they achieve this?
  > the investor should combine the original portfolio with a 40% short position in the GDP factor portfolio
  > the GDP factor beta one the 40% short position in the GDP factor portfolio equals -0.4, which perfectly offsets the original factor beta

Question 15

Assumptions of the APT

Answer 15

• well diversified portfolios can be formed
• no arbitrage opportunities exist
• returns follow a k-factor process

Question 16

Arbitrage Pricing Theory

Answer 16

E(Ri) = Rf + B1(RP1) + B2(RP2) + B3(RP3)
–> not factors, but risk premiums
RP represents the risk premium attacked to risk factor

Both CAPM and APT describe equilibrium expected returns for assets. CAPM can be considered a special case of APT in which there is only one factor.

Question 17

Fama-French Model

Answer 17

1. Size of the firm –> SMB (small minus big) is equal to the difference in returns between portfolios of small and big firms, Rs - Rb
2. Book to Market –> HML (high minus low) is equal to the difference in returns between portfolios of high and low book-to-market ratios (Rv-Rg)
3. Excess Return on the Market

E(Ri) = Rf + B1(MRP) + B2(SMB)+ B3(HML)

Question 18

What does the intercept alpha mean?

Answer 18

The intercept term equals the abnormal performance of the asset after controlling for its exposure to the market, firm size, and book-to-market factors

As long as the market is in equilibrium, the intercept should be equal to zero, assuming the three factors adequately capture all systematic risk.

Question 19

Slope of the CAL/CML

Answer 19

Sharpe Ratio - [E(Rp)-Rf] / SD(Rp) – CAL

becomes…

E(Rm)-rf/SD(Rm)