Factor Theory

Question 1

What is Factor Theory?

Answer 1

Factor theory is based on an analysis of factor risks, where risks represent exposure to bad times, where these exposures are rewarded with risk premiums

Question 2

What are the principles of factor theory?

Answer 2

1. Factors are important, not assets.
2. Assets represent bundles of factors.
3. Investors have differing optimal risk exposures.

Question 3

What are bad times?

Answer 3

Bad times represent economic bad times, like high inflation and low economic growth.

They could also represent bad times for investing, including poorly performing investments and markets.

Question 4

Implications of CAPM

Answer 4

1. Hold the factor not the asset
2. Investors have their own optimal factor risk exposures.
3. The average investor is fully invested in the market
4. Exposure to factor risk must be rewarded.
5. Risk is measured as beta exposure.
6. Valuable assets have low risk premiums.

Question 5

Capital Allocation Line

Answer 5

When investors hold portfolios that combine the risky asset and the risk free asset, the various risk return combinations are represented by the capital allocation line.

Question 6

Capital Market Line

Answer 6

When all investors invest in the same risky MVE portfolio, the capital allocation line for an investor is called capital market line

Question 7

How do you quantify investor’s risk aversion?

Answer 7

E(R (market)) - Risk Free Rate = risk aversion (lamda) X sigma squared (variance)

Question 8

What is the security market line?

Answer 8

Line that determines the risk premium of an individual asset.

Question 9

What is the formula for beta?

Answer 9

Cov(R(market),R(security))/variance(R(market))

Question 10

Assumptions of CAPM

Answer 10

1. Investors only have financial wealth. In reality, investors have many factors that contribute to their wealth.
2. Investors have mean variance utility, as in a symmetrical treatment of risk.
3. Investors have a single period investment horizon.
4. Investors have homogeneous expectations.
5. Markets are frictionless (no taxes or transaction costs)
6. All investors are price takers (in real world, they are price setters)
7. Information is free and available to everyone

Question 11

CAPM simplifying assumptions

Answer 11

The CAPM relies on several assumptions that are often considered overly simplistic or unrealistic, especially in illiquid or inefficient markets.

Question 12

Investors only have financial wealth (CAPM assumption)

Answer 12

CAPM assumes investors only have financial wealth, but in reality, they also have unique income streams, liabilities, and human capital, making inflation and income growth important factors.

Question 13

Mean-variance utility (CAPM assumption)

Answer 13

CAPM assumes investors treat risk symmetrically (mean-variance utility), but in reality, investors dislike losses more than they like gains, leading to different levels of downside risk.

Question 14

Single period investment horizon (CAPM assumption)

Answer 14

CAPM assumes a single period investment horizon, while real-world investors often need to rebalance portfolios over multiple periods.

Question 15

Homogeneous expectations (CAPM assumption)

Answer 15

CAPM assumes all investors have identical expectations, but in reality, investors have heterogeneous expectations, causing deviations from the model.

Question 16

Frictionless markets (CAPM assumption)

Answer 16

CAPM assumes no taxes or transaction costs, but real markets have both, especially for illiquid securities, leading to significant deviations from the model.

Question 17

Trading restrictions and heterogeneous beliefs

Answer 17

In the real world, trading restrictions (like short selling bans) and differing beliefs can prevent investors from fully acting on their expectations, causing market asymmetries.

Question 18

All investors are price takers (CAPM assumption)

Answer 18

CAPM assumes all investors are price takers, but in reality, large or institutional investors can influence market prices through their trades.

Question 19

Free and available information (CAPM assumption)

Answer 19

CAPM assumes information is free and available to everyone, but in reality, information can be costly and not accessible to all investors.

Question 20

Diversification in CAPM and multifactor models

Answer 20

Both models highlight the benefit of diversification—CAPM diversifies away idiosyncratic risk through the market, while multifactor models use tradable factors to remove this risk.

Question 21

Optimal exposures

Answer 21

Each investor has an optimal exposure to the market portfolio in CAPM or to factor risks in multifactor models.

Question 22

Average investor’s portfolio

Answer 22

Under both CAPM and multifactor models, the average investor holds the market portfolio.

Question 23

Reward for factor risk exposure

Answer 23

Exposure to factor risk must be rewarded; in CAPM, the market factor is priced, and in multifactor models, each factor has its own risk premium.

Question 24

Risk measurement in CAPM and multifactor models

Answer 24

In CAPM, an asset’s risk is measured by its beta; in multifactor models, risk is measured by factor exposures (factor betas)

Question 25

Assets with low risk premiums

Answer 25

Assets that provide positive payoffs in bad times are considered valuable and have low risk premiums.

Question 26

What is a pricing kernel?

Answer 26

Also known as a stochastic discount factor (SDF), which represents a random variable used in pricing an asset, represents an index of bad times, where bad times are indexed by different factors and states. It is denoted by m in the multifactor model. m=a+b1f1+b2f2+..... (multiple factor exposures)

Question 27

Bad times from the perspective of pricing kernels

Answer 27

With multifactor pricing kernels, bad times can be defined as periods when an additional $1 income becomes very valuable. Looking at bad times this way interprets SDF as a marginal utility.

Question 28

Price of “Bad Times” Risk (λm​)

Answer 28

The compensation investors require for holding assets that perform poorly in bad times, calculated as λm=−var(m)/E(m)

Question 29

Assets with Positive Payoff in Bad Times

Answer 29

Assets that provide returns during adverse economic periods are considered valuable and therefore have low risk premiums.

Question 30

How to explain behavioral biases which create inefficiencies in the market?

Answer 30

Rational explanation: Losses during bad times are compensated by high returns. Behavioral Explanation: Agents' overreaction/ under reaction to news which generate high returns.