Factor Models for Returns

Question 1

What are some Problems with the Markowitz Process?

Answer 1

• Too many inputs; for n securities:

* Independent correlations

Question 2

What is Sharpe’s Solution?

Answer 2

•Factor model: based on insight that a few factors drive security returns ◦Interest rates
◦World value of dollar
◦Unemployment rate
◦New housing starts
◦Consumer sentiment

• Unexpected change in factor, unexpected movement in security and returns
• Simplest, most common case: one factor—the market

Question 3

What is the market?

Answer 3

• Market aggregate of all the securities (e.g., S&P 500)
• Correlation between security returns and market returns
• Implements using excess returns on securities

Question 4

What are the three components excess return Ri(t)?into

Answer 4

iRM(t): component of total return related to the return on market
◦ei(t): nonmarket, random component of return E(ei)=0
◦αi: abnormal return, above what is expected in relation to market
•Known as single-index model and market model

Question 5

What are some advantages of the market models?

Answer 5

•Fewer inputs ◦n αs, βs, and σ(e)s
◦E(rM) and σ2M
◦Total of 3n + 2
◦n = 10, 32 inputs (65 for Markowitz)
◦n = 100, 302 inputs (5,150 for Markowitz)

•Economically consistant estimates

Question 6

What are some Disadvantages of the market model?

Answer 6

Approximate nature of the covariance estimate

Question 7

What are the 3 Steps to Estimating Market Model

Answer 7

1. Calculate monthly (or annual, weekly, or daily) realized returns for some period (60 months is typical) for: 1.Market index (S&P 500)
2. Risk-free security
3. Security or portfolio of interest
4. Calculate excess return for security and market.
5. Estimate α (intercept), β (slope), and residual variance or standard deviation.

Question 8

What are the 3 different straight lines?

Answer 8

1) Capital Allocation Line/ Capital Market Line
- E(r) vs σ for combinations of rf and ri
2) Security Market Line
- E(r) vs ß for any security/portfolio
3) Security Characteristic Line
- best fit line through the scatter-plot of Ri vs Rm

Question 9

What is the difference between CAPM vs. Market Model?

Answer 9

• CAPM (cross-sectional model): differentiates between expected returns of one stock and another
• Market Model (time-series model): describes security return at various points in time

Question 10

What are some Interpretations of β?

Answer 10

• Risk contributed to the market portfolio
• Sensitivity of a stock’s returns to the returns on the market portfolio
• Interpretations mathmatically identical
• β systemic risk for same period expectations generated, not past risk for future estimates

Question 11

What is the Markowitz Framework?

Answer 11

• Need E(r), σ, correlations.
• Use Markowitz formulas to calculate.
• Calculate slope of capital allocation line.
• Find portfolio weights to maximize slope.

Question 12

What are some Pros and Cons of Single-Index-Model-Based Process?

Answer 12

Advantages:
•Parsimonious, fewer inputs
•Consistent set of estimates

Disadvantages:
•Assumes linear relationship between security and market excess returns
•Approximates variance

Question 13

what is Estimating Prospective Statistics

Answer 13

• Inputs (prospective estimates) are needed for optimum portfolio-selection process.
• Security analysis may be needed for prospective estimates for individual securities.

Question 14

What are Abnormal Returns (α)?

Answer 14

• Efficient market believers can assume it to be zero for every security.
• Nonbelievers use security analysis to estimate it.
• Believers in momentum can assume historical α will persist.
• Believers in mean reversion can assume historical α will revert.
• 3 percent above/below historical mean should be the maximum change.