Using Multifactor Models

Question 1

Macroeconomic factor model

Answer 1

In a macroeconomic factor model, the factors are surprises in macroeconomic variables, such as inflation risk and GDP growth, that significantly explain returns.

ai represent the expected return.
b1F1 + b2F2 are returns resulting from factor surprises.
While the error term represents the asset specific risk

Question 2

Fundamental factor model

Answer 2

Attributes of Stocks or companies
Example Bv/MV, Market Cap, EPS

Question 3

Company Fundamental Factor

Answer 3

Part of fundamental factor models - Internal company performance
Earnings growth, Financial leverage

Question 4

Company Share Related Factor

Answer 4

Part of fundamental factor models - Valuation measure - Factors related to share price
EPS, B/MV

Question 5

What is categorized as an Macroeconomic factor

Answer 5

Sector/Industry
Sector or industry membership factors fall under this heading. Various models include such factors as CAPM beta, other similar measures of systematic risk, and yield curve level sensitivity—all of which can be placed in this category.

Question 6

If all factors are equal to their expected value (Macroeconomic Factor Models)

Answer 6

All factors are equal to zero (Actual - Expected)

Question 7

Application of Multifactor Models

Answer 7

Return Attribution
Risk Attribution
Portfolio Construction
Strategic portfolio decisions

Question 8

Return Attribution

Answer 8

Relative to a benchmark
Fundamental models are favored
Attribute active return Rp - Rb

Question 9

Investment Mandate

Answer 9

How we should perform relative to a benchmark

Question 10

Actual Investment Style

Answer 10

How we actually invest

Question 11

Active Risk

Answer 11

Standard deviation of the actual returns
Standard deviation (Return of portfolio - Return of benchmark)
Active risk is also known as tracking error

Question 12

Risk attribution of absolute returns

Answer 12

Sharpe Ratio

Question 13

Risk attribution of relative returns

Answer 13

Information Ratio (IR)
IR = (Rp - Rn) / Sd Ra

IR = (Rp - Rb) / Tracking error

Tracking error = Sd of (Rp - Rb)

Question 14

Portfolio construction: Passive management

Answer 14

Replicate benchmark factors exposure on a much smaller set of securities

In managing a fund that seeks to track an index with many component securities, portfolio managers may need to select a sample of securities from the index. Analysts can use multifactor models to replicate an index fund’s factor exposures, mirroring those of the index tracked.

Question 15

Portfolio construction: Active management

Answer 15

Use multifactor model to predict alpha or construct portfolio with a desired risk

Many quantitative investment managers rely on multifactor models in predicting alpha (excess risk-adjusted returns) or relative return (the return on one asset or asset class relative to that of another) as part of a variety of active investment strategies. In constructing portfolios, analysts use multifactor models to establish desired risk profiles.

Question 16

Portfolio construction: Rule based Active management

Answer 16

Overweight or underweighted specific factors

These strategies routinely tilt toward such factors as size, value, quality, or momentum when constructing portfolios. As such, alternative index approaches aim to capture some systematic exposure traditionally attributed to manager skill, or “alpha,” in a transparent, mechanical, rules-based manner at low cost. Alternative index strategies rely heavily on factor models to introduce intentional factor and style biases versus capitalization-weighted indexes

Question 17

The 3 assumptions of Arbitrage Pricing Theory (APT)

Answer 17

1. A factor model describes assets returns.
2. With many assets available - investors can form well diversified portfolios that can eliminate asset specific risk.
3. No arbitrage can exist among well diversified portfolios (All are priced correctly)

Additional information ..
Expected returns are a linear function of the risk of the asset with respect to a set of risk factors.

Explains the returns in equlibrium.

APT does not indicate the identity or even the number of risk factors.

Question 18

SMB

Answer 18

Small Minus Big: Average return on 3 small cap portfolio minus 3 average return big cap portfolios

Small cap factor

Question 19

HML

Answer 19

High Minus Low: Average return on 2 high Bv/Mv Portfolio minus Average return on 2 low BV/MV portfolios

Value factor

Question 20

WML

Answer 20

Winners Minus Losers: Past 12 month winners (top 30%) minus bottom 12 months losers (bottom 30%)

Momentum factor

Question 21

Surprise in a macroeconomic model is defined as

Answer 21

Actual - Forecasted

Question 22

Information Ratio (IR)

Answer 22

The higher the information Ratio, the better

Formula: (Rp - Rb) / Sdv (Rp-Rb)

Mean Active return / Tracking error

Active return / Active Risk

Question 23

Arbitrage opportunity in regards to Factor model questions

Answer 23

We want to earn a Risk Free Rate of return.
We want a zero factor exposure
Sell anything that is too high / overprices
Whatever we short - we will have a factor exposure of whatever we short (we have the Beta of the security we short), which means we have to long/invest assets that gives us the same factor (beta) exposure thus have a net factor of zero.

Question 24

When is the sensitivity determined in a Fundamental and Macro Factor model?

Answer 24

Fundamental factor model: Sensitivity (beta) is determined first
Macro factor model: Sensitivity (beta) is determined last

Question 25

What is the intercept of a Factor model

Answer 25

Expected return

Question 26

Which type of factor model is most directly applicable to an analysis of the style orientation (Growth vs Value)

Answer 26

Fundamental Factor Models
Company specific factor, therefore we want fundamental factor models

Question 27

Suppose an active equity manager has earned an active return of 110 basis points, of which 80 basis points is the result of security selection ability. Explain the likely source of the remaining 30 basis points of active return.

Answer 27

Active return = Active factor risk + Security selection

110 = x + 80

The remaining 30 BSP comes from active factor risk

Question 28

What is the information ratio of an index fund that effectively meets its investment objective?

Answer 28

Zero

because IR = (Rp - Rb) / Sdv (Rp - Rb)

If it meet its investment objective, hence performed equally to its bench mark, then there is no difference between portfolio and benchmark

Question 29

Active risk

Answer 29

Standard deviation of (Rp - Rb)

Question 30

Active factor risk

Answer 30

Return of portfolio (Rp)

Question 31

Asset Specific Risk / Security Selection

Answer 31

Return on Benchmark

Question 32

Formula for Active-Squared Risk

Answer 32

Active Factor Risk + Active Specific Risk