CAIA L2 - 6.3 - Multivariate Empirical Methods and Performance Persistence Flashcards
List
3 major categories
of factors
6.1 - Valuation and Hedging Using Binomial Trees
- Macro factors include economic determinants such as inflation, gross domestic product, and economic growth.
- Dynamic factors describe different stock return strategies such as value, momentum, and size
- Statistical factors - PCA
Explain
Principal Component Analysis - PCA
6.3 - Multivariate Empirical Methods and Performance Persistence
Identifies the set of othogonal factos by the percentage of return variance explained.
Examples of common attributes include sectors, geographic areas, governance, and sustainability
How to do a PCA?
1. Build a return matrix of the assets
2. apply a statistical software program to perform PCA
3. program process estimates variance-covariance matrices
3. program determine the eigenvalues and factor loadings for principal components.
4. program identifies a vector of loadings that maximizes the percentage of return variance explained by a single factor
5. process is repeated
6. software identifies a second factor that explains most of the remaining variance of returns
7. process is repeated until the software can no longer explain variances in returns, and the marginal percentage of variance explained will decrease without altering the percentage explained by previous factors
6.3 - Multivariate Empirical Methods and Performance Persistence
Define
Eigenvalue
and factor loadings
of the PCA - Principal Component Analysis
6.3 - Multivariate Empirical Methods and Performance Persistence
eigenvalue represents the percentage of return variance that is explained by a specific factor
Factor loadings are a vector of values for each asset that determine the sensitivity of each asset for each principal component.
Example of common attributes include sectors, geographic areas, governance, and sustainability.
Example:
The eigenvalues for the first four factors were 4.5, 0.8, 0.4, and 0.2. For the 5-7th = 0.1
Determine the marginal and cumulative percentage of return variance explained by each eigenvalue.
R:
Total eigenvalue amount = 6.0
Marginal: 4.5/6.0 = 75%; 0.8/6.0 = 13.3% …
Cumulative: 4.5/6.0 = 75%; 5.3/6.0 = 88.3% ….
6.3 - Multivariate Empirical Methods and Performance Persistence
Contrast
Principal Component Analysis
vs.
Factor Analysis
6.3 - Multivariate Empirical Methods and Performance Persistence
- PCA does not require a model with specific assumptions. PCA identifies factors by maximizing the percentage of explained return variance. FA makes specific statistical and modeling assumptions regarding the return process of the underlying asset.
- PCA factor loadings do not change when more factors are considered. Factor scores for FA vary when the number of factors or variables in the model is changed.
- PCA can identify a factor that is related to only one security. FA requires at least two securities to identify a factor.
6.3 - Multivariate Empirical Methods and Performance Persistence
Define
Multicollinearity
and its
two primary adverse effects
and a way to correct for multicollinearity
6.3 - Multivariate Empirical Methods and Performance Persistence
occurs when two or more independent variables in a regression model are highly correlated with each other
2 adverse effects:
1. coefficient estimates for the correlated independent variables are inaccurate.
2. the standard errors for the correlated independent variables are overstated.
A sign that multicollinearity exists in a regression model is when there is a high R-squared for the model but the coefficients of the independent variables do not have significant t-statistics.
‘–
How to correct?
Change one of the correlated independent return variable, by creating a spread (ex:return of US stocks and international stocks)
6.3 - Multivariate Empirical Methods and Performance Persistence
Define
Stepwise regression
in multifactor models
6.3 - Multivariate Empirical Methods and Performance Persistence
iterative process for determining variables that should be included or removed from the regression model
for each step:
- add variable with most significat t-stat
- remove variable with insignificant t-stat
danger: data mining or overfitting the model (fit past data, but poor job of explaining future return variations.
=> only add variable that are economically sound
6.3 - Multivariate Empirical Methods and Performance Persistence
List and explain
3
dynamic risk exposure
models
(that estimate returns for nonlinear exposure)
6.3 - Multivariate Empirical Methods and Performance Persistence
Dummy Variable Approach
Dummy D’1’ = 0 or 1, depending if markets are rising or falling
R’it’ – R’f’ = a’i’ + {[b’i,d’ + (D’1’ × b’i,diff’)] × (R’mt’ – R’f’)} + e’it’
* Rmt – Rf = market excess return
* ai = intercept term
* bi,d = responsiveness of the fund return to market returns when Rmt – Rf < 0
* D1 = a dummy variable equal to 1 when Rmt – Rf > 0
* bi,diff = difference between return beta sensitivities to up and down markets
’–
Separate Regression Approach
Breaking sample in two or more subsamples
(no formula)
‘–
Quadratic Model
for strategies like market-timing (U-shaped payoff diagram)
R’it’ – R’f’ = a’i’ + b’im’(R’mt’ – R’f’)^2 + e’it’
6.3 - Multivariate Empirical Methods and Performance Persistence
Define
Conditional Correlation
6.3 - Multivariate Empirical Methods and Performance Persistence
A correlation between two variables
under specific circumstances
an analyst can examine the correlation between hedge fund strategies and equity returns for more than two market conditions, such as stable, increasing, or decreasing inflation
6.3 - Multivariate Empirical Methods and Performance Persistence
List and Explain
4 common approaches for organizing data
(in order to compare historical performance and explain past performance)
6.3 - Multivariate Empirical Methods and Performance Persistence
Asset classes
* 90% of mutual fund returns are explained by the returns of a few underlying asset classes
* asset classes explain less than 25% of hedge fund returns
Strategies
* Mutual funds with same style = very closely related to underlying assets and other mutual funds with the same stated style
* hedge fund performance can be very diverse, even if the hedge fund claims to use the same stated strategy
* PCA: 45% of the variation in cross-sectional hedge fund returns is attributed to the following trading strategies: systems/opportunistic, global macro, value, systems/trend following, and distressed
Market-wide factors
* Fama-French approach: divide sample in 2 (based on a varible to be tested; one = long / other = short); test if return is explained by the return spread.When tradable factors are identified, the intercept of the model in an efficient market should equal the risk-free rate and the model is described as an arbitrage-free relationship. In other words, there are no opportunities for risk-free arbitrage returns.
* 90% of the return variation in diversified hedge funds is explained by the following seven factors that are observable and tradable:
1. Market return minus the risk-free rate (market risk premium)
2. Small-cap stock returns minus large-cap stock returns (size premium)
3. 10-year T-bond return minus risk-free rate (maturity premium)
4. Baa rated bonds minus risk-free rate (default premium)
5. Portfolio return of call and put options on bonds
6. Portfolio return of call and put options on currencies
7. Portfolio return of call and put options on commodities
The payoff of a look-back option (5;6;7 above) is based on the underlying value of the asset over a reference period rather than the value of the underlying asset when the option expires
Specialized market factors
* Hedge fund replication is another approach for analyzing hedge fund returns
* Specialized market factors in a specialized factor approach are specifically designed to represent the returns to a specific hedge fund. Such an approach tries to replicate the returns of a specific hedge fund with the returns of specifically chosen factors that are designed to match the alpha and beta of the fund.
6.3 - Multivariate Empirical Methods and Performance Persistence
Explain
Performance persistence of Hedge funds based on
* return correlations
* risk-adjusted returns
* portfolio returns
6.3 - Multivariate Empirical Methods and Performance Persistence
Performance persistence of Hedge funds based on
Return correlations
* no evidence of performance persistence (one study)
* However, in some hedge fund cases, such as those using appraisal values, the serial correlation of returns may be an indication of true skill persistence. Thus, in the short run, the manager may exhibit skills that are not possible to duplicate because appraisal values are lagged and are not market values.
Risk-adjusted returns
* The results of annual rankings suggested substantial evidence that hedge fund manager skills persist for some managers over time
Portfolio returns
* Evidence from research studies is mixed regarding the ability of alternative hedge fund managers to persistently outperform the market
6.3 - Multivariate Empirical Methods and Performance Persistence
Define
Nonlinear exposures
Nonlinear exposures (for an investment position)
occurs when the value of the investment changes based on
the size of the change in the factor
Examples
* Long and/or short options
* event-driven HF strategies (similar to short put)
* market timing strategies (~ straddle)
Obs:
* Models like CAPM = Single-factor linear model
* Models like Fama-French = Multiple regression linear model
* Models like Dummy Variable approach, separate regression approach, Quadratic Model are Dynamic risk exposure models, and estimate returns for nonlinear exposures
What does multivariate analysis involve?
Multivariate analysis involves including macro and dynamic factors by testing known variables with historical returns,
multivariate analysis is required to capture multiple factors and nonlinear relationships. Macro factors include economic
determinants such as in inflation, gross domestic product, and economic growth.
Dynamic factors describe different stock return strategies such as value, momentum, and size.
Macro and dynamic factors are identified by testing known variables with historical returns.
A third major category of factors is referred to as statistical
factors,
Lo 6.3.1
Why would an analysts most likely favor the use of Fama-French three-factor model over the CAPM?
Multifactor models like Fama-French provide more accuracy in measuring coefficient estimates.
These models result in lower intercept terms because the return variations are explained by two additional independent variables. Multifactor models also result in an
increase in R-squared values. Multifactor models are effective in explaining expected returns of assets but might not necessarily offer better or more accurate predictions of future asset return.
The predictive power of multifactor models relies on a number of mostly external factors. Hence, there is no guarantee that multifactor models will provide better predictions of future asset return.
LO 6.3.2
The practice of identifying and describing an underlying investment return to explain the return performance of the overall hedge fund strategy is most likely known as:
Style Analysis
Style analysis is a process of identifying an underlying investment return that defines and can explain the performance of a hedge fund strategy. This practice involves identifying the main contributor to the overall return performance of the hedge fund.
LO 6.3.6
Provide the steps in Fama-French adopted in identifying relevant market-wide factors
- Develope an idea related to a spcific variable that may explain returns
- Divide the full sample into two subsamples based on the specific variable.
- Estimate the investment return spread by holding one group long and the other group short.
- Empirically test whether the returns from the full sample are explained by the return spread.
LO 6.3.6
