# Macquarie Research Equities, The A-Z of Quant

February 4, 2024

## Factors

- embody information about a company
- used to predict relative returns of financial assets (implicitly assumes a benchmark against which fund performance is measured)

## Factor groups

- overview
- correlated, calculated similarly
- may be based on historical performance, future expectations, behavior, investor composition
- different factors may drive the market at different points in time, and may work against each other at other

- types
- value factors, probability factors, momentum factors, forecast factors, event-driven factors

## Building a model

- search for factors
- select and test factors
- univariate tests (IC, IC decay, fractiles)
- multivariate tests (pure factor returns)

- combine factors
- construct portfolios
- risk model, real-life constraints (active bet size, exposure to risk factors, liquidity constraints)

## Searching for factors

- requirements
- meaning
- economically, financially or behaviourally justifiable

- significance
- statistically significant, in-sample and out-of-sample

- stability
- through time, in different market conditions

- meaning
- pitfalls
- matching across data sources
- survivorship bias
- look ahead bias
- diluting per share data

## Selecting factors

- cross-sectional regression
- univariate tests (one factor at a time)
- monthly time series of information coefficients (Rank ICs)
- a ranked IC therefore measures the predictive power of a factor by looking at the correlation between the factor scores and subsequent period’s stock returns
- average of IC of 4% and above
- twelve month rolling average too account for volatility

- IC delay profiles
- IC decay profiles measure how fast or how efficient the market is at pricing in new information
- some factors exhibit short term predictive power, while others work over longer investment horizons
- involves lagging the stocks forward return and calculating the average of the ICs for each lagged return
- ideally we like to see high average ranked ICs in the initial lags of an IC decay profile that gradually decays as the lag increases (ie the IC decay profile has a gradual slope down to the right)
- factor autocorrelations also provide information about how fast a signal changes

- fractiles
- fractiles are the first portfolio simulations we use that test the efficacy of a factor strategy
- fractile portfolios are formed by dividing the universe of stocks each month based on stock factor scores
- fractile 1 would have stocks with the top x% of factor scores, and so forth
- rebalance each month
- calculate series and metrics
- may calculate market-weighted return of each fractile, to account for illiquid stocks

- useful information is mainly derived from the tails of a factor distribution, rather than the middle where there is more noise involved
- return-based performance metrics
- total return - measures the return to the portfolio
- active return - measures return in excess of the benchmark
- volatility - measures the deviation in total returns
- tracking error - measures the standard deviation of the active returns
- information ratio - measures the active return per unit of risk
- t-stat (information ratio)
- monthly success rate - measure the proportion of months with a positive active return
- monthly turnover - measures the amount of trading activity
- sharpe ratio - measures total return per unit of risk
- t-stat (sharpe ratio)
- CAMP beta - measures the correlation between fractile and benchmark returns
- CAPM alpha - measures the non-benchmark related component of fractile performance

- monthly time series of information coefficients (Rank ICs)
- multivariate tests (pure factor returns)
- multivariate cross-sectional regression
- a pure factor return therefore measures the notional return to a factor after controlling for key risk factors (eg size, sector and/or book to price)
- a pure factor return is the return to a one standard deviation exposure to the factor after controlling for all risk factor exposures

- multivariate cross-sectional regression
- heuristics
- high and significant one and two month lagged rank ICs
- Well-distinguished active returns and information ratios for top and bottom fractiles
- Lower turnover for top and bottom fractiles
- Strong relative pure factor returns

## Building the model

- two-stage factor models
- first stage
- involves combining all successfully screened candidate factors within the same factor group into an optimal mix (ie: determining the sub-model factor weights)

- second stage
- repeating the above process but at a factor group level

- considerations
- increased model transparency
- what general factor groups the multi-factor model has exposure to

- increased model control
- it is easier to qualitatively re-weight factors within factor blocks and factor blocks within the final model to take into account other practicalities

- while the correlation between factors from different factor groups is less likely, there will still be some correlation
- to combine factors they need to be comparable, normalise the data
- all factor group sub-models should have similar distributions (ie: normally distributed, zero mean and unit standard deviation)

- increased model transparency

- first stage
- putting it all together
- optimally combine correlated factors to avoid double counting and to avoid creating a model that only works in-sample Sophisticated formula is used to strip our factor correlations that uses average rank ICs and average time series rank correlations between each factor
- considerations
- factor weights
- negative weights
- small final weights
- large final weights
- a qualitative overlay to reweighting factors
- consistent measurement periods

- data
- missing dominant factor scores
- missing non-dominant factor scores
- factor weight threshold

- diversity
- a diverse array of factors to protect against some factors not working
- improves predictive power and consistency

- parsimony
- don't want too many factors, risk over-explaining past results and relying on specific combinations of factors for the future, which may or may not generalise
- more than 10 factors becomes questionable (?)
- avoid over-fitting the sample data

- time horizon
- the way to deal with this in model construction is to use Rank ICs relevant to your time horizon
- for example, if you wish your portfolio to be rebalanced monthly, you should use monthly ICs

- factor weights
- sweet spot analysis
- different stock groupings can behave differently within markets and separate models are advisable for these stock groups so long as there is sufficient breadth and it is not simply a data mining exercise

- testing model robustness
- in-sample information analysis
- in-sample multi-factor cross-sectional regressions
- out-of-sample information analysis
- out-of-sample multi-factor cross-sectional regressions

## Portfolio simulations

- constructing investible portfolios
- overview
- maximise the expected portfolio active return while minimising expected portfolio risk subject to appropriate real life constraint
- inputs: alphas (active returns), risk model, initial portfolio, fund constraints (maximum active bets, target tracking error, sector neutrality, transaction costs, liquidity considerations, market impact)

- converting the model to an alpha
- ALPHA = VOLATILITY x IC x SCORE
- normalisation process address problems caused by extreme outliers and a skewed distribution

- dealing with stock and portfolio risk
- characterise risk matrix
- full covariance – variance matrix
- This linear model involves the full history of each stock’s price returns. Both individual stock’s variances and covariances between stocks need to be calculated.

- structural full covariance – variance matrix
- This linear model involves splitting risk in two components. The first component is along various common risk dimensions also know as risk factors. Risk factors are forces that affect groups of stocks26. Well known risk factors are price to book and company sectors27. The second component is the specific or idiosyncratic risk of the stock. This is the risk not explained by the common risk factors.
- less cumbersome to calculate
- more stable and less subject to estimation errors
- don't result in selection bias
- estimate covariances of sticks with little historic data

- full covariance – variance matrix
- risk factors
- size (lof of market cap), sector, momentum
- risk factors should be meaningful and stable over time
- look for a risk model with overall explanatory power > 30%

- characterise risk matrix
- performing portfolio optimisation
- optimisation allows an active manager to get exposure to quantitative views (as characterised by the return factors), while minimising active risk (as characterised by exposure to the common risk factors and stock specific risk of the risk model).
- Value Added = Risk Tolerance x Portfolio Alpha – Portfolio Risk

- portfolio inputs and constraints

- overview
- performance analysis (including turnover, transaction costs and market impact)
- performance analysis
- see "return-based performance metrics" above

- sensitivity to portfolio constraints
- generally speaking the information ratio drops as: the size of the portfolio increase, the smaller the active bet, the smaller the liquidity constraints, the larger the tracking error, the lower the information ratio

- factor attribution
- for ex-post portfolio performance, determine the contribution of various factors to the actual return. The procedure employed for the attribution involves using regression over each performance period to estimate the market return associated with each factor. These returns are then multiplied into the portfolio exposures to these factors, giving an indication of the contribution made by each factor.
- which factors are performing well or not, which are driving returns, which constraints and risk controls are eroding alpha
- for ex-post tracking error, we can compare this with the predicted tracking error based on the risk model allowing us to assess the risk model

- performance analysis

## Appendix

- typical factor examples
- Analyst Sentiment
- Consensus Recommendation
- 1 Month Change in Consensus Recommendation
- 2 Month Change in Consensus Recommendation

- Forecast Revisions
- 1 Month % Change in FY1 EPS
- 2 Month % Change in FY1 EPS
- 3 Month % Change in FY1 EPS

- Other Factors
- Relative Trading Intensity (3/12 Month by Value Traded)
- Size (Log Market Capitalisation)

- Price Momentum
- 1 Month Momentum
- 3 Month Momentum
- 6 Month Momentum
- 12 Month Momentum

- Profitability
- Historic ROE

- Prospective ROE
- Value
- Prospective 12 Months Forward Dividend Yield
- Prospective 12 Months Forward Earnings Yield
- Prospective FY1 Dividend Yield
- Prospective FY1 Earnings Yield
- Historic Earnings Yield
- Historic Dividend Yield

- Analyst Sentiment