1. Foundations of Financial Econometrics
1.1. Definition and Core Process
Financial econometrics is defined as the field that “uses statistical techniques and economic theory to address a variety of problems from finance.” These problems include building financial models, estimating volatility, managing risk, testing economic theories, and informing portfolio allocation. The development of the field has been driven by three key factors:
- The availability of data at any desired frequency.
- The availability of powerful desktop computers.
- The availability of off-the-shelf econometric software.
The application of financial econometrics follows a structured, three-step process:
| Step | Description | Key Considerations |
| 1. Model Selection | A family of models with specific statistical properties is chosen based on financial economic theory. For example, deciding to use regression analysis to forecast stock returns based on macroeconomic variables. | Avoids data mining, which is the imprudent use of data exploration that can lead to misrepresentation of risks and opportunities. Judicious use, however, may suggest true relationships. |
| 2. Model Estimation | The parameters of the chosen model are estimated from sample data. This links the theoretical model to reality. For example, calculating the α and β coefficients in a regression. | Financial data is characterized by a small amount of information within a large amount of noise. Samples are often small, leading to uncertain estimates that must be supported by economic theory. |
| 3. Model Testing | The model’s ability to forecast is evaluated using new data not used in the estimation phase (out-of-sample testing). This process is known as backtesting. | A common method is using moving windows, where the model is repeatedly estimated on a rolling sample of data and tested on the next period, creating a long series of test forecasts. |
1.2. The Data Generating Process (DGP)
The fundamental principle of financial econometrics is that there are underlying quantitative relationships that hold consistently across different times and asset classes, much like the laws of physical sciences. This underlying structure is referred to as the Data Generating Process (DGP). While asset price behavior may appear random, the goal of a financial econometrician is to identify and model the stable laws of the DGP.
1.3. Applications in Investment Management
Financial econometric techniques are integral to several phases of the investment management process:
- Asset Allocation: This involves deciding how to distribute funds among major asset classes (e.g., stocks, bonds, real estate). Models rely on forecasting returns, risks, and the covariance matrix between asset classes.
- Policy Asset Allocation: A long-term, normal asset mix.
- Dynamic Asset Allocation: The mix is mechanistically shifted based on market conditions.
- Tactical Asset Allocation: Active, opportunistic shifts from the policy mix based on objective measures of value.
- Portfolio Construction: This involves selecting individual assets within an asset class.
- Active Strategies: Use forecasting techniques to outperform a benchmark. This requires models for forecasting returns for every candidate asset and estimating their covariance matrix.
- Passive Strategies: Rely on diversification to match a market index, assuming the market is efficient.
- Portfolio Risk Management: This involves setting risk objectives, estimating portfolio risk, and taking corrective action.
- A key risk measure is tracking error, which is the standard deviation of a portfolio’s active return (Portfolio return – Benchmark return).
- Backward-looking (ex-post) tracking error is calculated from historical returns.
- Forward-looking (ex-ante) tracking error is a predicted measure based on the portfolio’s current holdings and their exposure to risk factors, often derived from factor risk models.