CHAPTER 1
Introduction

After reading this chapter you will understand:

• What the field of financial econometrics covers.
• The three steps in applying financial econometrics: model selection, model estimation, and model testing.
• What is meant by the data generating process.
• How financial econometrics is used in the various phases of investment management.

Financial econometrics is the science of modeling and forecasting financial data such as asset prices, asset returns, interest rates, financial ratios, defaults and recovery rates on debt obligations, and risk exposure. Some have described financial econometrics as the econometrics of financial markets. The development of financial econometrics was made possible by three fundamental enabling factors: (1) the availability of data at any desired frequency, including at the transaction level; (2) the availability of powerful desktop computers at an affordable cost; and (3) the availability of off-the-shelf econometric software. The combination of these three factors put advanced econometrics within the reach of most financial firms such as banks and asset management firms.

In this chapter, we describe the process and the application of financial econometrics. Financial econometrics is applied to either time series data, such as the returns of a stock, or cross-sectional data such as the market capitalization1 of all stocks in a given universe at a given moment. With the progressive diffusion of high-frequency financial data and ultra high-frequency financial data, financial econometrics can now be applied to larger databases making statistical analysis more accurate as well as providing the opportunity to investigate a wider range of issues regarding financial markets and investment strategies.2

FINANCIAL ECONOMETRICS AT WORK

Applying financial econometrics involves three key steps:

1. Step 1. Model selection
2. Step 2. Model estimation
3. Step 3. Model testing

For asset managers, traders, and analysts, the above three steps should lead to results that can be used in formulating investment strategies. Formulating and implementing strategies using financial econometrics is the subject of the final chapter of this book, Chapter 15.

Below we provide a brief description of these three steps. More details are provided in later chapters. Model selection is the subject of Chapter 14 and model estimation is covered in Chapter 13.

Step 1: Model Selection

In the first step, model selection, the modeler chooses a family of models with given statistical properties. This entails the mathematical analysis of the model properties as well as financial economic theory to justify the model choice. It is in this step that the modeler decides to use, for example, an econometric tool such as regression analysis to forecast stock returns based on fundamental corporate financial data and macroeconomic variables.

In general, it is believed that one needs a strong economic intuition to choose models. For example, it is economic intuition that might suggest what factors are likely to produce good forecasting results, or under what conditions we can expect to find processes that tend to revert to some long-run mean. We can think of model selection as an adaptive process where economic intuition suggests some family of models which need, however, to pass rigorous statistical testing.

On the other hand, financial econometrics might also use an approach purely based on data. “Let the data speak” is the mantra of this approach. An approach purely based on data is called data mining. This approach might be useful but must be used with great care. Data mining is based on using very flexible models that adapt to any type of data and letting statistics make the selection. The risk is that one might capture special characteristics of the sample which will not repeat in the future. Stated differently, the risk is that one is merely “fitting noise.” The usual approach to data mining is to constrain models to be simple, forcing models to capture the most general characteristics of the sample.

Hence, data mining has to be considered a medicine which is useful but which has many side effects and which should be administered only under strict supervision by highly skilled doctors. Imprudent use of data mining might lead to serious misrepresentations of risk and opportunities. On the other hand, a judicious use of data mining might suggest true relationships that might be buried in the data.

Step 2: Model Estimation

In general, models are embodied in mathematical expressions that include a number of parameters that have to be estimated from sample data, the second step in applying financial econometrics. Suppose that we have decided to model returns on a major stock market index such as the Standard & Poor’s 500 (S&P 500) with a regression model, a technique that we discuss in later chapters. This requires the estimation of the regression coefficients, performed using historical data. Estimation provides the link between reality and models. We choose a family of models in the model selection phase and then determine the optimal model in the estimation phase.

There are two main aspects in estimation: finding estimators and understanding the behavior of estimators. Let’s explain. In many situations we simply directly observe the magnitude of some quantity. For example, the market capitalization of firms is easily observed. Of course there are computations involved, such as multiplying the value of a stock by the number of outstanding stocks, but the process of computing market capitalization is essentially a process of direct observation.

When we model data, however, we cannot directly observe the parameters that appear in the model. For example, consider a very simple model of trying to estimate a linear relationship between the weekly return on General Electric (GE) stock and the return on the S&P 500. When we discuss the econometric technique known as simple linear regression analysis in Chapter 2, we will see the relationship of interest to use would be3

The two parameters in the above relationship are α and β and are referred to as regression coefficients. We can directly observe from trading data the information necessary to compute the return on both the GE stock and the S&P 500. However, we cannot directly observe the two parameters. Moreover, we cannot observe the error term for each week. The process of estimation involves finding estimators. Estimators are numbers computed from the data that approximate the parameter to be estimated.

Estimators are never really equal to the theoretical values of the parameters whose estimate we seek. Estimators depend on the sample and only approximate the theoretical values. The key problem in financial econometrics is that samples are generally small and estimators change significantly from sample to sample. This is a major characteristic of financial econometrics: samples are small, noise is very large, and estimates are therefore very uncertain. Financial econometricians are always confronted with the problem of extracting a small amount of information from a large amount of noise. This is one of the reasons why it is important to support econometric estimates with financial economic theory.

Step 3: Model Testing

As mentioned earlier, model selection and model estimation are performed on historical data. As models are adapted (or fitted) to historical data there is always the risk that the fitting process captures characteristics that are specific to the sample data but are not general and will not reappear in future samples. For example, a model estimated in a period of particularly high returns for stocks might give erroneous indications about the true average returns. Thus there is the need to test models on data different from the data on which the model was estimated. This is the third step in applying financial econometrics, model testing. We assess the performance of models on fresh data. This is popularly referred to as “backtesting.”

A popular way of backtesting models is the use of moving windows. Suppose we have 30 years of past weekly return data for some stock and we want to test a model that forecasts one week ahead. We could estimate the model on the past 30 years minus one week and test its forecasting abilities on the last week. This method would have two major drawbacks. First, we would have only one forecast as a test; second, the model would be estimated on data that do not reflect the market situation today.

A sensible way to solve the problem of backtesting is to use samples formed from a shorter series of data (say, three or four years), estimate the model on the sample data, and then test the forecast on the week immediately following the sample data. We then move the window forward one week and we repeat the process. In this way, we can form a long series of test forecasts. Note two things about this procedure. First, for each window there is a strict separation of sample and testing data. Second, we do not test a single model, but a family of models that are reestimated in each window.

The choice of the length of the estimation window is a critical step. One must choose a window sufficiently long to ensure a reasonable estimation of the model. At the same time, the window must be sufficiently short so that the parameters don’t change too much within the...