Are the terms quantitative methods, modeling, and financial engineering used interchangeably?

 No. The term “quantitative methods” refers in general to methods based on quantitative measurements as opposed to judgment. Example: selecting a firm based on the positive trend of its earnings as opposed to a qualitative judgment on its management. “Modeling” refers to mathematical and statistical relationships, typically embodied in computer programs, that describe the behavior of prices, returns, rates, and other financial quantities. “Financial engineering” is the model-based construction of products (i.e., contracts or portfolios) that satisfy specific financial objectives. Most financial engineering problems can be represented as optimization problems.

 

How are models used in equity portfolio management?

In equity portfolio management, models are primarily used to 1) make forecasts (of, for example, prices, returns or rates), 2) identify factors/predictors, and 3) compute the exposure of assets and portfolios to risk factors. Models are also used in the equity research phase, to understand specific characteristics of assets and portfolio returns. Example: to identify the best predictors. Once identified, these predictors might then be integrated into a factor model.

 

Quantitative methods have traditionally been associated with benchmark replication in passive management. As firms apply quantitative methods to active management on a large scale, what, if anything, is changing in the modeling approach?

Passive management tries to replicate a benchmark in the most economic way (i.e., using a smaller number of stocks and minimizing transaction costs). Active management, on the other hand, tries to find subsets of the benchmark that beat the benchmark or that produce positive returns in the absolute. Passive management is often based on sampling techniques that can replicate but not beat the benchmark; what they do is bring down the management costs; active management is based on predictors that allow to identify alpha sources. Active strategies typically accept higher turnover than passive strategies.

 

It is often said that models do not work because the future does not repeat the past.

 Should the future not repeat the past, no knowledge is possible. That holds for qualitative and quantitative analysis alike. All knowledge is based on the existence of regularities. The problem is: Just what repeats what? Clearly, the future does not repeat the past in a naïve sense. Example: if the price of an asset has been going up, there is no assurance that it will continue to go up. Modeling is the quest for those relationships between financial quantities that remain approximately stable (i.e., invariant). The most common relationship found in financial modeling is some constant proportionality (in a statistical sense) between a number of past and present predictors (example: past and present financial ratios such as book to price or earnings to price) and future returns. The second most common regularity is the existence of empirical averages that remain relatively stable in time (i.e., momentum). The third most common regularity (but not everybody agrees on this) is the fact that “what goes up must come down,” that is, that price processes are cointegrated with global market processes.

 

Do models forecast better than humans?

Humans can effectively integrate information to produce qualitative judgments but have limited computing capability. We can evaluate corporate management but we cannot compute numerous correlations between different markets and stocks. Example: considering only stocks in the S&P 500, there are about 125,000 different correlations; no human can compute this number of correlations. Models are better at making a large number of forecasts on a large number of assets; skilled humans, if properly trained, can probably make better forecasts on individual assets. However, one has to bear in mind that skilled humans base their knowledge on statistical analysis. Pure intuition without the support of data does not work.

 

Why does the same type of model (e.g., momentum models) give good results (i.e., produce above-market returns) for some and bad results for others?

There might be different explanations. The most common explanation is that the same model is being applied to different markets and does not “fit” them all equally well. Another explanation is implementation: models require the estimation of parameters. For example, the performance of momentum models depends on the time window used to estimate momentum effects. If the window is not correctly estimated, momentum profits disappear or even turn into losses.

 

It is often said that models “break down”. Why might a model that has been performing well see its performance degrade?

Models used in finance are not universal laws, only approximate, partial representations of markets. A model might capture a phenomenon that is present at a particular moment but less relevant in other moments. The most obvious example is trends: trends change from time to time, a characteristic exploited by regime shifting models, though these are still not much used in the industry. Also, as models are calibrated on past data, they require time before they can be re-calibrated on more recent data. Example: in the year 2000, markets experienced a downturn after 20 years of steady growth. The (rather simplistic) models being used were not able to capture the change in trend.

 

When modeling markets, is more data always better?

From the purely statistical point of view the answer is: Yes. That is, if models captured real features of the economy and the economy did not change in time, more data would allow more accurate estimates. However, models are only approximate and the economy changes in time; thus there is a trade-off. We also have to distinguish between longer time series and data at shorter intervals. Estimating models on very long time series produces a kind of model average that does not necessarily improve the accuracy of forecasts: both the economy and markets change and using data on markets twenty years back might not be appropriate. As for the use of data at shorter intervals such as intraday data, while this should in principle be beneficial, it makes modeling more complex: the benefits might be offset by the increased complexity.

 

Risk is generally equated to uncertainty. How can we measure risk if we are uncertain about the future?

There are two levels of uncertainty. The first level is due to the fact that our models are statistical models subject to random errors. We measure uncertainty (i.e., risk) as the size of errors of our models. By estimating the models, we estimate risk. There is more than one way to measure the amount of error, but the mostly widely used method is variance. Some models, typically simple models, make errors whose size, when measured by variance, is predictable. This is the ARCH behavior discovered by Robert Engle, who was awarded the Nobel Memorial Prize in economics for his work. The second level of uncertainty is due to the fact that our models might be mis-specified. This risk is generally referred to as model risk. This type of risk is very difficult to estimate, both conceptually and in practice.

 

There are various measures of risk: variance, VaR, conditional VaR, downside risk measures, and EVT (extreme value theory). Is one better than the others?

When we measure the size of errors in our models (i.e., risk) with one single number, whatever that number, we trade off different characteristics of our uncertainty. By and large this happens in two ways. The first trade-off is between measuring the risk inherent in “business-as-usual” situations versus the risk inherent in extreme events. For example, VaR concentrates on business-as-usual risk; EVT concentrates on tail risk (i.e., extreme events). The second trade-off is between 1) risk measures that are good for some distributions but perform poorly for others (e.g., variance performs well for Gaussian distributions and poorly for distributions with fat tails) and 2) risk measures that perform reasonably well for a broader set of distributions (e.g., robust risk measures such as median absolute deviation or MAD). There are other considerations. For example, risk measures must be coherent. Coherence places a number of constraints on risk measures. Subadditivity is one such constraint. Enlarging a portfolio reduces the amount of risk as there are more diversification opportunities. VaR is not subadditive, conditional VaR (CVaR) is.

 

Why is there now so much interest in optimization?

 Optimization is the basis of portfolio construction; until recently, it has been difficult to perform. When constructing a portfolio, asset managers look for the best risk-return trade-off - a typical optimization problem. Essentially a process of trial and error, optimization is computationally intensive and sensitive to errors in parameter estimation. If correlations are incorrectly estimated, an optimizer might construct inefficient portfolios as it will try to exploit mistaken diversification opportunities. To avoid errors one has to 1) "smooth" estimations to make them robust and 2) put constraints on the optimization process. The first problem is conceptually complex and only recently have we learned how to solve it in practice. The second problem, constraining optimization, is simple to describe but hard to solve in practice; we are now beginning to tackle it. The present interest in optimization is due to the fact that optimization can now be effectively performed.

 

 

If you have additional questions, please contact:

Sergio Focardi

email: sfocardi@theintertekgroup.com

Tel: + 33 1/45 75 51 74

Cell: +39 348/530 85 28