Styles of Quantitative Finance

“Quants” is the nickname given to the financial analyst community’s quantitative analysts and sometimes also to the products they manage and produce. Although it is hard to think that asset or investment management could somehow not be quantitative, when the key figure is whether you have more at the end than you did at the beginning, the term really refers to the degree of quantitative knowledge necessary to manage and take part in some new processes that have recently become practical largely because of advances in computing technology and data networks. Traditional analysis of companies required comfort with algebra and perhaps a little calculus, but not necessarily a great deal more. Modern derivative products, on the other hand, typically demand an understanding of more complex procedures, such as stochastic integration, matrix algebra, and others.

In 1973, when Burton Malkiel published A Random Walk Down Wall Street and concluded that index funds offered better risk-adjusted results than any kind of active management, Malkiel divided active analysis methods into two camps. “Fundamental” analysis looks at company financial statements, management quality, and corporate strategy, whereas “Technical” analysis looks at pricing patterns and exchange volume for signals of when to buy and sell securities. Today, Quantitative Analysis presents a third strategy, possibly imagined, but certainly not available in 1973.

Emanuel Derman, one of the pioneering quants at Goldman Sachs and now at Columbia University, wrote in My Life as A Quant that the three essential ingredients to a good quantitative analyst are 1) an understanding of finance theory, 2) strong mathematical training, and 3) computer programming ability. Certainly these are the ingredients that are requested in quantitative job ads, but it is a mistake to think of quantitative analysis as a single thing. There are at least four different realms of quantitative analysis in modern finance, and they demand a different balance of these and other skill sets. The four types of quantitative analysis I see are Econometric Forecasting, Portfolio Optimization, Risk Management, and Derivatives/Arbitrage Pricing.

Econometric Forecasting is the use of statistical and regression techniques to predict rates of return on assets and the dispersion of that prediction. Major issues in econometric forecasting have to do with identifying the proper factors to include in the model and and reducing or at least predicting the spread of the residuals (essentially the error between what the model predicts and what you observe in reality). The major advance in the last 20 years has been the availability of data and improvements in computing speed, so that these regressions can be calculated for 1000s of securities, rather than the 10-20 per analyst that is feasible with fundamental analysis. What is necessary for this type of quantitative analysis is an understanding of the key factors to include in the model, the proper methods of model specification, and the effects of breaking key econometric assumptions.

Portfolio Optimization is the application of techniques introduced by Harry Markowitz in the 1950s to determine the optimal weightings for a portfolio of risky assets in order to ensure either the minimum degree of risk for a given expected return or the maximum possible return for a given amount of risk. Markowitz’s principal insight is to use the correlations (or lack of correlation) between assets to reduce the overall volatility of a portfolio beyond the volatility of its components - basically a mathematization of the portfolio diversification principle. The key issues in post-Markowitz portfolio optimization have to do accounting for potential errors of inputs to the optimization, the incorporation of trading costs when portfolios that drift from their target weights are rebalanced, and for computer coders to write numerical algorithms that can quickly converge on an optimal set of portfolio weights. These techniques demand a familiarity with statistical theory, matrix algebra, and an ability to produce efficient computer code.

Risk Management is closely related to portfolio optimization in its goal. Whereas portfolio optimizers seek to minimize the risk associated with a given level of expected return, risk managers seek to understand the risk a collection of funds or portfolios presents to a business operation. The difference arises where an individual portfolio may be optimized and have the minimum volatility for the desired level of return, but that level of volatility is still too great from the perspective of the business entity as a whole, in part because other funds in the organization may all be exposed to the same types of risk. Therefore even if an individual portfolio is optimized, it may be necessary to reduce the total risk exposure for the sake of the organization, and it is the risk manager’s job to go tell the portfolio manager to “cool it down a little.” This puts the risk manager in an unenviable position - in good times, risk managers are politically unwelcome because they tell portfolio managers that they can’t make all the bets they want; in bad times, they can take the blame for not having prevented the portfolio managers from taking those very same bets. A good risk manager generally needs broad quantitative skills because they need to understand the models of many different portfolios and asset classes and be able to combine them into models of enterprise risk. Thus, they need to be strong quantitative generalists across all classes.

Derivatives/Arbitrage Pricing is probably the most mathematically intensive of modern quantitative analysis, and makes use of stochastic differential equations to link the random behavior of underlying assets to the fair price. For the more timid, some derivatives can be priced using Monte Carlo simulation, provided that one has modeled the random behavior with the right random process, and some more exotic derivatives may have to be modeled with the Monte Carlo method. Derivatives are generally priced on arbitrage principles, which is to say that they are priced so that the derivative is equal to the cost of manufacturing an equivalent payoff with combinations of other securities (which may include other priced derivatives). There are several talents that can do well in these areas. First, a special ability to spot the combinations that will replicate the payoffs and then combine the prices efficiently is necessary to generate the arbitrage possibilities. Then, one needs to understand stochastic calculus sufficiently to derive analytic solutions, or one needs to be a highly efficient programmer to manage the Monte Carlo process rapidly enough to price items while they are still available. Ideally, one is good at both.

My own quantitative background is more in econometric forecasting and modeling, although I do find the derivatives and arbitrage pricing very interesting, and I like the application of portfolio optimization to investment problems. Still, I have often felt intimidated by the mathematics, engineering, and physics Ph.D.s who dominate the arbitrage and derivatives pricing world (and to some extent in risk management), and it has taken me some time to realize that econometric insights into asset valuation are still highly valuable, especially when needing to manage traditional assets. Indeed, the more mathematical an approach, the more assumptions typically need to be made about human and market behavior, and the more easily a model can fail to apply to economic reality. In these situations, a student of psychology, politics, and economics brings some very important advantages.

To some extent, we may be observing just this issue in the current subprime mortgage / CDO crisis which threatens to engulf other asset classes. I have a feeling that there may be considerable overreaction to the crisis in some sectors, but the increasing cost of leverage may force many asset managers to sell, driving down prices, and so there is certainly some danger of contagion from the mortgage market to the general equities market. The big question in my mind is about the credit default swap (CDS) market. Many asset managers may think that they are covered because their CDSs effectively have them insured against credit defaults. But if enough defaults occur, someone eventually will have to come up with money to pay out that insurance, and if their models have not adequately priced the insurance costs, then we are in for a very interesting ride.