5 Some choices in forecast construction
5.1 Introduction
102 Forecasting Expected Returns in the Financial Markets
and highly non-linear. They are also plagued with measurement problems such as the inconsistent reporting standards for company accounting data in different jurisdictions, or the frequent revision of macroeconomic data series by national statistics offices. Even when the data are accurate and consistent, the reporting may be infrequent and delayed or the available time series may be very short.
Our view on financial markets is that asset returns are highly state-dependent non
linear functions of underlying exogenous variables wherein the key parameters, if they can be identified, exhibit profound degrees of time-dependence. Faced with such a bleak description, it may be thought that quantitative finance has little to offer; however, these problems do not affect all investors equally, and this is what drives the diversity of forecasting and risk management strategies that can be observed in the marketplace.
For example, it is of interest to some long-term ‘buy and hold’ investors to establish equilibrium states toward which the economy can be expected to mean revert. For these purposes we can use large sample theory to mitigate some of the above difficulties, because it allows us to make simplifying assumptions such as stationarity and ergodicity.1 These properties allow us to get closer to the true, unknown data-generating process simply by observing long enough time series, because the departures from this simplified model become ‘lost in the noise’.
Another investment style is driven by the quarterly, semi-annual and/or annual assess
ment of a fund manager’s performance. For this group the transient behaviour of the market and how it moves between states is all-important, as this is what generates short-term investment returns. For these investors, ‘one-off’ events and non-linearities are of dominant importance because they are what disturb the equilibrium (if it is ever fully achieved following earlier exogenous shocks to the system). Hence for this class of investors we need to move from a frequentist view of modelling to a likelihood view where we can augment the available noisy data with logical extrapolation, using theory, judgement and experience.
In addition to these differences in the time horizon between investors, there exist many other differences of investment approach depending on the particular skill of each individual or organization. Some investors are specialists in top-down or macroeconomic analysis. Their role is to pick asset classes, regions or sectors that are likely to outperform, based on the large-scale economic factors. Others believe that their skill lies in bottom-up stock picking, based on careful analysis of each company’s market, management and product strategy.
Hence we have short- and long-term, top-down and bottom-up investors. To this we can add relative or absolute, and quantitative versus technical approaches to investment management. The reality is that all these dimensions are important in any forecasting process, and either they should be accommodated in it, or the risks implicit in not forecasting a dimension should be hedged away.
To further complicate this picture, the importance of each style of forecasting varies over time. For example, top-down macroeconomic views are critical at turning points in the business cycle. Stock-specific issues dominate mid-cycle, when the macroeconomic environment is benign and predictable.
1Intuitively, a stochastic process is ergodic if its sample properties mirror its population properties. For example, we might expect the average sample return to be close to the unknown population return.
103 Some choices in forecast construction
An idealized investment strategy therefore needs to be tailored to the detailed character
istics of each investor, and then varied continuously as circumstances change. Of course this is much easier to suggest than it is to do in practice, because of the ever-changing kaleidoscope of factors and one-off events that drive investment returns. However, what we can do is provide a framework within which investors can exploit a mixture of objec
tive analysis for those aspects that are amenable to quantitative modelling combined with the theory, experience and judgement, cited above, for those aspects that are not. Our objectives are to make the most of all available information, record and discuss our views as concisely and realistically as possible, avoid inconsistencies and inefficiencies in our implementation, manage our risk exposure as realistically as we can, and learn from our experience to maximize our performance in the future.
We do not claim to be able fully to meet all these aspirations; they do, however, provide the context for this chapter, which is primarily concerned with one stage in this process design – that of forecasting. Our contention is that investment models can be designed to have certain properties, and that when you approach the task from this perspective you arrive at some very interesting conclusions that are of crucial importance to the practising investment professional.
This chapter follows on from previous work where we used rank information in portfolio construction (see Satchell and Wright, 2003). There, we showed that this dealt with many of the difficulties encountered when building portfolios using knowledge of forecast alphas.
In a later paper, we extended this rank approach to include forecast construction where the resolution of the aggregation both in return space and across your classification structures is related to the quality of the information contained in that forecast (Satchell and Wright, 2005). In particular, in that paper we showed how this rank scorecard approach can be related to a classic linear factor structure model and its generalization into a mixture of normals model, hence allowing the rank scorecard to be used as a reduced form model or reporting format for a wide range of more complex models.
In this chapter, we outline some of the more common model forms used by practitioners and relate these to this mixture of normals approach. The problem with this type of approach is that it can result in highly non-normal expected return distributions that are not handled well by classical mean-variance analysis. However, we show that a Mean- Conditional-Value-at-Risk (CVaR) optimization approach agrees with the classical model when the forecast is a normal distribution, while giving more reliable recommended holdings when the underlying expected return distribution is in reality non-normal.
In Section 5.2, we review the fundamental building blocks for our approach – the linear factor model; this is central to all quantitative portfolio analysis. Another important notion is what we could call ‘local normality’; this is not to claim that returns are normal, but that returns over short periods of time and/or conditional upon particular states of the world are normal. Such an approach allows for unconditional returns being non-normal;
it also encompasses log normality and the style of analysis used in the option-pricing literature.
In Section 5.3 we consider issues of modelling the returns distribution as a mixture of normals; in Section 5.4 we cover practical issues in constructing models as a mixture of normals. Section 5.5 discusses the mean-CVaR approach to optimization given a Monte Carlo distribution, and we present our conclusions in Section 5.6.
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104 Forecasting Expected Returns in the Financial Markets