Holding Period Return-Risk Modeling: Ambiguity in Estimation

In this paper we explore the theoretical and empirical problems of estimating average(excess) return and risk of US equities over various holding periods and sampleperiods. Our findings are relevant for performance evaluation, for estimating thehistorical equity risk premium, and for investment simulation.Using a unique set of US equity data series, comprising monthly prices anddividends based on consistent definitions over the 132 year period 1871-2002, weinvestigate the complex effect of temporal return aggregation and sample estimationerror. Our major finding is that holding period risk and return statistics show anextraordinary sensitivity to the choice of the starting point in calendar time. Forexample, over the period 1926-2002 there is a difference of almost 140 basis pointsbetween the average annual total return starting in January compared to starting inJuly, and a difference of almost 7 (!) percentage points in estimated annual volatility.This is yet another way in which stock price seasonality manifests itself, but thisambiguity in the underlying estimation process seems completely neglected in thecurrent literature.temporal aggregation;holding period return;stock price seasonality;equity risk premium

A Multidimensional Framework for Financial-Economic Decisions

Most financial-economic decisions are made consciously, with a clear and constant drive to ???good???, ???better??? or even ???optimal??? decisions. Nevertheless, many decisions in practice do not earn these qualifications, despite the availability of financial economic theory, decision sciences and ample resources. We plea for the development of a multidimensional framework to support financial economic decision processes. Our aim is to achieve a better integration of available theory and decision technologies. We sketch (a) what the framework should look like, (b) what elements of the framework already exist and which not, and (c) how the MCDA community can co-operate in its development.decision making;finance;decision analysis;financial decisions;multiple criteria

The effects of decision flexibility in the hierarchical investment decision process

Large institutional investors allocate their funds over a number of classes (e.g. equity, fixed income and real estate), various geographical regions and different industries. In practice, these allocation decisions are usually made in a hierarchical (top-down), consecutive way. At the higher decision level, the allocation is made on basis of benchmark portfolios (indexes). Such indexes are then set as targets for the lower levels. For example, at the top level the allocation decision is made on the basis of asset class benchmark indexes, on the second level the decisions are made on the basis of sector benchmark indexes, etc. Obviously, the lower levels have considerable flexibility to deviate from these targets. That is the reason why targets often come with limits on the maximally allowed deviation (or "tracking error") from these targets. The potential consequences of deviations from the benchmark portfolios have received very little attention in the literature. In this paper, we discuss and illustrate this influence. The lower level tracking errors with respect to the benchmark indexes propagate to the top level. As a result the risk-return characteristics of the actual aggregate portfolio will be different from those of the initial benchmark-based portfolio. We illustrate this effect for a two level process to allocate funds over individual US stocks and sectors. We show that the benchmark allocation approaches used in practice yield inferior solutions when compared to a non-hierarchical approach where full information about individual lower level investment opportunities is available. Our results reveal that even small deviations from the benchmark portfolios can cause large shifts in the top-level risk-return space. This implies that the incorporation of lower level information in the initial top-level decision process will lead to a different (possibly better) allocation.decision flexibility;multi-level decision process;porfolio management;tracking error analysis

An Improved Estimator For Black-Scholes-Merton Implied Volatility

We derive an estimator for Black-Scholes-Merton implied volatility that, when compared to the familiar Corrado & Miller [JBaF, 1996] estimator, has substantially higher approximation accuracy and extends over a wider region of moneyness

Holding Period Return-Risk Modeling: Ambiguity in Estimation

In this paper we explore the theoretical and empirical problems of estimating average (excess) return and risk of US equities over various holding periods and sample periods. Our findings are relevant for performance evaluation, for estimating the historical equity risk premium, and for investment simulation. Using a unique set of US equity data series, comprising monthly prices and dividends based on consistent definitions over the 132 year period 1871-2002, we investigate the complex effect of temporal return aggregation and sample estimation error. Our major finding is that holding period risk and return statistics show an extraordinary sensitivity to the choice of the starting point in calendar time. For example, over the period 1926-2002 there is a difference of almost 140 basis points between the average annual total return starting in January compared to starting in July, and a difference of almost 7 (!) percentage points in estimated annual volatility. This is yet another way in which stock price seasonality manifests itself, but this ambiguity in the underlying estimation process seems completely neglected in the current literature

Cross- and Auto-Correlation Effects arising from Averaging: The Case of US Interest Rates and Equity Duration

Most of the available monthly interest data series consist of monthly averages of daily observations. It is well- known that this averaging introduces spurious autocorrelation effects in the first differences of the series. It is exactly this differenced series we are interested in when estimating interest rate risk exposures e.g. This paper presents a method to filter this autocorrelation component from the averaged series. In addition we investigate the potential effect of averaging on duration analysis, viz. when estimating the relationship between interest rates and financial market variables like equity or bond prices. In contrast to interest rates the latter price series are readily available in ultimo month form. We find that combining monthly returns on market variables with changes in averaged interest rates leads to serious biases in estimated correlations (R2s), regression coefficients (durations) and their significance (t-statistics). Our theoretical findings are confirmed by an empirical investigation of US interest rates and their relationship with US equities (S&P 500 Index)

An Alternative Decomposition Of The Fisher Index

Aside from the aggregated information provided by price and quantity indexes, there is growing interest in index decompositions that reveal the contribution of each index component to overall index change. In this paper, we derive a “natural” decomposition of the Fisher price index that is directly implied by its linear homogeneity in price relatives. The proposed “Euler” weights not only indicate the total contribution of each component to total index change but also reveal which component had the highest or lowest marginal impact. Our results can readily be generalized to any index that satisfies the linear homogeneity property

Holding Period Return-Risk Modeling: The Importance of Dividends

In this paper we explore the relevance of dividends in the total equity return over longer time horizons. In addition, we investigate the effects of different reinvestment assumptions of dividends. We use a unique set of revised and corrected US equity data series, comprising monthly prices and dividends based on consistent definitions over the period 1871-2002 (132 years). Our findings are relevant for performance evaluation, for estimating the historical equity risk premium, and for investment simulation

Financial Modelling: Where to go? with an illustration for portfolio management

The definition of Financial Modelling chosen by the EURO working group on financial modelling is ‘the development and implementation of tools supporting firms, investors, intermediaries, governments and others in their financial-economic decision making, including the validation of the premises behind these tools and the measurement of the effectivity of the use of these tools’. Clearly, in this definition, the decision and its solution is central. Unlike financial modelling in our definition, the theory of finance is not so much concerned with individual decisions, but rather with the effects of the decisions and actions of many individuals on the formation of prices in financial markets. It is therefore no wonder that the assumptions underlying financial theory, which at best describe ‘average individuals’ and ‘average decision situations’, are not suited to describe specific individual decision problems. In our view it is the role of financial modelling to support individual decision making, taking account of the peculiarities of the actual case, where possible taking benefit from the results of the financial theory. This philosophy towards financial modelling is illustrated by a framework for portfolio management

The Relevance of MCDM for Financial Decisions

For people working in finance, either in academia or in practice or in both, the combination of ?finance? and ?multiple criteria? is not obvious. However, we believe that many of the tools developed in the field of MCDM can contribute both to the quality of the financial economic decision making process and to the quality of the resulting decisions. In this paper we answer the question why financial decision problems should be considered as multiple criteria decision problems and should be treated accordingly