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 monthlyaverages of daily observations. It is well-known that this averaging introduces spurious autocorrelation effectsin the first differences of the series. It isexactly this differenced series we are interested in when estimatinginterest rate risk exposures e.g. This paperpresents a method to filter this autocorrelation component from theaveraged series. In addition we investigate thepotential effect of averaging on duration analysis, viz. whenestimating the relationship between interest rates andfinancial market variables like equity or bond prices. In contrast tointerest rates the latter price series are readilyavailable in ultimo month form. We find that combining monthlyreturns on market variables with changes inaveraged interest rates leads to serious biases in estimatedcorrelations (R2s), regression coefficients (durations)and their significance (t-statistics). Our theoretical findings areconfirmed by an empirical investigation of USinterest rates and their relationship with US equities (S&P 500Index)

Duration & Dimension

In fixed income analysis, duration plays a central role as a proxy for interestrate risk exposure. Althoughthis role relies on the interpretation of duration as (minus) theyield elasticity of the bond price, duration ismeasured as a bond's present value weighted average time to maturity andexpressed in terms of years. Hence duration is regarded as an elasticity with a time dimension. Inthis note we resolve this apparentduration paradox and show that duration is a pure number

Holding period return-risk modeling: the importance of dividends

En este trabajo se estudia la relevancia de los dividendos como componente del rendimiento de los activos financiero en el horizonte del largo plazo. Adicionalmente, se estudian varias alternativas de reinversión para estos dividendos. Se osaran series de datos procedentes del mercado americano con información sobre precios y dividendos para el periodo comprendido entre 1871 y 2002. Los resultados son relevantes de cara al estudio de la rentabilidad, de la estimación de la prima de riesgo así como para la simulación de distintas alternativas de inversión

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 monthlyaverages of daily observations. It is well-known that this averaging introduces spurious autocorrelation effectsin the first differences of the series. It isexactly this differenced series we are interested in when estimatinginterest rate risk exposures e.g. This paperpresents a method to filter this autocorrelation component from theaveraged series. In addition we investigate thepotential effect of averaging on duration analysis, viz. whenestimating the relationship between interest rates andfinancial market variables like equity or bond prices. In contrast tointerest rates the latter price series are readilyavailable in ultimo month form. We find that combining monthlyreturns on market variables with changes inaveraged interest rates leads to serious biases in estimatedcorrelations (R2s), regression coefficients (durations)and their significance (t-statistics). Our theoretical findings areconfirmed by an empirical investigation of USinterest rates and their relationship with US equities (S&P 500Index).interest rates; duration; averaging; time series properties; spurious autocorrelation

Decomposing Portfolio Value-at-Risk: A General Analysis

An intensive and still growing body of research focuses on estimating a portfolio’s Value-at-Risk.Depending on both the degree of non-linearity of the instruments comprised in the portfolio and thewillingness to make restrictive assumptions on the underlying statistical distributions, a variety of analyticalmethods and simulation-based methods are available. Aside from the total portfolio’s VaR, there is agrowing need for information about (i) the marginal contribution of the individual portfolio components tothe diversified portfolio VaR, (ii) the proportion of the diversified portfolio VaR that can be attributed toeach of the individual components consituting the portfolio, and (iii) the incremental effect on VaR ofadding a new instrument to the existing portfolio. Expressions for these marginal, component and incremental VaR metricshave been derived by Garman [1996a, 1997a] under the assumption that returns are drawnfrom a multivariate normal distribution. For many portfolios, however, the assumption of normally distributedreturns is too stringent. Whenever these deviations from normality are expected to cause seriousdistortions in VaR calculations, one has to resort to either alternative distribution specifications orhistorical and Monte Carlo simulation methods. Although these approaches to overall VaR estimation have receivedsubstantial interest in the literature, there exist to the best of our knowledge no procedures for estimatingmarginal VaR, component VaR and incremental VaR in either a non-normal analytical setting or a MonteCarlo / historical simulation context.This paper tries to fill this gap by investigating these VaR concepts in a general distribution-freesetting. We derive a general expression for the marginal contribution of an instrument to the diversifiedportfolio VaR ? whether this instrument is already included in the portfolio or not. We show how in a mostgeneral way, the total portfolio VaR can be decomposed in partial VaRs that can be attributed to theindividual instruments comprised in the portfolio. These component VaRs have the appealing property thatthey aggregate linearly into the diversified portfolio VaR. We not only show how the standard results undernormality can be generalized to non-normal analytical VaR approaches but also present an explicitprocedure for estimating marginal VaRs in a simulation framework. Given the marginal VaR estimate,component VaR and incremental VaR readily follow. The proposed estimation approach pairs intuitiveappeal with computational efficiency. We evaluate various alternative estimation methods in an applicationexample and conclude that the proposed approach displays an astounding accuracy and a promisingoutperformance.Value-at-Risk; marginal VaR; component VaR; incremental VaR; non-normality; non-linearity; estimation; simulation

Cross- and auto-correlation effects arising from averaging: the case of US interest rates and equity duration

Most available monthly interest data series consist of monthly averages of daily observations. It is well known that this averaging introduces spurious autocorrelation in the first differences of the series. It is exactly this differenced series that one is interested in when estimating interest rate risk exposures, for example. This paper presents a method to filter this autocorrelation component from the averaged series. In addition, the potential effect of averaging on duration analysis is investigated, namely, when estimating the relationship between interest rates and financial market variables like equity or bond prices or exchange rates. In contrast to interest rates the latter price series are readily available in ultimo monthly form. It is found that combining monthly returns on market variables with changes in averaged interest rates leads to substantial biases in estimated correlations (R2), regression coefficients (durations) and their significance (t-statistics). These theoretical findings are confirmed by an empirical investigation of US interest rates and their relationship with US equities (S&P 500 Index).