The Derivation of a New Model of Equity Duration

This paper sets out to address the issue of equity duration, one of several risk measures available for asset and liability management. Equity duration, as derived from the use of traditional dividend discount models, results in extremely long duration estimated for equities - often in excess of 50 years for growth stocks. Leibowitz, in his seminal paper (1986), identified an alternative framework for assessing equity duration empirically. This methodology yields equity duration measures more consistent with the experience of practitioners, implying that equities behave as if they are much shorter duration instruments. In our paper, based on an application to UK data, we develop the intuition behind the Leibowitz approach to generate equity duration as a by-product of asset pricing, Our analysis suggests that the equity premium puzzle may comprise an important element in reconciling the Leibowitz approach to equity duration, with the more traditional dividend discount model alternative

A New Risk Factor based on Equity Duration

We introduce a new risk factor linking a firms equity duration to investment opportunity risk. Low-duration firms generate short-run cash flows and face strong reinvestment risk. High-duration firms have long-run cash flows and their present value increases when discount rates decrease as a result of a deteriorating investment environment. Our empirical analysis reveals a significant return premium of low-duration stocks, confirming that investors charge a risk premium for stocks with returns that are positively related to the investment environment. Our newly introduced risk factor carries significant risk premiums in cross-sectional asset pricing tests. These premiums are robust to including further risk factors and a variety of different test specifications. Notably, our duration risk factor retains high explanatory power on the cross-section of stock returns in a model including direct measurement of the investment environment via state variable innovations

A comparison of UK equity and property duration

This paper considers the duration of property and equity. A general formula for duration of asset classes is derived. It is shown that calculations which assume, usually implicitly, that the flow-through of inflation to cash flow is zero, produce misleadingly high durations for property and equities. These are typically in the range 15 to 25 years. Simulations using the formulae show that property has some bond-like characteristics. The results indicate that, for realistic flow-through rates, equities have a higher duration than property. The flow-through rate is the most important variable in the estimation of equities. Using historical data, equity duration is estimated at 8.65 years and property’s at 3.15 years. These are substantially lower than those commonly cited. If these values can be substantiated, and if higher values are used in practice, portfolio immunisation strategies may need to be reconsidered

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)

A short note on the problematic concept of excess demand in asset pricing models with mean-variance optimization

Referring to asset pricing models where demand is proportional to excess returns and said to be derived from a mean-variance optimization problem, the note formulates what probably is common knowledge but hardly ever made an explicit subject of discussion. This is an insufficient distinction between the desired holding of the risky asset on the part of the speculative agents, which is the solution to the optimization problem and usually directly presented as excess demand, and the desired change in this holding, which is what should reasonably constitute the excess demand on the market. The note arrives at the conclusion that in models with a market maker the story of the maximization of expected wealth should be dropped

Constructing a GDP-based Index for Use as Benchmark

The gross domestic product [GDP] is a fundamental economic indicator that is frequently used as a benchmark for local equity indices. The widespread appeal of this association is understandable because an equity index, especially if broad, could, like the GDP, also manifest the state of the economy. At the same time, however, the validity of a direct relation between the two is debatable since the GDP is known to be characteristically different from the typical equity index, however broad. In this work, we review some of the key elements that separate the GDP from a typical broad equity index in order to explain why the two cannot be compared directly with each other. We then incorporate a readily available mapping technique to create a GDP-based index that circumvents their inherent disparities and, thus, enable us to benchmark one against the other.GDP; equity index; benchmark; relative valuation; duration;

Evaluating Methods to Estimate the Implied Cost of Equity Capital: A Simulation Study

We evaluate accounting-based methods to estimate the implied cost of capital using a simulation approach. We simulate a model economy in which the true cost of capital is known and calibrate it to the CRSP-Compustat universe. We then compare the true cost of capital to the implied cost of capital estimates from ten different methods proposed in the literature in terms of bias, accuracy, and their correlation with the true cost of equity capital. Methods based on the residual income model perform better than those based on the abnormal earnings growth model. Methods that estimate the cost of capital and expected growth simultaneously work reasonably well if they rely on analyst forecasts instead of ex post realized values, even if analyst forecasts are biased. We suggest combined methods that are chosen so that the distortions from individual methods compensate each other and show that some simple combinations outperform all individual methods

Multi-asset minority games

We study analytically and numerically Minority Games in which agents may invest in different assets (or markets), considering both the canonical and the grand-canonical versions. We find that the likelihood of agents trading in a given asset depends on the relative amount of information available in that market. More specifically, in the canonical game players play preferentially in the stock with less information. The same holds in the grand canonical game when agents have positive incentives to trade, whereas when agents payoff are solely related to their speculative ability they display a larger propensity to invest in the information-rich asset. Furthermore, in this model one finds a globally predictable phase with broken ergodicity

Why is Long-Horizon Equity Less Risky? A Duration-Based Explanation of the Value Premium

This paper proposes a dynamic risk-based model that captures the high expected returns on value stocks relative to growth stocks, and the failure of the capital asset pricing model to explain these expected returns. To model the difference between value and growth stocks, we introduce a cross-section of long-lived firms distinguished by the timing of their cash flows. Firms with cash flows weighted more to the future have high price ratios, while firms with cash flows weighted more to the present have low price ratios. We model how investors perceive the risks of these cash flows by specifying a stochastic discount factor for the economy. The stochastic discount factor implies that shocks to aggregate dividends are priced, but that shocks to the time-varying price of risk are not. As long-horizon equity, growth stocks covary more with this time-varying price of risk than value stocks, which covary more with shocks to cash flows. When the model is calibrated to explain aggregate stock market behavior, we find that it can also account for the observed value premium, the high Sharpe ratios on value stocks relative to growth stocks, and the outperformance of value (and underperformance of growth) relative to the CAPM.

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)