The need for pension funds to match their assets more closely to their liabilities has put the topic of duration at the top of the agenda. 

Pension funds are faced with the problem of finding fixed income instruments with the right durations. The problem is greatest at the long end, where there is a shortage of long-dated instruments. 

Governments have tried to help with the issue of 30- and 50-year bonds. Companies like Coca Cola, Disney and IBM have even issued 100-year paper. Yet the demand for long-dated bonds outstrips the supply, depressing bond yields still further. 

One solution is to use the duration of equities to match liabilities. It is argued that equities are reasonably long duration assets that are suited to longer-term liabilities such as pensions. 

As part of a diversified portfolio, equities can do as good a job as bonds, if not better, at providing the necessary durations. 

The concept of equity duration is relatively recent, and the debate about its usefulness dates back no more than 20 years. Most of the debate has centred on how to measure equity duration. 

Unlike the measurement of bond duration, estimating equity duration is not an exact science. Most admit it is difficult to measure, and some wonder whether it is worth measuring at all. 

The proponents of equity duration say the difficulties in estimating duration should not detract from its importance as a tool for pension fund and asset managers. They argue that it is a particularly useful tool in three areas: immunisation, risk management and tactical asset allocation. 

Immunisation means matching asset and liabilities in such a way that they are insensitive to interest rate movements. Since equities account of for a significant percentage of many pension plans, some idea of their duration would be helpful. 

If equities are sensitive to interest rate changes, investment managers need to be able to make allowance for this sensitivity in their risk management plan. 

Similarly, with tactical asset allocation investment managers who are aware of the sensitivity of equities can take full advantage of any changes in interest rates. 

The idea of duration has been around for more than 60 years. It is defined as the sensitivity of a security to changes in interest rates. The longer the duration, the greater this sensitivity is likely to be. 

In fixed income analysis, the economist Frederick Macaulay calculated duration back in 1938 as the ‘weighted average maturity’ of a bond, or portfolio of bonds. The weights are the present values of each of the anticipated cash flows, both coupons and principal, as a percentage of the price of the bond, and the weight of each cash flow is its contribution to the total price. The duration of a bond is therefore the point around which the weighted present value is distributed. It has been described as the ‘centre of gravity’ of an investment’s cash flow. This why it is the duration rather than the maturity of fixed income instruments that matters to pension funds looking to match their liabilities. The cash flow characteristics of a bond with a long duration will coincide with the cash flow requirements of a long-term liability. 

Although the concept of duration is usually applied to bonds, it can be applied to any security with a prospective payment stream, including equities. 

In the case of equities, the dividend can be seen as the equivalent of the bond coupon, and the share price as the equivalent of the bond principal. 

Yet there are significant differences between bond and equity duration, which may explain why equity duration is still not widely used by asset or pension fund managers. 

One key difference is the maturity. The terminal value of equities, unlike bonds, is not fixed.

Another difference is the certainty of payment. Bondholders know what interest payments they will receive. Shareholders cannot be certain what dividend payment they will receive. 

The most widely used method of estimating equity duration is the Gordon model, named after Myron Gordon, now a professor at the University of Toronto. This is a version of the dividend discount model (DDM), a method for valuing a stock. 

According to the model, the value of equity is based on its estimated dividend, the equity discount rate and the dividend growth rate. 

Srikant Dash, index strategist at Standard & Poor’s in New York, and Kevin Gardiner, head of global equity strategy at HSBC in London, have shown in their paper ‘On the duration of equity’ how a DDM-based estimate of European and US equity duration might have looked over the past 20 years. 

The simplest way of estimating this in the DDM approach is to treat equity duration as the inverse of the actual dividend yield. The dividend yield suggests that equity duration has been rising steadily, Dash and Gardiner says, to around 30 to 40 years in the US and 20 to 25 years in Europe, though the rise here is less steep. 

The main objection to adopting the DDM framework as a tool for pension and asset management is that it tends to provide unrealistically high estimates of equity duration – often more than 50 years for high-growth stocks. 

Observation by asset managers what actually happens to companies suggests it must be lower. 

Long equity durations also turned asset management practice on its head by suggesting that the fixed income portion of a fund manager’s portfolio could be used to shorten the overall duration of the asset pool. 

In conventional fund management practice, the equity component of a portfolio is likely to have much shorter durations than those estimated by the DDM. 

What bothered proponents of equity duration was the duration lengths implied by the DDM. Fifty years seemed an implausibly long time. Experience showed that duration were often much shorter. 

In the mid-1980s Martin Leibowitz, a former CIO of TIACREFF, was one of the first people to look at effective equity durations empirically – that is, on the basis of experience rather than theory. 

Leibowitz suggests a different way of estimating equity duration empirically, by looking at historical changes in equity prices and interest rates. The method produced far shorter estimates of duration – on average between two to six years and 2.8 years for the US market. This seemed more plausible to practitioners. 

Jim Moore, product manager for PIMCO’s long duration and pension products, says: “If you dig deeper and think through the nature of some businesses out there, particularly the cyclical businesses, this makes more sense. The cyclicality in their earnings streams is driven by many of the same factors that affect interest rates. So you would expect their earnings streams to drop at the same time interest rates drop, effectively shortening duration. 

“Also, if you think about the nature of financial innovation, and the active management of a firm, there’s a lot of embedded optionality that effectively shortens duration. So if you look empirically over the last 25 to 30 years, the implied duration of equities is between two and three years. 

“This is logical when you start to think that you could create a coupon paying 30-year bond that has anything from a zero to 14-or 15- year duration or more. The bond could have a high duration if the coupon is fixed and doesn’t move or - if the coupon is responding to interest rates and is influenced by the same factor that’s driving the discount factor - you could have a very short duration.” 

Two UK economists, Richard Lewin and Stephen Satchell of, respectively, the Judge Institute of Management Studies and the Faculty of Economics and Politics at Cambridge University, have tried to resolve the problem of the wide divergence of the DDM and Leibowitz calculations. 

In their paper ‘The derivation of a new model of equity duration’, Lewin and Satchell develop the idea of equity duration as a by-product of asset pricing, and suggest that the equity premium may be an important link between the Leibowitz approach to equity duration and the more traditional dividend discount model DDM alternative. 

They base their computation of equity duration on the historic correlation between UK stocks and bonds. Their methodology uses this correlation, together with a measure of bond market duration, to arrive at an estimate of equity duration. 

Crucially, they attempt to resolve the controversial issue of the average expected lifetime of equities. The DDM approach implies equities are financial assets with infinite lives in terms of a prospective investment horizon. This in turn generates excessively long equity duration estimates. 

In some respects, equities do appear to have infinite horizons. Investors own businesses, which could theoretically stay in business indefinitely. 

Yet Lewin and Satchell argue that equities cannot be treated as undated instruments, with an infinite horizon, when there is a clearly observable corporate failure rate of 1% and 2% a year in the UK. 

They therefore calibrated their model to reflect the fact that equities behave as assets with finite horizons. They chose 100 years as an average lifetime benchmark for equities. The resulting calculations, they say, square with the liability structure of most pension funds, which have upper liability durations that are far below the 49-year maximum contribution period for a male worker in the UK. 

Besides the DDM and the Leibowitz approach, Dash and Gardiner identify a third approach to the estimation of equity duration – what is called the ‘flow through’ approach. This is an attempt to build on DDM to measure the sensitivity of growth to interest rates. 

Leibowitz and a colleague proposed calculating equity duration by looking at two factors separately. One factor is ‘assets in place’, which they term tangible value. The other is growth opportunities, which they term franchise value. The duration equity is the weighted average sum of duration of each of these two valuations. 

Separating the valuations is useful because it showed that factors like inflation affect them differently. Standard & Poor’s uses these models to calculate an annual estimate of the duration of the S&P 500. This ranges from 15 to 25 years, lower than the calculations using the DDM but much higher than the duration of most government bonds. 

Yet Dash and Gardiner suggest that the flow-through approach has one serious shortcoming. It finds it difficult to model the sensitivity of growth to interest rates. 

“If theory and intuition both suggest stocks are long-duration investments why are they so insensitive to changes in interest rates?” they ask. 

They suggest several possible answers. One is that higher interest rates cause growth to fall, softening the impact on duration and price sensitivity. 

However, they add that the fact that equity duration cannot be measured objectively with any precision does not mean that it is necessarily short. 

One way of analysing equity duration more objectively is to look at how it might be used at the equity portfolio level rather than asset allocation level. Dash and Gardiner suggest that it might be more useful to focus less on absolute duration and more on how duration is ranked across equity styles and sectors. 

“Investors often choose to follow a growth or value style and we can imagine some investors opting for a duration bias. Just as many investors believe that value outperforms in the long term, so others might believe that duration will,” they suggest. 

In a given equity sector, duration will be longer if growth is higher or if beta (market risk) is lower. In other words, they say, investors looking for high duration sectors should look for growth prospects that are not cancelled out by a similar level of risk. 

They call this style the pursuit of “growth at a reasonable risk”. 

Dash and Gardiner believe that they can rank sectors of equities according to their duration characteristics by calculating their prospective growth rates and riskiness. The calculate growth by looking at dividend growth over the past 10 years, and risk by looking at beta, the measure of the market risk that investors face. 

Having calculated growth rates and betas, they then rank the sectors according to their growth/risk ratios, which act as a proxy for their duration. 

Plotting the sectors of the S&P Europe BMI in mid-2005 according to their relative duration, they show that sectors with a long duration include food, healthcare and property – an asset class that is under-represented in the portfolios of many European pension funds. 

Sectors with short durations include computer software and hardware, telecom equipment and electronics, reflecting the fallout from the TMT episode has resulted in very high levels of market risk. 

The main drawback to this method, Dash and Gardiner warn, is that the past may not be a useful guide to the future. 

Yet duration does appear to be a significant factor in sector performance. By splitting duration estimates into two equal weighted basked to high and low duration sects, Dash and Gardiner show that high duration baskets have mainly outperformed since 1999. 

So does equity duration explain some of the effects of style investing? In particular, can the relative performance of value and growth stock be explained in terms of their duration? 

Some proponents of equity duration believe that it can. In their paper ‘Implied equity duration: a new measure of equity risk’, Patricia Dechow and Richard Sloan of the University of Michigan Business School and Mark Soliman of Stanford Graduate School of Business argue that the book-to-market ratio provides a crude measure of equity duration. 

Eugene Fama and Kenneth French identified book to value as an important driver of returns in their three-factor model. They showed that firms with low book-to-market ratios have higher equity betas; in other words, are more susceptible to market risk. 

Dechow, Sloan and Solomon’s equity duration framework, constructed from an analysis of financial statements, suggests that firms have higher market risk because equities with low book-to-market durations have longer durations, and so are more sensitive to expected return shocks. 

They say that their measure of equity duration provides a better ranking of equities; style characteristics on the value/growth dimension than value and growth index providers such as S&P, Dow Jones and Russell, whose growth and value classifications are based on “ad hoc reasoning and data-motivated statistical procedures”. 

So is equity duration of use to pension funds, principally for immunising assets against interest rate risk? Or has the behaviour of the market changed in such a way that equities are no longer an attractive duration play? 

One market change in the past two years has been the switch from a positive to negative correlation between the global equity and fixed income markets. 

Bob Litterman, director of quantitative resources at Goldman Sachs Asset Management, has argued that, for this and other reasons, equity duration is no longer a useful construct for pension funds – if it ever was one. 

He points out that two recent developments have reduced the usefulness of relying on estimates of equity durations. 

First, long-term instability and negative correlations between the bond and equity markets have made any stable measure of equity duration impossible. 

Second, a liquid market in derivatives, such as interest rate swaps, has enabled pension funds to use derivatives to hedge against changes in the overall measure of interest rates measured by duration. 

Litterman says the small and unstable relationship between domestic equities and domestic interest rates “is not an interesting or important consideration in this broader return generating context”. 

He concludes that the term equity duration suggests a stable structural relationship between equity returns and interest rate changes. “Unfortunately such a relationship does not exist.” 

In short, there may be arguments in favour of pension funds increasing their exposure to equities in the current climate, but equity duration is not one of them.