[This article is more than 15 years old. For a more recent IPE article about equity duration please click here or see our equity asset class reports]

Whether the concept ‘equity duration’ is useful has been a topic of debate for several decades and there is still no consensus on its validity. However, over the past five years empirical evidence has accumulated of significant and long-lasting changes in the global correlations between returns on bonds and returns on equities. While the historical correlations were never particularly stable, they tended in the 1980s and 1990s to be small positive values, whereas since 2000 they have tended to be negative values.

This empirical evidence convincingly demonstrates the shortcomings of depending on equity duration as a useful, stable construct, particularly as a metric to measure and manage risk. In this article we will consider the historical attraction of the equity duration concept, discuss why it has turned out not to be particularly viable, and briefly review the academic literature on the topic.

The equity duration concept became popular about 20 years ago, when duration itself became widely used in managing the risk of fixed income portfolios and when pensions increasingly focused on the risk of their surplus, the difference between the value of their assets and a measure of their liabilities.

The idea of measuring the duration of equities probably reached a zenith of credibility when Marty Leibowitz won Graham and Dodd and Q-group awards for his September 1986 Financial Analysts Journal paper ‘Total portfolio duration: A new perspective on asset allocation’, which generalised the concept of duration to cover the total portfolio.

In this paper Leibowitz made the case that the empirically estimated variances and covariances of equities and bonds could be used to estimate a positive equity duration of around two years and that such estimates, rather than much longer estimates that had previously been derived from dividend discount models (DDM), should be included in the measure of total portfolio duration, the fund’s exposure to interest rate changes.

Unfortunately, the long-term instability and recent significantly negative correlations realised between equity and bond returns have dramatised the danger of trying to measure and rely upon a stable relationship between yield changes and changes in equity valuations. These issues are readily seen in the graph above of one-year rolling estimates of equity duration based on weekly yield changes in 10-year constant maturity US treasury bonds and weekly returns on the S&P 500 stock price index.

The concept ‘duration’, defined loosely as the sensitivity of the present value of anything to changes in the level of interest rates, has a long and useful tradition in the management of fixed income assets relative to liabilities.

Pension liabilities typically contain a significant component of long-dated obligations that induces a large (and, sadly, often unrecognised) economic exposure to changes in the level of interest rates. Lower discount rates increase the present values of long-dated liabilities. Managing asset duration relative to liability duration is thus a first-order risk issue for pension funds.

Despite the continued concern over interest rate risk, we believe that equity duration is no longer a useful construct for pension funds. To better understand why not, we briefly review the pension investing context. Pension funds invest their capital for two purposes: to hedge the risks of their liabilities and to create increased returns from consciously taking risk.

Historically, pension funds had access to a fixed amount of capital which created a tension in their asset allocation between these dual objectives.
Increased allocations to bonds offset more of the interest rate exposure of the liabilities and reduced risk, but also reduced expected returns relative to increased allocations to equities. Extending the duration of the bonds helped free up capital for increased equity allocation, but this approach was limited by the availability and liquidity of long-duration bonds.

In most cases pension funds were left with significant risk from declining interest rates because of the size of their equity allocations. These significant equity allocations and the combination of negative equity returns and declining interest rates in 2001 and 2002 created the perfect storm that has ravaged pension funds’ funded status globally.

[This article is more than 15 years old. For a more recent IPE article about equity duration please click here or see our equity asset class reports]

In this context, if a pension fund had relied on a stable positive duration for equities, particularly a long duration such as that derived from a DDM, it would have been encouraged, at the margin, to make an even larger allocation to equities because such an allocation would have been seen as reducing the size of the interest rate exposure while increasing expected returns.

Two developments in recent years have significantly reduced the viability of relying on estimates of equity duration. First, as already mentioned, the hope for a stable measure of equity duration (if there ever was one) has been largely eliminated by empirical instability (including even a change in sign from positive to negative).

More importantly, the development of liquid markets in financial derivatives, including especially interest rate futures, swaps and swaptions, has largely eliminated the old tension between the dual objectives of hedging and return generation.

It is widely recognised today that pension funds can, and should, separate their liability hedging function from their return generating portfolio. Limited capital is no longer a constraint: liability exposures to interest rates may be hedged not only by bonds, but also by derivative instruments which require very little capital.

Moreover, funds can use derivatives to hedge not only changes in the overall level of interest rates measured by duration, but other risks such as changes in the term structure of rates and exposure to inflation. Many of the major pension funds around the world today actively pursue this approach.
Once the liabilities have been hedged, the return-generating portfolio can be optimised independently. It will almost certainly include equities, but should be broadly diversified and structured largely on the basis of maximising expected return for a given level of asset risk. Alternative asset classes such as private equity, property, commodities, and sources of active returns such as hedge funds and overlay strategies also should be considered.

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. Exposure to interest rate changes in the return generating portfolio can be managed like all other risks, which is to say that exposures should be taken only when there is a commensurate expected excess return.

Beyond the pension management context there have been several equity duration threads in the academic literature which may be of independent interest, but primarily as explanations of the divergence of dividend discount measures of duration from empirical estimates of duration. Leibowitz’s early empirical findings led to a number of attempts to explain why the realised durations do not exhibit the large positive values that might be expected from a naïve change in the value of the discount rate (holding all other values fixed) in the dividend discount model.

Leibowitz, in his (July 2004, Wiley) book ‘Franchise value: A modern approach to security analysis’, provides one explanation by distinguishing between two components of a business’s value: the existing ‘tangible’ business and expected growth which leverages the firm’s unique characteristics, its ‘franchise’.

Leibowitz summarises the issues as follows: “From standard DDMs, one would expect equities to exhibit a super-sensitivity to changing interest rates. However, while equities do statistically exhibit some correlation with interest rates, it is quite low, very unstable, and even switches signs from one regime to another. In other words, the market experience has no resemblance to the extremely long ‘stretch durations’ predicted by the DDM. The franchise value framework points one way toward resolving this paradox by noting that (1) a company’s future earnings can respond to changing inflation, and (2) there can be significant difference in this inflation adjustment between the tangible value and the franchise value components.”
Related literature on ‘real options’ uses the option valuation framework to attempt to clarify the factors affecting the value of growth options available to a business. Bradford Cornell noted for example, in ‘Equity duration, growth options, and asset pricing’, the Journal of Portfolio Management, Spring 2000, that much of the corporation’s expected future cash flow depends on future investments which can be viewed today as options whose value will increase with increases in interest rates.

In another academic thread there have been several attempts to decompose the relationship between equity returns and interest rates into the real rate and expected inflation components, but perhaps not surprisingly given the instability of the empirical correlations, the results have been inconclusive.
A final thread in the literature focuses on which types of equities are most sensitive to changes in interest rates. For example, a number of papers have looked at the interest rate sensitivities of value stocks versus growth stocks. Based on a DDM approach one might expect growth stocks, with a larger proportion of cash flows projected to occur further into the future, to have a higher duration than value stocks. In practice, the empirical durations of growth stocks tend to be lower. This can be explained by the franchise value approach since the longer dated cash flows of growth stocks can be adjusted more easily to changes in inflation than those of tangible businesses.

In some cases academics have tested whether the excess performance of value stocks relative to growth stocks might be due, at least in part, to their different exposures to interest rate risk. While these tests have not rejected this hypothesis, the power of these tests tends to be low.
In summary, the term ‘equity duration’ suggests a stable, structural relationship between equity returns and interest rate changes. Unfortunately, such a relationship simply does not exist. While interest rate and equity risk are two of the most fundamental risk exposures in financial markets, a better approach is to recognise that their covariance is dynamic and subject to many influences.

Bob Litterman is managing director, director of quantitative resources at Goldman Sachs Asset Management in New York


[This article is more than 15 years old. For a more recent IPE article about equity duration please click here or see our equity asset class reports]