The difficulty in developing a model that accurately predicts equity duration means few managers pay much attention to the concept. And yet, just because it’s a tricky task, doesn’t mean it should be ignored.

 

The concept of duration – a measure of the sensitivity of an asset’s price to a change in interest rates – is a familiar one to bond investors. That is for good reason, since movements in interest rates are often the primary determinant of a change in the price of a bond or portfolio of them. After all, the value of a bond, like that of any other financial asset, can be viewed simply as the ‘net present value’ of a series of future cash inflows. The higher the discount rate used to convert those future payments into today’s money, the lower the value of the asset.

But the term is probably far less familiar to the majority of equity investors. That too is for a good reason. Whereas measuring a bond’s duration is fairly straightforward, in the case of a share, or portfolio of them, it’s an altogether trickier task.

The cash flows expected to accrue to the owner of a bond are pretty much known in advance, except in the relatively rare event of a default. That is because the issuer of a bond is contractually obliged to make pre-determined coupon payments and to repay the principal upon maturity.

By contrast, payments to shareholders, largely in the form of dividends, are not obligatory and as a result fluctuate. During good times they tend to rise in tandem with company profits. But when profits fall, they can be slashed or even stopped altogether. And if working out future dividend streams seems hard enough, how do you value a share in a young company that has yet to make any payouts, or value a firm that ends up being acquired.

These difficulties haven’t stopped financial market practitioners and academics from attempting to find a method of estimating equity duration. Most have entailed using the dividend discount model – a widely recognised procedure for determining a theoretical valuation of a stock by estimating the sum of future dividend payments and discounting them back to the present.

It contends that the current price of a stock, or stock index, depends on three variables: next year’s dividend, the required rate of return – which can itself be broken down into a risk-free rate of interest and an equity risk premium – and the expected dividend growth rate in perpetuity – such that: 

Where S0 = the current stock price; D1 = next year’s dividend; r = the required rate of return; and g = the expected dividend growth rate.

By inputting different estimates of r into the model while holding the other variables constant, it is possible to try to anticipate how sensitive a share price is likely to be to a given change in interest rates. Unfortunately, for a host of different reasons – not least the sensitivity of the model to the estimates of r and g, and the difficulty in estimating g in the first place – the model has not been a good predictor of the sensitivity of equity prices to changes in interest rates. Whereas it predicts most equities have extremely high durations, empirical evidence suggests they tend to be far lower.

Furthermore, while in reality there does appear to be some relationship between equity prices and interest rates as one might expect, the correlation between the two is quite low, very unstable, and can even be negative on occasion.

The difficulty in developing a model that accurately predicts the sensitivity of share prices to changes in interest rates means few equity fund managers tend to pay a great deal of attention to duration. And yet, just because it’s a tricky task, doesn’t mean it’s a risk factor that should be ignored.

We believe duration warrants especially close monitoring in the current environment with record-low interest rates having significantly lengthened the duration risk attached to pretty much every financial asset, including shares. Equity investors should be no different to their bond-market brethren in wanting to have an idea how sensitive their investment portfolio is likely to be to a change in interest rates. After all, just as falling interest rates have been a major factor behind the strong advance in equity prices over the past seven years, so a sustained rise in rates could send share prices sharply lower.

But since finding a precise measure of the duration of a share, or portfolio of them, is likely to prove elusive, it seems like a better idea is to settle for a rough and ready reckoner such as the price:earnings (P:E) ratio.

The rationale for this approach is intuitive when one considers that an alternative definition of a bond’s duration is the weighted average time to maturity of all coupon and principal payments. After all, the P:E ratio is merely an estimate of the number of years’ worth of profit investors are prepared to pay for up front when buying the share.

So in the current environment we believe there is a strong argument for investors to pay closer attention than usual to a share’s P:E ratio when screening it for inclusion in a portfolio. Other things being equal, the higher the P:E ratio a share is trading on the more duration risk it would appear to carry.

In the event interest rates do rise, equities trading on high P:E ratios ought to be more vulnerable. For instance, there has been no shortage of commentators warning of the danger of owning so-called bond proxies – shares in ‘defensive’ companies offering high yields such as utilities and ‘consumer staples’ firms.

As the chart below shows, US utility share price valuations – as measured by P:E ratios – have risen sharply relative to the wider market in recent years, as investors, including large pension funds, craved their predictable cash flows.

 

 

However, just as these shares have been driven up by the collapse in bond yields, so any rise in rates has the potential to inflict heavy losses on shareholders. We were given a preview of this in the third quarter of this year when speculation that stronger economic data could lead to US interest rates rising faster than previously envisaged led to a sharp sell-off in utility share prices which fell 6 per cent over the period.

Meanwhile other sectors such as biotech and technology are widely seen to be far less sensitive to interest rates. This too appears a dangerous assumption to make. Many companies in these sectors make no money and furthermore are not expected to do so for a number of years. That means investors are pinning their faith in these firms making money long into the future.

As such investments in these shares should typically be seen to involve a high level of duration risk. At least from a theoretical perspective, any rise in interest rates ought to lead to investors bidding down the value of the sum of these companies’ future dividend payments.

At the same time, it’s important to recognise that biotech and technology companies tend to have low levels of debt. As such their profits are less vulnerable to any increase in interest rates than in the case of many other types of company. So in attempting to assess an individual stock’s duration, it’s vital to simultaneously estimate how much impact higher interest rates could have on a company’s profitability.

In contrast, shares in many industrial companies look attractive. They tend to trade on low P:Es due to investors’ scepticism over these firms’ ability to maintain, let alone grow, profits. Although once again, one should recognise that at least in the US, industrial companies tend to be more indebted than the average company.

Investors also need to distinguish between those shares which are indeed bond proxies and others which offer growth potential. For example, some commentators have labelled consumer products maker Unilever a bond proxy. We believe this is wrong as the company’s focus on emerging markets means the shares offer strong growth potential.

Of course, financial markets often don’t behave in the way theory suggests they should. One only has to look at the fact that in the third quarter – just as utility and real estate stocks sold off sharply – biotech was the best performing sector, returning 13 per cent.

That is understandable. In an environment of rising rates, it’s no surprise to see that investors’ first move was to switch out of defensives into what they perceive to be ‘growth’ stocks. But just because a stock has a growth label attached to it doesn’t mean to say its future stream of dividends shouldn’t be valued at an appropriate discount rate. After all, it’s highly likely that many of today’s growth stocks will become tomorrow’s income investment.

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