- Stuart Fowler

# Are equities overvalued?

Following a series of articles and letters in the FT disputing whether US equities are under- or overvalued, I sent a letter. My contribution to the debate reflects our company’s use, in wealth management, of a ‘long-term asset model’ which, amongst other clever things, generates projections for future real returns from market indices. The model relies on time series data for returns alone, rather than modeling all the variables affecting returns, such as profits and profit margins. It is a method that brings objectivity which is generally a good thing when trying to value markets. But you can only do this when you have the luxury of long histories of reliable data.

The letter referred only to the US, which we find to be normally, or ‘fairly’, valued. But what of the other markets, including the UK? We can observe that the UK is about 35% overvalued – but this is still not by any means extreme. Europe is also overvalued (but has much less history). Only Japan offers above-average long-term returns. Read on if you would like to see the numbers and read the letter.

Here’s the letter. The preceding items I refer to are briefly explained even if you did not see them.

**Sir,**

*It has to be striking when two respected experts with similar views on the equity return process reach opposing conclusions about the current valuation of US equities. Disputing Professor Siegel’s bullish case for US equities (Insight, April 26th), Andrew Smithers (letters, April 30th) says both profit margins and price/earnings multiples are well above their averages and, because the return to equity investors is stable over the long term, the market is therefore ‘clearly overvalued’.*

*I believe there is a sound way to test their conclusions. The answer is that both are wide of the mark: US equities are not at all unusually valued.*

*Andrew Smithers rejects (and sees as uncharacteristic) Professor Siegel’s idea that lower transaction costs and lower economic volatility might permanently lower the future required return, justifying much higher share prices. It is true that it has generally proved foolhardy to bet against the theory that real returns, however volatile, revert to some sustainable rate which is ‘systematic’, stable over the long term and probably not even unique to individual markets. But if you hold this view, which both have espoused in the past, it is logical to use past returns themselves to test conclusions based on analysis of the fundamental factors that are thought to be the drivers of those returns.*

*For both wealth planning and portfolio management purposes, we generate horizon-specific, real, total-return estimates for equity indices derived from observations of the slope of the full-history regression (or fitted trend), the current residual (or deviation from trend) and assumptions about the reversion coefficient (or strength and speed of mean reversion). Favouring the S&P 500 Index that Professor Siegel has previously used to demonstrate his case for a systematic return trend, we find that the trend (continuously compounded) for the US is 6.9% pa.*

*Treating the present residual as a measure of over- or undervaluation, we note that the market is 14% above trend (offering a 10-year mean return of 5.7% pa and a 20-year return of 6.2% pa). It has traded on similar terms since the end of 2003.*

*Considering the historic range (free of hindsight) is from about half to twice the trend, the present level is not significantly different from normal, or ‘fair value’.*

*Whilst valuation is important if long-term return ranges are being relied on, such as for projecting outcomes or setting funding rates, it is of little use when calling the market, and then only if truly extreme. It was from a similar valuation level (against the then observed trend) that the S&P went on to double between 1996 and 1999. But it was also the level at which the 40% drop in 1974/5 started.*

*Yours faithfully,*

SF

Valuations in the UK, Europe, US and Japan

Fitting a trend to a time series of continuously compounded, real (inflation-adjusted) total (income plus capital) returns for a market index is a simple regression exercise. The idea that the ‘slope’ of the trend is a meaningful measure of some economically sustainable rate of return from investing in a fully-diversified market index is not quite so simple. This involves buying in to some very high-level theories of economic and investor behaviour. Are there, for instance, opposing but self-equilibrating forces, such as between labour and capital, that lead to this mean reversion? Is it to do with risk premiums – investors’ required reward for providing capital or liquidity in conditions of uncertainty – in which case is there a typical investor ‘utility function’ and an average risk aversion level that cause extreme deviations to correct? These ideas are all necessary to give meaning to the data. They are also all open to dispute.

Even if you regard reversion to a sustainable mean rate of return as a true description of the equity return-generating process, you can never have so much data to work with to be sure you have correctly estimated the slope and, therefore, that you know where you are in relation to the trend. However, estimation errors related to the length and quality of data can at least be allowed for in the ‘standard deviation’ assumed for each market.

With those caveats here is a quick summary of the model outputs at the end of April for four markets where we have about enough data. The projection period in this example is 15 years.

The first column is the trend rate. Go to the last column to see how Europe’s standard deviation is penalised, and Japan’s somewhat less so, relative to the UK and US, because neither has as long a usable history.

The second column is the mean expected rate of return. If this is close to the trend rate it means a market is ‘normallly’ valued. Note that only Japan is offering a rate of return above its ‘normal’ rate. The UK is the most overvalued. The min and max rates are the best and worst-case rates at 99% confidence. The returns are for a single investment made to day with the expectation of holding for 15 years. (Regular investments benefit from ‘averaging’ of the returns and so are typically closer to trend but still influenced by ‘initial conditions’ at the outset.)

Expressed as a ratio of the trend, and hence as an approximate degree of relative value, the UK is 35% overvalued, Europe 23% and the US 12% (I actually said 14% in the letter). Japan is 20% undervalued.

By way of example, I show below the plots for the UK market. The magenta line is the level of the trend using all the data up to that point. The yellow line is the whole-history trend referred to in the table.