Many metrics have been developed for equity valuations. Conventionally, there is a focus on short-term measures of profits and cashflows. However, these are vulnerable to cyclical changes in profits and embedded margins. For example, profits vary with the level of turnover, and embedded margins vary owing to changes in expenses, such as labour costs.

The shortcomings of short-term valuation metrics have influenced the development of medium-term valuation indicators such as the cyclically adjusted price earnings ratio (CAPE), for example, which smooth out the cyclicality of profits. However, CAPE does not adjust for embedded margins.

The price-to-sales ratio focuses on factors such as gross revenue, sales and turnover. It ignores current earnings, thus providing a medium-term valuation metric that is not directly sensitive to cyclical changes in profits and margins. Of course, there are implicit assumptions, but there is an argument that this metric is less sensitive to them, and there is some comfort in offsets and unknowns over the medium term.

Stepping back further, the ratio of total equity market capitalisation to GDP (gross domestic product) provides another medium-term valuation metric that is less sensitive to cyclical changes in profits and margins. This metric became known as the ‘Buffett indicator’, since Warren Buffett referred to it as a most useful indicator when the technology bubble burst. Analysis of decades of medium-term valuation metric data leads to three important and straightforward observations:

**Consistency** – medium-term valuation metrics move broadly in line with one another.

**Equity valuation cycles** – equity valuations fluctuate relative to smoothed ‘fair value’ trend lines. Equities can be over-priced (or under-priced) relative to fair value trends for considerable periods of time. However, importantly, the fluctuations are mean-reverting, so equity prices have tended to revert to fair value over time.

*Figure 1*

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Equity valuation auto-correlation – if equity valuations are high (or low) today, they are likely to be so tomorrow. However, equity valuation auto-correlation diminishes with increased time horizon. Statistically, auto-correlation decays over a decade or so. In the late 1960s, equity valuations were not discounting the early 1970s oil crisis. In 1990, equity valuations were not discounting the technology bubble. Equity market valuation 10+ years in the future is a known unknown, and consequently the best estimate might be the long-term historic average.

These observations lead naturally to the conclusion that medium-term equity returns will be influenced significantly by medium-term valuation levels at the beginning of any period. This conclusion is supported by decades of data.

**Expected return distributions**

As an investor, one is interested in the expected return distribution. Analysis shows that equity expected return distributions are influenced significantly by two variables: valuation level and time horizon. We can illustrate this with two simple examples – short-term time horizon and medium-term time horizon.

First, take a one-week horizon. Suppose we have 100 years of data, so we have 5,200 data points. The distribution looks quite normal, with a positive mean, but slightly fatter tails and a slight left skew (because markets tend to fall faster and more sharply than they rise). Now, if we divide our data set into two sets of 2,600 data points, conditional on the valuation level at the start of each week, do we think the two distributions are identical? No, of course not. The distribution of returns from lower valuations will have a higher mean, and vice versa. So far, so good.

Now, take a 10-year horizon. Our equity valuation auto-correlation observation tells us that a sensible estimate of valuation in 10 years is the long-term historic average value. This has a significant impact on our 10-year expected return distribution. Indeed, analysis of 10-year expected return distributions leads to the important and straightforward conclusion that the mean of the distribution is closely correlated with the valuation level at the beginning of the period. Higher initial valuations lead to lower expected returns, and vice versa. There are exceptional periods owing to bubbles and deep bear markets, but the general validity of this conclusion holds with a number of medium-term valuation metrics: CAPE, price-to-sales ratio and the Buffett indicator.

To illustrate this, *Figure 1* shows both actual and expected 10-year returns on US equity, where expected returns have been estimated as a simple function of the ratio of market capitalisation to GDP, calculated as ((1.25–Ratio)×20) to scale and align the historic data. One can see how closely these lines move together – higher market capitalisation to GDP ratios being followed by lower 10-year returns, and vice versa.

**Executive summary**

Equity medium-term expected return distributions are primarily a function of current valuation levels and time horizon

US equity market medium-term valuation metrics are at levels not seen other than at the top of the technology bubble in 2000

The 10-year forward expected return for the US equity market from these valuation levels can be shown to be less than zero Investing in the US equity market today relies on an implicit assumption that equity valuation levels will be high 10 years from now, but history provides no comfort that this is a reasonable assumption

Non-US equity market valuation levels are less than the US but still high

Medium-term expected returns are dismal, and actuarial investment assumptions ought to take this into account.

**Price-to-sales ratio**

Price-to-sales ratio is a good metric for medium-term equity valuation for three reasons:

**Availability** – total revenue and sales data are available readily.

**Reliability** – this figure is less open to manipulation, with a few notorious exceptions, in contrast to reported earnings (where there is considerable evidence that results have been manipulated).

**Stability** – this metric figure is more stable than earnings.

More importantly, like market capitalisation to GDP, the price-to-sales ratio is highly correlated with medium-term returns.

Over decades to mid-2017, the US equity price-to-sales ratio averaged about 100%, but varied from as low as 40% to as high as 215%! Back in 1981, government bond yields were 15% or more, and equities had performed poorly for years. You could buy the average company at just 40% of revenue. If you invested then for 10 years, you would have made 16% per year as earnings grew and valuations increased. During that time, inflation averaged just 4% per year (although over 10% in 1981), generating a 12% real return.

In contrast, there was something very different and special about the market peak of 2000. Equities were selling at 215% of revenue—more than five times the price in 1981. Using a simple rule-of-thumb indicator described below, 10-year returns would have been forecast to be -2% per year. The actual return turned out to be -1%, but, adjusted for inflation, the real return was -3.4% per year. That is what happens after a big bubble. The ingredients of bubbles have not changed since the tulip mania that gripped Holland hundreds of years ago – easy money and the illusion that a market will go up for ever because this time it’s different.

The predictive power of the price-to-sales ratio metric as a sufficient statistic can be captured with a simple rule of thumb: for every 10% that the price-to-sales ratio is over 100%, deduct 1% per annum from a 10-year expected return of 10% per annum. So, with a price-to-sales ratio of 100%, assume a 10-year expected return of 10% per annum; with a ratio of 110%, assume 9% per annum; and... with a ratio of 200%, assume 0% per annum.

**Equity 10-year expected return distribution today**

Well, of course, this brings us to the interesting question of where are we now? The fact is that, as at early January 2018, the US equity market was priced at 231% of sales – higher than at the top of the technology bubble in 2000. This suggests that we may be at the very late stage of what will be looked back on as the ‘central bank bubble’ or ‘quantitative easing bubble’.

The implications for investors are clear. Our simple rule of thumb suggests US equity market returns of less than 0% per annum for a decade from here. Of course, the likely scenario would be a big drop followed by decent returns, again.

Consequently, equities are unlikely to be an attractive investment in the medium term from here, and there is significant downside. While it is true that European equity valuation levels are lower than in the US, and emerging markets are lower still, if the US equity market suffers a significant fall, other markets are likely to fall in sympathy.

Looking at the picture since 2000, the last 17 years might be summarised as ‘technology’ bubble, to slightly expensive valuations, to ‘housing’ bubble, to reasonable valuations, to ‘everything’ bubble. Arguments are made for why valuations are justified and will be higher permanently. But, if you look at history, these arguments do not hold water. For example, there have been long periods of very low interest rates and low price/earnings ratios.

The concerning fact is, with demographics, debt and non-debt obligation burdens where they are, economic growth in the next

10 years is more likely to disappoint than surprise on the upside.

The alarming fact is that great US equity market valuations, with a price-to-sales ratio back at 40% say, would require an 80% fall from here.

Consequently, if one has been fortunate enough to be invested until today, one might consider whether one wants to continue to be invested until the medium-term upside clearly outweighs the downside again.

Of course, there are arguments of detail that can be made with the foregoing analysis, but I have yet to be presented with one that undermines the substance of the conclusions.

**Expected return assumptions**

Actuaries make assumptions about investment expected returns. To highlight one important example, for UK defined benefit pensions, these assumptions are particularly important right now, because liabilities are likely to peak in the next decade or so. Investors recognise that equity market valuation levels are currently ‘high’.

However, current levels suggest that many investors are not exploring and understanding the implications of these valuations for future medium-term returns. This is remarkable, given that the mathematics of medium-term expected returns is relatively straightforward. Right now, the implications are clear and extremely uncomfortable.

Global equity market valuation levels are very high. Non-US equity market valuation levels are less than the US, but still high. 10-year forward expected returns are dismal. Actuarial investment assumptions ought to take this into account.

**Arno Kitts **is founder and chief investment officer at Perspective Capital Management