When I wrote recently that the All-Share index seemed cheap, some of you replied that you find it hard to find attractive stocks. This might not be as contradictory as it seems. It’s perfectly possible for the aggregate market to be underpriced while individual stocks seem fair value. The prices of one stock relative to another might be right, even if the aggregate price level is wrong.
To see how, start with my chart. It shows that the dividend yield has often predicted changes in the All-Share index in the subsequent three years. High yields in 1990 and 2009 led to big price rises, and low yields in 1999 and 2006 led to falls. Since 1987 the correlation between the dividend yield and subsequent three-year changes in the All-Share index has been 0.65 in monthly data, which means the yield alone has explained more than two-fifths of the variance in subsequent three-year returns.
This tells us that the aggregate market can indeed sometimes be too dear or too cheap. And with the yield well above its historic average, it’s possible it is too cheap now – assuming, that is, that past relationships continue to hold.
If, however, we look at how yields predict returns for individual FTSE sectors, we see a different picture. Correlations between yields and subsequent three-year price changes are much lower. Across the 25 main FTSE sectors, since 1987 they average only 0.3, meaning they explain less than 10 per cent of subsequent returns. For sectors such as construction, food retailing, IT and non-life insurance the correlations are insignificant. Only utilities and life insurers have ones close to the All-Share index’s.
This tells us that while the aggregate market is often mispriced, individual sectors and stocks are less so – the 1999 tech bubble being the obvious counter-example. As the late Nobel laureate and founder of modern economics, Paul Samuelson, said, stock markets are “micro efficient” but “macro inefficient”.
This fits US evidence, gathered by Yale University’s Robert Shiller. He showed that for the overall US market dividend yields predicted returns, consistent with the market overreacting and so becoming too cheap or too dear. For individual stocks, though, yields didn’t predict price changes but dividend growth instead. This is what the efficient market hypothesis tells us: a high yield should be a sign not of a cheap stock, but of low future growth or high risk. In 2006, for example, construction stocks and mortgage lenders were on high yields – but this led to big price falls. High yields were a sign not that the stocks were cheap but that disaster was coming.
What we have here is an example of something like Simpson’s paradox – that what is true of the whole need not be true of any particular part. This is not uncommon in economics. Maynard Keynes thought the labour market was micro efficient but macro inefficient: the workers who were in jobs were doing the right things, but there weren’t enough people in work. Consumers in aggregate can predict equity returns and economic conditions even though individual consumers are typically wrong or irrational. And Alan Kirman at the University of Aix-Marseilles has shown that the bedrock of economics – the downward-sloping demand curve – is sometimes found in aggregate data but not in any individual buyer.
In fact, there’s a simple reason why stock markets can be macro inefficient but micro efficient. Imagine you think a particular stock is cheap. You can buy it, but lay off the risk that it will be dragged down by falls in similar stocks by reducing your holdings of those stocks or even by shorting them. You can therefore mitigate the risk of being wrong. This makes it easier to pile into mispriced shares – and if enough investors do so, of course, they will bid away the mispricing.
But what if you think the overall market is cheap? Of course, you can buy it. But this exposes you to the risk that the cheap market will get even cheaper. You cannot lay off this risk by shorting or underweighting other stock markets because these tend to be highly correlated in the short term.
Arbitrage – in the sense of low-risk means of eliminating mispricings – is easier in individual stocks than it is in the aggregate market, which means that the aggregate market is more likely to be mispriced than are particular individual stocks.
It is not, therefore, as paradoxical as it seems to say that the All-Share is cheap while individual stocks are not. If you believe this to be the case, there is of course a simple solution – to buy a tracker fund.
