by Nicholas Barberis
I n the US alone, pension funds control more than $4,000bn in retirement assets. One of the basic questions facing these long-term investors is how to allocate this money between broad asset classes such as stocks and government bonds. This article examines what finance theory has to say about long-term allocation policies and why financial practice often differs from these recommendations.
Good news for stocks
The two most important factors to consider when weighing up different investment opportunities are risk and reward. The simplest way to quantify the reward from holding a security is to measure its average annual return. It will come as no surprise to most people that the reward from holding stocks has historically been higher than that for bonds. However, few realize just how much higher.
For example, the average annual real, or inflation-adjusted, return on the US stock market over the 1926—93 period was 6.6 per cent. This is considerably more than the average return on long-term government bonds over the same period, a mere 1.7 per cent. The difference between the two, 4.9 percentage points, is known as the ‘equity premium’. The story is the same across many countries worldwide. The annual return on the UK stock market was 5.7 per cent over this period, 4.6 percentage points higher than the average bond return of 1.1 per cent.
The reward from holding stocks has, therefore, historically been substantially greater than that for bonds. This does not mean, of course, that we should automatically allocate all our money to stocks. It is possible that the superior performance of stocks is simply compensation for their higher risk. In other words, while stocks do earn more than bonds on average, over any one year stocks may significantly underperform bonds. Given the much higher reward from stocks, we might expect to find that they are also considerably riskier. In fact, looking at the data from a longer-term perspective, this does not appear to be the case.
Jeremy Siegel of the Wharton School of the University of Pennsylvania has used data on US stock and bond returns going back to 1802 and presented intriguing evidence about the risk of stocks. Over the 1802-1992 period, the highest real return on stocks in any one year was 66 per cent; the lowest was —39 per cent. The corresponding numbers for bonds are 35 per cent and -21 per cent. This is not very surprising. We typically think of stocks as being the riskier investment and these numbers are consistent with this view: the spread for stocks is wider than that for bonds.
For a long-term investor, though, this may not be the most relevant calculation. It may be more reasonable to use a 20-year rather than a one-year time-frame. The highest real return on stocks over any 20-year period was 12 per cent on an annualized basis and the lowest, one per cent. For bonds, the numbers are 9 per cent and -3 per cent. In other words, over any 20-year period, stocks have always earned a positive real return, something that cannot be said for bonds. Moreover, the spread between the
highest and lowest 20-year return on stocks is smaller than that for bonds. The remarkable fact is that at long horizons, stocks appear less risky than bonds.
These results are confirmed by calculating a more direct measure of risk known as standard deviation, which measures the dispersion in returns. The standard deviation of annual stock returns has been 21 per cent historically, compared with 10 per cent on bonds, again confirming the usual notion that from a short-term perspective, stocks are riskier. Once again, though, our focus is on long-term investors with horizons much longer than one year. Therefore a more relevant statistic is the standard deviation of average returns over 20-year periods. For stocks, this is three per cent — lower than the corresponding figure for bonds of 3.4 per cent.
This is a remarkable reversal: from a short-term perspective, stocks are riskier than bonds. At long horizons, though, it is stocks that are less risky. Why do stocks offer a 4.9 percentage point average annual premium over bonds when they are not obviously more risky? It is worth thinking about these standard deviation figures a little more. Why is it that stocks appear riskier than bonds at short horizons but less risky at long horizons?
Some economists believe this is caused by mean-reversion in stock returns. Mean- reversion means that a particularly bad year for the stock market is slightly more likely to be followed by a good year, rather than by another bad year. Similarly, a good performance is more likely to lead to weak subsequent returns than to another good year. The effect of this is that bad years ‘cancel’ out good years, and vice-versa, so that over long periods of time, the risk of stocks is reduced. If there is more mean-reversion in stocks than bonds, stocks may eventually become less risky than bonds.
The evidence so far casts stocks in a very favorable light. On the one hand, their average return is almost five percentage points a year higher than the average return on government bonds. Moreover, this higher reward does not appear to carry a substantial price in terms of increased riskiness. Over long horizons, stocks are not noticeably riskier than bonds. Taken at face value, the historical data seem to suggest that stocks are a far superior investment and that even quite risk-averse investors should weight them very highly in their portfolios.
Many prominent investment analysts disagree strongly with the preceding analysis of risk and reward. They claim, for example, that the 4.9 percentage point figure for the US equity premium, or indeed the 4.6 percentage points for the UK, greatly exaggerate the future rewards from holding stocks over bonds. They point out that the magnitude of the historical equity premia is largely explained by the very low returns on government bonds in both countries in the 1960s and early 1970s, which they in turn put down to the unexpectedly high inflation of the time.
Today, we have a much better understanding of the inflation process and it is unlikely that bondholders will be caught by surprise in the same way. Therefore, they say, we should not expect bond returns to be as low in the future as they were in the past century. There is undoubtedly some truth to this. But in fact it is not so clear why bonds suffered the way that they did. If inflation were the whole story, why did shortterm government bonds perform just as poorly as the longer-maturity bonds? Would not short-term rates have quickly incorporated the rising inflation figures? If we do not fully understand the cause of the poor performance of bonds, it may be premature to argue that their historical performance is unlikely to be repeated.
The question of the long-run risk of stocks is even more controversial. The fact that the standard deviation of annual stock returns over 20-year periods is as low as three per cent suggests that mean-reversion in stock returns is making the risk of stocks fall faster than that of bonds. The problem is that our data only goes back a few decades and we do not have very many independent 20-year periods from which to draw reliable inferences. Formal statistical tests have been unable to establish convincingly that there is any mean-reversion in stock returns, even if the raw numbers do suggest it. If there is no mean-reversion in stock returns then there is no reason to believe that stocks become less risky than bonds at long horizons.
All the same, there are some good reasons for believing in mean-reversion. Here is one possible story. Suppose that investors become overly optimistic about the prospects of the economy and push the stock market to levels that are unreasonably high. A piece of sobering news will lead investors to correct their mistake, pushing the market back down. Any overreaction/correction story of this type automatically generates mean- reversion in returns.
Mean-reversion is often viewed with considerable scepticism because the predictability it implies appears to conflict with the idea that markets are ‘efficient’ and that prices are ‘correct’. It is a common misconception that when prices reflect true fundamental value they should move randomly. In fact, mean-reversion can be completely consistent with a world where prices are set rationally. All that is required is that the risk of stocks changes over time. Suppose, for example, the market has plunged dramatically in the past few months. Such a move may lead to a shift in risk perceptions: investors may decide that stocks have become riskier. Basic finance theory tells us that risk must be compensated by a higher expected return. Therefore, following a stock market plunge, we would subsequently see higher returns on average, a phenomenon resembling mean-reversion.
The risk of a market collapse
Instead of arguing over how to interpret the standard deviation numbers, some analysts have claimed that standard deviation is an inadequate number to begin with. They say that simply looking at the dispersion of historical stock returns on existing stock markets misses a subtle but crucial form of risk: the risk of complete stock market collapse.
Proponents of this view point out that of the stock exchanges that existed at the turn of the century, as many as half subsequently experienced significant interruptions or were completely abolished. The Russian stock market, for example, was one of the world’s largest in 1900, yet only a few years later investors had lost their entire holdings. Simply looking at the variability of US stock returns misses this kind of risk for the simple reason that the US market has never experienced such a collapse. This does not mean, however, that the risk of a future collapse is not present. Perhaps the observed high return on stocks relative to bonds is simply compensation for the unlikely but calamitous possibility of a complete stock market collapse.
The problem with this argument is that it is not clear why this kind of risk would confine itself to the stock market. Presumably something so devastating as to bring down the stock market should also affect the bond markets. Indeed, a more careful look at the historical facts shows that most of the time, it is in fact bond markets that suffer more. The Second World War, for example, reduced the value of the German stock exchange to a mere 10 per cent of its pre-war level. At the end of 1945, the Japanese
8 • Portfolio investment
stock market was worth only 35 per cent of its value just before the Japanese surrender. Political turmoil and labor unrest in the UK in 1973 and 1974 caused the British stock market to fall to a mere $50bn.
Striking as these events were, they had no lasting consequences. The Nikkei index’s post-war performance is now legendary, rising as it did from 176 in 1949 to 20,000 in 1993. From 1948 to 1960, the German stock index provided real annual returns of more than 30 per cent. In spite of the effect of the war on the stock markets of these two countries, long-term investors eventually reaped rewards comparable to those of US investors. The same cannot be said, however, for the German and Japanese bond markets.
Japanese bondholders were devastated by the post-war inflation there while in Germany the hyperinflation of 1922-23 completely wiped out the value of German bonds. These facts make the 4.9 percentage point equity premium all the more surprising. Why is the average return on stocks so much higher than on bonds when the risk of catastrophic collapse actually seems higher for bonds than for stocks?
The numbers so far suggest the average return on stocks has been surprisingly high given that, over the long run, they appear not much riskier than bonds. What do these numbers imply for the portfolio holdings of long-term investors? Finance theory offers formal models for thinking about reasonable portfolio allocations across different classes of securities. The best known framework is mean-variance analysis, developed in the 1950s by Harry Markowitz, who later received a Nobel Prize for his work.
When historical numbers for bonds and stocks are fed into these quantitative models, the recommended long-term allocations to stocks are very high, often close to 100 per cent. Given the facts outlined earlier, this should not be surprising. The model sees that stocks have offered very high average returns historically and those returns have not been accompanied by a high level of risk over the long-run. Naturally, it recommends shifting most of one’s wealth into the stock market.
How does this recommendation compare with actual portfolio holdings? By all accounts, both individuals and institutions hold rather less in stocks than it appears they should. In the US the typical asset allocation of a pension fund is 60 per cent to stocks and 40 per cent to bonds. Moreover, the asset allocation recommendations of leading brokerage houses published regularly in the financial press hover between 50 per cent and 60 per cent in stocks. These numbers raise a puzzle of their own. Given that historical data points to an allocation approaching 100 per cent in stocks, why do investors hold so much of their wealth in bonds?
One response is that even investors who, in principle, have a long-term outlook are forced for institutional or psychological reasons to take a short-term view, thus reducing their desired allocation to stocks. It is only when we cumulate returns over long time-periods that the risk of stocks falls below that of bonds. Annual returns on stocks are undeniably more variable than annual returns on bonds and a short-term investor will, therefore, limit his holdings of stocks.
Take pension funds, for example. Given the long-term nature of their liabilities, these funds should have a long-term investment outlook. However, behind every pension fund is a pension fund manager whose performance is frequently evaluated. To be sure of keeping their job, managers have to worry about short-term performance. This shortens their investment horizon and deters them from allocating too much to
stocks. A different argument has been used to explain why individuals may act as if they have shorter horizons than would seem optimal.
Suppose you have an investment horizon of 20 years and are trying to decide on the right split between bonds and stocks. Would it matter that you are going to watch the year-by-year performance of your portfolio as opposed to going to sleep for 20 years and then awakening to see only the final outcome? At first sight, these distinctions may seem irrelevant. Why should it matter whether or not you are allowed to watch a blow- by-blow account of the performance of your portfolio? The remarkable fact is that psychologists who have simulated these types of experiments find that it does matter. Even if in principle you only care about the cumulative performance of your portfolio over a 20-year period, seeing poor performance over any one year may make you unhappy.
Given the regular updates from their investment managers and all the financial information at their fingertips, it is almost impossible for investors to avoid noticing occasional losses on their portfolios. Unwilling to watch these losses occur, investors may lean away from strategies that can produce poor short-term returns. Since stocks are more variable in the short-term, this reduces investors’ desired allocation to stocks. The question of the right long-run mix of basic securities such as bonds and stocks is far from being resolved.
On the one hand, many investors are convinced by the historical data and are allocating larger and larger fractions of their portfolios to the stock market. In the US, for example, a government panel recently recommended that Social Security funds be invested in stocks, largely on the basis of their historical performance. On the other hand, even with two centuries of data, basic quantities such as the equity premium and risk, can only be measured very imprecisely, a problem known as ‘estimation risk’.
This problem has led some investment managers to abandon the quantitative mean- variance models developed by academics precisely because these models appear to require accurate estimates of parameters that in practice we have little knowledge of. A better approach, though, may be to develop new models that explicitly incorporate our uncertainty about quantities such as the equity premium. It is models of this type that represent the current state of the art in practitioner and academic research on asset allocation.
An important challenge for long-term investors is how to allocate money between stocks and government bonds. So what does finance theory tell us and do practitioners take any notice?
Nicholas Barberis reminds us of the vastly superior returns achieved by equities over bonds, yet he suggests that equities are not noticeably risker.
One explanation for this is mean-reversion, whereby ‘bad’ years cancel out ‘good' ones and vice versa. Others counter that the equity premium greatly exaggerates future rewards from holding equities over bonds - because of the distorting effect of high inflation on historical bond returns - and that looking at the dispersion of returns on existing stock markets ignores the risk from a complete stock market collapse. This said, equity weightings are lower than theoretical models would support, reflecting perhaps how even long-term investors are forced to take a shortterm view.