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Long Term Risk and Return

Between 1926 and 2010 $1.00 invested in the S&P 500 with dividends reinvested, would have produced a cumulative real return of $242.69. In comparison, a $1.00 invested in US Treasury Bills would have grown to only $20.40 in today’s purchasing power. Equities win hands-down; their long term superiority is undeniable. The annualized real return on the S&P 500 was 6.67%. The annualized real return on US Treasury Bills averaged 0.60% percent. The difference, or 6.07 %, is the equity premium or the long-term reward for taking the risk of investing in equity markets.

The fact that there is a measurable, significant long-term premium for investing in equities is a fundamental building block for all investors. But what this data doesn’t tell you is how rough the ride has been along the way for any investor who lived through the plunge in 1929, the decline in 1973-1974, the collapse in 1987, the bursting of the technology bubble in 2000, and the credit blowup in 2008 and 2009. Higher returns are always paired with higher risk. Sometimes volatility can wipe out years of gains in just a few months. Other times, the market chips away at a portfolio through long painful downturns.

The Equity Premium

Assumptions about the equity premium drive allocation of funds between stocks and bonds, and direct investment decisions among asset classes within those segments. Assumptions about the equity premium also reflect what returns investors can expect from equities and what the future risk-reward tradeoff is likely to be.

Because the equity premium for owning stocks has swung widely over periods of one, ten, and twenty, and fifty years the question of what equity premium we can expect is a source of controversy. And judgments about it should really be based on the full extent of financial market history and not just by looking at the United States, but at other countries as well. If long-term historical average returns are reasonable estimates of expected returns, the implications for long-term investors are rising real spending levels over time. When more conservative adjusted means are used, investors may have to adjust their future wealth expectations.

Prior to the end of the technology bubble in 2000 the most widely cited US source of the long-term US equity premium was Ibbotson Associates. Ibbotson Associates risk premium estimates are based on data from the Center for Research in Securities Prices (CRSP) whose data history starts in 1926. Based on CRSP data from 1926-2000 Ibbotson estimated that their long-term data implied that the annualized US equity premium relative to US Treasury bills is 7.3 percent.

In the spirit of using the longest possible data to analyze expected stock returns Fama and French (Equity Premium, 2002) analyzed returns on the S&P 500 Index from 1872 – 2000 and calculated 5.57% for the equity premium on  the index. The average annual equity premium reported in the Fama French paper is around 1 and 3/4% lower than the equity reported in the Ibbotson study. Some of the difference arises from the choice of time frame. The Fama French study dates back to 1872 and includes the pre-1926 period for the United States when returns were lower, partly due to events leading up to, and including World War I. A comparison between the 1872 to 1950 period and the 1950 – 2000 periods in the Fama French research study makes the point that the equity risk premium could change over time. The equity premium for 1872 to 1950 is 4.40%. In contrast the equity premium for 1951 to 2000 is 7.43%. The difference in returns between the two periods is significant.

Jim Davis (DFA) says there are two schools of thought on how to explain the variation in returns. Some attribute it to rational variation in response to Macro Economic factors (Fama and French,1989), while others judge that irrational swings in investor sentiment are the prime moving forces (Schiller, 1989). Whatever the story for variation in expected return, and whether it is temporary or partly permanent, the message from end-of sample dividend and earnings yield ratios in the Fama and French research is that although the US economy has been remarkably successful it may face a period of low expected returns.

To help put the US equity premium record in perspective, Elroy Dimson, Paul Marsh and Mike Staunton (London School of Economics) compiled a database of long-run international returns  including reinvested income for 16 countries over the 102 year period from 1900-2001. In “Triumph of the Optimists” (Princeton, 2002) Dimson, et al. cover the U.S., the U.K., Japan, France, Germany, Canada, Italy, Spain, Switzerland, Australia, the Netherlands, Sweden, Belgium, Ireland, Denmark, and South Africa. The authors show that some historical indexes overstate long-term performance because they are polluted by survivorship bias and that long-term stock returns in most countries are overestimated, due to a focus on periods that in retrospect are known to have been successful. Over the entire 102 year period, the annualized equity risk premium, relative to bills, was 5.8% for the United States, and 4.90% for the world index. The US equity premium reported in the Dimson et al. study has a standard error of about 2 percent and is similar to the equity premium reported in the Fama French study. In the global study Dimson et al. show that only Australia, France, Italy, Japan, and South Africa had had higher equity premiums than the US over the 102 year period. France led the field with a 7.4 percent premium, while the lowest premium was the 1.8 percent for Denmark. Of the three market leaders in 1900 (US, UK and France) only the US managed to outperform the world during this period.

The Forward Looking Premium

Will the forward equity premium on the S&P 500 index deliver 5 ½ to 6.0% real returns like it did over the past century? Or will the equity premium be closer to 3 or 4% as some analysts currently suggest? The answer provides direction not just for allocation decisions, but for how much and for how long investors need and to save in order to reach their goals.

Ibbotson and Chen (Source) estimated the forward-looking equity risk premium by constructing a supply-side earnings model with data from 1926 to 2000. They factored in inflation, real earnings growth and the historical dividend yield.  Their conclusion: the forward-looking equity premium is 3.97 percent annualized.

Fama French (2002) use fundamentals (dividends and earnings) to estimate expected returns. Fama French estimate the expected equity premium from the fundamentals to help them judge whether the realized average return was high, meaning the market was too kind to investors, or low. The estimate of the expected premium for 1872 – 2000 from the dividend growth model is 3.54% per year. The estimate of the equity premium for 1872 to 1950 from the dividend growth model is 4.40%. In contrast the estimate of the expected premium for 1951 to 2000 from the dividend growth model is 2.55%. Fama and French reason that the lower estimates from dividend growth fundamentals is more precise because the standard error of the estimate from the dividend growth model is less than half the standard error from the average return.

Fama and French reasoned that higher average 7.43% returns from 1951-2000 were due to a decline in the discount rate that produced larger than expected capital gains. The discount rate is the current dividend yield plus the expected growth rate for dividends. There is a sharp decline in the discount rate between 1951 and 2000.  Specifically, the dividend yield ratio falls from 5.34 percent in 1950 to 3.70 percent in 2000. In estimating dividend growth rates, Fama and French found that they are largely unpredictable, and concluded that historical average growth rates are the best forecasts of future growth. Based on this logic, assuming 1.8 percent current yield and 1.17% dividend growth rate from 1950 to 2010, it stands to reason that the prospective equity premium on the S&P 500 Index from the dividend growth model is 2.97 percent. This definition is far lower than the historical average equity premium of around 5.50% to 6.0%. But again it also quite conservative because it ignores the benefits of international diversification, and the opportunity to lift expected portfolio returns back to long-term historical levels by tilting portfolios toward more promising investment options like small cap and value stocks, asset classes with above market expected returns.

Long-Term Assumptions May Not Hold

Stocks are thought to perform so much better than bonds over the long run. Is that really true? In Stocks for the Long Run (McGraw Hill, 2002) Jeremy Siegel analyzes US stock returns from 1802 to 2001 and makes the case for US equities. According to Siegel’s analysis the real return on US equities averaged 6.9% percent per year over the past 200 years. This means that purchasing power in the stock market about doubled every 10 years. According to Siegel US stocks have never fallen behind inflation whereas bonds and bills once fell as much as 3% per year behind the rate of inflation whenever the time interval is 20 years or longer.  And second, for all investment holding periods of around twenty years or more, US equity premiums have always been positive or within a fraction of a percentage point on the wrong side of zero. Third, over 20-year horizons US stocks beat bonds and bills over 90% of the time.

To what extent should we rely on such patterns persisting in the future? In Triumph of the Optimists, the authors (Dimson, Marsh and Staunton) present evidence that spans more countries. They show that the equity premium is not constant across markets. And more often than not they show stock market volatility has been larger in other countries than the United States. From their global perspective, and looking forward to the future, equities are far from risk free over the long-term. To focus on the international dimension Dimson et al. looked at the experiences of all 16 countries. Only when they look at periods of 40 years or more does the equity premium turn consistently positive for the Netherlands. Several countries studied in Triumph of the Optimists went through even longer periods before showing consistently positive premiums. In fact, for more than half the 16 countries, including Germany, Sweden and Switzerland, there was a greater than 10% chance that the 20-year equity premium would be negative. Poor long-term performance for these countries can be attributed to a variety of social, economic and political factors. For investors, the point is that a twenty-year investment horizon in these countries was far from risk-free. Diversification isn’t a panacea but by holding a globally diversified portfolio investors can reduce the portion of variance tied to the volatility of a single country, and lower overall portfolio volatility.

What does the future hold for the equity premium? Dimson et al., estimate the prospective equity premium for their sixteen country world index to be approximately 3 percent annualized. They examined the range of expected risk premium that can be anticipated over various future time horizons.  In Triumph of the Optimist’s Dimson et. al., retain Siegel’s interpretation that 20 years may be considered a long time and concluded that based on their assumption on a forward-looking equity premium of 3% and applying a standard deviation of 16% (typical for the United States and UK), there is an 18% probability that global equities will underperform T-bills over 20 years. What happens when the researchers applied a standard deviation of 24%? That standard deviation would not be unrealistic for a poorly diversified portfolio, or if the world became a riskier place in which to do business. With this higher margin for error, there is a 17% probability that equities would underperform T-bills even over 50 years. As the standard of error increases, the assumption that single country stock returns are always triumphant over longer periods falls apart. There is clearly a substantial probability of achieving a negative premium, even over longer investment horizons.

To sum up, in the pursuit of returns, history and theory confirm that the expected return on equities exceeds the expected return on fixed income. Yet downside risk in equities is always present, which at times can be extreme. The first line of defense in risk reduction is diversification. Investors reduce the risk of equities in portfolios by diversifying; they spread the risk among domestic and foreign equities, large companies and small companies, and growth stocks and value stocks and real estate securities, etc. But given the volatility of stock returns even a highly diversified equity portfolio may have higher volatility than is desired by the investor. Investors are then advised to adjust total risk in the portfolio by adding fixed income to their asset allocation. Adding fixed income, particularly short-term bonds, to an equities portfolio will reduce the overall portfolio volatility.

How Should Assumptions About the Equity Premium Guide Investors?

  • Base Investment Strategy on Realistic Assumptions: Equities are likely to outperform risk-free T-bills in the long-run, but current dividend yields suggest that the forward-looking equity premium will be lower than in the past; how much lower is a matter of debate.  With a smaller risk premium the opportunity cost of being out of stocks might look smaller. The reward from risk for society as a whole might therefore be lower in relative terms than was previously thought.


  • Tilt Allocations to Value and Small Cap Stocks: Stock market researchers have identified a number of persistent patterns in stock returns: preeminently the small and value effect, over the long haul, providing better returns than the broad market. There is little doubt that these phenomena contribute to explaining stock returns. Skilled investors can therefore buttress their portfolios against the risk of diminished long-term broad market returns by deviating from the market benchmark and taking on more size and value risk in their portfolios.


  • Reduce Risk through International Diversification: Investment risk is lowered in worldwide portfolios. Global investors can therefore afford to allocate relatively more of their portfolio to risky assets, such as equities. Since riskier assets have a positive expected reward for risk, investors in globally diversified portfolios have a higher expected return in relation to their risk.


  • Control Investment Costs: A declining equity premium argues for careful control of costs, including advisory fees, management fees, and trading fees. Investors who fail to diversify efficiently and who overpay for investment management services have a lower expected return than those investors who control these costs. See discussion about our low fixed fees elsewhere on this site.


  • Manage Taxes: The risk of a lower forward looking equity premium also argues for a tax aware approach, a hallmark of passive and index investment strategies. Those who do pay tax suffer a dead weight burden on their stock returns. That burden can be large. Dimson et al. reference Siegel and Montgomery (1995), for example, estimate that the twentieth century annualized real return on US equities is roughly halved if the investor is taxable at the maximum rate on income and capital appreciation.


  • Carefully Explore Assumptions:There is no guarantee that the past is an indicator of future results. And many asset pricing models predict a much lower equity premium than observed in historical returns. This implies that equities should be held as part of a diversified portfolio, including multiple asset classes worldwide.

Cardiff Park simulates portfolio performance against a range of equity premium assumptions. For many investors, knowing the worst that can happen to their portfolio provides direction and clarity. If long-term historical average returns are reasonable estimates for expected returns, the implications for long-term investors are rising real spending levels over time. If stock returns are low for long periods, investors may need to save more, and spend less.

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