Updated January 2021

INVESTMENT RISKS AND RETURNS

Abstract:  This article examines quantitative historical data on risk and return, risk premiums, modern academic mean-variance models, the limitations in these models, and EAM's "worst case" model for estimating maximum potential portfolio declines.  Returns data from DFA and Dimson et al. indicate that over long time samples globally diversified equity portfolios are likely to give an inflation adjusted return around 5% in equities, 1.5% in fixed income and 0.5% in cash or cash equivalents although historical averages differed a little in 2019 due to strong returns in stocks and bonds since 2009.  Investors need to hold realistic expectations about the trade-off between risk and return and possible worst case declines and accept that no one can know or predict future returns with any precision.  Even long bonds, generally not recommended or considered for portfolios due to the risk of large price declines in rising interest rate scenarios, have on occasion outperformed equities for 30 years.  Thanks to modern computing technology and numerous academic studies we now have extensive data on long-term U.S. and international stock and bond returns, earnings growth, dividend growth, probable risk premiums for various asset classes, and other financial and economic variables.  Dimson et al's data covers 25 countries from 1900 through 2017 and Ibbotson's data employed in DFA's return analyses covers multiple countries from 1927 through 2017.

RETURNS AS RISK PREMIUMS

Passive and index allocation models are simply statistical extrapolations from historical data on financial markets.  Just as there is scant evidence that active money managers can predict future market moves and outperform the market using past information, there are substantial limitations in passive and index allocation models based on historical data that are used to estimate future portfolio risks and returns.  It is assumed that past is roughly prologue.  In addition, the structure and operation of financial markets has changed greatly since the 1980's.  This includes the advent of high frequency trading in 2005 from expensive computers which process data sold by exchanges nanoseconds before retail investors, the removal of Glass-Steagull in 1999 which let investment banks to do pretty much what they want with client deposits, the switch to mark to model accounting for many assets after the 2008 financial crisis, a US derivative market with over $200 trillion of notional assets, and an endorsement of "Keynesian" economic growth models driven by debt.  Many of these changes are discussed elsewhere on this site in "Financial Superstructures".  Past financial market data is drawn from a non-homogeneous sample of ever changing market structures and it's unlikely it will ever be precise because financial structures are always changing, complexly multivariate, and unexpected events occur fairly often.  Never-the-less, this historical data is all that we have to peer into the future of probable market returns, volatility about those returns and worst case declines in various portfolio allocation mixes.

Risk premiums are the additional returns investors may receive for committing funds that could be left in risk free cash or cash equivalents to riskier assets like stocks and bonds and real estate.  These additional returns are the reason for committing money to investments as opposed to putting it into an FDIC insured bank checking account, C.D.'s or Treasuries.  Premiums are usually expressed, as they are here, in inflation-adjusted terms otherwise known as real return after inflation.  Dimson and his London Business School and Princeton research teams have accumulated a large and comprehensive historical data base of investment returns.  The data presented here are largely an update of Dimson et al's original work published in 2002, "Triumph of the Optimists".  His team's studies now cover 1900 through 2018, 119 years of data for 25 countries though not all data is available for all countries for the full time period.  Updates are available free online in Credit Suisse's "Annual Investment Returns Yearbooks" every year in February or March.

Dimson's team (2015 Credit Suisse Returns Review) estimates a global historical real geometric return of 0.8% on cash and cash equivalents, the risk free rate of return, 1.8% for bonds, and 5.0% for equities based on data from a globally diversified market-capitalization weighted world index for 1900 through 2015 for 25 countries, 116 years of data in total.  Prior to 2015 their estimates were typically running 0.5% on cash and cash equivalents, 1.5% on bonds, and 5% on equities.  The equity premium is the difference in returns for equities minus the risk-free rate of return in cash and T-bills and was thus 4.5%.  In Dimson's 2018 update, he reports real returns for the World Index from 1900 through 2017 of 5.2% in equities, 2.0% in bonds and 0.8% in cash and cash equivalents.

Dimson's numbers are close to those estimated by Fama and French and DFA from Ibbotson data going back to 1927 but generally lower than those presented by most of the financial services industry and financial press.  Breaking the sample period into three parts shows very similar numbers for equities but much higher numbers for bonds from 1966 through 2015, 5.0% in equities, 4.2% in bonds, and the same 0.8% for T-bills with 2000 through 2015 showing 1.6% in equities, 4.9% in bonds, and -0.4% in cash and cash equivalents.  These high historical returns in bonds are a function of record high interest rates in the mid-teens in bonds in 1982 and their general decline up until their record low levels during 2008 through 2016, effectively at 0% or below after inflation for most maturities.  Not all market researchers agree on long-term returns.  For example, Siegel, in "Stocks for the Long Run", estimates an equity premium of 7.2% based on almost 200 years of data but his data is open to several critiques.  Differences in estimates stem from the use of different time samples or data sets of questionable quality from prior to 1900.  Dimson and his group unquestionably have the broadest, deepest and most carefully researched data base for financial markets and DFA and Ibbotson are close in this regard.

Dimson et al's "Global Investment Returns Yearbook 2018" presents historical returns data for 21 countries with continuous data going back 118 years beginning in January 1900 and ending in December 2017.  Long term historical returns differ a little year to year due to variations in equity returns and fixed income and cash yields.  For 117 years through end-2016 world equity returns gave a real inflation adjusted annual return of 5.1%, bonds gave a real annnual return of 1.8%, and cash returns varied greatly over the time frames sampled and returned -0.3% annually.  This differs little from Dimson's previous long term studies.  Prior to 2008 real bond returns back to 1900 were 1.5% and as of 2018 both historical returns for stocks and bonds are higher than they have been previously.

Dimson, in "The Low-return World" (2013 Credit Suisse Investment Returns Yearbook), makes a number of points all investors should consider when looking at past returns as guides to allocation.  Returns were very high in both stocks and bonds since 1980, far higher than returns which include long-term data from 1900-1979.  From 1980 through 2012, a 33 year sample, long maturity bonds slightly outperformed equities despite claims that equities are often promoted as the best choice for the long run.  The long decline in record high interest rates from 1982 drove stock and bond returns for the 1982 through 2000 and 2008 through 2013 periods along with multi-trillion dollar injections of liquidity by central banks and US taxpayers after the 2008 credit crisis, something in the range of $14 trillion and as of early 2021 US debt is around $34 trillion.  For the full range of 20 countries since 1900 whenever short inflation adjusted interest rates were 0% or below, as they were in 2021, forward equity returns averaged -1.0% for the subsequent five years and bond returns averaged -6.0%.  They also note that the world equity premium since 1900 is 3.5% excluding the US and 5.3% including the US.  Dimson proposes that aging US demographics and the need for boomers to sell assets during retirement will likely reduce future US equity returns and mentions that the extraordinarily fortunate position the US found itself in after WWII, "the world's most successful economy during the 20th century", is unlikely to repeat.

Dimson estimates a forward geometric equity premium of 3.5% for 20 to 30 years from 2013 and references a similar conservative estimate from Fama and French.  Dimson estimated a 3.5% world equity premium in 2000 and for 2000-2017, 3.4%.  Total return was 2.9% per annum but T-bills returned -0.5% per annum for 2000-2017 creating a 3.4% equity risk premium.  Whatever the true equity premium might turn out to be in the future it is pretty likely it won't be the 7% to 10% real inflation adjusted premiums widely promoted and mentioned by the financial press and used in financial planning programs, pension fund calculations and insurance investment pools.  Based on 2013's zero or negative real interest rates Dimson estimated close to zero real returns on inflation-protected bonds and a negative to zero yield on cash for 20 years from 2013.  Not many investors are expecting equity returns that low and investor optimism is at record highs, as are major stock and bond indexes, as of early 2021.

Across countries equity returns vary greatly.  Dimson's 1900 through 2013 data show equity premiums as low as 2.2% in Belgium and as high as 6.5% in Australia, bond premiums as low as -1.7% in Italy up to 3.0% in Denmark, and bill premiums of -3.7% in Italy up to 2.3% in Denmark.  Dimson also looked at size and value premiums, additional probable returns from small cap and value stocks with high book to market valuations.  Over the longest available time samples they estimate an annualized size premium of 1% to 1.5% and an annualized value premium of 1% to 1.5%.  The time sampled matters greatly.  From 1900 through 1949 world equity index returns were about 3.5% while for 1950 through 1999 they were 9.0%.  Events in the real world obviously created very different returns in the first half of the 20th century when compared with the second half.  We cannot, of course, know what lies in store for the first half of the 21st century.  For bonds, Dimson et al. stated in 2013 that "bond returns have been remarkably high, but extrapolating this level of performance into the future would be fantasy."

When considering risk tolerance and designing portfolio allocations we urge investors to hold conservative and realistic expectations about returns and risk in equities and fixed income and understand that markets and returns and market narratives are always changing and always unpredictable.  It is human nature to base one's expectations on the relatively recent past, a "recency" effect, and most investors have been indulged in the extraordinary bull markets in stocks and bonds since 2013.  We recommend that estimates of forward risk and return and worst case declines rest upon the type of detailed very long-term data gathered by the Dimson team, Fama/French/DFA, and Ibbotson rather than the recent past.  Investors should probably not expect future returns to match the returns they've been seeing for most of the past twenty five years up to 2021.  We simply have no way of being certain about future returns and no one is guaranteeing future returns while major changes in market structures render markets even more unpredictable than ever.  See "Financial Superstructures" elsewhere on our website on some of these changes.

DEFINING RISK

Wall Street, the financial press, and most financial professionals focus investors on returns, constantly boasting manager skill, new ideas, market timing, and stock and fund picking skills.  As we examine in more detail in "Active vs. Passive Management" and "Portfolio Design" elsewhere on our website, past returns do not predict future returns reliably.  However, marketing material and the financial press and media keep investors focused on how much money they could have made in some past investment and how much they might make when they make the right investment choices, prices rather than risks are Wall Street's almost exclusive focus.  It is in their interest to do so.  Even during financial crises Wall Street remains optimistic about "selected" stocks and other investments because pessimism doesn't sell as well as optimism and even crises make Wall Street money.

Most of modern finance, both active and passive, defines risk as standard deviation.  For investors without a strong background in statistics it's important to understand a few facts about standard deviation.  Standard deviation is not a measure that describes risk as most investors experience risk.  Standard deviation in finance is merely a quantitative way of expressing the average variation about the mean return for an asset.  It is a measure of variability or volatility in investment returns.  An investor's definition and experience of investment risk, however, will most likely be composed of two factors:  (1) How much their investment portfolio declines in a worst case, the maximum drawdown, and (2) How long it stays down and takes to return to breakeven, in some cases decades.  We'll examine both of these issues in detail below but first let's look a bit more at standard deviation.

Most of modern financial theory and portfolio management employs mean-variance models, means being the average returns and variance being the standard deviation or variation about a presumed bell-shaped curve of distributions of financial market returns.  For example, the total U.S. stock market gave a nominal return (not inflation adjusted) of 9.6% annualized with a standard deviation of 20.5% for 1926 through 2009.  A normal range of returns in a standard distribution would be plus or minus two standard deviations covering about 95% of observations with the other 5% termed outliers that split 50/50 on both ends of the distribution.  Put in simple terms, the US equity market gave an average return of 9.6% annually for 1926-2009 with most returns lying within two standard deviations or about +/- 41% around the average return, not very precise.  Thus "normal" returns ranged from -31.4% to +50.6%.  This illustrates what would be a "normal" roll-a-coaster ride for equities but may not have been what investors had in mind when they heard the word "volatility" expressed.  During 1926 through 2009 a few return samples were big outliers and the ride was even more extreme.  The Dow Industrials dropped over 85% from 1929 through 1932 and didn't breakeven, excluding dividends, until 1954.  The financial industry, of course, would like to give the impression that good returns can pretty much be counted on and declines will be small and quickly correct.

THE LIMITATIONS OF MEAN-VARIANCE MODELS

One problem with using standard deviation as a measure of risk is that real investors are more concerned about that 31.4% decline than the long-term 84 year nominal return of 9.6%.  During the 2008 financial crisis US equities declined over 45% and foreign equities over 50%.  Getting through bear markets is the hard part about investing.  Making money in bull markets is the easy part.  Investors need to keep in mind other considerations when looking at historical risk and return data.  First, standard deviations are not constants but variables.  They change over time.  That's because the entities which influence market returns are always changing and market returns are changing as asset classes shift in and out of favor and economies grow and contract .  In order to be certain about standard deviations and returns we need a much longer time sample than is available.  Market structures even very roughly resembling today's market structures have only been around for a little over a century.  If we wish to make a statement with strong statistical confidence for returns and standard deviations in a portfolio for a 25 year holding period we should have at least 20 independent 25 year periods or 500 years of data.  This is obviously not possible.

Second, distributions in financial markets are not nice normal bell-shaped curves like we find when plotting height differences in human beings and many other variables.  Distributions of returns in financial markets suffer from kurtosis and skewness, forms of distortion in the normal curve, and particularly, the tendency for financial markets to generate outliers, extreme negative returns on the left side of the distribution (losses) that should rarely or never occur but do.  This is of utmost importance since the basis for estimating risk probabilities from standard deviations assumes a bell-shaped curve.  The more the data deviate from that curve the less trustworthy returns estimates of risk will be.

It is also important to remember that past asset class risk and return numbers are dependent variables and not independent variables.  Passive and index allocation strategy puts little if any, analysis into what produced these numbers.  Often past risk and return data are discussed as if they are almost constants in nature yet past investment numbers are the results of unpredictable events in the real world which are never constant and the numbers they produce are never constant.  These events include globalization, new technologies and industries, new investment instruments like derivatives and CDS's, high frequency trading computers, changing societal values regarding consumption and debt, new central banking theories, changes in market regulation and countless other factors.  Such events are unpredictable yet influence economies which in turn influence future asset class prices, risks, and returns.  We examine this elsewhere on our website in "Financial Superstructures".

In one study, DFA provides historical data covering July 1926 through December 2013 and finds that the S&P 500 beat T-bills 69% of the time for 1 year, 84% of the time for 10 years and 95% of the time for 15 years.  Value equities beat growth equities 60% of the time for 1 year, 88% of the time for 10 years, and 95% of the time for 15 years.  Small cap equities beat large cap equities 58% of the time for 1 year, 72% of the time for 10 years, and 95% of the time for 15 years.  High profitability equities beat low profitability equities 71% of the time for 1 year, 100% of the time for 10 years and 100% of the time for 15 years.  Our recommendation to investors is that they define "long term" as at least 10 years and not place money in equities unless they have a 10 year time frame or longer.  Historical probabilities vary significantly depending upon the timing of equity purchases.  About 95% of the time equity markets are making up previous losses if investors purchased equities at or near previous all-time highs.  About 5% of the time markets are at or near new highs as is the case in in early 2021.

And, there's another serious problem with basing estimates of future risk and return on historical data generated in financial markets during 1900 through 1999.  The long-term case for owning stocks is based on data going back 118 years but for most of that period financial markets and currencies were largely tied to gold.  Nixon took the US off the gold standard in 1971.  When this occurred the Keynesian theory of debt based economic stimulation began to become popular in governments and banking systems (similar to MMT) and that boosted financial market returns.  After 1971 unlimited amounts of money could be added to the US economy, money that was simply borrowed from the future and no one earned or paid in taxes.  Basing investment allocations today on historical data derived from a different financial system in the past where money supply was limited by gold production is statistically questionable.  As of 2019 the "shadow banking system" is a major contributor to this discontinuity, as well as high frequency algorithmic computer trading and considerably relaxed regulatory and accounting standards compared to those in place prior to the 1990's.

Paul McCulley of Pimco in 2007 first defined the shadow banking system as "the whole alphabet soup of levered up non-bank investment conduits, vehicles, and structures with its birth beginning in 1970 with the creation of money markets."  In 2008 Treasury Secretary Geithner noted that lending through the shadow banking system slightly exceeded lending via the traditional banking system based on loan balances and capital ratios, then about $10 trillion.  In 2012 he estimated it had grown to $15 trillion and as of end-2020 about $34 trillion.  As of 2016 the top four US megabanks held over $200 trillion of derivatives, linking counterparties and assets in long collateral chains like those that failed in 2008 and required bail-outs by the US taxpayer.  The shadow banking system includes asset backed commercial paper conduits that securitize mortage, auto, and other loans, structured investment vehicles, hedge funds, tender option bonds, variable rate demand notes, and triparty repos.  It supports an enormous amount of trading activity in the OTC derivatives market and was over $700 trillion in notional value globally according to IMF data as of 2013.  OTC derivatives include CDO's and CDS's.  CDS's are a form of quasi-insurance against risk but the issuers of the CDS insurance are not required to maintain significiant capital reserves to pay off potential claims.  This increases counterparty risk between financial instititutions and can lead to domino chains of failing commitments.  For example, AIG was a large underwriter of CDS's for Goldman Sachs, BofA, and other major financial institutions in 2008.  The US Treasury deemed the $165 billion rescue of AIG essential for the banking system since major investment banks like Goldman were in danger of failing from their CDS losses if they weren't paid by AIG.

Risks to financial stability created by the shadow banking system greatly contributed to the 2008 financial crisis. Yet, almost all financial experts and central bankers failed to see 2008 coming and still argue against regulating the shadow banking system or derivatives.  Most do not see increasing risk in ever-rising global debt and leverage.  As of end-2020 US equity markets are the most levered they have ever been and also the most overvalued they've ever been in metrics which strongly correlate with 10 year forward returns.  Fed chairman Bernanke, Treasury Secretary Geithner, and many others promoted the idea of a "Great Moderation" and consequent reduction in risk created from "financial engineering", translate that mostly as stock buybacks, which dominate today's financial system and prices.  The 2008 credit crisis was also fueled by two decades of greatly increased borrowing and a continual rise in government, corporate, and consumer debt.  OECD data as of 2019 shows that the world is awash in debt, having more than doubled debt relative to global GDP since the 1980's.  This is in no small part the result of Keynesian economic models espousing government and central bank economic stimulus through debt and money creation.  This is often called printing money though most new "money" today is simply created in the form of digital computer money from central banks and costs nothing other than a keystroke to produce.

Borrowed money, of course, allows people to live better today but eventually the credit card debt comes due, the debt must be paid, and growth slows.  There is every indication that the bill for decades of excessive borrowing and leverage began arriving in 2007 and resulted in a crash in 2008 in mortgage debt that triggered the large equity market declines and a recession.  It is not coincidental that easy money policies of the Federal Reserve, rising US government debt, and the shadow banking system accompanied the biggest bull equity and fixed markets in US history from 1982 through 2000 and the US housing bubble from 2002 through 2006.  David Stockman's book, "The Great Deformation", reviewed elsewhere on our website, examines deformations in the US economy and financial markets created by three decades of borrowing and very low interest rates in the 2000's.  He makes a strong case that the price of money determines the price of all financial assets.

Dimson et al. provide a variety of revealing statistics about economies and financial markets.  Many of these clearly contradict more optimistic numbers frequently presented in the mainstream financial media.  For example, real global GDP growth averaged 2% last century not the 3% often mentioned in the press and assumed by central banks in their models.  The correlation of GDP growth and equity returns is somewhere around +/-.2, not much, though it would seem logical that the two would be more strongly associated. Real long-term dividend growth averaged only 0.6% yearly, roughly doubling dividends in 80 years.  Dividends on the S & P 500 are under 2% as of end-2020 while for the 1900 through 2012 period they averaged 4.6%.  High securities prices mean low dividends.  At the historical rate of dividend growth it will take several decades to return the dividend payout ratio to its historical norm if stock prices don't decline from 2020 levels.

Research shows high dividend yielding stocks are value stocks.  Other studies indicate that real earnings growth in the S & P 500 averaged 1.4% yearly for 1891 through 2000 so investors expecting earnings or dividends growth to eventually justify high price earnings ratios and low dividend payouts in 2020 may be sorely disappointed with median price/earnings at an all time record high in late 2020.  Financial statistics are always changing.  Up until 1959 stock investors always received higher dividends than bond investors due to the perception of a greater risk in stocks.  It was assumed that would always be the case but since 1959 that has not been the case.  The key insight to be had from detailed historical financial data is that returns data is always changing because markets are always changing, financial narratives are always changing and always unpredictable, past presumed relationships change and virtually everything is a dependent variable and not a constant.

Dimson's sobering conclusion on equity risk comes from a detailed analysis of the equity premium in "Triumph of the Optimists" 2002.  Dimson et al. note that, "there is clearly a substantial probability of achieving a negative risk premium (losses in equities), even over long investment horizons."  They estimate there is an 18% probability that equities will underperform T-bills for a 20 year period of low volatility and a 17% probability that this will occur over 50 years during a period of high volatility.  Fifty years is undoubtably more than most investors have in mind when they are thinking "long-term".  WWW.dshort.com, is a technical trading site and posts many analyses of the S&P 500.  They found that, adjusted for inflation but not dividends, it took the S&P 56 years to breakeven if an investor bought at the 1929 top.  Including dividends it took until 1949 but dividends as of 2020 are about one-third what they were during the first half of last century.  In "The Low Return World", 2013, Dimson states "To assume that savers can confidently expect large wealth increases from investing over the long term in the stock market, in essence that the investment conditions of the 1990's will return, is delusional."

Often, digging into returns details reveals a different story than return data.  John Hussman, Ph.D. (5-25-19, www.hussmanfunds.com) notes that "in the Summer of 1929 the surface of Wall Street was a mixture of placidity and mania" and that "dissenters were momentarily routed".  Then, from September 3, 1929 to July 8, 1932 the Dow Jones Industrial Index fell by 89.2% but not in one swoop.  Wall Street never predicts market crashes or bear markets in advance and if they do so significant declines have already taken place.  The decline known as the "1929 Crash" took the Dow down an initial 47.9% by November 13, 1929, followed by a 48.0% recovery by April 17, 1930.  In mid-1930 the financial industry had no concern about a bear market or recession.  But, by the 1932 low the Dow had plunged 86% below its April 1930 peak.

Merrill Lynch economist David Rosenberg estimates that the increase in price/earnings ratios for U.S. shares from 9.2:1 in 1980 to a record high of 30:1 in 2000 accounted for 70% of the share price appreciation during that period with the remaining 30% coming from true earnings growth.  We have seen record high price/earnings ratios again from the very strong bull market from 2014 through 2020.  From 2009 through end-2018 the US economy grew in inflation adjusted compound returns by about 20% while the S&P 500 rose by a remarkable 350%. This was about the same US GDP growth rate as 1929 through 1939.  Raging bull markets like that we've seen in the recent past can be profitable but grossly overvalued, seductive and lead to large investor losses..

If there's one rule that applies to stocks over very long time frames it's that periods of high optimism, high stock ownership, and high valuation metrics have always been followed by periods of great pessimism, distrust of stocks, and low valuation metrics.  On January 26, 2018 the S&P and major indexes hit record price highs.  For two years prior the S&P rose to new highs continuously with very shallow and brief declines.  As of Spring 2019 valuation metrics were at or near all time record highs on those metrics which strongly predict future 10 year returns (the Shiller CAPE, price/revenue, EV/EBITDA, etc.).  If "this time is different" from all prior times when valuations have been stretched large declines in US equity prices lie ahead in the near future.  As of early 2021 a decline to merely average valuation metrics would take US equity markets down about 50%, bargain prices would be reached with a 65% to 70% decline and crisis lows would be 80% to 90% below today's prices.  Most retail investors are not looking in that direction.  Historical price data strongly supports regression to the other side of the mean when price returns and valuation metrics have become excessive .

A study of "buy and hold" equity strategies published on David Stockman's website (1-25-16) makes an important points regarding long term equity portfolios.  Compounding is not linear.  If equities give  an annual return of 10% for three years, compounded, then lose 10% in year 4, they will have gained 33.1% in the first three years and lost 13.3% of that in year 4, netting a 19.8% 4 year gain at the end of year 4.  Individual investors always have a finite investment time horizon and most investors don't have significant investment assets until their 40's and may have only 20 years of work left to build their investment assets for retirement.  Buy and hold is integral to passive and index investment strategies, it is likely to outperform security selection and trading and market timing but it is not a magic elixer that guarantees consistent and positive long term returns because equity and fixed income markets can be very volatile.

Several historical periods show 20 year inflation adjusted compound trailing equity returns close to zero or even negative and we have no way of predicting when this will occur.  For example, compound total 20 year trailing equity returns were 0% in 1932, 3% in 1943, 3% in 1950, 2% in 1975, 0% in 1984 and 5% in 2010.  This data is unlikely to wet investor appetites.  Twenty years is a long time to wait for flat or very low compound positive returns in equities but it occurred six times last century.  DFA has looked at equity prices 1, 3 and 5 years after the equity market has hit new highs and found equity prices rose 13.6%, 9.8% and 8.7% respectively.  It has also looked at average annualized equity returns after the market has declined 10% or more and found 1, 3 and 5 year returns of 11.2%, 10.2%, and 9.6% respectively.  While this is encouraging for shorter time frames investors should always keep in mind that equity markets and bond markets can and have failed to deliver returns for very long periods.

A compelling reason for caution in assuming that equities are always the best choice for long-term portfolios is illustrated by the 31 year period from 1981 through 2011.  Long-term US Treasury bonds gained an average of 11.5% per year versus the S&P 500 with a gain of 10.8% a year, and Treasury bonds carry a US government guarantee and show far less price volatility then equities.  Least that be construed as a reason to own long-term bonds, DFA presents data showing that from 1940 through 1990, a 51 year period, the inflation adjusted return on long-term Treasury bonds was merely breakeven, 0%.  There is simply no asset class for all seasons and any asset class can fail to produce positive returns for 20 years or longer.

RISK, RETURN, AND ASSET CLASS DIVERSIFICATION

Extensive academic research, much of it undertaken by DFA, has carefully examined the sources of portfolio returns and found that additional returns are likely if value stocks and small cap stocks are overweighted relative to the total equity market and if REIT's and international stocks are included along with other factors like profitability.  Both Fama and French and Dimson et al., found evidence for small cap and value effects across U.S., international developed, and emerging markets.  They also found a better risk/return ratio when short-term bonds, under three years, are included in fixed income allocations.

The next table shows annualized returns, standard deviations, and best and worst single year returns for highly diversified passive portfolios from DFA for the 42 year period covering 1973 through 2015.  DFA's models draw upon quantitative historical data gathered by Ibbotson and its analysis by Fama and French.  Portfolios include U.S. and international large and small and growth and value stocks, and U.S. and international short-term bonds.  Weightings are roughly 1:1 large/small, 1:1 value/growth, and 70% U.S./30% international.  Bonds are referred to as fixed income, run from 1-6 years, and are U.S. and international.  The mix or overall allocations vary from 100% fixed through 100% equity.

  Table 1:  DFA "Balanced" Portfolios: 1973-2017

Inflation averaged 4.1% for this period so inflation adjusted annual returns are approximately 4.1% lower than those shown in the table but still high by historical standards thanks to the 1982 through 2000 and 2009 through 2020 bull markets and bubbles in equities and fixed income.  As columns move from left to right portfolios become increasingly weighted towards stocks until they are 100% in stocks and 0% in fixed income on the far right.  These figures assume monthly rebalancing, adding or subtracting from one sector of the market if its weight relative to others grows or shrinks, and it includes simulated as well as real returns.  Rebalancing yearly or less frequently increases the returns and standard deviations slightly.

Continual modifications in the methodology underlying the construction of the CPI inflation metric by the Bureau of Labor Statistics has almost always resulted in a lower reported inflation rate over the last three decades.  Real returns are a function of inflation and the US government's statistical agencies are very likely underreporting the inflation rate in the opinion of many experts.  Higher inflation is politically unpopular.  The methodology for measuring inflation is debatable but continually changes.  This calls into question the accuracy of the methodology for the calculation of inflation rates by US government statistical agencies and hence real inflation adjusted returns in all financial markets.  Removing housing prices from the CPI in 1984 and adjusting "market basket" consumer prices hedonically and substitution weighting of commodities from the 1990's on distort and reduce the true cost of living and reduce the CPI.  The effects of inflation are significant for investors.  From January 2000 through end-2017 the S&P gave an inflation adjusted average yearly return of 4.75% and a true geometric compound return of 3.16% annually with a total return of 87.6% with dividends reinvested.  The official government agency CPI-U cumulative compound inflation rate for that period was 46.5%.  Although these returns are not particularly strong numbers by historical standards the mainstream financial press continues to tout investing in stocks and bonds and proclaims the US is a "solid economy" as of early 2021.

It is obvious from looking at Table 1 that a strong relationship exists between potential portfolio returns and the ratio of stocks to bonds.  More stocks means more risk as defined by standard deviation.  It also illustrates the benefits of a tilt towards small, value, and international stocks.  For 1973 through 2012, the US total equity market (CRSP 1-10th deciles) gave a return of 10.0%, not adjusted for inflation.  A globally diversified 100% DFA "balanced" equity portfolio added over 3% annually to returns versus the S&P 500 for that period, a clear advantage.  DFA views fixed income primarily as a volatility dampener for equity portfolios and employs only short and intermediate investment grade bonds.  Investors should not count on added returns from tilting towards value stocks though historical data clearly show value stocks outperform the broad market long term.  Rod Cole, an MIT based statistician, calculated that the optimal or superefficient portfolio from 1927 through1966 held only 25% in value stocks while the optimal portfolio from 1967 through 2006 held only 25% in growth stocks.  Asset classes go in and out of favor over very long unpredictable time frames.

In 1999, growth stocks shone brightly as value trailed growth by the largest annual percentage in the history of the Russell indexes.  Value is again trailing growth as of early 2021.  At year-end 1998 value stocks had underperformed growth stocks over the previous 1, 3, 5, 10, 15 and 20 year periods.  But, in a dramatic reversal, by February 2001 value stocks had outperformed growth stocks over the previous 1, 3, 5, 10 and 20 year periods.  Growth stocks cratered as the Dot.com bubble imploded in 2000.  That makes sense since getting a good value and a bargain in anything is always a wise move.  Unfortunately, the investment public repeatedly gets overinvolved in overvalued and glamourous growth stocks and frequently discussed story stocks as a road to quick wealth.  An example would be Amazon.  As of 2018 Amazon's retail site has yet to make a profit since its inception 23 years ago.  Yet, Jeff Bezos, its founder, is intermittently the richest man in the world from stock issuance.  Amazon has a breathtaking p/e ratio around 80:1 as of early 2020 and its tiny profit comes from server rentals in a highly competitive industry.  Amazon makes little sense as a good value since historically anything over 20:1 in any security has been considered too high by most market participants.  From 1928 through 2017 DFA's US large value index gave a total return (price growth plus dividends) of 11.3% annually versus the S&P 500's at 7.1%.  From 1990 through 2017 DFA's US large value fund returned 11.4% annually to the S&P 500's 7.2%.  From 2009 through 2017 DFA's US large value fund returned 15.9% annually to the S&P 500's 13.2% despite record high prices and enthusiasm for US large cap growth stocks.  As of late 2020 US mega-cap growth stocks, particularly popular glamour stocks like Amazon, Facebook, Apple, Alphabet, Google have driven indexes up and led to occasional articles in the financial press arguing that the value effect has permanently disappeared.

Since asset classes have largely unpredictable long-term cycles of underperformance and outperformance, time of market entry will make a significant difference in portfolio returns but investors can do nothing about that other than make investment choices based on current valuations.  Table 1 doesn't capture the downside disappointments that investors have encountered when entering bull markets at long-term secular tops.  An investor entering the equity market in 1968 only received a breakeven return after inflation in 1981, a 0% return for fourteen years, and a twenty year annual return through 1987 of a modest 4.19%.  A lucky investor who happened to enter the market at the beginning of the new bull market in 1981 received a twenty year annual return through 2000 of 12.91%, 8.72% more per year than our unlucky 1968 investor.  Time of market entry matters greatly though extensive research shows that market timing cannot be done consistently and profitably and we never know what lies ahead.  This issue is examined elsewhere on our website in "Tactical Asset Allocation".

Another issue is how well highly diversified equity asset class portfolios do in bear markets.  From April 2000 through March 2003 the S & P 500 gave a total return of -40.9%.  A DFA globally diversified 100% equity portfolio gave a total return of -14.25%, far less loss than the S&P 500, and DFA portfolios with 50% or less in equities gave positive returns.  A moderate balanced portfolio with 40% equities rose 6.8% and preserved capital nicely.  For Q202, the worst quarter during that period, a diversified 100% DFA equity portfolio was down 3.37% versus a decline of 13.39% for the S & P 500, again showing the value of broad global equity asset class diversification in difficult markets.  Relationships between equity asset classes are always changing.  Globally diversified DFA portfolios during the 2008 financial crisis declined about 50% to 55% versus 41% for the S & P 500.  From 2010 through 2015 the S&P 500 outperformed almost all other asset classes.  Nothing in equity markets is certain and returns across asset classes are always changing.

As noted above, it is always important that investors keep in mind that correlations between different asset classes or different slices of the equity market, like value versus growth, are dependent variables, not independent constants.  This adds statistical noise to predictions.  A big surprise for the investment community during the 2008 financial market crisis and accompanying equity market collapse was how "all correlations went to 1.0" between all asset classes as they declined.  Just when diversification was most needed it didn't work and all asset classes declined simultaneously.  Richard Bernstein of Bernstein Advisors (April 12, 2012) emphasizes that correlations are dynamic rather than static and that one can make short-term correlations yield any desired result by using different time samples or frequency of returns.  Agreed. He presents a chart showing correlations for major asset classes (real estate, gold, corporate bonds, etc.) with the S&P 500 index for five year periods preceding 2002 and 2012.  The majority of the correlations shifted from negative to positive, indicating that markets were much more correlated in 2012 than in 2002.  Returns can also show up infrequently.  Siegel, for example, ("Stocks for the Long Run") points out that if the nine-year period from 1975 through 1983 is eliminated, the total return in large and small cap stocks for 1926 through 2006 is the same even though the 1900 through 2006 shows a 2% or so annual advantage for small cap stocks.

WORST CASE PLANNING

EAM recommends that investors plan from a "worst case" perspective rather than relying exclusively on past returns and standard deviations as a measure of risk.  In layman's terms, how much is a given asset mix likely to decline and how long could it stay down?  This can, of course, only be a rough estimate based on past high and low equity valuations and declines.  EAM provides an estimate of worst case potential declines in our quarterly reports to our clients or upon request.  Our estimate, based on long-term global MSCI data, is that a fully diversified equity portfolio with value and small cap tilts and Reits and emerging markets could decline up to 65% in an extreme financial crisis from prices in 2020.  Prior to the big bear market of 2008 and early 2009 historical data only indicated a worst case decline around 35%.  DFA's data now show a worst 12-month decline of 51.9% in a globally diversified 100% equity portfolio due to a large decline between March 2008 and February 2009.  Looking to the past does not guarantee that we can predict what will occur in the future.  From data on American equities in the 1930's and Japanese equities since 1990 it is clear and indisputable that major indexes can decline 80% or more and stay down for ten to twenty-five years.  Although international diversification may help ameliorate declines, global markets and capital are increasingly interlinked in collateral chains, counterparties and hidden derivatives and that may increase future declines.  The true risk is largely unknowable.  In 2008 global equities all went down together.

Our advice is to look at risk and return in terms of additional expected returns from riskier assets and additional declines possible in portfolios from that additional risk.  If we can reasonably expect a global long-term geometric equity premium around 4.5% above risk free returns in cash equivalents we can then consider risk and return in terms of the equity to fixed ratio.  Starting at 0% equities and 100% cash or cash equivalents, our worst case decline before inflation is 0% and our probable inflation adjusted yield is 0.5%.  If we assume our worst case decline for a globally diversified 100% equity portfolio is 65%, it could be as high as 90%. then each 10% added to equities, starting from 0% equities, adds an additional potential downside of 6.5%.  For a high quality bond mix in the short/intermediate range, worst case declines are probably in the 10% range and the bond premium is about 1.0% to 1.5% over the risk free rate of return.  If we assume an equity premium of 4.5% above cash and T-bills, then each 10% allocated to stocks adds about 45 bps. above the risk free rate of return in T-bills.  And, each 10% added to bonds from cash adds a bond premium of 0.1% above cash.  If we estimate real probable forward returns above the risk free rate of return for a portfolio with 60% equity and 40% fixed, a simple formula presents itself: a .6 x 45 bps (annual real equity premium) + 0.4 x 1.0% (real bond premium) equals an inflation adjusted probable long term return premium of 3.1% greater than risk free cash and cash equivalents.  The approximate worst case decline for a portfolio with 60% equity and 40% fixed income would be roughly 0.6 x 65% = -39% along with a 0.4 x -10% = -4%, thus about -40%+ for a 60/40 equity/fixed poretfolio mix.  These estimates of maximum drawdowns can, of course, only be approximate and drawdowns could be greater than the numbers shown here.  They do, however, illustrate two key points.  Investment returns are probably far lower than most investors expect and risks of maximum declines are probably far higher.

Each investor should assess whether they could live through a worst case probable decline emotionally and whether their portfolio allocations are likely to meet their investment objectives in terms of growth and income.  If the risk is too high equity allocations should be adjusted downwards and more fixed income should be added.  As investors move into retirement and distributing income from their accounts equity allocations and risk are usually reduced.  Whatever conclusions an investor may draw from research on past equity and fixed returns they should always bear in mind that past performance for markets and asset classes, just like for mutual funds, does not predict future performance.  Before deciding on an overall allocation, each investor should look carefully at the potential downside and at worst cases as well as oft-quoted historical data showing that over very long time-frames stocks outperform all other asset classes.  Detailed information on designing a passive and index portfolio is found in "Portfolio Design" elsewhere on this website.

References:

Investment Dimensions 1926-2020, Dimensional Fund Advisors

Dimson, Marsh, and Staunton.  Triumph of the Optimists.  Princeton, 2002.  Updates on their studies can be found in the Credit Suisse, Annual Investment Returns Yearbooks, 2009-2015.

Ibbotson Associates, 2001, Stocks, Bonds, Bills, and Inflation Yearbook.  Chicago: Ibbotson Associates

Siegel, Jeremy.  Stocks for the Long Run.  McGraw-Hill, 1998 (4th Ed. 2008)