after-inflation stock returns. Furthermore, fixed-incomereturns in countries that experienced major wartime dislocations, suchas Italy, Germany, and Japan, were decidedly negative, so that the supe17See Stephen J. Brown, William N. Goetzmann, and Stephen A. Ross, “Survival,” Journal of Finance,vol. 50 (1995), p. 853–873.
CHAPTER 1 Stock and Bond Returns Since 1802
19
riority of equities relative to other financial assets was decisive in allcountries.The average annual real stock, bond, and bill returns of the 16countries analyzed from 1900 through 2006 are shown in Figure 1-6.18Real equity returns ranged from a low of 2.7 percent in Belgium to ahigh of almost 8 percent in Sweden and Australia. Stock returns in theUnited States, although quite good, were not exceptional. U.S. stock returns were exceeded by the returns in Sweden, Australia, and SouthAfrica. And the average real-world return on stocks is not far from theU.S. return.18Elroy Dimson, Paul Marsh, and Mike Staunton, “Global Investment Returns Yearbook 2007,”ABN-AMRO Bank NV, February 2007.
FIGURE
1–6
Average Annual Real Stock, Bond, and Bill Returns of the 16 Countries Analyzed from 1900 throughDecember 2006
SOURCE: Based on information from Elroy Dimson, Paul Marsh, and Michael Staunton, Triumph of the Optimists: 101Years of Global Investment Returns, (Princeton, N.J.: Princeton University Press, 2002).
20
PART 1 The Verdict of History
When all the information was analyzed, the Triumph of the Optimistsconcluded “that the US experience of equities outperforming bonds andbills has been mirrored in all sixteen countries examined. . . . Every country achieved equity performance that was better than that of bonds.Over the 101 years as a whole, there were only two bond markets andjust one bill market that provided a better return than our worst performing equity market.”Furthermore, “While the US and the UK have indeed performedwell, . . . there is no indication that they are hugely out of line with othercountries. . . . Concerns about success and survivorship bias, while legitimate, may therefore have been somewhat overstated [and] investorsmay have not been materially misled by a focus on the US.”19,20This last statement is significant. More studies have been made ofthe U.S. equity markets than the equity markets of any other country inthe world. Dimson, Marsh, and Staunton are saying that the resultsfound in the United States have relevance to all investors in all countries.The superior performance of U.S. equities over the past two centuries isnot a special case. Stocks have outperformed fixed-income assets inevery country examined and often by an overwhelming margin. International studies have reinforced, not diminished, the case for equities.
CONCLUSION: STOCKS FOR THE LONG RUNOver the past 200 years the compound annual real return on a diversifiedportfolio of common stock is nearly 7 percent in the United States, and ithas displayed a remarkable constancy over time. The reasons for the persistence and long-term stability of stock returns are not well understood.Certainly the returns on stocks are dependent on the quantity and quality of capital, productivity, and the return to risk taking. But the ability tocreate value also springs from skillful management, a stable political system that respects property rights, and the capacity to provide value toconsumers in a competitive environment. Swings in investor sentimentresulting from political or economic crises can throw stocks off theirlong-term path, but the fundamental forces producing economic growthenable equities to regain their long-term trend. Perhaps that is why long19
Elroy Dimson, Paul Marsh, and Michael Staunton, Triumph of the Optimists: 101 Years of Global Investment Returns, Princeton, N.J.: Princeton University Press, 2002, pp. 52–53 and 175.20In fact, Triumph of the Optimists may have actually understated long-term international stock returns.The U.S. stocks markets and other world markets for which we have data did very well in the 30years prior to 1900, when their study begins. U.S. returns measured from 1871 outperform those returns taken from 1900 by 32 basis points. Data from the United Kingdom show a very similar pattern.
CHAPTER 1 Stock and Bond Returns Since 1802
21
term stock returns have displayed such stability despite the radicalpolitical, economic, and social changes that have impacted the worldover the past two centuries.Yet one must be aware of the political and legal framework inwhich these returns were generated. The superior returns to equity overthe past two centuries might be explained by the growing dominance ofnations committed to free-market economics. Who might have expectedthe triumph of market-oriented economies during the Great Depressionof the 1930s and the tumult following World War II? The robustness ofworld equity prices in recent decades might reflect the emergence of thegolden age of capitalism—a system in ascendancy today but whose fortunes could decline in the future. Yet even if capitalism declines, it is unclear which assets, if any, will retain value. In fact, if history is any guide,government bonds in our paper money world may fare far worse thanstocks in any political or economic upheaval. As the next chapter shows,the risks in bonds actually outweigh those in stocks over long horizons.
APPENDIX 1: STOCKS FROM 1802 TO 1870The first actively traded U.S. stocks, floated in 1791, were issued by twobanks: the Bank of New York and the Bank of the United States.21 Bothofferings were enormously successful and were quickly bid to a premium. But they collapsed the following year when Alexander Hamilton’s assistant at the Treasury, William Duer, attempted to manipulatethe market and precipitated a crash. It was from this crisis that the antecedents of the New York Stock Exchange were born on May 17, 1792.Joseph David, an expert on the eighteenth-century corporation,claimed that equity capital was readily forthcoming not only for everyundertaking likely to be profitable but also, in his words, “for innumerable undertakings in which the risk was very great and the chances ofsuccess were remote.”22 Although over 300 business corporations werechartered by the states before 1801, fewer than 10 had securities thattraded on a regular basis. Two-thirds of those chartered before 1801 were21Until recently, the oldest continuously operating firm was Dexter Corp., founded in 1767, a Connecticut maker of special materials that was purchased in September 2000 by Invitrogen Corp. Thecurrent oldest is Bowne & Co. (1775), which specializes in printing; the second is Wachovia Bank,which acquired First Union, the successor of the First National Bank of Pennsylvania founded in1782; and the third is the Bank of New York Corp., founded in 1784, which was involved in the successful 1791 stock offering with the Bank of the United States that was eventually involved in thecrash of 1792.22Werner and Smith, Wall Street, p. 82.
22
PART 1 The Verdict of History
connected with transportation: wharves, canals, turnpikes, and bridges.But the important stocks of the early nineteenth century were financialinstitutions: banks and, later, insurance companies. Banks and insurancecompanies held loans and equity in many of the manufacturing firmsthat, at that time, did not have the financial standing to issue equity. Thefluctuations in the stock prices of financial firms in the nineteenth century reflected the health of the general economy and the profitability ofthe firms to whom they lent. The first large nonfinancial venture was theDelaware and Hudson Canal, issued in 1825, which also became an original member of the Dow Jones Industrial Average 60 years later. In 1830,the first railroad, the Mohawk and Hudson, was listed, and for the next50 years railroads dominated trading on the major exchanges.
APPENDIX 2: ARITHMETIC AND GEOMETRIC RETURNSThe average arithmetic return rA is the average of each yearly return. If r1to rn are the n yearly returns, rA ⫽ (r1 ⫹ r2 ⫹ . . . ⫹ rn)/n. The average geometric, or compound, return rG is the nth root of the product of one-yeartotal returns minus 1. Mathematically this is expressed as rG ⫽ [(1 ⫹ r1)(1⫹ r2) . . . (1 ⫹ rn)]1/n ⫺ 1. An asset that achieves a geometric return of rGwill accumulate to (1 ⫹ rG)n times the initial investment over n years. Thegeometric return is approximately equal to the arithmetic return minusone-half the variance ␴2 of yearly returns, or rG ⬇ rA – 1⁄2␴2.Investors can be expected to realize geometric returns only overlong periods of time. The average geometric return is always less thanthe average arithmetic return except when all yearly returns are exactlyequal. This difference is related to the volatility of yearly returns.A simple example demonstrates the difference. If a portfolio falls by50 percent in the first year and then doubles (up 100 percent) in the second year, “buy-and-hold” investors are back to where they started, witha total return of zero. The compound or geometric return rG, definedabove as (1 ⫺ 0.5)(1 ⫹ 1) ⫺ 1, accurately indicates the zero total return ofthis investment over the two years.The average annual arithmetic return rA is ⫹25 percent ⫽ (⫺50 percent ⫹ 100 percent)/2. Over two years, this average return can be turnedinto a compound or total return only by successfully “timing” the market, specifically increasing the funds invested in the second year, hopingfor a recovery in stock prices. Had the market dropped again in the second year, this strategy would have been unsuccessful and resulted inlower total returns than achieved by the buy-and-hold investor.
2
CHAPTER
RISK, RETURN, ANDPORTFOLIO ALLOCATIONWhy Stocks Are Less RiskyThan Bonds in the Long RunAs a matter of fact, what investment can we find which offers real fixity or certainty income? . . . As every reader of this book will clearlysee, the man or woman who invests in bonds is speculating in thegeneral level of prices, or the purchasing power of money.I RV I N G F I S H E R , 1 9 1 2 1
MEASURING RISK AND RETURNRisk and return are the building blocks of finance and portfolio management. Once the risk and expected return of each asset are specified, modern financial theory can help investors determine the best portfolios. But1
Irving Fisher et al., How to Invest When Prices Are Rising, Scranton, Pa.: G. Lynn Sumner & Co., 1912,p. 6.23Copyright © 2008, 2002, 1998, 1994 by Jeremy J. Siegel. Click here for terms of use.
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PART 1 The Verdict of History
the risk and return on stocks and bonds are not physical constants, likethe speed of light or gravitational force, waiting to be discovered in thenatural world. Despite the overwhelming quantity of historical data,one can never be certain that the underlying factors that generate assetprices have remained unchanged. One cannot, as in the physical sciences, run repeated controlled experiments, holding all other factorsconstant while estimating the value of the parameter in question. AsNobel laureate Paul Samuelson is fond of saying, “We have but one sample of history.”Yet one must start by analyzing the past in order to understand thefuture. The first chapter showed that not only have fixed-income returnslagged substantially behind those on equities but, because of the uncertainty of inflation, bonds can be quite risky for long-term investors. Inthis chapter one shall see that because of the changing nature of risk overtime, portfolio allocations depend crucially on the investor’s planninghorizon.
RISK AND HOLDING PERIODFor many investors, the most meaningful way to describe risk is by portraying a “worst-case scenario.” The best and worst after-inflation returns for stocks, bonds, and bills from 1802 over holding periodsranging from 1 to 30 years are displayed in Figure 2-1. Here stock returnsare measured by dividends plus capital gains or losses available on abroad capitalization-weighted index of U.S. small and large stocks.Note that the height of the bars, which measures the difference between best and worst returns, declines far more rapidly for equities thanfor fixed-income securities as the holding period increases.Stocks are unquestionably riskier than bonds or Treasury bills overone- and two-year periods. However, in every five-year period since1802, the worst performance in stocks, at –11 percent per year, has beenonly slightly worse than the worst performance in bonds or bills. Andfor 10-year holding periods, the worst stock performance has actuallybeen better than that for bonds or bills.For 20-year holding periods, stock returns have never fallen belowinflation, while returns for bonds and bills once fell as much as 3 percentper year below the inflation rate for two decades. This wiped out almostone-half the purchasing power of a bond portfolio. For 30-year periods,the worst returns for stocks remained comfortably ahead of inflation by2.6 percent per year, a return that is not far from the average return onfixed-income assets.
CHAPTER 2 Risk, Return, and Portfolio Allocation
FIGURE
25
2–1
Maximum and Minimum Real Holding Period Returns, 1802 through December 2006
It is very significant that stocks, in contrast to bonds or bills, havenever delivered to investors a negative real return over periods of 17years or more. Although it might appear to be riskier to accumulatewealth in stocks rather than in bonds over long periods of time, preciselythe opposite is true: the safest long-term investment for the preservationof purchasing power has clearly been a diversified portfolio of equities.Some investors question whether holding periods of 10 or 20 ormore years are relevant to their planning horizon. But one of the greatest mistakes that investors make is to underestimate their holding period. This is because many investors think about the holding periods ofa particular stock, bond, or mutual fund. But the holding period that isrelevant for portfolio allocation is the length of time the investors holdany stocks or bonds, no matter how many changes are made among theindividual issues in their portfolio.The percentage of times that stock returns outperform bond or billreturns over various holding periods is shown in Table 2-1. As the hold-
26
PART 1 The Verdict of History
TABLE
2–1
Holding Period Comparisons: Percentage of Periods When Stocks Outperform Bonds and Bills
ing period increases, the probability that stocks will outperform fixedincome assets increases dramatically. For 10-year horizons, stocks beatbonds and bills about 80 percent of the time; for 20-year horizons, it isover 90 percent of the time; and over 30-year horizons, it is virtually 100percent of the time.As noted in the last chapter, the last 30-year period in which bondsbeat stocks ended in 1861, at the onset of the U.S. Civil War. This is apoint worth remembering: never in any of the past 175 years would abuyer of newly issued 30-year government bonds (had they been issuedon an annual basis) have outperformed an investor in a diversified portfolio of common stocks held over the same period.Although the dominance of stocks over bonds is readily apparentin the long run, it is also important to note that over one- and even twoyear periods, stocks outperform bonds or bills only about three out ofevery five years. This means that nearly two out of every five years a
CHAPTER 2 Risk, Return, and Portfolio Allocation
27
stockholder’s return will fall behind the return he or she would get onTreasury bills or bank certificates. The high probability that bonds andeven bank accounts will outperform stocks in the short run is the primary reason why it is so hard for many investors to stay in stocks.2
INVESTOR RETURNS FROM MARKET PEAKSMany investors, although convinced of the long-term superiority of equity, believe that they should not invest in stocks when stock prices appear high. But this is not true for the long-term investor. Theafter-inflation total return over 10-, 20-, and 30-year holding periodsafter the eight major stock market peaks of the last century is shown inFigure 2-2.Even from major stock market peaks, the wealth accumulated instocks is more than four times that in bonds and more than five timesthat in Treasury bills if the holding period is 30 years. If the holding period is 20 years, stock accumulations beat those in bonds by about twoto-one. Even 10 years after market peaks, stocks still have an advantageover fixed-income assets. Unless investors believe there is a high probability that they will need to liquidate their savings over the next 5 to 10years to maintain their living standard, history has shown that there isno compelling reason for long-term investors to abandon stocks no matter how high the market may seem.Of course, if investors can identify peaks and troughs in the market,they can outperform the buy-and-hold strategy that is advocated in thisbook. But, needless to say, few investors can do this. And even if an investor sells stocks at the peak, this does not guarantee superior returns.As difficult as it is to sell when stock prices are high and everyone is optimistic, it is more difficult to buy at market bottoms when pessimism iswidespread and few have the confidence to venture back into stocks.A number of “market timers” have boasted that they yanked alltheir money out of stocks before the 1987 stock crash or the 2000 bearmarket. But in 1987 many did not get back into the market until it had already passed its previous highs. And many of the bears of the most recent decline are still out of the market, despite the fact that most marketaverages have hit all-time highs. In the long run, getting out of the market at the peak does not guarantee that you will beat the buy-and-holdinvestor.2
Chapter 19 on behavioral economics analyzes how investors’ aversion to taking losses, no matterhow small, affects portfolio performance.
28
PART 1 The Verdict of History
FIGURE
2–2
Average Total Real Returns after Major Twentieth-Century Market Peaks ($100 Initial Investment)
STANDARD MEASURES OF RISKThe risk—defined as the standard deviation of average real annual returns—for stocks, bonds, and bills based on the historical sample of over200 years is displayed in Figure 2-3. Standard deviation is the measure ofrisk used in portfolio theory and asset allocation models.Although the standard deviation of stock returns is higher than forbond returns over short-term holding periods, once the holding periodincreases to between 15 and 20 years, stocks become less risky thanbonds. Over 30-year periods, the standard deviation of a portfolio of equities falls to less than three-fourths that of bonds or bills. The standarddeviation of average stock returns falls nearly twice as fast as for fixedincome assets as the holding period increases.
CHAPTER 2 Risk, Return, and Portfolio Allocation
FIGURE
29
2–3
Risk for Average Real Return over Various Holding Periods, 1802 through December 2006 (HistoricalRisk versus Risk Based on Random Walk Hypothesis)
Theoretically the standard deviation of average annual returns isinversely proportional to the holding period if asset returns follow a random walk.3 A random walk is a process whereby future returns areconsidered completely independent of past returns. The dashed barsin Figure 2-3 show the decline in risk predicted under the random walkassumption.But the historical data show that the random walk hypothesis cannot be maintained for equities. This is because the actual risk of stocks declines far faster than the predicted rate, indicated by the dashed bars. Thisoccurs because of the mean reversion of equity returns that I described inChapter 1.3
In particular, the standard deviation of average returns falls as the square root of the length of theholding period.
30
PART 1 The Verdict of History
The standard deviation of returns for fixed-income assets, on theother hand, does not fall as fast as the random walk theory predicts. Thisis a manifestation of mean aversion of bond returns. Mean aversionmeans that once an asset’s return deviates from its long-run average,there is an increased chance that it will deviate further, rather than return to more normal levels. Mean aversion of bond returns is especiallycharacteristic of hyperinflations, such as those that impacted Japaneseand German bonds, but it is also present in the more moderate inflationsthat have hit the United States and the United Kingdom. Once inflationbegins to accelerate, the inflationary process becomes cumulative andbondholders have virtually no chance of making up losses to their purchasing power. In contrast, stockholders who hold claims on real assetsrarely suffer a permanent loss due to inflation.
VARYING CORRELATION BETWEEN STOCK AND BOND RETURNSEven though the returns on bonds fall short of that on stocks, bonds maystill serve to diversify a portfolio and lower overall risk. This will be trueif bond and stock returns are negatively correlated, which means that bondyields and stock prices move in opposite directions. The diversifyingstrength of an asset is measured by the correlation coefficient. The correlation coefficient, which theoretically ranges between –1 and +1, measures thecorrelation between an asset’s return and the return of the rest of the portfolio. The lower the correlation coefficient, the better the asset serves as aportfolio diversifier. Assets with negative correlations are particularlygood diversifiers. As the correlation coefficient between the asset andportfolio returns increases, the diversifying quality of the asset declines.The correlation coefficient between annual stock and bond returnsfor six subperiods between 1926 and 2006 is shown in Figure 2-4. From1926 through 1965 the correlation was only slightly positive, indicatingthat bonds were fairly good diversifiers for stocks. From 1966 through1989 the correlation coefficient jumped to +0.34, and from 1990 through1997 the correlation increased further to +0.55. This means that the diversifying quality of bonds diminished markedly from 1926 to 1997.There are good reasons why the correlation became more positiveduring this period. Under the gold-based monetary standard of the1920s and early 1930s, bad economic times were associated with fallingcommodity prices; when the real economy was sinking, stocks declinedand the real value of government bonds rose.Under a paper money standard, bad economic times are morelikely to be associated with inflation, not deflation, as the government at-
CHAPTER 2 Risk, Return, and Portfolio Allocation
FIGURE
31
2–4
Correlation Coefficient between Monthly Stock and Bond Returns
tempts to offset economic downturns with expansionary monetary policy. This inflationary policy accompanies a weak real economy, such asoccurred during the 1970s. The negative short-term effects of inflationon equity returns are detailed in Chapter 11.But this has changed in recent years. Since 1998 there has been adramatic reversal in the short-term correlation between stock and bondprices, as shown in Figure 2-4. Over the past decade stock prices havebeen negatively correlated with government bond prices. From 1997through 2001 the world markets were roiled by economic and currencyupheavals in Asia, the deflationary economy in Japan, and then theevents of September 11.4 The collapsing currency markets, combinedwith falling commodity prices, had an eerie resemblance to the 1930s,4
The causes and consequences of these events are discussed in Chapter 10.
32
PART 1 The Verdict of History
when deflation ruled and government bonds were the only appreciatingassets. As a result international investors fled to the U.S. government security market when turmoil hit equities and other currencies. Long-termU.S. government bonds became “safe havens” for investors fearing ameltdown in the stock market.5This tendency for investors to hide in long-term U.S. Treasury issues when equities experienced sudden declines persisted, despite theAsian recovery and the improving Japanese economy. As central bankshave held firm against inflation, government bonds can be an island ofstability when there is financial stress.But it is an open question whether bonds will be good long-term diversifiers, especially if the specter of inflation looms once again. Nevertheless, the premium now enjoyed by Treasury issues generated byinvestors seeking short-term safe havens means that the return on government bonds will be low and they will become less desirable to longterm investors.
EFFICIENT FRONTIERS6Modern portfolio theory describes how investors may alter the riskand return of a portfolio by changing the mix between assets. Figure2-5, based on the 200-year history of stock and bond returns, displaysthe risks and returns that result from varying the proportion of stocksand bonds in a portfolio over various holding periods ranging from 1to 30 years.The square at the bottom of each curve represents the risk and return of an all-bond portfolio, while the cross at the top of the curve represents the risk and return of an all-stock portfolio. The circle fallingsomewhere on the curve indicates the minimum risk achievable bycombining stocks and bonds. The curve that connects these points represents the risk and return of all blends of portfolios from 100 percentbonds to 100 percent stocks. This curve, called the efficient frontier, is theheart of modern portfolio analysis and is the foundation of asset allocation models.Investors can achieve any combination of risk and return along thecurve by changing the proportion of stocks and bonds. Moving up the5Short-term Treasury securities such as bills have often enjoyed safe-haven status. Rising bond pricesin a tumultuous equity market also occurred during the October 19, 1987, stock market crash, butmuch of the rise then was predicated on the (correct) belief that the Fed would lower short-term rates.6This section, which contains some advanced material, can be skipped without loss of continuity.
CHAPTER 2 Risk, Return, and Portfolio Allocation
FIGURE
33
2–5
Risk-Return Trade-Offs for Various Holding Periods, 1802 through December 2006
curve means increasing the proportion in stocks and correspondingly reducing the proportion in bonds. As stocks are added to the all-bondportfolio, expected returns increase and risk decreases, a very desirablecombination for investors. But after the minimum risk point is reached,increasing stocks will increase the return of the portfolio but only withextra risk.The slope of any point on the efficient frontier indicates the risk-return trade-off for that allocation. By finding the points on the longerterm efficient frontiers that have a slope equal to the slope on theone-year frontier, one can determine the allocations that represent thesame risk-return trade-offs for all holding periods.
34
PART 1 The Verdict of History
RECOMMENDED PORTFOLIO ALLOCATIONSWhat percentage of an investor’s portfolio should be invested in stocks?The answer can be seen in Table 2-2, which is based on standard portfolio models incorporating both the risk tolerance and the holding periodof the investor.7 Four classes of investors are analyzed: the ultraconservative investor who demands maximum safety no matter the return, theconservative investor who accepts small risks to achieve extra return,the moderate-risk-taking investor, and the aggressive investor who iswilling to accept substantial risks in search of extra returns.The recommended equity allocation increases dramatically as theholding period lengthens. Based on the 200 years of historical returns onstocks and bonds, ultraconservative investors should hold nearly threequarters of their portfolio in stocks over 30-year holding periods. This allocation is justified since stocks are safer than bonds in terms ofpurchasing power over long periods of time. The historical data suggestthat even conservative investors should hold nearly 90 percent of theirportfolio in stocks for these long horizons, while the analysis indicatesmoderate and aggressive investors should have over 100 percent in equity. Borrowing or leveraging an all-stock portfolio can achieve this allocation, although if such borrowing is not desired, investors with thesepreferences would do quite well to hold 100 percent of their long-termportfolio in stocks.Given these striking results, it might seem puzzling that the holding period has almost never been considered in portfolio theory. This is7
The one-year proportions (except minimum risk point) are arbitrary and are used as benchmarksfor other holding periods. Choosing different proportions as benchmarks does not qualitativelychange the analysis.
TABLE
2–2
Portfolio Allocation: Percentage of Portfolio Recommended in Stocks Based on All Historical Data
RiskTolerance
1 Year
Holding Period5 Years
10 Years
30 Years
Ultraconservative(Minimum Risk)
9.0%
22.0%
39.3%
71.4%
Conservative
25.0%
38.7%
59.6%
89.5%
Moderate
50.0%
61.6%
88.0%
116.2%
Aggressive Risk Taker
75.0%
78.5%
110.1%
139.1%
CHAPTER 2 Risk, Return, and Portfolio Allocation
35
because modern portfolio theory was established when the academicprofession believed in the random walk theory of security prices. Asnoted earlier, under a random walk, the relative risk of various securitiesdoes not change for different holding periods, so portfolio allocations donot depend on how long one holds the asset. The holding period becomes a crucial issue in portfolio theory when the data reveal the meanreversion of stock returns.8
INFLATION-INDEXED BONDSUntil the last decade, there was no U.S. government bond whose return was guaranteed against changes in the price level. But in January1997, the U.S. Treasury issued the first government-guaranteed inflation-indexed bond. The coupons and principal repayment of thisinflation-protected bond are automatically increased when the pricelevel rises, so bondholders suffer no loss of purchasing power whenthey receive the coupons or final principal. Since any and all inflationis compensated, the interest rate on this bond is a real, or inflationadjusted, interest rate.When these bonds were first issued, their real yields were about 31⁄2percent, and they rose to over 4 percent at the height of the 2000 bullmarket. However, these yields have declined markedly since 2001, andat the end of 2006, their real yields fell to about 2 percent, less than onethird the historical return on equity. Nevertheless, these bonds may bean attractive alternative for investors who do not want to assume theshort-term risks of stocks but fear loss of purchasing power in bonds. In20 percent of all 10-year periods from 1926, stocks have fallen short of a2.0 percent real return. For most long-term investors, inflation-indexedbonds should dominate nominal bonds in a portfolio.
8
For an excellent review of this literature see Luis M. Viceira and John Y. Campbell, Strategic AssetAllocation: Portfolio Choice for Long-Term Investors, New York: Oxford University Press, 2002. Also