Smithers & Co. Ltd. St. Dunstan's Hill, London ECR HL Telephone: 7 Facsimile: 7 Web Site: www.smithers.co.uk E-mail: info@smithers.co.uk Was the Yield Curve a th Century Aberration? Report No. 7 1 st July Andrew Smithers. This research is for the use of named recipients only. If you are not the intended recipient, please notify us immediately; please do not copy or disclose its contents to any person or body, as this will be unlawful. Information and opinions contained herein have been compiled or arrived at from sources believed to be reliable, but Smithers & Co. Ltd. does not accept liability for any loss arising from the use hereof or make any representation as to its accuracy or completeness. Any information to which no source has been attributed should be taken as an estimate by Smithers & Co. Ltd. This document is not to be relied upon as such or used in substitution for the exercise of independent judgment. Registered office: Lincoln s Inn Fields, London WCA LH Registered number: 91 England
Was the Yield Curve a th Century Aberration? Summary. 1. Real interest rates were much higher in the 19 th than in the th Century and there was a downward sloping yield curve. It is generally agreed that the fall in real yields in the th Century was the result of unanticipated inflation. We present the case that the perceived risk of continuing uncertainty over inflation caused the emergence of an upward sloping yield curve.. Returns on different assets should be proportionate to the risks involved. It has generally been assumed that risk should be measured by the volatility of short-term returns. If this is correct, then the yield curve will normally be upward sloping. But investors time horizons differ and their risks include fluctuations in income from jobs as well as from savings.. Short-term interest rates tend to fall in periods of economic weakness, when income from employment becomes more uncertain. Long-term investors may thus rationally perceive bonds as less risky than short-term deposits, provided only that inflation is not seen as a threat. Such a perception would have been rational in the 19 th Century, when the long-term volatility of real bond returns was similar to that from month Treasury bills and long-term inflation was low and stable.. Thus the most obvious explanation of the change in slope of the yield curve between the 19 th and th Centuries is that the bulk of investors have long-term time horizons, but they responded in the th to the rise in the risk of unanticipated inflation. If fears of unanticipated inflation have now receded, the 1 st Century s yield curve may resemble that of the 19 th rather than the th Century.. An alternative hypothesis is that the upward sloping yield curve was caused by the rise in government debt. Governments generally choose to fund these debts at the long end, unlike companies, which are more prone to try to keep debt costs low. A rise in the proportion of government to private sector debt will thus tend to steepen the yield curve. If, as many believe, government debt is related to inflation uncertainty, then the two hypotheses will tend to reinforce each other.. From 1 to 17 US CPI inflation was only.1% p.a.; during this period the real return was.1% on short-term government debt and.% on long dated bonds. With targets for inflation at %, this points to nominal interest rates on bonds and short-term debt of 7%. Even if real rates were above equilibrium levels from 1 17, current expectations for short-term rates seem too low, unless a recession is looming. 1
1. The Differences Between Interest Rates in the 19 th and th Centuries. Table 1. Real US Returns (Source: Jeremy Siegel, Stocks for the Long Run. ) Long-term Short-term CPI Inflation Government Government 1-17..1.1 171-19.7.. 19-199 1.7..1 Table 1 has two interesting features. First, it shows that real returns on both long and short-term government bonds have fallen as inflation has picked up and, second, that the yield curve has steepened at the same time. Chart 1. UK: Yield on Consols minus Yield on Month T-bills or Equivalent. Yields on long bonds minus yields on T-bills. - - - - 1 1 17 1 19 191 19 19 19 197 199 Sources: NBER for yields on Consols and open market discount rates to 19 then T-bills. - - Yield Gap 1 Year Average As Chart 1 shows, UK experience matches that of the US. Prior to World War II the yields on Consols (an effectively irredeemable government bond) were usually below those on months interest rates and, from the end of World War II to 199, they were habitually higher.. Risk and Return. Relative returns on assets will naturally tend to reflect the relative risks of holding them. There are, however, different ways of measuring risk. The standard method is to equate risk with the short-term volatility of the return. On this basis short-term assets, such as months Treasury bills, are less risky than long-term bonds and equities are even more risky than bonds. This can be
illustrated by comparing the impact of a rise of 1% in the required return on each type of asset. As we show in Table below, there is almost no impact on the value of month T-bills, but year bonds fall by 1.% and equities 1 fall by twice as much as bonds. Table. Impact of a 1% Rise in the Required Return on Different Assets. % Fall in Price month T-bill with an initial % return -.% year bonds with an initial % return -1.% Irredeemable Equity type bond with an initial % -.% yield rising at % p.a. to give a % return This measure of risk is, however, only appropriate for short-term investors. For investors with a longer investment horizon, longer term volatilities need to be used. The longer term volatilities of the real returns on T- bills, bonds and equities are, in each case, disproportionate to their short-term ones and in none of these cases do the relationships between long and shortterm volatility change in a similar way. For bonds, the relationship between long and short-term volatility of real returns depends on the level of uncertainty over future inflation. If the rate of inflation is known in advance, then the volatility of both the final real capital value and the real income stream from a bond over its life will be zero. While there will also be no volatility with respect to the final real capital value, there will be some volatility with regard to the income stream derived from holding month T-bills over the same timeframe. The risks of the income streams considered in isolation will therefore be less, from this perspective, for bonds than for short-term paper or deposits. The bulk of savers will also have income from employment and, as real short-term interest rates tend to fall with economic weakness, investors in bonds will have greater overall security of income, if both income from savings and from employment are considered together. If fears of unanticipated inflation have now receded, this element of risk should become more important to investors and encourage the 1 st Century s yield curve to resemble that of the 19 th rather than that of the th Century. 1 We use a bond of equity type rather than equities as such, because this removes the problem that the required return on equities cannot be changed without changing the equilibrium return on them and thus, in equilibrium, they will always be correctly valued at net worth, irrespective of any changes in the required return. For equities, the relationship between long and short-term volatility comes from their negative serial correlation, which applies over time independent of the rate of inflation. See, for example, Report No. 1 The Perils and Opportunities for Leveraging Equity Portfolios. 1 st September,.
The above description, of how long-term investors may rationally perceive risk, differs from the way in which it is usually measured. This is done by comparing the volatilities of the relative returns, not once the decision to invest has been made, but as these volatilities vary over time. Even on this basis, however, there is no reason why bonds should be more risky than shortterm paper, provided that the volatility being measured is for returns over, say, twenty years rather than one, and the historic evidence, taken from periods with low and stable inflation, is that it will not be. It follows that the yield curve will depend on the time horizon of investors, the perceived uncertainty of future inflation and the importance that investors place on having income from savings, which does not tend to fall at the same time as their income from employment becomes more uncertain. The most likely explanation, therefore, for the change in the yield curve between the 19 th and th Centuries is that the time horizon of investors remained generally quite long but that their perception regarding the uncertainty of future inflation rates rose from one century to the next.. Real CD and Bond Returns in the Past. Chart. US: Real Returns on CDs and Bonds over Previous Years. Real returns % p.a. over previous years. 1 1 1 - - 177 17 197 197 1917 197 197 197 197 197 1977 197 1997 Sources: NBER, BLS, Federal Reserve & Professor Shiller's website. 1 1 1 - - Bonds CDs Chart shows fluctuations in real returns over the previous years of portfolios invested in US CDs and bonds and Chart below, shows the similar pattern that ruled in the UK, when returns on Treasury Bills, or their nearest available equivalent, are compared with Consols.
Chart. UK: Real Returns on Consols and Treasury Bills over Years. Real returns % p.a. over previous years. 1 - - - 1 17 19 19 19 19 19 19 19 199 Sources: NBER and Ecowin. 1 - - - Consols T-bills Chart. US: Inflation and the Real Return From Bonds. Real returns on bonds % p.a. over previous years. 1 1 1 - - 177 17 197 197 1917 197 197 197 197 197 1977 197 1997 Sources: NBER, BLS, Federal Reserve & Professor Shiller's website. - - - Annual inflation rate over previous years % p.a. (inverted scale). Inflation over Previous Years Bonds Chart shows the way in which real returns on US bonds were the mirror image of rises and falls in inflation. No such relationship would be likely if changes in the level of inflation had been expected. As is generally agreed, the rises and falls in the real returns from bonds were almost certainly the result of the considerable fluctuations in inflation being largely unanticipated.
. Long and Short-term Volatilities. Chart. UK: Volatility of Real Returns from Treasury Bills and Consols. Standard deviation of annual real log returns over previous 1 years. 1 1 11 1 11 19 1911 19 191 19 1971 19 1 Sources: NBER and Ecowin. 1 1 Consols T-bills Chart. UK: Volatility of Real Returns from Treasury Bills and Consols over Years. Standard deviation of year returns over previous 1 years.. 1. 1.. 1. 1. 19 1 199 191 199 19 199 197 199 Sources: NBER and Ecowin. Consols T-bills
Chart 7. UK: Differences in Long and Short-term Volatilities of Real Returns from T-bills and Consols over 1 Years. Differences in standard deviations of real returns on T-bills and consols over previous 1 years. 1 1-11 1 11 19 1911 19 191 19 1971 19 1 Sources: NBER and Ecowin. 1 1 - Year Real Returns Annual Real Returns Charts, and 7 show the volatility of the returns on UK Treasury bills and Consols over 1 year periods, both for their annual real returns and their real returns over years. As Chart 7 shows, the differences in both the long and short-term volatilities were much smaller in the 19 th than in the th Century and the average difference in long-term volatilities in the 19 th Century was only.%, compared with.% in the th Century.. The Past Volatility of Inflation. Chart below shows how the pattern of inflation has changed. In the short-term, inflation has become far less volatile, and this will also have had a tendency, other things being equal, to reduce the longer term volatility. At the same time, however, the rate of inflation over years has been on a rising trend. The perception of the risks of inflation is likely to be influenced by both its volatility and its longer term trend. 7
Chart. US: Inflation over 1 and Years. % change in CPI over year. 1 1 1 1 9 - - -9-1 -1-1 17 17 19 1917 19 197 19 1977 199 Source: Professor Shiller's website. 1 Year Years - - - % change in CPI over past years. The reduction in the volatility of inflation over the short-term is likely to be permanent, if only because of the declining importance of food and the reduction in the impact of the weather on its output. If, therefore, central banks are successful in stabilising the longer term level of inflation, the volatility of inflation over year periods should be lower than it was in the 19 th Century. If, at the same time, investors become convinced that the long upward trend in inflation, shown in Chart, has ended, investors perception of the risk of unanticipated inflation should fall back to, or even below, its 19 th Century level.. Equilibrium Yields with a Flat Yield Curve. The evidence thus points to an upward sloping yield curve being the response of investors to uncertainty regarding inflation, rather than to an equilibrium that should exist in the absence of such doubts. If we have therefore entered into a new, or rediscovered world, in which inflation will be low and stable we must expect the recent flatness of the yield curve to be a continuing feature of the world economy, rather than an aberration. One important question which follows from this is what the equilibrium levels of real long and short-term interest rates should be in such an environment.
The first obvious guides are the returns that ruled when the yield curve was flat to downward sloping, as it was in the US from 1 to 17 and in the UK from 1 to 191. In the first instance the real returns from long bonds were.% and short ones.1% and in the second.1% and.% respectively. The lower returns in the UK relative to the US over this period fit the assumption that investors will have a home bias with regard to perceived risk. During the 19 th Century the UK consistently ran a large current account surplus. For the last years of the Century, for which reasonably reliable data are available, the surplus averaged over % of GDP (Chart 9 below). Chart 9. UK: Current Account Surpluses 17-19. Net investment abroad as % of GDP. 1 9 7 1 17 17 17 179 1 1 1 191 19 197 Source: Statistical Tables of National Inc etc., C.H. Feinstein. % of GDP Average 1 9 7 1 Over the same period the US was moving from deficit to surplus. An average of these yields would thus seem to be the most likely equilibrium level, and this gives a real yield of.%.. Supporting Evidence. In a previous report we showed that the historic real return on bonds, if allowance is made for errors in forecasting inflation, has been around %. We illustrate this in Chart 1 below. Sources include Historical Statistics of the United States, Colonial Times to 197. U.S. Department of Commerce and Bureau of the Census. See Report No. 1 The Equity Risk Premium or believing six nearly impossible things before breakfast. th May,. 9
By deducting the error in inflationary expectations from the realised real return on bonds the expectations-neutral return can be estimated and we show the results of this exercise in Table below. Chart 1. Returns on Equities, Bonds and Cash: The Impact of Inflation Expectations. 1 1 Real returns % p.a. - Average % Error In Inflation Expectations -1 11-1 1-1 1-19 19-19 19-19 19-197 197-191 191-199 cash bonds equities Table. Expectations-Neutral Average Real Long-term Bond Returns. All relevant data.1% Only th Century.% 7. US Growth and US Returns. Although US GDP has been volatile, its trend growth rate has been extremely stable at.% p.a. (Chart 11 below). 7 It is often claimed that the equilibrium rate of interest is related to the growth rate of an economy. If this were correct, then the long-term stability of US growth would support the case for a stable long-term rate of real interest. Appendix of Report No. 1 explains how we estimate the probable extent to which investors will have errors in forecasting future inflation. Cash and bond returns are calculated as compound averages over samples in which inflation expectations were realised, weighted by sample size (hence some data are excluded from averages). Stock returns are calculated as trough-to-trough compound averages (hence excludes impact of data after 197). 7 The ADF statistic for GDP growth from 19 to is -.1. 1
However, the model on which this case is based, requires the assumption of a single immortal representative investor, which is a concept lacking, at least to us, in credibility. Chart 11. US: Growth of GDP. % change in GDP over year. 1 1 - -1-1 19 19 191 19 19 19 19 19 197 19 199 Sources: NIPA since 199, various before. 1 1 - -1-1 Average Growth in US Real GDP The model has additional problems. First of all, it seems inconsistent with other, better established, economic principles, notably the tendency for rapidly growing economies to have rising real exchange rates and thus for their equilibrium returns to be below, rather than above, the returns in mature economies. Secondly, over years, the fluctuations in real returns from CDs (Chart ), year bonds (Chart 9) and equities (Chart 1) in the US seem to have been unrelated to growth. If the natural rate of interest was related to economic growth, then large year fluctuations in the real short-term rate of interest is difficult to explain in the light of the stability of the real growth rate of the economy. The nature of the fluctuations makes any relationship between real growth and real returns even more improbable. 9 We include equity returns as the model assumes that returns over all asset classes need to be in excess of the growth rate of the economy, though this raises the secondary problem as to why the representative investor should ever hold any asset but equities. 9 The correlation coefficient between year real CD returns and year GDP growth is. and that with year bonds and GDP growth is -.7. 11
Chart 1. US: Growth and Real Short-term Interest Rates. Growth % p.a. and real returns on CDs over previous years. 7 1-1 - - 199 1919 199 199 199 199 199 1979 199 1999 Sources: NIPA & NBER. 7 1-1 - - Real CDs GDP Chart 1. US: Real Growth of GDP and Real Returns on Year Bonds. % change p.a. in real GDP over previous years. 1 1 - - 199 1919 199 199 199 199 199 1979 199 1999 Sources: NIPA, NBER & Professor Shiller's website. 1 1 - - Real return % p.a. on long bonds over previous years. Real Bonds GDP 1
Chart 1. US: Growth and Real Returns on Equities. % growth p.a. in GDP over previous years. 1 1 1 199 1919 199 199 199 199 199 1979 199 1999 Sources: NIPA, NBER & Professor Shiller's website. 1 1 1 % real return on equities over previous years. Real Equity Returns GDP Despite the absence of a satisfactory economic model for the level of returns, it remains the case that, over time and in equilibrium, the cost of capital must equal its return. Chart 1. US: Real Returns on Equities to Investors. Real returns over previous years % p.a. 1 1 1 191 191 1911 191 191 191 191 191 1971 191 1991 1 Source: Professor Shiller's website. 1 1 1 Average Real Equity Return 1
As the real return on equities has been extremely stable over the longterm (Chart 1), a fall in the equilibrium return on debt is only likely if the total return on equity had recently been below trend and thus needed either a reduction in the cost of debt, or an increase in the ratio of debt to equity, in order to restore returns to trend. Chart 1. US: Non-financial Corporate RoE. Profits after tax, including those retained abroad as % of net worth. 7 19 197 19 197 197 1977 19 197 199 1997 Sources: NIPA Tables B. 1 and F. 1. 7 Average RoE The return on non-financial corporate equity (Chart 1) has been stable, as it must if the long-term return on investors equity is to be stable. But, as the current level is very high, 1 it would need a below average level of debt to make a below average level of interest rates reasonable. However, as Chart 17 shows, while debt levels are currently below peak levels, they are very high by longer term standards. The return on equity is likely to fall from its current high level and a rise in real interest rates is likely to make a contribution to this decline. 1 On the data shown in the Flow of Funds ( Z1 ) accounts, the return on corporate equity has averaged well below the return on investors equity. This is one of several pieces of evidence that point to US profits being overstated, probably because of an understatement of depreciation. See Report No. The Overstatement of US Profits. 1 th July,. 1
Chart 17. US Non-financial Corporate Leverage. Debt ratio as defined %. 1 19 197 19 197 197 1977 19 197 199 1997 Sources: Z1 Tables B. 1 & L.1. Domestic Liabilities as % of Domestic Assets Domestic Net Debt as % of Domestic Net Worth 1. Current Levels of G Interest Rates. Table. G Interest Rates % p.a. (Source: Financial Times 17 th July.) Months 1 Years Index-Linked Maturity for Index Linked Bonds US.9..9 US.7 UK.7. 1.9 9 UK 1. Germany..9 Japan. 1. France..99 1.1 9 Table shows current months and 1 year nominal interest rates and, where available, indexed linked ones. In the case of the three European Countries, where the current rate of inflation is near % p.a. and in line with their central bank targets, it seems reasonable to assume that both bond and short-term rates would, if at their equilibrium rates, be around.% to % respectively, if the yield curve has indeed flattened on a secular rather than a temporary basis. 1
For the US, where the current inflation rate (to March ) has been.% over 1 months and.% over months, but the target rate seems to be nearer %, there is greater uncertainty. If it is assumed that the short-term rate should allow for short-term fluctuations in inflation, then these should be at least 7%; if not, then both short and long rates should be around.% to %. In Japan real short and long-term interest rates are low, even compared with the current level of inflation, which is effectively zero. 9. Looking Ahead. Chart 1. US: Yield Gap and Weak Growth. 19 19 19 197 197 19 19 199 199 Source: Ecowin. Down Quarters Yield Gap Less Than.% A feature of all G bond markets is that yield curves are flat and this has in the post-world War II period been a good, but not infallible, indicator of economic weakness. We illustrate this for the US in Chart 1. This shows that a difference between 1 year and month yields at the end of a quarter has been nearly always followed by at least one negative quarter for GDP growth during the next 1 months. The only major exception was from Q 19 to Q1 197. If, however, the world is returning to a 19 th Century pattern, then the current flat yield curves should cause no concern. As Chart 1 shows, a downward sloping yield curve was normal in the UK in the 19 th Century, without any deleterious impact on the economy. 1
1. Government Debt. There has been a marked change between the 19 th and th Centuries in the relative importance of government borrowing, compared with that by the private sector. The 19 th Century opened with the Napoleonic Wars, which led to UK government debt rising to over 1% of GDP. This had fallen dramatically by the end of the Century, only to rise again under the impact of two World Wars and the influence of Keynes. Chart 19. UK and US: Government Debt to GDP. General government debt as % of GDP. 7 199 199 199 199 199 Sources: UK Eurostat, US NIPA 1.1. and Z1 D. 7 UK US In the UK and US, however, there have been some signs that the ratio of government debt to GDP has stopped rising and may well be falling. Both governments have habitually sought to borrow at relatively long maturities, while private sector borrowing has usually been more flexible, seeking either to minimise the longer or, possibly more frequently in recent years, the shorter term cost of debt. It follows that the greater the importance of government debt relative to private sector debt, the greater will be the relative supply of long dated debt and this is likely to have helped steepen the yield curve. A high level of government debt has also been considered by many to indicate a proclivity to higher inflation. While we are rather doubtful about the importance of government borrowing in effecting the shape of the yield curve, any influence it may have is likely to act in the same direction as a change in inflationary fears by investors. 17
11. Conclusions. There seems good reason to believe that the habitual upward sloping yield curve of the th Century was an aberration attributable to rapid and unpredictable inflation. In the absence of unanticipated inflation the perceived and actual risks for investors with a longer term horizon appear to be little if at all greater in bonds than in short-term paper. If the current faith in central banks is not disrupted by inflation rates in G countries moving persistently above % or so, then the current flat yield curve, similar to that ruling in the 19 th Century, will become accepted as normal. The bond market s view of the economy may therefore not be as negative as it appears and, if this is influencing central banking policy, it will be contributing to excessive ease. If the yield curve is now flat on a secular basis, the equilibrium level of interest rates is likely to be significantly above current levels. As current asset prices reflect excessive liquidity, they are likely to fall if interest rates rise sharply. This may well precipitate a recession before the long-term equilibrium level of real interest rates is reached. www.smithers.co.uk This research is for the use of named recipients only. If you are not the intended recipient, please notify us immediately; please do not copy or disclose its contents to any person or body, as this will be unlawful. Information and opinions contained herein have been compiled or arrived at from sources believed to be reliable, but Smithers & Co. Ltd. does not accept liability for any loss arising from the use hereof or make any representation as to its accuracy or completeness. Any information to which no source has been attributed should be taken as an estimate by Smithers & Co. Ltd. This document is not to be relied upon as such or used in substitution for the exercise of independent judgment. 1