- While equities have fallen sharply in the past year, rebalancing is less attractive now than in the past because spread sector valuations have declined just as significantly as equities.
- Current valuations suggest that the prospective return premium for equities over corporate bonds is as slim as it has been at almost any time in the postwar era.
- Relative to historical norms, corporate bonds have fallen much more sharply below long-run return trends than equities.
- Over the past 45 years, equity returns exceeded those on corporate bonds by approximately 2% per year, at a “cost” of an additional 10-20% per year of volatility. If anything, the equity premium should be smaller in the years to come.
- Corporate bonds appear to bear less additional downside risk should an adverse economic environment continue, thanks to their senior credit position and more strained current valuations.
With the broad stock market down nearly 50% since December 2007, some institutional investors are considering rebalancing their portfolios, shifting fixed-income allocations to equities to re-attain the equity exposure they would normally target (that exposure having declined because of the drop in equity valuations). We believe such a response is much less appropriate now than might have been the case after past sell-offs.
The major difference is that the relative drop in corporate bond valuations this time around is even more severe than that of equities. Investment-grade corporate bonds currently offer prospective returns that investors could previously have hoped for only in the stock market. Still higher prospective returns are available in the high-yield corporate and non-agency mortgage sectors even upon allowing for historically high levels of default. Furthermore, fixed-income spread sectors offer these equity-like returns alongside a senior claim on corporate assets, an historical risk profile far tamer than that of stocks, and, for defined-benefit pension plans, a much tighter coherence with strategic investment goals.
If “fixed-income” meant only Treasuries, then rebalancing would be attractive given very low current Treasury yields. However, corporate bonds and other spread sector assets are major components of the fixed-income universe, and the very attractive loss-adjusted yields available there put rebalancing in a different light. A recent white paper, “Credit: An Historic Opportunity,” touted the attractiveness of corporate bonds compared to Treasuries. Here, we will make a similar case for corporate bonds versus equities.
Current market pricing indicates that the prospective return premium for stocks over bonds is less than at virtually any time in post-WWII history. This “equity premium” has been about 2.0–2.5% over the past 45 years, so current pricing suggests a premium somewhat lower in the foreseeable future.
Equity market pricing has indeed become more attractive over the past year. Historical analysis indicates that the large-cap stock market is currently two to three standard deviations below long-term return trends. However, investment-grade corporate bonds are six to seven standard deviations below their trends. In statistical terms, current stock market valuations are thousands of times more likely to recur than current bond market valuations. In more intuitive terms, if stocks are priced for an extended recession, then corporate bonds are priced for something worse than the Great Depression.
Corporate bonds have less relative downside risk should recession persist or deepen and more relative upside potential when and as the economy recovers. In the final analysis, the present expected return on stocks is higher than that on corporate bonds. However, once relative risks are considered, corporates look every bit as or more attractive than stocks.
Prospective returns on corporate bonds are clearly indicated by yields to maturity.1 An analogous prospective return measure for equities can be constructed by utilizing the Capital Asset Pricing Model (CAPM). CAPM specifies a relationship between current valuation, horizon earnings and the current prospective rate of return.2
For stocks in aggregate, total earnings equal after-tax corporate profits. Furthermore, over time, aggregate profits can grow no faster than corporate GDP.3 So horizon earnings for the aggregate stock market can be modeled via current after-tax profits and the prospective growth in GDP. CAPM then reduces to a statement that the prospective yield on stocks equals the inverse of current market P/E plus the expected rate of growth in nominal GDP.4
Exhibit 1 plots historical values of this estimated prospective yield on nonfinancial stocks in aggregate against contemporaneous yields on Baa corporate bonds. Expected nominal GDP growth rates are taken as the average rate of growth in real corporate GDP over the preceding 10 years plus the average rate of corporate-sector inflation over the preceding three years. (These are quite charitable assumptions to use for the stock market presently, given current risks of either deflation and/or sluggish real growth.)
As seen in Exhibit 1, prospective yields on stocks have indeed risen lately, thanks to the decline in equity prices. However, prospective stock yields are still substantially lower now than during the non-inflationary (and low-interest-rate) days of the late 1950s and early 1960s, and hugely lower now than during the early days of the 1980s’ bull market. Corporate bond yields have risen even more sharply recently than have equity yields, so that the “spread” of prospective stock yields over those on corporate bonds has declined steadily for the past two years. This spread is smaller presently than it was at virtually any other point in postwar history, the exceptions being the eve of the 1987 stock crash and the peak years of the late 1990s stock bubble.5
To repeat, only at the beginnings of sharp equity market plunges—in October 1987 and over 2000–2002—have corporate bond valuations looked more attractive relative to equities than they do now. We hopefully stand at the end of an equity plunge at present and are looking for upside potential. However, it appears the behavior of corporate bond valuations during the recent sell-off provides them a much better competitive position currently relative to equities than was the case in past rebalancing environments.
Equity and Bond Valuations Relative to Trend
The previous section looked at prospective returns. Much the same perspective on corporate bonds versus stocks is provided by looking at current pricing in terms of historical trends. It is commonly argued that long-run stock market returns average about 7% per year over inflation. This is verified by Exhibit 2, utilizing real returns on large-cap stocks as reported by Ibbotson and Associates. Exhibit 2 also shows a one standard deviation band around stocks’ trend line. As of the end of March 2009, equities were 1.9 standard deviations below long-run return trends.
To fairly compare stock and bond returns going forward, the focus should be on periods of stable inflation, as inflation causes permanent losses to bonds but only temporary losses to stocks.6 Bond market data are thus analyzed here over a sample period from 1986 to the present. It is apparent from Exhibit 2 that stocks’ volatility relative to trend was lower over the post 1985 period (shaded area) than before. Focusing only on returns after 1986, present stock valuations are 2.7 standard deviations below trend.
Ibbotson and Associates also publish returns on high-grade corporate (Aa or better) long bonds. For such bonds, the period from 1986 to the present provides a sample of returns unaffected by either accelerating inflation or the initial effects of disinflation. That experience is summarized in Exhibit 3 similarly to the depiction of stocks in Exhibit 2. At their October 2008 low, long corporates were 7.2 standard deviations below trend. Even with some rebound since then, high-grade long corporates were 6.1 standard deviations below trend as of the end of March.
Spread widening has been even more pronounced further out the ratings spectrum, as mentioned in the “Historic Opportunity” white paper. Exhibit 4 shows the Barclays Capital Long Credit Index, which includes all investment-grade long-term corporates (Baa or better). At its October 2008 low, this aggregate was 9.1 standard deviations below long-run return trends. Even after a recent bounce, the March 2009 level was 6.9 standard deviations below trend. Outside of the investment-grade space, high-yield bonds were similarly undervalued. At its November 2008 low, the Barclays Capital High-Yield Index was 5.0 standard deviations below trend. As of the end of March, it was 3.9 standard deviations below trend.
The extremes observed for bond valuations presently are much rarer than those observed in the stock market. Assuming normal distributions for cumulative returns, current valuations in the stock market would be 40,000 or more times more likely to be observed than those in the investment-grade credit markets or hundreds of times more likely than current high-yield valuations. In an era of black swans (i.e. rare events beyond normal expectations), one might understandably be skeptical of the relative frequencies stated here, grounded as they are in statistics.
Both the visuals of the charts and the statistics cited make clear that recent bond market movements are much more of a departure from historical trends than what has been observed in the stock market.
As discussed in the “Historic Opportunity” white paper, corporate bond valuations imply prospective default rates far worse than those experienced during the Great Depression. Hence our statement that the corporate market is priced for an economic environment a good bit worse than that of the Depression. At a minimum the trends analyzed here indicate that stocks are priced for an environment a good bit less severe.
Equity Premia and Risk-Adjusted Returns
In discussing prospective yields, we found that equities were currently priced to deliver a yield about two percentage points per year higher than that on corporate bonds (before allowing for incidences of default and prior to compounding). Meanwhile, historical data show the compound yield on equities exceeding that on corporate bonds by about 1% per year over the last two decades. Even though we might argue that the relative attractiveness of corporate bonds is greater than that of stocks, it should be conceded that the present expected return on stocks is higher than that on corporate bonds. The questions remain, though, as to just how large the expected equity premium is and whether that expected premium is worth the much higher rates of volatility and economic risk that equity investments entail.
It is commonly stated that stocks have unlimited upside potential. This is a misconception. While it is certainly possible to strike it rich on a single (small-cap?) issue, no reasonable investor would put all his eggs in one basket. And just as surely as diversification reduces risk, so it also reduces upside potential. At the aggregate level, historical returns on the S&P 500 have clearly been bounded. Even at the conceptual level, aggregate corporate-sector earnings are bounded above, as argued earlier, and P/Es for stocks do not have any more upside potential than do P/Es for bonds. (There is no presumption that the potential returns from active equity investing are unlimited, but that is another story.)
Exhibit 6 shows rolling 10-year compound averages of the equity premium over high-grade corporates across the range of the Ibbotson data. As stocks recovered from The Depression and WWII over 1945–60, equities vastly outperformed long bonds. However, since 1964, the equity premium has been dramatically smaller, only about 2.5% per year, and it has been much lower than that in the last two decades, as well as prior to and during the Depression (1926–44).
Careless computations can make this premium look larger. For example, studies often claim an equity premium of 4% per year in recent decades, but those results are based on average percent returns. It is compound average returns that are important for long-run return comparisons, and it is well known that volatility of returns causes arithmetic average (percent average) returns to be a good bit higher than compound average returns; this overstatement rises with volatility.7 While arithmetic average equity premia have been around 4% per year, the compound average premium is much lower.
Even the 2.5%± equity premium comes at a cost of a much larger increase in volatility. Exhibit 7 shows moving 10-year measures of both the incremental increase in volatility moving from corporates to equities as well as the tracking error of equities over corporates. For defined-benefit pension plans and other long-term investors, long bonds are the relevant risk-free asset, and this tracking error of equities over corporates is the relevant measure of the riskiness of stocks. Tracking error is also relevant in determining the information ratio for stocks relative to corporates.
Equity volatility has typically been 10-15 percentage points per year higher than that for long bonds, with higher incremental equity volatility during the Depression/WWII era and lower incremental volatility during the early days of disinflation (early 1980s). The tracking error of equities over corporates has typically been on the order of 15–20% per year, higher still during the Depression/ WWII era and also recently, lower early in the disinflation era.
This large extra volatility puts additional perspective on the equity premium. Exhibit 8 shows moving 10-year information ratios for large-cap equities over corporate bonds. Only briefly during the last 80 years have equities enjoyed an information ratio of 0.5 or higher versus long bonds. Over the 1964–2006 era, that information ratio was just 0.17 (and the 1964–2008 value is even lower).
In sum, over the last 45 years, equity investors have endured an extra six percentage points per year of risk for each one percentage point of equity premium. We believe this is the relevant trade-off metric for defined-benefit plans contemplating rebalancing. Even for other investors, while stocks are commonly thought of as the best investment for the long-run, on a risk-adjusted basis, they have not provided an attractive alternative to long bonds. Nor do present valuations look likely to provide different results in the future, as we have already seen.
Considering the Economy
Describing equities or corporate bonds as currently attractive presupposes a benign economic environment where defaults remain relatively low and corporate cash flows are sustained and eventually improved upon. The thrust of the analysis so far is that even in the event of a reasonably prompt, satisfactory recovery in the economy, relative valuations are such that equities would likely only slightly outperform corporate bonds and that corporate bonds offer better prospects on a volatility-adjusted basis. None of this directly considers the senior claims on corporate assets that bonds enjoy relative to stocks. That seniority would be a very important factor in other, less propitious economic outcomes.
If the U.S. were to experience an extended period of deflationary growth, similar to that of 1865-1895, bonds would likely vastly outperform stocks, as yields would fall sharply and as corporate earnings would decline with the aggregate price level. This is, admittedly, a most unlikely scenario. However, a less unlikely scenario would be one of extended economic funk, not necessarily as severe nor as protracted as the Great Depression, but more severe and longer than other recessions of the post-WWII era.
Such a development would result in elevated corporate default rates, which would impair the performance of corporate bonds. However, as detailed in the “Historic Opportunity,” white paper and as already discussed above, implied default rates on corporate bonds are already priced for something worse than the Great Depression, so even the perverse default experience mentioned here should not prevent corporate bonds from outperforming Treasuries. Those default levels would be as much or more chilling for equity valuations, precisely because of the lower seniority of equities. Our analysis of historic valuations relative to trend suggests that the stock market is not nearly sufficiently priced to withstand such an environment as is the corporate bond market. Thus, under these more dire economic scenarios, there is reason to believe that corporate bonds would outperform stocks and Treasuries.
Stock-market multiples have declined sharply in the last year, making equities more attractive. However, corporate bond market pricing has also deteriorated sharply, and various prospective and historical perspectives indicate that corporate bonds are more attractive than stocks. Yes, equities will most likely provide a higher realized return than will corporate bonds. However, that prospective premium would appear to be smaller now than it has been at virtually any other time in the last 50 years, even while equity allocations will most likely subject the investor to much greater short-run volatility of returns and much higher exposure to downside risks should the economy endure a prolonged funk.
Other analysts have pointed out that even without regard to relative return considerations, the case for rebalancing into stocks at present is diminished by the elevated state of transactions costs given distressed financial market conditions.8 While we didn’t detail this issue here, it clearly augments our findings.
The rebalancing argument is most relevant with Treasuries as the implicit model for fixed income. We have no problem with analysis touting stocks over Treasuries from current market pricing. However, confining fixed-income to Treasury issues is unnecessarily myopic. More to the point, it ignores the historic attractions currently offered by the corporate bond market and other spread sectors.
- Of course, even if one holds a portfolio of corporate bonds to maturity, the realized return will differ from yield to maturity by the incidence of defaults. However, for the prospective returns estimates calculated in this section, defaults are an ever greater detractor for equity returns than for corporates, because of equities’ junior credit claim relative to bond debt. In effect, this section estimates historical “yields to maturity” for stocks to compare with those for bonds. Since default considerations would be expected to be more of an issue for stocks than bonds, comparing prospective yields for stocks versus corporate bonds actually overstates the attractiveness of stocks relative to corporate bonds.
- CAPM says that the market capitalization of the stock market should be equal to the present value of the future earnings stream of the corporate sector. This is the same dictum that allows us to calculate yields-to-maturity on bonds from coupon rates and market pricing, the only difference being that coupon rates are fixed over time, while corporate earnings are expected to grow over time.
- If profits continually grew faster or slower than GDP, then their share of corporate GDP would eventually go to 100% or 0%. Over time, the share of profits in GDP has moved within a bounded interval, indicating that it is valid to use the expected long-run growth rate of corporate GDP as a measure of the long-run growth rate in corporate profits.
- That is, under the assumption that corporate earnings grow over time at the same rate as the economy, say ρ, and if R is the prospective rate of return on the aggregate stock market, then CAPM reduces to P = E/(R-ρ), where P is current market cap, E is current earnings, and R and ρ are as already defined. This equation, in turn, is equivalent to R = E/P + ρ.
- Nonfinancial corporate market cap estimates used in the chart are taken from the Federal Reserve Board’s flow-of-funds data set. These data begin in 1952, which is why this chart extends only back to 1952.
- When inflation was accelerating from 1965–1979, the associated rise in inflation expectations and in the volatility of inflation and business cycle swings led to sharp losses on both equities and bonds. In fact, equities actually under-performed bonds during the early years of rising inflation. When inflation was finally curbed in the early 1980s, both interest rates and equity P/Es moved back toward pre-inflation levels. Because corporate earnings also eventually rose fully in line with the higher price level, equity returns eventually fully recouped the losses they suffered early in the inflation period. However, because bonds feature fixed coupon returns, bond-holders never recovered the losses of purchasing power incurred on bonds issued prior to or early in the inflation era.
Thus, to fairly compare bonds and stocks in a prospective non-inflation era, one should restrict the sample period not just to a period of generally stable inflation, but also to a period long enough after the inflationary episode that the sharp gains on both stocks and bonds early in any disinflation period don’t dominate performance. As stated in the text, with inflation declining in early 1980s, bond and stock valuations had moved sufficiently back toward normal by 1986 that the period from 1986 to the present provides a fair comparison of the two asset classes. Certainly, as seen in Exhibits 1 and 2, both stock and bond returns held very stable on average from 1986 until the recent disruption.
What if inflation comes back? Both stocks and bonds were clobbered during the early days of inflation, and stocks actually appeared to have suffered more than bonds. Deflation is probably a more relevant contingency for investors presently, but if inflation is your concern, then you shouldn’t regard either stocks or bonds as attractive at present.
Finally, even apart from inflation-cycle considerations, the fact is that detailed data on corporate bond returns below the high-grade tranche exist only for the last 30 years. This is another reason to focus the stock/bond comparison on post 1985 experience.
- For an asset with normally distributed logarithmic returns, compound mean μ, and compound volatility σ, the arithmetic mean of percent returns is μ+σ2/2. In other words, the compound average return is less than the average percent return by half of the square of volatility. This formula provides a good approximation for average compound returns under other, non-normal distributions. With the broad stock market typically showing annual volatility of 20% per year, stocks’ compound average return will be less than their average percent return by about (0.2)2/2, or 200 bps per year. For bonds, annual volatility is typically above 8% per year, so that their compound average returns fall short of average percent returns by (0.08)2/2, or 32 bps per year. In other words, using average percent returns will typically overstate the equity premium by about 168 bps per year, and the overstatement will be worse during periods of especially large volatility.
Also, when monthly or quarterly returns are annualized, the typically positive auto correlation of equities means that “annualizing” monthly or quarterly returns serves to understate their true annual volatility, while the typically negative auto correlation of bond returns means that annualizing monthly or quarterly returns overstates their annual volatility. Therefore, comparing monthly or quarterly average percent returns of stocks and bonds will further exaggerate the equity premium.
- See Callan Associates, “Rebalancing in a Time of Extreme Volatility,” November 2008.