Larry Swedroe
Most investors are well aware of the SEC's warning that past performance isn't an indicator of future performance. That warning often leads to questions like: "If past performance isn't predictive, why do you believe that the past outperformance of value stocks over growth stocks and small stocks over large stocks is predictive?" The answer lies in understanding two key points.
First, the SEC's warning relates directly to the performance of actively managed mutual funds. The warning is required because an overwhelming body of evidence demonstrates that for these funds even long periods of outperformance aren't predictive -- while some funds do outperform, it's no more than is randomly expected.
Second, the SEC's warning doesn't apply to asset classes, a group of assets with similar risk and reward characteristics. To address the question of whether the past performance of asset classes is predictive of future performance, we'll begin by thinking about stocks and their performance relative to riskless one-month Treasury bills.
It's safe to say that most investors not only know that stocks have provided higher returns than Treasury bills but that they also expect stocks will continue to provide higher returns. That's because stocks are riskier than Treasury bills, and investors demand a risk premium in return for accepting the increased risk.
They also know there's no guarantee that stocks will outperform. It's an expectation, not a guarantee. And they know that the longer the time horizon, the more likely it is that stocks will outperform.
Why can they have that expectation and be confident about it? Because not only is there a logical risk explanation, but the evidence of an equity premium is both persistent (over long periods and covering many economic cycles) and pervasive (all around the globe). It's that persistence and pervasiveness (with sample tests to reduce the risks of what's called data mining) that gives us confidence.
The risk explanation also means it cannot be arbitraged away. And statistical analysis can be helpful by demonstrating that the outcomes are statistically significant -- reducing the odds that the results are nothing more than a random outcome.
The same persistence, pervasiveness and statistical significance apply to the value premium and the size premium. They also apply to the momentum premium and the profitability premium (highly profitable firms outperform). An earlier post offers a detailed look at the different premium types.
While there's little debate that risk explains the size premium, there are disagreements about the other three premiums. The greatest concerns the source of the value premium. For example, economists have found that value stocks have characteristics that are intuitively risky.
On the other hand, many studies find that the source of the value premium is at least to some degree a behavioral error, an anomaly. These studies find that investors persistently overprice growth stocks and underprice value stocks. The source of the mispricing is that investors persistently underestimate the power of the reversion to the mean of abnormal earnings growth, be it abnormally high or abnormally low. They may also confuse the familiar (growth stocks) with the safe, and thus overpay for growth stocks.
Given that both sides have good arguments, a third explanation seems likely -- there should be a value premium because of the incremental risks, but the premium has been too large for the risks to fully explain. In other words, it may not be a free lunch, but it might at least be a free stop at the dessert tray.
While both the momentum and profitability premiums also have explanations on both sides, the weight of the evidence favors a behavioral story. And if it's behavioral, it runs the risk that once it's discovered the very act of exploiting it will cause it to disappear. Is that likely in these cases?
While that's certainly a possibility, the existence of the momentum premium has been well known for decades. Yet, the momentum premium persists not only in the
The evidence for the profitability premium is relatively more recent, giving perhaps less confidence that it will continue (because the weight of the evidence seems to be on the behavioral explanation). However, the evidence is persistent across cycles and pervasive across the globe.
Summarizing, the longer the premium's persistence and pervasiveness, the more we can have confidence that we should expect it to continue. And the weight of the evidence suggests that just as we should expect that the equity premium over Treasury bills will continue, we should also expect value stocks, small stocks, high-momentum stocks and highly profitable stocks to provide premiums as well.
Still, the expectation should come with a warning that there's no guarantee this will happen.
The bottom line is that because risk explanations provide more confidence than behavioral ones, you might consider allocating more of your portfolio to the factors that rely more heavily on a risk story. However, it doesn't mean you should ignore the other factors.
Copyright © 2014, The BAM
By Thomas J. Emmerling and Jared Kizer
Much has been written about the risks that rising interest rates pose to fixed income portfolios. However, much of this analysis has been simplistic or focused on historical periods, which are of little relevance in today’s environment of ultra-low nominal rates. On the simplistic side, market commentary has regularly focused on the certainty of upward rate movements when rates are by no means guaranteed to increase, particularly over shorter horizons. Market commentary has also focused on the notion that the impact of rate movements on fixed income portfolios is as straightforward as determining whether rates will go up or down. At first glance, it appears this is true since bond prices move in the opposite direction of interest rates. However, this viewpoint misses the vitally important notion that the right question to ask is whether rates will move by more or less than the market has already accounted for. This is a completely different question and one that market timers find more difficult to answer correctly.
This piece provides insight into the risks that fixed income investors face over the next year using today’s rate levels and a model of interest rate volatility. While no one knows exactly what the future holds, we believe this is a much better way to examine interest rate risk compared with historical analyses of rate movements and fixed income returns and compared with analyses that do not account for the market’s expectations for rate increases and maturity premia.
The Flaws in Historical Analyses
Historical analyses of rate movements and fixed income returns suffer from at least two flaws:
We can illustrate both of these flaws by looking at five-year Treasury rates, returns and inflation in the early 1980s. In 1980, the five-year Treasury returned 3.9 percent even in the face of interest rate increases of more than 2 percent. One might think this result shows that investors should not worry about interest rate risk today, because in some past periods rates have moved up sharply but returns have still been positive. We would argue though that this historical result has virtually no relevance for today’s fixed income environment. First, while the nominal return on a five-year Treasury was
3.9 percent in 1980 the real return, or net-of-inflation return, was –7.6 percent due to high inflation in 1980. This is a significant loss in purchasing power. More important for today’s environment, the five-year Treasury yield was 10.4 percent at the start of 1980, which provided a significant nominal return buffer against the increase in rates that occurred during 1980. This “starting condition” of high rates is obviously not relevant today.
Over a one-year period, the return on a bond or portfolio of bonds can be approximated by the following equation:
R = Y = Dur x ΔY
In this equation, R is the one-year return, Y is the starting yield, Dur is the duration of the bond or portfolio of bonds and ΔY is the actual change in the yield over the one-year holding period.
Duration is a measure of interest rate risk and is always positive (unless you are shorting fixed income securities or dealing with relatively exotic fixed income securities). Therefore, during periods when rates move up, the second part of the equation will be negative and detract from overall portfolio return. Let’s assume the starting yield of a portfolio is 5 percent, duration is 5 percent and that rates move up by 1 percent.
R = 5% - 5% x 1% = 0%
Here we see that the 5 percent yield helped completely offset the 1 percent increase in rates. However, if we assume the starting yield is 2 percent but leave the other aspects of the equation unchanged, the result is:
R = 2% - 5% x 1% = -3%
Instead of earning no return when the starting yield was 5 percent, we have lost 3 percent when the starting yield was just 2 percent (again keeping in mind this equation is an approximation). This illustrates the fundamental flaw of extrapolating past historical results into today’s low-rate environment.
This example also demonstrates an important fact concerning duration when evaluating an investment’s return. Namely, the value of the duration does not necessarily dictate the return of the investment under a 1 percent change in yield. In fact, only when the starting yield is 0 percent will the return match its duration if the yield changes by 1 percent.
Understanding How Interest Rate Increases Actually Affect Returns
Before reviewing our forward-looking analysis, it is important to understand that market pricing can help protect investors against sizable rate increases. Most investors wrongly believe that interest rate increases mean returns will be “bad” while interest rate decreases mean returns will be “good.” The more nuanced reality is that a steep yield curve — that is, a yield curve in which longer-term rates are higher than shorter-term rates — provides some protection against rate increases. This is important to understand since yield curves have generally been steep over the past few years.
Consider an investor with a one-year investment horizon and suppose a one-year, zero-coupon bond is yielding 1 percent, and a two-year, zero-coupon bond is yielding 2 percent. Given these two rates, the investor who purchases the two-year bond will earn a higher return over the next year compared with the investor who purchases the one-year bond, as long as the one-year interest rate does not increase by 2 percent or more. Said differently, as long as the one-year rate — which is 1 percent today — is less than 3 percent in one year, the two-year bond will earn a higher return than the one-year bond. For example, assume the one-year rate increases from 1 percent to 2.5 percent over the next year. In that case, the return on the two-year bond will be[i]:
Return = ($97.56/$96.12 - 1) x 100% = 1.5%
We see that the 1.5 percent return on the two-year bond exceeded the 1 percent return on the one-year bond even though interest rates increased.
A Forward-Looking Analysis of Interest Rate Risk
Our first equation above shows that an investment’s return depends upon the change in the investment’s yield. When this investment consists of more than one bond, such as with a laddered bond portfolio, the change in yield depends upon several rates for different bond maturities. In other words, a 1 percent change in the portfolio’s yield can result from many different changes to the shape of the yield curve. Arguably, an effective analysis of the future return of such portfolios should include a consideration into different evolutions of the whole yield curve.
Given today’s interest rates and reasonable expectations of interest rate volatility, what is the range of returns that a fixed income investor could expect over the next year? We answer that in this section by examining the forward-looking risk profile of a laddered bond portfolio with starting maturities ranging from one year to eight years.[ii] Generally, interest rates could change in countless ways over the next year, so the only way to get an assessment of the risk of a portfolio is by simulating different changes in interest rates and calculating portfolio returns for each simulation. We simulated 100,000 different interest rate paths. Figure 1 shows returns for a selected number of simulations.
|
Bond Latter Returns (%) |
|
| 5th Percentile | -5.3 |
| 10th Percentile | -4.1 |
| 25th Percentile | -2.2 |
| Median |
0.0 |
| Average | 0.1 |
| 75th Percentile | 2.3 |
| 90th Percentile | 4.5 |
| 95th Percentile | 5.8 |
This analysis shows that if interest rates were to rise sharply, the laddered portfolio would decline by 5.3 percent, which is the 5th percentile result. If interest rates were to decline sharply, the laddered portfolio would increase by 5.8 percent. Further, in many of the positive return scenarios, rates actually increased over the next year. Nevertheless, they did not increase enough to lead to negative portfolio returns.
This analysis also shows that relative to bad equity market returns, which could easily be –20 percent or worse over a 12-month period, bad returns on a short-duration fixed income portfolio are not nearly as negative. Further, it could be that some of the scenarios in which rates increase sharply are also periods when equity market performance is strong, offsetting the negative returns of the fixed income portion of the portfolio. Finally, long-horizon investors should keep in mind that while interest rate increases may lead to portfolio losses in the short term, higher real interest rates are a positive over longer periods of time for short-to-intermediate maturity bond portfolios. That is, as a lender of money, ask yourself whether you would prefer lending at higher or lower interest rates over the next 20 years.
Summary
We show that historical analysis of bond returns during periods of rising rates potentially suffers from two flaws. First, since many of these historical periods were also periods when inflation was high, focusing only on nominal returns greatly understates the loss of purchasing power that many fixed income investors incurred. Second, during many of these periods, beginning interest rates were much higher than they are today. Today’s “starting” interest rates provide less cushion against interest rate increases.
Using current interest rates and a model to simulate future interest rates over the next year, we examine how a portfolio of short- and intermediate-term bonds might perform. We find that if interest rates were to move up sharply over the next year, the portfolio value would fall by about 5 percent (in inflation-adjusted terms, assuming 2 percent inflation, this would be a decline in purchasing power of approximately 7 percent). While no one enjoys negative returns, the magnitude of the downside risk of the bond portfolio we examined is significantly less than the downside risk of stocks, a point often missed in many of the popular media articles that warn about the risks of rising interest rates.
Finally, fixed income investors in short- and intermediate-term bonds should actually root for increases in real (net-of-inflation) interest rates since higher rates should improve returns for long-horizon investors.
Thomas J. Emmerling, PhD, is a post-doctorate research assistant at Whitman School of Management at Syracuse University. Jared Kizer, CFA, is the director of investment strategy at the BAM ALLIANCE.
[i] Assuming a maturity value of $100, the original cost of the two-year bond is $100/1.02^2=$96.12 and the value of the two-year bond after one year is $100/1.025=$97.56.
[ii] Our implementation methodology, a one-factor Heath, Jarrow and Morton (HJM) term structure model, simulates the evolution of the entire zero-coupon Treasury yield curve forward in time beginning with today’s current yields. After simulating future yields every month over one year, we compute the monthly returns and then the annualized return on a laddered bond portfolio consisting of eight zero-coupon bonds, i.e., one bond for each maturity: 1-year, 2-year,…, 8-year. With this construction and given current yields, our bond portfolio has a duration of approximately 4.3. After computing the annual portfolio return for each simulation of 100,000 yield curve evolutions by compounding the monthly returns, we analyze the distribution of the annual returns and compute distribution statistics to assess the portfolio’s performance and risk.
To simulate actual yield curve evolutions, we closely follow the simulation algorithm prescribed in Section 3.6 of Glasserman (2004) Monte Carlo Methods in Financial Engineering. For implementation, we first need to identify a reasonable market price of risk for the one-factor driving the uncertainty in the model. For our purposes, we choose the short rate (the interest rate used for short-term borrowing/lending) as a proxy for this quantity. As a second ingredient for the implementation, we need to specify the volatility of returns for Treasury zero-coupon bonds across all available maturities. We estimate these volatilities using historical yield curve rates between January 2004 and December 2013. This historical data is continually updated and freely available on the Federal Reserve website. The methodology used for obtaining these historical yield curves is based upon the academic research carried out by Gurkaynak, Sack, Wright (2006). We also use this Federal Reserve data to obtain the most current Treasury yield curve from which each simulation begins. We utilized the May 20, 2014 yield curve estimate for the initial specification of our simulation.
By Jared Kizer
The financial media are full of conjecture about which strategies might effectively hedge inflation risk or not. Here we explore which asset classes, if any, have been effective at protecting against inflation risk. First, it is helpful to address some common logical and analytical misconceptions about hedging inflation risk.
Focus on Correlation, Not Volatility
When evaluating whether an asset class effectively protects against inflation, the focus should be on the correlation between that asset class’s returns and inflation and not the relative volatility of the asset class’s returns when compared with the volatility of inflation. This misconception often leads to assumptions, such as commodities as an asset class cannot effectively hedge inflation because its returns are about 8–10 times more volatile than inflation. This is simply false.
For example, if commodities were perfectly correlated with inflation but had returns that were 10 times more volatile than inflation, it would still be a perfect hedge against inflation risk. In that case, a 10 percent allocation to commodities with the balance of the portfolio in short-term fixed income would be very close to a perfect hedge. We recognize that commodities are not perfectly correlated with inflation and therefore are not a perfect hedge. The point, however, is that correlation is what matters and not relative volatility.
Focus on Correlation, Not Returns
Another common error is categorizing an asset class such as equities as a good inflation hedge because its long-term returns have been significantly higher than the rate of inflation. Here again, correlation is what matters. The reality is that equities have had very low correlation with inflation over almost all time horizons. If your spending is highly correlated with inflation, the fact that equities eventually should outpace inflation is not nearly as helpful as knowing that an asset class tends to do well at the exact same time inflation is high.
There Are No Perfect Inflation Hedges
Although there are no perfect hedges against inflation risk, this, however, does not mean it is a waste of time to explore which asset classes can provide some protection against inflation. There are meaningful differences in inflation protection across different asset classes.
Further, even though individual rates of inflation are often significantly different from the consumer price index (CPI) rate of inflation, they are likely highly correlated with CPI. This means asset classes with attractive inflation hedging properties are generally useful to investors who are highly exposed to this risk.
Evaluating Inflation Hedges
We examined the returns of 10 different asset classes relative to CPI inflation from the period covering January 1981–December 2013, and the period covering September 2002–December 2013.* (Our definition of “hedge” is general, and it is not meant to imply that any asset class is a perfect hedge.) The only asset class that did a decent job of hedging monthly inflation over this period was commodities. The two asset classes that tended to perform the worst were two-year and 30-year Treasury notes with 30-year Treasury notes doing significantly worse than two-year Treasury notes.
The results over the shorter time period included Treasury Inflation-Protected Securities (TIPS), and we found that commodities and short-term TIPS both did a decent job of hedging monthly inflation risk. Also, there is some evidence that the relationship between inflation and the returns of certain asset classes tends to strengthen over longer horizons. Note that equities, REITs, gold and foreign currency did not have a consistent relationship with inflation and therefore have not been good hedges of inflation.
Overall, these results suggested that only two asset classes have consistently protected against inflation over relatively short horizons: short-term TIPS and commodities.
*Asset classes included are as follows: U.S. stocks (proxied by S&P 500 Index), international developed stocks (proxied by MSCI EAFE Index), short-term bonds (proxied by 2-Year Treasury notes), long-term bonds (proxied by 30-Year Treasury notes), short-term TIPS (proxied by TIPS 0-5 Year Maturity Index), TIPS (proxied by Full TIPS Index), commodities (proxied by S&P GSCI Index), real estate (proxied by Dow Jones U.S. Select REIT Index), gold (proxied by spot gold prices from the Federal Reserve) and foreign currency (proxied by USD$ Index).
Copyright © 2014, The BAM