Abstract

Inflation, a quiet but growing concern, is complicated by its unpredictability in timing and severity. A survey of 110 years of inflation data suggests that Treasury Bills track inflation better than equities or bonds, and this result is robust across 19 countries. In most periods of high inflation in these countries, however, equities produced much higher, though […]

Introduction

Inflation can decimate the value of any investment portfolio. The average annual inflation rate from 1900 to 2011 (112 years) was 3.07%. In the 1970s and 1980s the average annual inflation rate was 6.28%. Treasury Bills offered returns averaging 7.62% during that period, commensurate with the high inflation levels. Within the last 20 years, from 1992 to 2011, however, a more benign inflation environment has prevailed with average annual inflation rates of 2.50%. In the last 4 years, from 2008 to 2011, annual inflation rates averaged just 1.82%. If inflation spikes, will investors be prepared?

A cursory examination of annual inflation, employing data from Dimson, Marsh, and Staunton (DMS)¹, is presented below in Figure 1. Visual examination reveals the high period of prolonged inflation in the period from 1970s to 1980s. Prior to the mid-1950s, inflation appears to have exhibit much more volatility with even some years having negative inflation. We have not experienced a negative inflation year since 1954. Inflation decreases purchasing power alternatively negative inflation would have increased purchasing power.

Fig. 1: US Inflation Rates 1900-2011

Annual US inflation rates based on Dimson et al. (2012)

Consulting the DMS dataset, we identified 75 periods of high inflation across the 19 countries in our sample. High inflation periods are defined as 5% or greater annual inflation. In these periods, we find that the decrease in purchasing power averaged 53% with an inter-quartile range of (32%, 80%), the worst case in the data set was in Germany over the period from 1913 to 1923 with a 99.999% drop in purchasing power. These periods averaged 10.67 years with an inter-quartile range of (5, 14.5) years. The high inflation periods cover 24% of the total country-years in the data set.

Looking at the total returns for the three asset classes (bills, bonds, and stocks) represented in the DMS set, we find that stocks had the best chance of beating inflation during these periods, more than twice that of bills or bonds. An investment in equities outstripped inflation in 37 of these 75 cases (49%) while an investment in bills or bonds outstripped inflation in, respectively, only 24% and 21% of the cases.

Bills performed better than bonds in that the average return on bills outstripped that of bonds in 68% of our high-inflation periods. However the number of periods in which bills beat inflation was only marginally better than that of bonds. Care must be taken however, as even equities’ real returns are negatively skewed: the mean real return across inflationary periods was -10.42%. Furthermore, these figures assume reinvestment of all interest and dividends; that is, no spending or payments for taxes were deducted. While taxes are not payable by pension plans or charities, even those institutions require annual distributions to pensioners or for charitable purposes. For this reason, the chances of emerging unscathed from a period of inflation are substantially lower than these numbers suggest.

Fig. 2: Number of Countries in Our Sample Experiencing 5% or Greater Annual Inflation

Additionally, equities were far more volatile than Treasury Bills. The most recent period of sustained high inflation in the US was from 1968 to 1982. From 1968 to 1972, an investor would have made 23.7% on his stock investment, during which time inflation increased only 19.6%, but then would have lost all of those gains (and then some!) by the end of 1974, ending the year with just 58.4 cents for every dollar invested at the end of 1972 while inflation continued to increase by a total of 30.6% from 1972. At the end of 1974, the investor’s stock portfolio would have lost 27.2% in nominal value and 50.6% in real value from its previous peak at the end of 1968. How many individuals or investment committees are able to “stay the course” after two consecutive years of such massive losses (18.5% and 28.4% in 1973 and ’74, respectively), during which time an investment in Treasury Bills gained 42.1%, losing only 2.7% in real terms? Only later did stocks recoup these losses but even then, over this period, they were less profitable than an investment in Treasury Bills.

Though volatile, stocks generally outperformed bills and bonds during periods of very high inflation, that is periods in which the value of the currency dropped 75% or more. Out of our 75 high-inflation periods, there were 23 periods of varying length, each having such a drastic total loss in currency value. Interestingly all of them had an average annual inflation rate over 7%. The returns on stocks exceeded inflation in 52% of those periods, while bonds exceeded inflation in 30% of the periods, and bills exceeded inflation in only 4%. Average annual real returns during such periods were: stocks -1.42%; bonds -0.11%; bills -5.97%.

The situation becomes even more dire once spending and taxes are factored in. Let us assume that the investor spent 3% of the portfolio value each year (e.g. for retirement living expenses, pension or charitable distributions)—this is not a high number considering that private foundations are required by law to expend 5% of their portfolio value each year. With the 3% spending assumption, portfolios invested in stocks, bonds, and bills would have lost the percentages of real value (that is, losses after adjusting for inflation) set out below in Table 1. Consider the same numbers for an investor who, unlike a pension plan, university, or foundation, must pay taxes. Assume that each year such an investor pays 25% of the nominal increase in portfolio value in state and federal taxes. Tax rates, of course, are not constant and can be deferred by various strategies, but nominal earnings that do not even keep up with inflation are still taxed. Based on the assumption of a 25% tax rate, the figures are as set out below:

Loss of Real Portfolio Values in the United States 1968 to 1981

	Stocks	Bonds	Bills
Before Spending and Taxes	-10.42%	-42.80%	-4.79%
At 3% annual spending	-41.52%	-62.66%	-37.84%
3% Spending and 25% Taxes	-59.74%	-67.65%	-50.88%

There were periods of widespread high inflation around World War I (1914-1918), World War II (1945-1949), and again in the 1970s. Grouping the country periods roughly into these categories, the average loss of value of currencies during the periods around the wars was about 56%; during the ‘70s the loss was 77%, during the other periods 30%. The 1970s offered the best chance to beat inflation by investing in stocks, bonds, and bills; the war periods offered the worst chance. The full results are set out by period in total below.

Asset Performance During High-Inflation Periods

Period	Currency Devaluation Due to Inflation	Countries with Stocks Beating Inflation	Countries with Bill Beating Inflation	Countries Bond Beating Inflation	Countries with Bonds Beating Bills	Countries with Stocks Beating Bills
WW I	57%	21%	11%	5%	95%	68%
WW II	55%	35%	0%	0%	59%	94%
1970s	77%	84%	63%	53%	68%	84%
Other	30%	52%	33%	33%	48%	71%
Overall	53%	49%	21%	21%	68%	77%

Losses from inflation may be tolerable when inflation is “low,” but at higher numbers, however, these losses can become ruinous. Of the 75 high-inflation periods we identified, 23 resulted in currency losses of over 75%. To recoup such losses, a portfolio would have to quadruple in value.

The Fischer Effect

The Fischer Effect (1930) hypothesizes that in any period, with well-functioning capital markets, nominal interest rates equal expected real interest rates plus expected rates of inflation. With US Treasury Bills paying close to 0%² as of July 2, 2012 and inflation nearly 1.81%³ as of June 2012, the “real rate” for investors, recently, has been essentially minus 1.8%. Skeptics of this calculation argue that the joint hypothesis test fails in that either Fischer’s hypothesis is mis-specified or inapplicable because of failure of the assumption of well- functioning capital markets. One could also argue the Federal Reserve has provided for capital markets that are non-normal in nature by intervening to keep nominal interest rates at or close to zero. In any case, Treasury Bills currently offer very low to zero returns to investors.

The stock market has offered no refuge from negative real returns: stock market indexes are selling at or below their levels of 2000, so that the nominal return on stocks is approximately 0% over the last 12 years. The purchasing power of one US dollar, as measured by the Consumer Price Index (CPI), has fallen to just under seventy-five cents over this same period, according to the US Bureau of Labor Statistics inflation calculator⁴. The real value of a stock portfolio, therefore, has actually fallen about 25% since 2000.

This paper examines the relationship between inflation and asset prices and investment strategies. Using the DMS data set, we first examine this relationship over the very-long term—112 years’ annual inflation data, and then over the medium-term, approximately 50 years of monthly inflation data. Our methodology centers upon creating “optimal inflation tracking” baskets of traditional assets and other, less traditional investment strategies. Our inquiries focus on the following: the optimal composition over time, how the composition changes over time, and whether the composition is consistent.

We find that for the majority of time, Treasury Bills have been the largest allocation within the optimal tracking basket for inflation. This result appears robust to examination across different countries. Also, we find that long term bonds have been extremely unpopular in our inflation tracking optimal portfolios. Interestingly enough, within the US, we find evidence linking Fama-French (1993)’s factors mimicking portfolio returns, HML and SMB, to inflation as well.

Prior Research

The volume of published research concerning inflation is vast and ever growing. Interested readers are referred to excellent reviews by Fabozzi (2001) and Cooray (2002). We briefly highlight some of the more relevant research papers on inflation and asset prices. Fama (1975) examines Treasury Bills and expected inflation and finds that from January 1953 through July 1971, the one- to six-month nominal rates of interest correctly employs all available information about expected inflation. Real rates are constant and nominal rates are a good predictor of expected inflation. Fama and Schwert (1977) examine various assets ability to hedge against expected and unexpected inflation over the period from 1953 to 1971. They find evidence that short-term US Government Bonds and Treasury Bills completely hedged against expected inflation and that private residential real estate hedged against both the expected and unexpected component of inflation. They also found that common stocks were actually negatively related to the expected component of inflation.

Gorton and Rouwenhorst (2006) studies equally-weighted portfolio of long commodity futures over the period from July 1959 to December 2004. They find that commodity futures are positively correlated with inflation, unexpected inflation, and changes in expected inflation. Twomey, Foran, and Conor (2011) examine whether managed futures can provide a hedge against inflation. They employ the CISDM Index which is an equally weighted index of underlying managers over the period from January 1980 to February 2011. Arnott (2011) argues given the effects of the 3Ds – deficits, debts, and demographics, investors should start preparing for the wealth eroding effects of inflation. He proposes employing tactical management across “an expanded inflation-protection asset class.”

Fama and French (1993) factors SMB and HML were originally linked to macro-economic variables by Liew and Vassalou (1999). Moreover, their relationship to the macro economy has been extended to include inflation initially by Kelly (2003), and was further examined by Fajardo and Fialho (2010). The results in this paper support such research findings; we postulate, however, that this relationship is much more complex than previously hypothesized.

The structure of the paper begins with the first section describing the methodology of building inflation optimal tracking portfolios. Next, we describe the different data sets employed highlighting the limitations and cautioning readers with regards to interpreting our results. Finally, we present our empirical results and conclusion.

Methodology

In order to track inflation, we employ a very simple optimization technique. The objective function is to minimize the squared deviations from a basket’s return and the target’s return. The target is percentage change in inflation over non-overlapping periods. The basket consists of a given set of assets. To solidify the understanding for our readers, we will present a simple example.

Our data set consists of four vectors: (1) inflation, (2) bills, (3) bonds, and (4) stocks. Each element within the vector is an annual rate of return. If we employ 10 years of data, each vector is 10×1. The objective is to find weights on the vectors (2), (3), and (4), such that the sum of squared errors is minimized. These weights in turn determine the “optimal” tracking basket for inflation over that given period. In mathematical notation:

Assuming a ten-period sample with three assets, R is a matrix (10×3) of asset returns, and is a vector (3×1) of weights. The objective is to find weights w such that the sum of squared excess returns over inflation, (3×1), is minimized. Additionally, non-negativity constraints are added so that no shorting is allowed for all three assets (k=3) and weights sum to unity⁵.

It is important to note that this is an in-sample optimization. Our goal is not to create a trading strategy that attempts to predict inflation; rather, we aim to determine ex-post what composition of assets and investment strategies best tracked inflation from the historical perspective. The optimization process is rolled forward each period while including the next period’s observation and dropping the oldest observation. The reason we roll this analysis is to determine the time-series behavior of the weights and the composition. Second, this methodology assumes the optimal weights to be non-negative (no shorting) and sum to one (no leverage or holding cash) over the entire period under consideration. We assume rolling 10-year windows from 1900 to 2011 for the first part of our analysis.

Tracking Error

Tracking error measures the standard deviation of the time series of differential returns. Differential returns are defined by optimal portfolio returns minus inflation rates over time. We see that over our long history tracking error and volatility of inflation appears to move closely together. In the high-inflation period of 1970s to 1980s, tracking error increases as inflation becomes more volatile. Both inflation volatility and tracking error is measured over a 10-year rolling window. Of particular note is how closely inflation volatility determines tracking error (R²=0.92).

Fig. 3: Tracking Error for US Inflation Employing Treasury Bills, Bonds, and Stocks

Optimal Weight to the “Classic” Portfolio US Evidence

We define the “Classic” portfolio as that basket that consists of only bills, bonds and stocks. In the latter section we shall expand the assets and investment strategies examined to include a larger cross-section of candidates. Additionally, we will examine monthly data which allows for potentially more variation of the weights intra-year. Cautions, however, should be taken as the number of observational years becomes more limited.

Fig. 4: Tracking Portfolio Weights Based on Annual Data

In the analysis above, we notice that for the majority of the time, the biggest weight within the optimal tracking portfolio belongs to Treasury Bills. Our result supports Fama (1975), which concludes that the Treasury Bills are the best predictor of future inflation. Notably apparent is the low weights to both bonds and equities over this long history. When we focus on the most recent period, however, we notice that bonds and stocks have started to gain more relevance as their summed weighted breach the 10% allocation range. In the latter section, we dig a bit deeper into these latter years to discover that other assets and strategies have recently gained favor in composition of the inflation tracking basket.

Long-History International Evidence

In Table 3, we examine whether such findings are limited to only the U.S. We note that this relationship is robust across 18 other countries. That is, short-term government debt is the strongest asset when the objective is to track inflation within a country given the Classic assets.

Looking at the U.S. (row 1), we display the quartile and median for tracking error and the Classic asset weights over the time period from 1900 to 2011. Note that the first observation starts in 1909, which is the tracking error determined from 1900 to 1909. The next columns contain quartiles and medians over time for Treasury Bills, bonds, and stocks, by country.

The weights in Treasury Bills by country dominate across the classic assets. In almost every case, the median weight assigned to bills is at least 95%. The lowest median bills weight belongs to Norway, and that is still 86%. The median weight allocation to bonds across countries is 0% consistently. The median weight allocation to stocks across countries is between 0 and 3%.

Country Inter-Quartile Range Analysis of Tracking Error and Weights for 10-year Rolling Optimization

	Tracking Error			Bills Weights			Bonds Weights			Stocks Weights
Country	25%	50%	75%	25%	50%	75%	25%	50%	75%	25%	50%	75%
U. S.	0.0155	0.0250	0.0467	0.9537	1.0000	1.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0304
Australia	0.0247	0.0344	0.0506	0.9192	0.9711	1.0000	0.0000	0.0000	0.0000	0.0000	0.0051	0.0385
Belgium	0.0148	0.0362	0.0741	0.8468	0.9685	1.0000	0.0000	0.0000	0.0575	0.0000	0.0092	0.0625
Canada	0.0142	0.0271	0.0473	0.9119	0.9655	1.0000	0.0000	0.0000	0.0009	0.0000	0.0239	0.0726
Denmark	0.0177	0.0362	0.0515	0.7697	0.9468	1.0000	0.0000	0.0000	0.0000	0.0000	0.0131	0.1240
Finland	0.0276	0.0462	0.0893	0.8042	0.9534	1.0000	0.0000	0.0000	0.0000	0.0000	0.0299	0.0913
France	0.0169	0.0365	0.1062	0.7986	0.9106	0.9876	0.0000	0.0000	0.0976	0.0000	0.0105	0.0602
Germany	0.0142	0.0184	0.1075	0.8591	0.9633	0.9962	0.0000	0.0000	0.0285	0.0000	0.0135	0.0467
Ireland	0.0250	0.0386	0.0541	0.9363	1.0000	1.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0424
Italy	0.0206	0.0375	0.1050	0.8648	0.9901	1.0000	0.0000	0.0000	0.0012	0.0000	0.0000	0.0303
Japan	0.0168	0.0552	0.0984	0.8850	0.9940	1.0000	0.0000	0.0000	0.0256	0.0000	0.0000	0.0114
Netherlands	0.0140	0.0236	0.0403	0.7933	0.9322	0.9936	0.0000	0.0000	0.0396	0.0000	0.0313	0.0917
New Zealand	0.0160	0.0259	0.0415	0.8803	0.9805	1.0000	0.0000	0.0000	0.0766	0.0000	0.0000	0.0194
Norway	0.0226	0.0286	0.0497	0.6859	0.8569	0.9767	0.0000	0.0000	0.1837	0.0000	0.0202	0.1275
South Africa	0.0254	0.0367	0.0455	0.8694	0.9824	1.0000	0.0000	0.0000	0.0643	0.0000	0.0000	0.0276
Spain	0.0262	0.0442	0.0627	0.8223	0.9643	1.0000	0.0000	0.0000	0.0001	0.0000	0.0132	0.1476
Sweden	0.0179	0.0276	0.0513	0.8572	0.9627	1.0000	0.0000	0.0000	0.0593	0.0000	0.0000	0.0412
Switzerland	0.0122	0.0216	0.0444	0.9158	0.9792	1.0000	0.0000	0.0000	0.0007	0.0000	0.0077	0.0376
U. K.	0.0177	0.0348	0.0476	0.9447	0.9992	1.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0305
Europe	0.0159	0.0239	0.0484	0.9230	0.9612	1.0000	0.0000	0.0000	0.0359	0.0000	0.0002	0.0514
World	0.0152	0.0244	0.0473	0.9193	0.9915	1.0000	0.0000	0.0000	0.0000	0.0000	0.0018	0.0502
World ex U.S.	0.0155	0.0231	0.0481	0.9058	0.9651	1.0000	0.0000	0.0000	0.0347	0.0000	0.0102	0.0592

Monthly Data Sets Employed

In this section we attempt to optimally track inflation within the US, employing popular assets and investment strategies. Examination of more recent data allows for a larger more diverse cross-section of potential candidates. We employ 16 candidates loosely grouped into four categories: Classics, Traditionals, Stealth Fighters, and Hedgies. Note that some care should be taken as our data set does not have history dating back to the 1900s as in the prior section. Additionally, our series have varying start times. Although the start dates do vary, the end dates are all consistent—June 2012. In total, 9,335 monthly observations are examined. The components of our groups are detailed below in Table 4.

Assets and Investment Strategies Employed

Strategy	Asset	Dates
Classics	1. Treasury Bills 30-days	Jan-1940-Jun-2012
	2. S&P500	Jan-1940-Jun-2012
	3. Long-Term Govt Bonds	Jan-1940-Jun-2012
Traditionals	4. CCI (Continuous Commodity Index)	Dec-1965-Jun-2012
	5. GSCI (Goldman Sachs Commodities Index)	Feb-1970-Jun-2012
	6. Barclays US Treasury TIPs	Mar-1997-Jun-2012
	7. Gold	May-1968-Jun-2012
	8. FTSE NAREIT All REITs	Jan-1972-Jun-2012
Stealth Fighters	9. Credit Suisse Leveraged Loan	Feb-1992-Jun-2012
	10. JPM ELMI+ (Emerging Local Market Index Plus)	Jan-1994-Jun-2012
	11. JPM EMBI Plus TR	Jan-1994-Jun-2012
	12. BofA ML Convertible Bonds All	Jan-1988-Jun-2012
	13. Barclays US Corporate High Yield	Jan-1983-Jun-2012
Hedgies	14. Fama-French’s SMB	Jan-1940-Jun-2012
	15. Fama-French’s HML	Jan-1940-Jun-2012
	16. CISDM CTA Equal Weighted Index	Jan-1980-Jun-2012

The Classics follow the prior sections and include Treasury Bills, stocks (as proxied by S&P500), and bonds (as proxied by Long-Term Government Bonds), with all data from Ibbotson obtained through Morningstar. Traditionals include two commodities series CCI and GSCI, TIPs, gold, and real estate investment trusts. The distinction between the commodity indices is that GSCI is well-known to have a larger energy weighting whereas CCI has a more balanced weighting methodology. Finally, TIPs have been constructed to give investors inflation exposure explicitly. Unfortunately, TIPs have a very short history. We do find some evidence that TIPs help tracks inflation but this occurs in the most recent periods which correspond to a steady, low-inflation environment. Gold and real estate have both been hotly debated as inflation hedges. Interestingly, both have seen euphoric returns in our data sample period. Unfortunately, our evidence neither favors gold nor real estate.

Data Limitations

We present the varying start dates over time by our four categories to allow for a visual presentation that clearly shows the limitation in our data set (see Figure 5). First, the Stealth Fighters have very limited histories, so their ability to deliver performance when inflation occurs must be evaluated with some caution. In particular, the Stealth Fighters miss the exciting 1970s-1980s period of high inflation. Our Stealth Fighters begin 1983 with the arrival of Barclays US Corporate High Yield. The other series enter our data set afterwards, beginning with BofA ML Convertible Bonds in 1988. Unfortunately, the Credit Suisse Leverage Loan, and JPM ELMI+ and EMBI Plus only arrive in 1992 and 1994, respectively. Thus, although Stealth Fighters may have intuitive appeal, they are unfortunately limited in their data length, which in turn limits our ability to test their efficacy. Extrapolation of hedging benefits to the Stealth Fighters should be undertaken with caution.

The Traditionals have a slightly longer track record coming into our data set in the mid-1960s to 1970, with TIPs arriving as late as in 1997. Finally, our Classics and Hedgies have the longest history, starting in the 1940s, excluding EW CTAs which began in 1980s.

Fig. 5: Count over Time of Potential Candidates to Track Inflation

Results

We begin our analysis by examining our longest data series of the Classics and Hedgies and their ability to optimally track inflation. Figure 6 below contains similar results from our analysis of annual data, namely, the Treasury Bills are the clear winner once again. The lookback period for the optimization is 2 years or 24 monthly observations.⁶ Interestingly enough, the Fama-French factors appear to enter the optimal portfolio in the periods of roughly 1948-1952, 1987-1989, 1992-1993, 1997-1998, and 2008-2009. At times their summed weights even exceed 20% of the optimal portfolio composition. Their dynamics are very interesting as they appear to ebb and flow into and out of the optimal tracking basket over time. Clearly there exists some time-variation structure to their relationship with inflation. Thus, some evidence appears to exist that these factor mimicking portfolio returns may be linked to the contemporaneous changes in inflation even in the presence of the classic assets. This result supports some of the prior research on inflation and Fama-French factors.

Fig. 6: Optimal Weights Over Time for Classics and Hedgies

Next we expand the asset and strategies that may be included in the optimal tracking portfolio to the full list of 16 candidates in Figure 7. Even with the expanded set, Treasury Bills are the dominate component of the optimal tracking portfolio over time. The optimal tracking portfolio continues to include HML and SMB, with very interesting compositions in the most recent 10 year period. In this period, evidence appears that favors some of the Stealth Fighters (leveraged loans and convertible bonds in particular).

Fig. 7: ortfolio Weights Using the Full Asset Basket

Treasury Bill Yields are Too Low

In this section we examine the need to protect against inflation from an investor’s perspective. Clearly, financial advisors and institutional consultants find it challenging to advise investors to include zero- or very low-return assets in their portfolios, limiting the practicality of bills as an inflation hedge. Investors could argue that when the bill rates increase to provide meaningful returns, they could then include them as they are readily accessible, highly liquid investment vehicles. In this section we examine what happens to the optimal allocation when we exclude the Treasury Bills from the candidate set of investments.

Excluding Treasury Bills will provide us with an interesting understanding of the dynamics of inflation basket over time. Surprisingly, our results which include only the Classics and Hedgies but exclude Treasury Bills show that the Fama-French factors receive meaningful allocations even in the presence of stocks and bonds. In the most recent period, at times, the Hedgies even dominate the allocations compared to the Classics (see Figure 8). Stocks and bonds appear to be overshadowed by Hedgies in the recent period from 1980 to June 2012. The CISDM EW CTA strategy receives an increasing but oscillating weight in the more recent period with an allocation of over 50% from February 2010 to October 2010. Our evidence supports the findings of Twomey, Foran and Conor (2011) in that trend-following strategies have some linkage to inflation, especially in the more recent periods.

This ebbing and flowing nature of the optimal trend-following strategy weights highlight the complexity in the structure of inflation. It appears that there is merit to the argument of dynamic strategies akin to trend-following that CTAs generally employ in the ability to hedge inflation.

Moreover, in light of this evidence, more thought should be employed when attempting to model inflation within the context of a linear framework. The relationship between inflation and asset returns and investment strategy returns is clearly not constant or simple over time. Models should incorporate some sort of oscillation and time-variation components. Linear models fail to capture the relationship between inflation and investment returns.

Fig. 8: Portfolio Weights Using Stocks, Bonds, and Hedgies

Finally in Figure 9, when we include all our candidates except Treasury Bills, we find that great beauty emerges. First, the Stealth Fighters show some promise entering into the fray in the periods from 1995 to 2008. Some examples within that period are Leveraged Loans, US Long Credit, Convertible Bonds and Leveraged Loans. The allocations as of the final period in our data set June 2011 are: 24.98% Leveraged Loans, 24.03% HML, 19.74% US Long-Term Government Bonds, 15.77% SMB, 11.38% US Treasury TIPs, and 4.10% ELMI+.

Fig. 9: Portfolio Weights with Just Bills Excluded

When Treasury Bills are excluded from our total sample, we notice many of the others enter into mix in a continued dynamic way. Once again we provide more evidence suggesting that the Arnott’s Stealth Fighters should be seriously considered for those that have no appetite for Treasury Bills.

Out-of-Sample Results

In this section we present out-of-sample cumulative returns from the period from 1980 to June 2012. Suppose one wanted to create an investable product for investors that helps them track inflation. What would be the characteristics of such a product? In order to produce weights that are tradable out of sample we must lag these weights to allow ample time to put on such trades. We lag our weights two month forward. Thus weights computed using data from December are employed in trading at the end of February the next year. Note that all results are gross of any transaction and rebalancing costs.

Fig. 10: Out-of-Sample Portfolio Returns for Various Tracking Baskets

Conclusion

High inflation rates have not been seen in about a quarter of a century. Younger investors may not remember the destructive power of inflation on wealth. In this paper, we refocus our community on an increasingly important risk factor, namely inflation. First, we show that over time the best hedge for inflation has been Treasury Bills. The optimal tracking basket does, however, include some lesser known strategies such as Fama-French factors. Surprisingly, real estate, GSCI, and gold appear much less frequently than less popular investment strategies. We find that investment strategies such as trend-following, as proxied by the CISDM Equally Weighted CTAs, and some Stealth Fighters enter into this portfolio in the absence of Treasury Bills. We also find evidence that some Stealth Fighters such as bank loans and convertible bonds are present in the optimal portfolio. This research seemingly raises more questions than it answers. Some of the difficulties of understanding inflation seem to arise from the complex nature of its dynamics. Time variation and oscillations appear in the fabric when we attempt to understand what constitutes the best tracking portfolios of assets and investment strategies over time. We have merely scratched the surface and we encourage others to further explore the mysteries of the relationship between investment returns and the macro economy.

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