My last post dove into the swirling waters of stocks as an inflation hedge. Today I intend to swim even deeper. Put on your life preservers, and take your sea-sickness pills. Here comes a deluge of data, and the ride is expected to be choppy. I can’t guarantee it will be all that thrilling, though I have a fair chance of making you queasy by the end.
If you missed my last post, you might want to read the conclusion there to catch up on the whole issue. In brief, I’ve made the case in the past that stocks provide a useful but imperfect hedge against inflation. Since then, I’ve come across articles and research indicating that stocks aren’t such a good inflation hedge. I feel that my last post successfully refuted the evidence presented in one of these articles. So, climb aboard the U.S.S. Mindfully Investing as we sail once again into the debate surrounding stocks as an inflation hedge.
“Conventional Wisdom” about Stocks and Inflation
Our first destination is an article by Howard Gold in 2012 at MarketWatch titled “Don’t Count on Stocks as an Inflation Hedge”.* The article starts with:
- “You’ve heard it so often you can probably repeat it in your sleep: Equities are the best protection against inflation.”
I was a bit perplexed when I first read this, because personally, I’ve seen this conventional wisdom applied to gold investments much more than it’s applied to stocks. Regardless, Mr. Gold mobilizes three ships to carry his assertion that stocks are a poor inflation hedge:
- Stocks and inflation have a “strong” negative correlation, meaning that stocks do poorly when inflation rises.
- People confuse the long-term return from stocks with their ability to hedge inflation, which are two different things.
- Academic research established long ago that stocks are a poor inflation hedge.
Looking across all the articles and research I’ve read, these three ships are a good synopsis of the most commonly used arguments against stocks as an inflation hedge. This post will test the sea-worthiness of the first ship, while my next post will examine the last two.
Navigating the Data
The Gold article provides useful links to research supporting the “strong” negative correlation between stocks and inflation. One link is to a great summary from 2012 about the relationship between stock returns and inflation by Credit Suisse, which is largely based on the work of Elroy Dimson, Paul Marsh, and Mike Staunton. Here’s one of the most compelling graphs in the Credit Suisse Report.
The graph uses stock and inflation data from 19 countries across 112 years. It seems to show a negative relationship between stocks and inflation. As inflation rises, inflation adjusted (real) stock returns decline. This seems to contradict my own analyses (see here and here) using U.S. S&P 500 data from Robert Shiller, which showed no clear relationship like this.
Why were my past results different from the Dimson et al. research? To answer that question, I created a similar graph using the U.S. data from Shiller as shown here.
Batten down the hatches! My new U.S. stock graph looks pretty similar to the Credit Suisse multi-country graph. Did my previous analysis only see the tip of the data iceberg? Before I abandon ship on the idea of stocks as a decent inflation hedge, I can’t resist looking below the surface.
To start, the above graph shows that U.S. stocks perform pretty consistently in real terms from moderate deflation (average -4%) to moderate inflation (average +4%). There’s actually no decline in real stock returns across this most common range of inflation rates. What’s causing real stock returns to decline somewhere around the 5% inflation threshold? A look at nominal stock returns instead of real returns could help answer that question.
Removing the inflation correction from stock returns clarifies that stocks have provided relatively consistent average annual nominal returns across a wide range of inflation rates. There’s no clear negative relationship between the two. Except for the extreme deflation case, the nominal returns were all within about 7 to 13%, regardless of the prevailing inflation rate.
Typically, if your going to look for a potential correlation between two variables, the first step is to create a scatter plot and calculate a correlation best-fit line. Going back to inflation adjusted returns, here’s the scatter plot of real returns versus inflation provided in the Credit Suisse report, although for some reason they decided not to show a best-fit line or the level of correlation.
Although I don’t see it, the Credit Suisse authors claim there is a slight downward slope in this plot. But they also note:
- “Nevertheless, the correlation between the series is only mildly negative and so this relationship must be interpreted with caution…There is a tremendous degree of return variation that is unrelated to inflation, reflecting the substantial volatility of equity returns.”
They resist saying it, but put another way, the negative correlation between real returns and inflation is actually poor. To verify that, here’s my graph using U.S. real stock return and inflation data.
For U.S. real stock returns, the correlation with inflation has a paltry R-squared value of 0.13. (R-squared is the “coefficient of determination” and shows how close the data are to the fitted regression line.) In my past work in environmental science, we like to see R-squared values above 0.3 before we would consider one variable potentially predictive of another. In my experience, the level of correlation between U.S. real stock returns and inflation is almost meaningless. Just to see what happens, let’s again dispense with the inflation correction and plot the same data using nominal returns.
Once again, the apparent relationship disappears using nominal stock returns.
Math to the Rescue
There’s an obvious math problem lurking below the surface that is rarely mentioned in the articles and research I found. A few sentences in the 64 page Credit Suisse report make brief note of this problem:
- “We are estimating a relationship between real returns and inflation. Inflation therefore appears in the regression both as an independent variable and (indirectly) as a component of the dependent variable…so the partial hedge indicated by [these data] may understate the hedging ability of the assets…” (my emphasis added).
Specifically, when you calculate real returns from nominal returns, the inflation rate is in the denominator. The dependent variable (returns) becomes a function of the independent variable (inflation) in the correlation. Here’s an example of nominal returns and inflation rates where I had a computer randomly select values between 0% and positive 20% for each variable. The top graph uses nominal random returns and the bottom graph uses real random returns (which I called “normalized”).
Converting to real returns creates an instant correlation! I ran this random simulation 20 times just to make sure the above graphs were not outliers, and the average nominal R-squared value was 0.01 and the average real R-squared was 0.50. So, the above graphs aren’t a fluke of random number generation.
Math tells us that looking at the relationship between real returns and inflation is double counting the inflation variable. The fact that the correlation between the two is so low for U.S. stocks indicates that stock returns are indeed highly variable, as Credit Suisse mentioned. I’d argue that a much cleaner way to look at the relationship between returns and inflation is to use only nominal returns. After the analysis is done, it would still be reasonable to consider how the real value of the stock returns under various inflation conditions might impact your investment plans and goals. But including real returns in the analysis upfront muddies the waters, biases the results towards negative correlation, and inherently favors a hypothesis that stocks are a poor inflation hedge.
Cruising Upstream
Let’s look again at a bar graph of real returns broken down by percentiles of historical inflation rates. But this time, let’s examine how stock returns versus inflation contribute to the real returns as shown in this graph.
The orange bars are just the same real returns shown in my first bar graph in this post. The blue bars take the all-time nominal Compound Annual Growth Rate (CAGR) since 1871 (a value of 10.1%) and subtract the average inflation rate for that inflation percentile. You’ll note that, except for the deflation case (low 5th percentile), the blue and orange bars for each percentile of inflation are nearly the same throughout the graph. This shows that inflation itself drives the apparent negative correlation between real returns and inflation. Although stock returns are highly volatile on a year-to-year basis, the overall average nominal returns of stocks, minus the inflation rate for any given inflation percentile, does a pretty good job of estimating the real returns across the entire range of historical inflation conditions.
A good analogy is cruising up a river in a boat. Nominal returns are the forward speed generated by the boat’s motor when the boat is cruising through still waters. When the motor is run steadily at a moderate power level, most of what determines the boat’s net rate of progress upstream (real returns) is the velocity of the opposing water currents (inflation), not the output of the motor (nominal returns). If the currents against the boat are strong enough (high inflation), the boat actually makes no forward progress and will be pushed back downstream (negative real returns). If the currents are travelling in the same direction as the boat (deflation), then the currents assist the boat’s forward progress (augmented real returns).
Of course, in real life, the motor of nominal stock returns is not steady. As noted in the Credit Suisse report, stock returns fluctuate wildly, which makes it difficult to differentiate inflation from other factors effecting returns at any given time. Because these other factors are myriad and complex, for most investors, variations in stock returns appear essentially random. And the data show that these random variations mostly overwhelm any potential correlation between nominal returns and inflation. Random chance means that stock fluctuations can sometimes coincide with inflation changes and sometimes not.
Leveraging the Data
I wondered if part of the problem with the poor correlation between the S&P 500 nominal returns and inflation might be due to the use of annual average returns, which limits the data set to just 147 points, one for each year of the entire history since 1871. More importantly, using annual returns assumes that all results are from a one-year investment period, but almost no one actually invests in stocks that way.
I was curious if annualized nominal returns (CAGR) over various investing periods might better represent real-life investors and show a better correlation with concurrent inflation rates. So, I calculated the CAGR and geometric inflation rate for all possible investing timelines since 1871. Each calculated data point represents starting and ending a stock investment at different times. Thus, one point represents investing in the period from, for example, 1871 to 1995. Another point represents, for example, a period from 1871 to 1900. Yet another point represents 1972 to 1982, and so on. This process is repeated until every possible long (up to 147 years) and short (down to 1 year) investing period for the entire S&P 500 stock history is calculated. Here’s a scatter plot of the more than 10,000 data points generated by this process.
It’s still looks random to me. And if anything, there is a slight positive relationship between nominal annualized returns and annualized inflation, though the correlation is very weak. It seems unlikely that the stock returns for any group of real-life investors, who invested at different times and over different periods, would be predictably related to the inflation rates occurring during their varying investing periods.
Conclusion
Closely examining the correlations between stock returns and inflation reveals a few leaks in the ship of “strong negative correlation” that is often mobilized in this debate. Both my simple analysis and many of the details in the Credit Suisse report show that the apparent negative correlation is not that clear or strong. Instead we see a weak negative correlation using real returns and a lack of correlation using nominal returns, which means nominal returns are essentially random relative to inflation.
Using the boating analogy, many people seem to argue that the poor relationship between returns and inflation means that there’s no experienced boat pilot prudently revving up the motor of nominal returns when inflation currents increase; this makes stocks a poor hedge against inflation. Instead, the motor of nominal stock returns seems to be operated by a drunken novice who fluctuates the motor’s output based on personal whim. Because of our drunken pilot, one could equally argue that stocks are mostly independent of inflation. Therefore, stocks can often resist the ebb and flow of inflation currents.
It seems to me that the first ship of “strong” correlation is swamped, although not quite sunk to the bottom. Unlike the Credit Suisse report, I didn’t look at data from any countries beyond the U.S. However, given that the U.S. represents more than half of the world stock market size, it seems like an analysis of U.S. data is more relevant to most investors than an analysis that includes developing countries like South Africa, India, etc.
In my next post, I’ll conduct leak inspections on the last two ships in this debate: 2) confusing long-term stock returns with their inflation hedging ability 3) the established academic research indicating stocks are a poor inflation hedge.
* It’s interesting that almost all the articles I found on this subject were written right around 2011 to 2012, when everyone seemed to be worried that inflation was about to accelerate and swamp their investment portfolios. In fact, inflation rates declined a little in the ensuring years, which shows, once again, the difficulty of predicting the future.
