At the onset of the financial crisis in 2008, the volatility of stock returns increased dramatically as the equity markets plunged. At the same time, U.S. Treasury bond prices shot up. The correlation of bonds and stock prices has been mainly negative ever since.

This makes sense: In times of trouble, we dump stocks and buy safe Treasury bonds, and their prices should move inversely. This also would mean that in better times, we buy stocks and sell bonds, implying that the correlation between Treasuries and stocks should always be negative.

It isn’t. The correlation between the aggregate stock market and long-term Treasury bonds has been mainly positive and rising from the 1960s to the end of last millennium. With the new millennium, the correlation between stocks and Treasuries turned negative, and strongly so, especially around the last two recessions.

What happened? Why did the behavior of stocks and bonds change so much in the last decade? More important, what does this tell us about economic fundamentals and investors’ behavior? In a recent article, we argued that investors’ uncertainty about economic growth and inflation regimes is at the root of the puzzling behavior of stock and Treasury prices.

We take into account that, at any point in time, investors don’t know which economic-inflation regime they are operating in, but they can use historical data and statistics to figure out at least which one is the most likely, as any skilled econometrician would.

Historical Data

Treating investors like econometricians who use historical data to form beliefs about economic regimes is illuminating. It follows from the laws of statistics that if investors are uncertain about the current economic regime, any new data observation leads to large revisions in expectations about long-term prospects.

Stock and long-term bond prices depend on these expectations, and thus large revisions imply large price movements. The constant flow of news into the market generates volatility and price co-movement (positive or negative) as investors’ uncertainty changes over time. Uncertainty decreases as investors observe more data, but it may also increase as the observation of outliers signals changes in economic regimes. We exploit this insight and use stock and bond data to learn about investors’ beliefs and especially their uncertainty about future economic growth and inflation.

Before describing the implications of our model for the last decade, we should look at the late 1970s. Our estimates suggest that at that time investors faced large uncertainty about whether the U.S. would enter a persistent stagflation regime. Any consumer-price data that were above expectations were taken as an indication that the U.S. was transiting into such a regime, which brings about low growth and high inflation. The former makes stock prices decline, the latter makes long-term yields increase. Thus, data-driven fluctuations in investors’ beliefs about a stagflation regime pushed the prices of stocks and Treasuries to move together, and increased volatility for both.

In the recent Great Recession, the opposite occurred. The market now fears deflation, which is accompanied by low growth, as we know from the Great Depression. In this case, CPI data above expectations are great news for the economy, as investors interpret them as a signal that the bad deflation regime could be averted.

Deflationary Regime

Stock markets cheer higher-than-expected CPI, and Treasury yields increase in expectation of accelerating inflation. Thus, data-driven beliefs about entering a deflationary state push the prices of stocks and Treasuries in opposite directions. Large uncertainty about deflation also increases the volatility of stocks and bonds, as we observed in the data. In other words, the signaling role of inflation dramatically alters the joint behavior of stocks and bonds, with important implications for risk and returns of stock and Treasury investments.

Our model’s estimates also suggest that investors may have had a relatively strong belief that the economy may enter into a deflationary regime in 2001. Federal Reserve Chairman Alan Greenspan expressed such concerns then as part of the central bank’s decision to cut interest rates to then-historic lows, which some commentators have designated as one of the causes of the housing bubble in the subsequent five years.

Our model has numerous implications for the behavior of stocks and bonds. For instance, researchers have been puzzling over why the new millennium brought the breakdown of the “Fed model” -- the positive relationship between stock earnings yields and Treasury yields. Our model shows that the signaling role of inflation would predict just that: An increase in the probability of entering a deflationary regime will lower Treasury yields (because expected inflation is lower) but increase stocks’ yields (because the expected economic growth is slower).

Similarly, the change in correlation between stocks and long-term Treasuries returns from positive to negative also implies that U.S. bonds moved from being a risky investment -- requiring a risk premium -- to a hedge, requiring a discount.

That is, investors purchasing long-term Treasuries in recent times would tend to receive a low average return on their investment, because bond prices have been bid up for their hedging properties. Treasuries are now considered a haven. However, this will only be true until the return of an inflationary regime. Caveat emptor.

(Alexander David is professor of finance at Haskayne School of Business at the University of Calgary. Pietro Veronesi is professor of finance at the University of Chicago Booth School of Business, and a contributor to Business Class. The opinions expressed are their own.)

Read more opinion online from Bloomberg View.

To contact the writers of this article: Alexander David at adavid@ucalgary.ca; Pietro Veronesi at Pietro.Veronesi@chicagobooth.edu.

To contact the editor responsible for this article: Max Berley at mberley@bloomberg.net.