The correlation of bond and stock returns

(MoneyWatch) Over the last four decades, the correlation between stock indexes and government bond returns has been highly unstable. For example, one study found that the daily correlation between stock and bond indexes is on average modestly positive, but has ranged anywhere from +0.60 to -0.60 over the past 40 years and exhibits sharp changes of 0.20 or more.

You can also see the instability when looking at the quarterly correlations. While the quarterly correlation was just 0.07 for the period 1970-2011, we see a very different story when we break the periods down:

• 1970-79: 0.49
• 1980-89: 0.36
• 1990-99: 0.19
• 2000-11: -0.55

The authors of a 2010 study, "Comovement and Predictability Relationships Between Bonds and the Cross-Section of Stocks," analyzed the links between government bonds and the cross-section of stock returns and found some interesting connections between stocks and bonds. The following is a summary of their findings:

• Bonds co-moved more strongly with "bond-like" stocks. Large stocks, long-listed stocks, low-volatility stocks, stocks of profitable and dividend-paying firms, and stocks of firms with mediocre growth opportunities were more positively correlated with government bonds. In other words, portfolios of bond-like stocks -- stocks with the characteristics of safety as opposed to risk and opportunity -- showed higher correlations with long-term bond returns.
• Stocks that are relatively more "speculative" were relatively less connected to bonds. Small-capitalization stocks, young stocks, high-volatility stocks, non-dividend paying stocks, and unprofitable stocks all displayed strongly negative coefficients.
• Both high-growth and distressed firms were less like bonds than were stable and mature firms.
• Bonds and bond-like stocks also exhibited similar predictability characteristics. The same yield curve variables used to predict returns on government bonds (such as the term spread and combinations of forward rates) also predicted the returns on bond-like stocks relative to speculative stocks. When predicted bond returns are high, the returns on bond-like stocks were also higher than the value-weighted average stock return. The returns of speculative stocks were significantly lower than the average. The explanation is that bonds and bond-like stocks are linked through common shocks to real cash flows. For example, a business cycle contraction is often associated with lower inflation and rising bond prices and will generally have less of an impact on the cash flows of stable, mature firms versus more speculative growth firms or already-distressed firms. Such effects contributed to the relatively stronger co-movement between bonds and bond-like stocks.
• These patterns remained even when bonds and stock indexes were moving in opposite directions.

The authors found that these relationships were driven by a combination of effects including correlations between real cash flows on bonds and bond-like stocks, correlations between their risk-based return premia and periodic flights to quality. For example, an increase in risk aversion increased the stock risk premium and may lead to better performance of long-term bonds and the stocks of stable, mature firms than the stocks of more speculative firms.

Investor sentiment is another link between bonds and bond-like stocks. Periods of high investor sentiment were characterized by high demand for speculative stocks relative to demand for bond-like securities. On the other hand, "flights to quality" are periods when investors shift money toward "safe" (bond-like) assets. In other words, bonds and bond-like stocks departed from riskier stocks as sentiment fluctuated.

The authors' findings complimented prior research, which found that bond returns tended to be high relative to stock index returns when the implied volatility of stock index options increased and that the positive correlation between stocks and bonds switched signs in stock market crashes.

These findings offer insights into the cross-section of stock and bond returns. For example, they help explain the performance of low-volatility stocks. (They have provided similar returns to high-volatility stocks, an apparent anomaly.) The answer seems to be that the low-volatility stocks are more bond-like. In fact, regression analysis shows that they do have exposure to the term premium (and the value premium as well).

In other words, while low-volatility stocks are an anomaly for the capital asset pricing model, their returns are well explained (they don't generate alphas) by a five-factor model (beta, size, value, credit, and term).