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Mirror Image Seasonality for Stocks and Treasuries?

December 20, 2007 • Posted in Calendar Effects

Do Treasury instruments exhibit a seasonal return pattern? If so, is the pattern related to that of stock returns? In their September 2007 paper entitled “Opposing Seasonalities in Treasury versus Equity Returns”, Mark Kamstra, Lisa Kramer and Maurice Levi investigate the calendar month dependence of returns for U.S. Treasuries and its relationship to that of U.S. stock returns. Using monthly returns for mid-term to long-term Treasury indexes and for a broad equal-weighted stock index over the period 1952-2004, along with contemporaneous economic data, they find that:

  • Over the entire sample period, the average monthly U.S. stock (Treasury) index return is about 1.2% (0.5%), with stock returns markedly more volatile.
  • The medium-to-long end of the U.S. Treasury market exhibits a striking annual cycle, with monthly returns varying by over 0.8% from peak (October) to trough (April).
  • The seasonality of Treasury returns is opposite that of equity returns.
  • These patterns are unlikely to arise from macroeconomic seasonalities, seasonal risk variation, cross-hedging between equities and Treasuries, investor sentiment, Treasury auction seasonality, Treasury debt seasonality, Federal Reserve action seasonality or peculiarities of the sample period considered (data mining).
  • The patterns coincide with that of the Seasonal Affective Disorder (SAD) observed clinically to induce depression among approximately 5-15% of North Americans, and depression is associated with reduced risk tolerance.

A chart in the paper (not shown by request of one of the authors) compares by calendar month for 1952-2004:

Average actual monthly raw returns for Treasuries (Monthly T-bill Return), calculated as a simple average by month across 5-, 7-, 10- and 20-year maturities and adjusted to remove the special January seasonal in bond returns (less than 0.06%).

Estimated monthly Treasury returns based on the change in the proportion of SAD-affected individuals actively suffering from SAD (Onset/Recovery Return), centered on the 0.5% mean return for Treasuries. This series represents the movement in the monthly return for Treasuries directly attributable to SAD.

The modeled effect of SAD tracks the actual raw seasonal pattern well. The peak and trough are within a month of matching. The decline from October to mid-spring and the rise from mid-spring to June are similar for the two plots.

Another chart in the paper (also not shown by request of one of the authors) compares by calendar month for 1952-2004:

Average actual monthly raw returns for a broad equal-weighted stock index, adjusted to remove the January tax-loss selling effect (roughly 4%).

Estimated monthly stock returns based on the change in the proportion of SAD-affected individuals actively suffering from SAD (Onset/Recovery Return), centered on the 1.2% mean return for stocks. This series represents the movement in the monthly return for stocks directly attributable to SAD.

While the model generally tracks the monthly pattern of actual returns fairly well, it does not explain the November peak in actual returns.

In summary, monthly returns for mid-term to long-term Treasuries exhibit a seasonality that is roughly the mirror image of that for stock returns, with November standing out as an exception (strong for stocks and Treasuries).

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