Forecasting Interest Rates

There was lots of action in financial markets last week, with much of the attention focused on the U.S. Federal Reserve. The interest rate on a 10-year U.S. Treasury bond edged up 10 basis points early in the week in anticipation that the Fed might finally raise its target for the short-term interest rate. But it shed all that and more after the Fed announced it was standing pat for now.

Price of CBOE option based on 10-year U.S. Treasury yield; to convert to the Treasury yield itself divide by 10. Source: Google Finance.

If bond investors were rational and unconcerned with risk, the 10-year rate should correspond to a rational expectation of what the average short-term rate is going to be over the next decade, a conjecture known as the expectations hypothesis of the term structure of interest rates. If instead the 10-year rate was above the average of expected future short rates, you’d expect a higher return from the long-term bond than staying short. If you were risk neutral, you’d prefer to go long in such a setting. But if more investors tried to do that, it would drive the long yield down and the short yield up.

If the expectations hypothesis held true, it’s hard to see how swings of the magnitude observed this week could be driven by news about the Fed. Although the Fed did not raise the overnight rate this time, it probably will by the end of this year or early next. A difference of 50 basis points for 1/4 of a year amounts to a difference of (1/40)(50) = 1.25 basis points in a 10-year average, only a tenth the size of the observed movement. Maybe people see the Fed’s decision as signaling a change in the interest rate that it will set over a much longer period, not just 2015:Q4. Or perhaps the nature of this week’s news altered investors’ tolerance for risk. To the extent that the answer is the latter, can we describe empirically the forces that seem to be driving the changes in risk tolerance and quantify the magnitude of the changes over time?