Friday, June 22, 2012

This post describes a methodology for using the current yield curve to forecast future interest rates.

In the current economic environment, the direction of interest rates is a critical issue for many investors -- especially for retirees. You probably know that you can use the yield curve to forecast the direction of the economy. But, did you know that you can also use the current yield curve to forecast the shape of the yield curve one, two or three years or more in the future? Read on.

The Bond Market's Forecast of Interest Rates 1, 2 & 5 Years From Now

 Market Forecast of Future Yield Curve/ Interest Rates

In the graph above (click to expand), the heavy black line is the current yield curve (as of June 15, 2012). The other three lines are the yield curves as they are expected to be 1, 2 and 5 years in the future. The shape of the future yield curves was derived directly from the current yield curve.  As you can see from the chart, the forecast is for rates to remain depressed, even as they rise gradually over the next five years. Two years from now (the green line), the one-year rate is forecast to be barely above 0.5%; five years from now (the dotted red line), the five-year rate is forecast to still be less than 3%.

Deriving Future Yield Curves From the Current Yield Curve

To understand how this model/spreadsheet works, consider the following. If we know the current one year interest rate and the current two year interest rate, we can calculate
what the market expects the one year interest rate to be one year from now. It is the rate such that the proceeds of a one-year treasury purchased now and re-invested one year from now will yield the same ending portfolio as a two-year treasury purchased now and held to maturity.

For example, according to the Department of the Treasury, as of June 15 the yield on one-year treasuries was 0.18%, and the yield on two-year treasuries was 0.29%. As a result, if you bought a \$1,000 one-year treasury bill it would be worth \$1,001.80 when it matures in one year; a \$1,000 two-year treasury would be worth \$1,005.81 when it matures in two years. This suggests that the market expects one-year rates to be 0.40% a year from now; in that case, if you invested the \$1,001.80 from the maturing one-year T-bill in a brand new one-year T-bill, two years from now you would have \$1,005.81 -- the same as you would have if you had bought a two-year note now.

(The above results are based upon the June yield curve. See below for an up-to-date forecast.)

Lather, Rinse, Repeat

Using a similar analytical process, one can derive the expected rate for one-year bills two years from now, three years from now, and so on. In fact, all of the remaining calculations in this model use a similar analytical technique. For example, by comparing 5-year treasuries to 8-year treasuries you can derive the expected rates for three-year notes 5 years from now. (Interested readers can see the appendix for additional discussion.)

No Guarantees

Of course, it goes without saying that this is all theoretical. There is no guarantee these forecasts will prove to be accurate any more than the yield curve's "forecast" of the economy is infallible. In addition, I have simplified some of the calculations.

Finally, in today's environment the interpretation may be clouded by the fact that market rates are being "manipulated" by non-free-market forces. With various forms of quantitative easing, the Fed has inserted itself into the picture to an extent we have not seen before. Still, this is the best way I know to capture what "the market" thinks; at a minimum, it is a useful starting point when thinking about future interest rates.

For More Up-to-Date Interest Rate Forecasts

Note: I update this graph very infrequently.  For the most recent forecast of 1 and 5-year rates five years from now, see the March 2013 market update. For an even more up-to-date, and more encompassing, forecast you can download the yield curve forecasting spreadsheet and input current yield curve data from the Treasury.

Note: calculations assume no taxes or commissions.

Related Materials

Interest Rate Forecast for 5-Year Treasury Notes: Uses this methodology to forecast rates for a single maturity (5-Year Notes) for the next 5 years.
100 Years of Interest Rate History: A graphic history of U.S. interest rates.
Daily Treasury Yield Curve Rates: the Department of the Treasury's constant maturity series. Updated daily.   Enter current data from this site into the interest rate forecast spreadsheet to get an updated forecast.
Barron's U.S. Treasury Notes & Bonds Listing: Allows more accurate estimate of interest rates for maturities not covered in the treasury constant maturity series (e.g., treasuries maturing in 4 years or 8 years). Updated weekly.
Al's Future Yield Curve Model/ Spreadsheet: My spreadsheet that derives future yield curves/ interest rates from the current yield curve.
The 10-Year Stock Market Projection: My methodology for projecting future stock market returns.
For lists of other popular posts and an index of stock market posts, by subject area, see the sidebar to the left or the blog header at the top of the page.

The Role of Arbitrage

In theory, in the first example above, if arbitragers expected one-year rates to be higher than 0.40% a year from now, it would pay arbitragers to sell two-year notes. They could then use that money to buy one-year bills, knowing that a year from now if they invest the maturing one-year bills in new one-year bills paying more than 0.40%, they will end the two-year period with more than they would have had if they had kept the original two-year notes. Theoretically, arbitragers would sell two-year notes and buy one-year bills. This would drive down the price of two-year notes and drive up two-year interest rates until we were in equilibrium -- i.e., until two-year treasury returns matched the returns available from buying one-year bills and rolling them over.

Similarly, if the market expected one-year rates to be lower than 0.40% a year from now, it would pay arbitragers to sell their one-year bills and buy two-year notes.

Generalizing

Comparing the current three-year treasury to the one-year treasury allows you to calculate the yield on a two-year note a year from now. Comparing the current four-year treasury to the one-year bill allows you to calculate the yield on a three-year note a year from now, and so on. In general, you can use n-year treasury rates along with one-year treasury rates to calculate the rates for n-1-year treasuries one year from now.

Even more generally, you can use n-year treasury rates along with m-year treasury rates (for n>m) to calculate the rates for n-m year treasuries m years from now.