# Estimating The Steady-State Fed Funds Rate

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At its simplest form, the Treasury yield curve shows bond payouts across different maturities. Therefore, the spread between maturities is equal to sum of the interest rate, liquidity, and default risks. Since the liquidity and default risk of Treasury bonds is essentially zero, the spread only represents interest rate risk.

The Federal Reserve sets a target for the overnight fed funds rate. If a dealer purchases a one-day bond, the yield would be equal to the fed funds rate. The yield on a two-day bond would be equal to the fed funds rate for the first day and the expected fed funds rate for the following day. A one-year bond would have a yield equal to the average expected fed funds rate for the entire year.

As long as the liquidity and default risks remain zero, the changes in yields for different maturities only reflect shifts in the expected fed funds rate over the duration of the bond.

We can capture the expectations of future fed funds rate hikes by looking at the fed funds futures data from the CME. If the economic data improve, suggesting a better-than-expected economy, the implied fed funds predictions shift higher.

Statistically, Granger causality tests show that shifts in the implied fed funds futures curve lead to changes in Treasury rates and not the other way around. Thus, the Treasury market is looking toward the fed funds futures market when determining the expected fed funds rate.

Unfortunately, the fed funds futures market only exists for the first 36 months on the yield curve. So we don't know exactly what the market is predicting for the fed funds rate at any point beyond the first 36 months. However, we can extrapolate fed funds predictions from the slope of the implied fed funds curve.

The slope of the implied fed funds curve represents the pace for fed funds rate hikes. For example, the fed funds futures market predicted on both April 4, 2014, and July 3, 2014, that the first rate hike would take place at the June 2015 FOMC meeting. However, the slope of the fed funds futures curve on April 4 was steeper, implying that the market believed in April that subsequent rate hikes would be more substantial than it did on July 3.

Likewise, the market predicted the first rate hike would be at the July 2015 FOMC meeting on both May 30, 2014, and July 11, 2014. The steeper slope in July suggested that the market believed more than it did in May that each rate hike would be larger.

Past experience shows that the FOMC increases rates on a relatively straight and linear path. The FOMC very rarely deviates from this trend and increases the size of the rate hike at a subsequent meeting. It is safe to assume that the fed funds futures market bases its predictions on linear trends. Therefore, a simple linear trend estimated from the slope of the fed funds futures curve tells us what the market believes the fed funds rate will be even beyond the first 36 months.

Remember, the yield on a Treasury bond is equal to the average expected fed funds rate over the duration of the bond. We can therefore determine what the market believes the steady-state fed funds rate would be based on a linear extrapolation from the fed funds and the yield on the 10-year Treasury bond.

The steady-state fed funds rate is the market's expectation for the FOMC's long-term fed funds rate. Essentially, the market expects the FOMC to raise interest rates until it reaches a maximum point and the rate will stay at that level, on average, for the duration of the bond.

For example, the chart below shows two bonds, bond "A" and bond "B", with the exact same yield of 2.65%. The known fed funds future curve for bond "A" - solid black line - averages 0.86% over the first 36 months of the 10-year bond. Assuming a linear extrapolation, the market perceives the FOMC will raise rates until the fed funds rate reaches 3.57% and then hold at that level for the duration of the 10 years. Thus, the average fed funds rate from the entire 10-years is exactly equal to the 2.65% 10-year rate.

Bond "B" has a steeper fed funds futures curve. The average fed funds rate is 1.16% over the first 36 months. Since the 10-year yield of Bond "B" is the same as Bond "A", the FOMC is expected to raise interest rates to only 3.30%. Like in Bond "A", the average fed funds rate for the entire duration is exactly 2.65%.

The fed funds rate does not need to hold exactly at the steady-state level for the entire duration to maturity. Oscillations in the fed funds rate due to normal business-cycle trends, such as in the dotted line below, can happen. The key is that the fed funds rate will average the steady-state level once it is reached.

**Using Forward Rates to Estimate the Steady-State Fed Funds Rate**

Using a linear extrapolation based on the fed funds futures is not the only way to calculate the steady-state fed funds rate. Another methodology is to use the forward rate for different Treasury bond durations.

Since Treasury bond yields are equal to the average expected fed funds rate for the duration of the bond, the difference in yields between the two durations has to be equal to the expected average fed funds rate during that time frame.

For example, the 10-year, 20-year forward - which measures the average fed funds rate for 20-years starting ten years from today - can be calculated using the current 10-year Treasury yield and the 30-year Treasury yield. On July 10, 2014, the average fed funds rate from July 11, 2024, through July 10, 2044, is expected to be 3.75%.

The 1-year, 29-year forward - using the one-year Treasury and 30-year Treasury bonds - shows an average fed funds rate of 3.49% for the 29 years after year one.

Both methods, the fed funds futures linear extrapolation and the forward rates, produce a similar steady-state fed funds rate. Differences in steady-state estimates occur during periods of time when the slope of the fed funds futures curve is so flat that the steady-state is not reached until after the duration of the near- term bond period.

For example, concerns about when the Fed would initially raise interest rates following the implementation of QE3 in late 2012 led to a linear slope of only 2.5 bps per month. In this case, the linear extrapolation from such a flat slope resulted in the fed funds rate not reaching its steady-state until 2024, 12 years after rates were expected to begin increasing.

The 10-year, 20-year forward produces a steady-state rate that is lower than the linear extrapolation. Forward rates are the average fed funds rate between the two durations. In this case, the average includes a two-year period where the fed funds rate is below the linear extrapolated steady-state.

Both methods, linear extrapolation and forward rates, produce a reasonable estimate of the Treasury market's long-term steady-state fed funds rate. Neither method is better than the other, but the forward rate is easier to calculate.

**Disclosure: **The author has no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.