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Estimating The SteadyState Fed Funds Rate http://seekingalpha.com/p/1tw53 Jul 17, 2014
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Estimating The SteadyState Fed Funds Rate 0 comments
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 oneday bond, the yield would be equal to the fed funds rate. The yield on a twoday bond would be equal to the fed funds rate for the first day and the expected fed funds rate for the following day. A oneyear 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.
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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 betterthanexpected 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.
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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 steadystate fed funds rate would be based on a linear extrapolation from the fed funds and the yield on the 10year Treasury bond.
The steadystate fed funds rate is the market's expectation for the FOMC's longterm 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 10year 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 10years is exactly equal to the 2.65% 10year 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 10year 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%.
(click to enlarge)
The fed funds rate does not need to hold exactly at the steadystate level for the entire duration to maturity. Oscillations in the fed funds rate due to normal businesscycle trends, such as in the dotted line below, can happen. The key is that the fed funds rate will average the steadystate level once it is reached.
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Using Forward Rates to Estimate the SteadyState Fed Funds Rate
Using a linear extrapolation based on the fed funds futures is not the only way to calculate the steadystate 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 10year, 20year forward  which measures the average fed funds rate for 20years starting ten years from today  can be calculated using the current 10year Treasury yield and the 30year 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 1year, 29year forward  using the oneyear Treasury and 30year Treasury bonds  shows an average fed funds rate of 3.49% for the 29 years after year one.
(click to enlarge)
Both methods, the fed funds futures linear extrapolation and the forward rates, produce a similar steadystate fed funds rate. Differences in steadystate estimates occur during periods of time when the slope of the fed funds futures curve is so flat that the steadystate is not reached until after the duration of the near term bond period.
(click to enlarge)
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 steadystate until 2024, 12 years after rates were expected to begin increasing.
The 10year, 20year forward produces a steadystate 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 twoyear period where the fed funds rate is below the linear extrapolated steadystate.
Both methods, linear extrapolation and forward rates, produce a reasonable estimate of the Treasury market's longterm steadystate 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.
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