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Measuring Market Expectations on Federal Funds Target Rate. Liang Wu & Isabel Yan City University of Hong Kong. 1. Agenda. Background of Fed funds market Literature review Existing models on Fed funds rate and their limitations Model set up Model evaluations Conclusions.

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liang wu isabel yan city university of hong kong

Measuring Market Expectations on Federal Funds Target Rate

Liang Wu & Isabel Yan

City University of Hong Kong

1 agenda
1. Agenda
  • Background of Fed funds market
  • Literature review
    • Existing models on Fed funds rate and their limitations
  • Model set up
  • Model evaluations
  • Conclusions
2 background fed funds target rate
2. Background - Fed funds target rate
  • Federal funds market:
  • banks borrow from or lend to, one another on an unsecured basis the reserves balances that they hold at the Fed Reserve accounts.
  • (b) Effective Fed Funds rate (FFR) = volume-weighted daily average overnight rate
  • The Federal Reserve Bank of New York collects data on the overnight trades
  • arranged each day by the major brokers in this market and uses the data to
  • calculate a volume-weighted daily average overnight rate.
  • (c) FOMC directs NY Fed to maintain, on average,
  • effective FFR = target rate (FFR*)
  • using open market operation.


Target error


FOMC meeting


3. Review on Fed funds models

  • Fundamental Approach --- Taylor Rule:
  • conventional(Taylor,1993),
  • smoothing (Clarida et al., QJE 2000; Rudebusch, 2002),
  • Bayesian VAR (system of equations on FFR, real time nonfarm payrolls and core CPI (Gurkaynak et al., 2007)


(i) Real time data availability (Orphanides, 2001)

(ii) Output gap hard to measure reliably

- various trends and filters (Orphanides and Norden, 2002; Orphanides,

Reifschneider, Tetlow and Finan 1999)

- output gap uncertainty affects optimal parameters in the policy rule (Smets, 1999)

(iii) Time-varying parameters

Fed may change the weighting on inflation, unemployment (Cochrane and Piazzesi, AER 2002).

(iv) Use of real-time data makes it difficult to determine the correct dynamics (Rudebusch, 1998, 2001, JME 2002b)


(2) Market-based Approach


(a) Surmounting the omitted-variables and time-lag problems:

Market expectations from liquid financial instruments can summarize the vast amount of information used by Fed in setting policy, and used by Fed- watchers in guessing Fed’s actions.

(b) Overcome the time-varying parameter problem

Financial instruments used:

(a) Fed Funds Futures:

spot-month (Krueger and Kuttner, 1996; Faust, Swamson and Wright, 2004); month-ahead (Bomfim, 2003; Poole and Rasche, 2000)

(b) Others:

Eurodollar futures: 1-month (Cochrane and Piazzessi, 2002); 3-month (Rigoben and Sack, 2002)

Yield spread: Lange, Sack and Whiteshell (2001); Rudesbusch (2002);

Piazzessi, 2005.



(i) Market-based approach is superior to the Fundamental Approach:

  • Even static forecast performs better than the Taylor rule with Greenbook forecasts.
  • Models using yield curve is better than the conventional Taylor rules (Piazzesi, 2001, 2005).
  • All of the financial instruments are clearly superior to the Bayesian VAR (Gurkaynak et al., 2007)

(ii) Among financial instruments in the market-based approach, Fed funds futures dominate all the other instruments at horizons out to six months (Gurkaynak et al., 2007)

(iii) For longer horizons, the predictive power of many of the instruments become more similiar (Gurkaynak et al., 2007)


(3) Risk-adjusted futures rate --- the hybrid approach

  • Adjust the risk premium term by business cycle variables such as non-farm payroll (Piazzesi and Swanson, 2008)


(i) Risk premia are well predicted by macro-economic indicators in real time

(ii) The risk-adjusted approach is better than the rule-of-thumb-adjusted approach that is currently used by the Fed


Figure 1. Fed Funds Futures Rates – Target Rates

Limitations in the Literature

(a) The maturity value of the Fed funds futures is linked to the monthly averageeffective Fed funds rate, not specifically on the new target rate for the upcoming FOMC meeting.

Objective #1 of this paper:

To somehow undo the time-averaging to get a correct measure of the expectation on the new target rate in the upcoming FOMC meeting.

(b) Use only the N-month futures contract for a N-month-ahead forecast. Hasn’t used the information embedded in the futures contracts of other horizons,

Objective #2 of this paper:

To obtain more expectation information by using the whole spectrum of futures contracts of different horizons.


Why is it useful to forecast the target rate instead of just the monthly average?

  • Starting from Feb. 1994, the FOMC began to inform the public about the scheduled meeting and announced the target rate immediately after the meeting. The practice has dramatically changed how market participants form their expectations:

(i) There was a structural break in February 1994 in the response of T-bill

rates to the Fed funds target. The term rates react much in unison during the announcement days after 1994 (Demiralp and Jorda, 2004)

(ii) The behavior of the U.S. prime rate changed significantly from before 1994

to after 1994. Until 1994, the US prime rate is irresponsive to short-term interest rate changes. After 1994, prime rate has come to react immediately to shifts in target rate. (Kobayashi, 2009)

Since 1994, the focal point of the market has changed to the target rate instead of the smoothed version of the interest rate.


4. Model set up (recursive identification approach)

month: tt+1t+2t+3

As in Piazzesi and Swanson (2008), we sample the futures data on the last day of the month.


Scenario(A): 1-Month-Ahead Expectations

month tt+1

weight on old target rate

weight on new target rate


Based on this relationship, we can extract the market expectation of the 1-month ahead new target rate by “purging” the carried-over effect of the old target rate from the 1-month-FFF:

Target errors should have an expected value of 0 because the FOMC directs the Federal Reserve Bank of New York (the Desk) to maintain the overnight Fed funds rate “at an average of around” the target rate(see Hilton, 2005).


Day of the month

Figure 3. FOMC meeting day frequency, Feb.1994 – Sept. 2008


Scenario(E): 5-Month-Ahead Expectations


and so on up to the 4-month-ahead expectations, we can obtain …


Scenario(F): 6-Month-Ahead Expectations


and so on up to the 5-month-ahead expectations, we can obtain…


4.2 Features of the “recursive identification” approach

  • The use of the recursive identification approach is expected to yield better prediction of the target rate than using the N-month futures rate alone, especially in the short-horizon when the bias caused by the risk premium term is smaller.
  • However, in the longer horizon, the effect from the leveraged risk premia is expected to accumulate whichcan drive a bigger wedge between the expectation and the realized target rate.
  • The leverage effect on the risk premium will magnify if the FOMC meetings are held close to the end of the month.

4.3 Method to alleviate the leverage effect when the FOMC meetings are held close to the end of the month

tt+1t+2 (no meeting)t+3

  • There are four months in a year when there are no scheduled meeting.
  • During these months the target rate is the same as the target rate after the
  • previous month’s FOMC meeting.
  • Usually the FOMC meeting before a non-meeting month takes place near
  • the end day of the month.
  • The leverage effect is close to maximum if we use the n-month futures
  • contract to recover the n-month-ahead target rate.
  • In this case, the (n+1)-month futures contract gives a better forecast for the
  • n-month-ahead target rate, as it is not suffered from the leverage effect.

4.3 Technical details

(A) Forecast of the target rate when the FOMC meeting is close to the end of the month, and when there is no meeting in the subsequent month


We therefore propose an end-of-the-month modified strategy

if and there is no FOMC scheduled meeting in month t+1.

  • For instance, at one-month forecast horizon, there are 11 cases in which the expected monetary policy rate using the recursive identification approach is more than 25 bps away from the actual target rate.
  • In these circumstances, 7 out of the 11 cases are when the FOMC meeting happened in the last 2 days of the month.
  • The modified strategy gives better predictions in all these cases.

Table 1. Observations with 1-month-ahead forecast errors greater than 25 bps


5. Evaluations of the recursive identification approach (RI approach)

Does the average effective FFR anchor to the expected target rates derived from the RI approach?

  • Test the cointegrating relationship:

If the expectations derived from the RI approach are good predictors of the target rates to which the effective fed funds rates anchor to, we expect:


6. Out-of-Sample Forecasts

I.Static Forecast: Using the previous meeting’s target rate as the forecast

II. Taylor Rule: Forecast version of Clarida et al. (2000),

III. Futures-alone: Directly using (100 - futures price) as the forecast value, adjusted by the end-of-the-month alternative strategy

IV. Risk-adjusted futures: Using futures, and adjusting for risk premia using real time business cycle variables (non-farm payroll and total capacity utilization).

V. Recursive identification approach:


Technical details for obtaining the risk-adjusted futures rates (Piazzessi and Swanson, 2008)

Step 1: Regress the proxy for risk premium on real-time business cycle variables:

Step 2: run rolling window regressions to get out-of-sample forecast for the risk premium term, then subtract it from the fed funds futures:


For the Taylor rule and risk-adjusted futures rates, we use half of the sample (55 data points) for in-sample training, and then use the obtained estimated coefficient to forecast the next out-of-sample point. The first out-of-sample forecast is for January, 2001.

  • All macroeconomic variables are based on real-time data.

6.1 Evaluations of the Out-of-Sample Prediction Performance

(a) Root Mean Square Error (RMSE)

(b) Modified Diebold-Mariano (MDM) test (Harvey et al., 1997)

It compares the out-of-sample forecast residuals of two models via the squared loss function L(.):

(c) Regression of the actual target rate changes on the expected changes

(d) Graphical analysis


(a) Root Mean Square Error (RMSE)

  • the recursive approach has the best performance for 1- and 2- month-ahead forecasts.
  • (ii) the risk-adjusted approach always yields better results than directly
  • using the Fed funds futures
  • (iii) The recursive approach, the risk-adjusted approach and directly using
  • futures all outperform static forecasts.
  • (iv) static forecasts is very similar to the Taylor rule
  • (v) for longer horizon forecasts, the forecasting performances of the
  • recursive approach and the risk-adjusted approach are quite similar.

In terms of the MDM test,

  • The expectations extracted from the recursive approach significantly outperform the other candidates for 1- and 2-month-ahead forecasts.
  • The recursive approach, the risk-adjusted approach and directly using futures all outperform static forecasts.
  • Static forecasts are not significantly different from the Taylor rule.
  • For longer horizon forecasts, the recursive approach, the risk-adjusted approach and the futures-alone approach are not statistically different.

(c) Regression of the actual changes on the expected changes

If the expectations have good predictive power, we expect .


In terms of the regression results,

  • The explanatory power (in terms of the ) is much higher for the market-based approaches than the fundamental approach (the Taylor rule).
  • The estimated slope coefficients of the recursive approach and the risk-adjusted futures are much closer to 1 compared with the futures-alone approach and the Taylor rule, suggesting that the expected changes track closer to the actual changes for these approaches.
  • The estimated intercepts of all three of the futures-based approaches are significantly negative, which is consistent with the fact that the expectation terms on the right hand side encompasses some (full or partial) risk premium which tends to bias up the expectations.
  • The estimated intercepts from the recursive approach is smaller than that of the futures-alone approach but are slightly larger than that of the risk-adjusted futures.
  • The estimated intercepts become smaller and less significant after we adjust the futures by the risk premium terms, suggesting that the risk adjustment procedure is useful in capturing at least part of the risk premium.

The estimated intercepts from the futures-alone regression indicate that the average risk premium is about:

3 bp for 1 month (~3 bp per month),

6 bp for 2 months (~3 bp per month),

16 bp for 3 months (~ 5 bp per month),

22 bp for 4 months (~5.5 bp per month)

34 bp for 5 months (~7 bp per month)

28 bp for 6 months (~5 bp per month).


In terms of the graphical analysis,

  • For 1-month and 2-month ahead forecasts, the recursive identification approach seems to be a better predictor of the actual target.
  • This is confirmed by the root mean square error (RMSE) and the Modified Diebold-Mariano (MDM) test.
        • Overall, the fundamental based models (the Taylor rules) lag behind.
        • During the recent financial crisis (2007-2008), the longer-horizon futures-based forecasts (4-6 months) tend to yield expectations that are significantly above the actual target rate, possibly indicating the dominant impact of positive risk premium, which bias upward the futures-based expectations.

7. Conclusions

        • Taylor rule:

Overall, in terms of predictive ability, the fundamental based models (the Taylor rules) lag behind. An accurate predictor of the Fed funds rate using Taylor rules would at least require an equally accurate predictor of output gap and inflation expectation, which by themselves are difficult.

  • Risk-adjusted futures:

- It outperforms the futures-alone approach at all

horizons out to 6 months.

- However, both our analysis and that of (Piazzesi and Swanson, 2008) suggest that macroeconomic variables explain only part of the risk premium, and the explanatory power at short horizons (especially one-

month-ahead forecast) is low.


7. Conclusions (Con’t)

  • Recursive identification approach:
          • We provide a new approach to back out recursively the expected target rate using the relationship between the Fed funds futures and expected target Fed funds rate.
          • The scheduled FOMC meeting days play a vital role in the relationship.
          • This approach does provide the most accurate forecasts for the target Fed funds rate at short horizons out to 2 months.
          • For longer horizon forecasts, we cannot walk away from the risk premium embedded in futures contracts, but the risk premium is not known in real time.