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
(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)
(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)
Eurodollar futures: 1-month (Cochrane and Piazzessi, 2002); 3-month (Rigoben and Sack, 2002)
Yield spread: Lange, Sack and Whiteshell (2001); Rudesbusch (2002);
(i) Market-based approach is superior to the Fundamental Approach:
(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)
(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
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?
(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.
As in Piazzesi and Swanson (2008), we sample the futures data on the last day of the month.
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).
Figure 3. FOMC meeting day frequency, Feb.1994 – Sept. 2008
We can obtain
and so on up to the 4-month-ahead expectations, we can obtain …
and so on up to the 5-month-ahead expectations, we can obtain…
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
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
if and there is no FOMC scheduled meeting in month t+1.
Table 1. Observations with 1-month-ahead forecast errors greater than 25 bps
Does the average effective FFR anchor to the expected target rates derived from the RI approach?
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:
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.
(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
If the expectations have good predictive power, we expect .
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).
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.
- 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.