Fama-Bliss Discount Bonds – Monthly Only
The Fama-Bliss Series (TREASNOX 2000047-2000051) use only fully taxable, non-callable, non-flower issues, including ITYPEs equal to 1 (Bonds), 2 (Notes), 3 (Certificates), and 4 (Bills).
Bond Selection for Term Structure
Four filters are used to select from the remaining bonds a subset from which to construct a term structure.
First Pass: Initial Choice of Instruments
The screen on the first pass is based on two moving averages of CRSP yields to maturity on the 3 longer and 3 shorter maturity instruments surrounding the bond being considered for inclusion. Issues with the same maturity may form part of the window. Whether they are considered shorter or longer depends on the relative CRSP coupon rates. Also, 1.5% notes are excluded from windows, since these are subject to large spurious errors.
A bond is included if its yield is within 0.2% (an absolute not relative yield difference) of either average, or if its yield is between either average. The latter rule allows rapid changes in the yield curve. Multiple issues with the same maturity are permitted. Included instruments with different maturities must have maturities at least 7 days apart. Conflicts are resolved using issues in this order of preference: bill with smallest spread, bills, maturity dates with multiple issues, or issue trading closest to par.
- There are refinements of the rules used to form the moving average yield windows that improve the screen. The moving windows are restricted to bills as long as they are available. There are well-known liquidity problems that affect the pricing of short bonds.
- Windows are bounded below by 0.0%.
- The longest maturity issue is always included.
Second Pass: Clean Up Big Yield Reversals
The second pass begins to refine the discount yield term structure by deleting suspicious bonds which cause large reversals in the discount yields generated from the set of bonds included in the first pass.
A reversal is defined as a sequence of changes in the discount yield function greater than 0.2% and opposite in sign. A reversal sequence ends when there is a change less than 0.2% in the discount yield function.
When there are multiple bonds at a given maturity, they are examined separately in looking for reversals. That is, first one bond is included in the sequence of yields. Then it is dropped and the other is included. Bonds at the same maturity tend to be priced the same way, so they will break reversal sequences if they are not treated separately.
To determine which bonds in a reversal sequence are to be deleted, we go to the end of the sequence. The change in yield less than 0.2% at the end of the sequence is assumed to mean that the last change greater than 0.2% is good. Thus, we delete the second from the last in the sequence, the fourth from last, etc.
Third Pass: Reconsider Excluded Bonds
With the bonds included after the second pass, a new term structure of discount yields can be calculated. The next step is to re-examine bonds excluded on the first and second passes for possible inclusion. Pass Three adds selected bonds from those previously excluded to the set of bonds included after Pass Two.
The inclusion criteria are similar to Pass One with the criteria applied to the discount yield rather than the yield to maturity.
- The mean yields of each of two moving windows of three strictly longer and three strictly shorter maturity bonds are computed.
- Bonds of the same maturity as the one being tested are excluded from the windows.
- Only bonds previously included, either on Pass Two or earlier in Pass Three, may form part of the window. The 1.5% notes are no longer specifically excluded.
- An excluded bond is put back if the discount yield at its maturity date which would result from its inclusion is within 0.2% of the mean of either the shorter or the longer window, or if it is between the two means.
Fourth Pass: Last Check for Reversals
Repeat reversal tests of Pass Two, using yields calculated from bonds included after Pass Three.
Calculation of Forward Rates, Discount Prices and Yields
The bills and bonds that survive Pass Four allow us to calculate monthly term structures of forward rates and yields for adjacent accepted maturities. Each successively longer maturity accepted allows us to calculate an additional forward rate. When there are multiple accepted bonds on a single quote date, the forward rates for each of them are calculated and the average is used as the rate for the quote date. Forward rates calculated from shorter maturity bonds are used to price the coupons for the subsequent available maturity. The coupon dates are unlikely to correspond exactly to the forward rate dates. To price coupons that fall within the period covered by a forward rate, the forward rate (always continuously compounded) is assumed to be constant during the period, so that it can be used for any subinterval. Likewise, there may be coupons as well as a principal payment during the period from the maturity date of the last included bond to the maturity of the next longer bond. In this case, the incremental forward rate is assumed to cover the whole incremental period to the maturity of the next longer bond.
The forward rates described above cover unevenly spaced periods between the maturities of accepted bills and bonds. Under the assumption that a forward rate applies to each day of the period it covers, the forward rates can be used to calculate implied prices of artificial discount securities for maturities corresponding to future end-of-month quote dates. Equivalently, one can think of the calculations as generating daily forward rates, which are then grouped to get implied forward rates for annual intervals.
These forward rates are used to calculate prices and yields on artificial discount securities for the maturities corresponding to end-of-month quote dates one through five years in the future. To avoid having single bonds introduce spurious results only annual maturity intervals were used. This increases the signal to noise ratio. Extension of the term structure beyond 5 years is impractical due to the scarcity of qualified issues and the erratic results produced by those quotes which are available.
TFZ_MTH_FB.* - Monthly Fama Bliss Discount Series
|(KY)TREASNOX||See table below for mapping to old columns||9d||9d|
|MCALDT||Last Quotation Date in the Month||8d||8d|
|TMNOMPRC||Monthly Artificial Bond Discount Price||11.6lf||20.12e|
|TMNOMPRC_FLG||Monthly Nominal Price Flag (Uniformly D)||1c||1c|
|TMYTM||Monthly Series of Yield to Maturity (TMYLD * 36500)||9.4lf||20.12e|
|MAPPINGS||Fama-Bliss TREASNOXs are between 2000047 though 2000051 and map to columns 2-6 respectively, in the legacy files|