A Model of the Convenience Yields in On-the-run Treasuries
Joseph A. Cherian
Banc America Securities
CIRANO, CIREQ, HEC Montreal
Robert A. Jarrow
Johnson Graduate School of Management, Cornell University
The convenience yield diferential between on- and off-the-run Treasury securities
with identical maturities has two components. A non-cyclical component may arise
due to the higher illiquidity of off-the-run bonds. Also, trading in the market for the
next issue often causes cyclical shortages of the on-the-runs. When this occurs, owners
of the on-the-run bond can earn riskless profits by borrowing at a special repo rate
while lending at the prevailing risk free market rate. This second component of the
convenience yield, induced by the auction, is cyclical.
We first show that special repo rates and the convenience yield are jointly cyclical
over the auction cycle. The patterns are statistically significant and pervasive. Repo
specials are highest around the announcement day and disappear by the issue day.
The off- minus on-the-run yield spread is highest at the beginning of the cycle and
collapses near its end, consistent with a decreasing present value of profits over a
decreasing horizon. Second, we develop a first no-arbitrage continuous-time model,
with both interest and special repo rates stochastic, that prices the on-the-run bonds
that command this convenience yield. A simple implementation of the model can
generate yields consistent with the evidence.