The convenience yield differential 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
next issue often causes cyclical shortages of the on-the-runs. When this occurs,
of the on-the-run bond can earn riskless profits by borrowing money at the special
rate and lending money at the prevailing risk free market rate. This second component
of the convenience yield, induced by the auction, is cyclical.
Autors first show that special repo rates and the convenience yield are jointly cyclical
over the auction cycle. The patterns are statistically significant and pervasive
bonds and auctions. Repo specials are highest around the announcement date and
disappear by the issue date. The off-minus on-the-run yield spread is highest at
beginning of the cycle and collapses near its end. This is consistent with a decreasing
present value of profits over a decreasing horizon. We then develop a no-arbitrage
continuous-time model, with stochastic interest and special repo rates, that prices
on-the-run bonds that command this convenience yield. A simple implementation of
the model generates yields consistent with the evidence.