STRIPS: a bond as a portfolio of zeros

In February 1985 the US Treasury’s STRIPS program (Separate Trading of Registered Interest and Principal of Securities) let dealers split a note into one zero-coupon security per payment date. A coupon bond is then exactly a portfolio of zeros. If the strips are worth more than the bond, dealers buy bonds and strip them. If they are worth less, dealers buy strips and reconstitute the bond. Either trade pulls the two prices back together.

import matplotlib.pyplot as plt
import numpy as np

from financialkit.fixed_income import NelsonSiegelCurve, bond_cash_flows, strips_curve, strips_decomposition, strips_value, yield_to_maturity

curve = NelsonSiegelCurve(0.05, -0.02, 0.01, 2.0)
bond = bond_cash_flows(100.0, 0.055, 10.0)
strips = strips_decomposition(bond)
quotes = 100.0 * curve.discount(bond.times)

Strip prices and the bond they rebuild

value = strips_value(bond, quotes)
print(f"{len(strips)} strips; replication cost {value:.4f}")
for market in (value - 0.25, value + 0.25):
    edge = value - market
    trade = "buy the bond, strip it, sell the strips" if edge > 0 else "buy the strips, reconstitute, sell the bond"
    print(f"bond at {market:.4f}: {trade} for {abs(edge):.2f}")

20 strips; replication cost 105.5217
bond at 105.2717: buy the bond, strip it, sell the strips for 0.25
bond at 105.7717: buy the strips, reconstitute, sell the bond for 0.25

One yield versus a curve of strip yields

implied = strips_curve(bond.times, quotes)
ytm = yield_to_maturity(value, bond)
fig, ax = plt.subplots()
ax.plot(bond.times, 100 * implied.rates, "o-", label="strip (zero) yields")
ax.axhline(100 * ytm, color="k", ls="--", label=f"bond yield to maturity {100 * ytm:.3f}%")
ax.set_xlabel("strip maturity (years)")
ax.set_ylabel("continuously compounded yield (%)")
ax.legend()
print("max strip-curve error vs the curve:", np.abs(implied.rates - curve.zero_rate(bond.times)).max())
plt.show()

max strip-curve error vs the curve: 6.245004513516506e-17