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TIPS-Treasury Arbitrage

Section: 14.2 | Asset Class: Miscellaneous (Fixed Income) | Type: Arbitrage

Overview

Based on the empirical observation that Treasury bonds are almost persistently overvalued relative to TIPS (Treasury Inflation-Protected Securities). The strategy shorts a Treasury bond and offsets the position with a synthetic portfolio that precisely replicates all Treasury bond cash flows using TIPS and zero-coupon inflation swaps. Because the synthetic portfolio costs less than the Treasury bond, the net cash flow at inception is positive, representing the arbitrage profit.

Construction / Mechanics

Short leg: Sell Treasury bond with price P_Treasury, fixed coupon rate r_Treasury, maturity T.

Synthetic replicating portfolio (long legs):

Buy TIPS with price P_TIPS, maturity T, fixed coupon rate r, and n coupon payments at times t_i (i = 1, ..., n, with t_n = T)
Simultaneously sell n zero-coupon inflation swaps with maturities t_i, fixed rate K, and notionals:
```
N_i = r + δ_{t_i, T}    per $1 of TIPS principal
```
where δ_{t_i, T} = 1 if i = n (maturity), 0 otherwise (to match principal repayment)

TIPS cash flows (per $1 notional; I(t) = CPI at time t):

C_TIPS(t_i)  = N_i × I(t_i)/I(0)                          (504)
C_swap(t_i)  = N_i × [(1 + K)^t_i - I(t_i)/I(0)]         (505)
C_total(t_i) = C_swap(t_i) + C_TIPS(t_i) = N_i(1 + K)^t_i (506)

The total cash flow replicates fixed coupon payments with effective coupon rates r_eff(t_i) = r(1 + K)^t_i.

STRIPS positions to match Treasury coupons exactly (small long or short positions in zero-coupon discount bonds):

S(t_i) = D(t_i) × {[r_Treasury - r_eff(t_i)] + δ_{t_i,T} × [1 - (1+K)^t_i]}   (507)

where D(τ) is the discount factor (STRIPS value) with maturity τ.

Net cash flow at inception:

C(0) = P_Treasury - P_TIPS - Σ S(t_i)      (508)
                               i=1

Empirically, C(0) > 0 even after transaction costs — hence arbitrage.

Return Profile

The profit is locked in at trade inception as a positive C(0). All subsequent cash flows net to zero by construction (the synthetic portfolio precisely replicates the Treasury). Returns are model-independent and driven purely by the persistent Treasury overvaluation relative to TIPS.

Key Parameters / Signals

C(0): the net cash flow at inception; must be positive (and cover transaction costs) for the trade to be worthwhile
STRIPS prices D(t_i): discount factors; observable from market
Fixed rate K on inflation swaps: the breakeven inflation rate
TIPS coupon rate r and Treasury coupon rate r_Treasury: the gap drives the size of STRIPS adjustments

Variations

Duration-neutral overlay: combine with duration hedges to isolate the mispricing from interest rate directionality
Partial replication: use a subset of STRIPS to approximately replicate, reducing transaction costs at the expense of perfect replication

Notes

Transaction costs (bid-ask spreads on TIPS, inflation swaps, STRIPS) can erode C(0); the trade is only viable when mispricing is large enough
STRIPS = "Separate Trading of Registered Interest and Principal of Securities" — zero-coupon discount bonds
The persistent Treasury overvaluation has been documented empirically but can narrow or temporarily reverse
Short selling Treasuries requires repo market access; repo rates affect the total cost of carry
Regulatory constraints on short positions in government securities may limit implementation

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