# Inflation-Linked Bonds & Asset Swap Spreads

I am trying to plot the asset swap spreads of government inflation-linked bonds (ILBs) versus the asset swap spread of government nominal (plain-vanilla) reference bonds.

I used the article in the link below:

My questions/concerns:

a.) I have conceptual concerns using the net-proceeds asset swap structure (let me qualify that that by saying, given my understandings). My understanding is that we are trying to solve for the asset swap spread (which is built into the floating leg of the asset swap) which sets:

PV(Fixed)-PV(Floating)=0


where Fixed denotes the fixed leg of the swap and Floating the floating leg of the swap. I felt more comfortable with the par asset swap structure - solving for the asset swap spread which sets:

AIP-PV(Fixed)-PV(Floating)=100

where AIP is the current bond all-in-price. Why I liked this was because if a bond was issued with a high coupon rate (relative to current interest rate environment) but had an all-in-price less than par (100), one would conclude the bond had poorer credit quality (relatively speaking - and just assume there is no liquidity premium, etc.) This was then matched by a larger asset swap spread - ie. as holder of the bond I am compensated more for its inferior credit quality.

But I don't see this mechanism in the net-proceeds asset swap because the all-in-price is not built into the structure (in the par asset swap structure, at initiation you pay par for a bond whose current value is the all in price, while under the net-proceeds structure, you pay the all-in-price (so that (AIP-100) term is not present in the net-proceeds structure as it is in the par-asset swap structure)

b.) Anyway having used the net-proceeds for the ILBs, the graph of the ILB asset swap spread is completely different to the Nominal asset swap spread - the ILB spreads are roughly around double the size of Nominal spreads and the shape of the graph (vs. maturity of the bonds) is erratic and wholly different to the shape of the Nominal curve

Now this may be due to the different credit risk profile of the ILB versus a plain vanilla nominal bond (explained in the article in the link above). But the article fails to cover how to account/compensate for this differing credit structure (so that we could compare the ILB spreads to its reference nominal bond's spread). How would one account for this?

Does anyone have an idea how one should go about this? or more generally to model the asset swap spread for ILBs?

Any help is greatly appreciated

a couple of ideas on the subject:

a) This is how swap are priced (PV[fixed] - PF[float] = 0). It is the same idea for bond if you think about it, but with two fixed legs (one is selling the bond at today's price, the other is receiving the stream of interest and final repayments).

b) In theory, the difference between Inflation linked and non inflation linked bonds is, well, inflation expectations. That gives you some idea of where the market participant see inflation realizing.

In practice, the inflation linked market is

• much smaller (so liquidity is not always great and your time series will not be as responsive as the vanilla one)

• some organizations (think pension plans with defined benefits) absolutely need those, pushing the price higher.

Credit is not really an issue here as you would expect the bonds to have the same kind of risk if the issuer is the same.

Say the bond is at 105. In a par asset swap, you are not really paying par for the bond. You are paying 105 for the bond, and receiving 5 on an off-market swap, which is being discounted at Libor flat (or maybe Fed funds) by the dealer. So you final spread is a sort of average of these two trades. To contrast, in a proceeds-swap, the swap is on-market to start with, and drifts 5 points off-market by the maturity date, hence you increasingly lend to the dealer. The different spreads are due to the differing amounts of "investment" in the swap part.

By either method, TIPS are cheap versus nominals on an asset swap basis, due to lower liquidity, and market supply and demand. The only way to arbitrage it is to do back to back asset swaps, for which you will suffer a significant (say 15-20bp) repo differential on the bonds, hence removing most of the arbitrage in my experience.