Choosing Fixed-Income Spreads for Relative Value and Risk Analysis

# Fixed income relative valuation with spreads


# Fixed income relative valuation with spreads












When one does fixed income relative (comparables) valuation there are different spreads quoted in markets,

while as I know Z spread (add-on swap rate) is used for fixed income with no optionalities, and OAS (add-on swap rate) is used for fixed income with options, in corporate markets, and g spreads generally used in sovereign (+supranationl?) markets

I am not clear we have different spreads quoted as shown below (swap spread, asset swap spread...), is there a general approach which spread to use, when and why, when doing relative valuation?

screen just for illustration

## Answer by Dimitri Vulis (score 1, accepted)

https://quant.stackexchange.com/a/81516

Follow-up to Asset Swap Spread

Spreads have many uses. Relative value analysis - are some bonds rich or cheap in relation to other - is one, but also other uses, and different kinds of spreads work better for various uses and different kinds of bond features - callables, floaters, credit-risky, amortizing, toggle coupons, etc. And in relative value, you should consider whether the bonds have different seniority/subordination, trade special (i.e. funding cost is other than the general collateral curve), have different bondholder rights like the collective action clause, have collateral, etc. In some markets (notably Brazil), risky bonds coupons use gearing (e.g. index x 145%) rather than a spread over index - surely you want to solve for a spread equivalent to compare with other bonds.

The risk-free rates in various currencies are market observable. The bond prices are observable, but there are different ways to quote them, as I discuss below. CDS quotes are sometimes observable. Underlying credit assumptions - actual probabilities of default (PD) and loss given default (LGD) are important for credit-risky bonds and aren't directly observable, but you can get risk-neutral PDs from the CDS quotes.

P&L attribution - how much did the bond's fair value (dirty price) change from carry & roll-down, from the changes in risk free / funding rates (by tenor bucket), from the change in the spread (it sounds circular because the spread is derived from the price, but is actually useful), or maybe the change in CDS spreads and the bond-CDS basis, higher-order gammas and cross-gammas between spreads / rates / time (needed if you want to minimize unexplained P&L)...

Quotes, e.g. on runs or broker screens. Typically clean price (or dirty price for distressed bonds, or for all bonds in some markets), or yield, or one of the many possible spreads over risk-free/treasury rates, or in rare cases the bond-CDS basis, and other exotics.

Market risk management: you can put limits on the sensitivities to spreads, you can use the sensitivities to spreads and rates to calculate VaR / ES, and to decide how much to hedge...

You can calculate a yield (to maturity) of a bond, discounting its cash flows using the same yield, not considering the possibility of a credit event, and not considering the shape of any risk-free curve when discount cash flows. Several commonly used spreads are the vertical difference between the yield and some risk-free rate, e.g. interpolated point on the swap curve at the bond's maturity, or treasury yield interpolated to the bond maturity, or a standardized on-the-run treasury benchmark. These are easy to calculate and are commonly used to communicate quotes. "Yield01" - the price change from a 1bp change in yield - is not a great risk measure, but is an easy estimate for the actual sensitivities to interest rates and spreads.

Different spread methodologies, taking the shape of the risk free curve into account, work better for uses other than quotation. Also there's a bit of "founder's effect": U.S. desks tend to like Z-spreads / coupon adjusted spreads, because USD is their only important currency - few care about CAD or LatAm currencies. U.K.,Europe, Asian, and other non-U.S. desks, where they work with many currencies with very different interest rates, and historically had even more currencies pre-EUR, prefer asset swap spreads for everything, assuming swapping the bond cash flows into one currency, because just comparing Z-spreads across currencies ignores the cross-gamma effects. Asset swap spreads have many little details, so if you communicate them

But both Z-spreads and asset swap spreads overstate the sensitivity to interest rates of bonds with material credit risk. But the higher the probability of defaulting, the less is the bond's price driven by the interest rates / funding cost, and then more - by the actual LGD/recovery assumptions like "if a credit event occurs, then we'll receive 65% of the face value in one year". I've seen yield spreads, and Z / coupon adjusted / asset swap spreads used for rich-cheap comparisons and P&L explanations, and they're usable, but, especially for higher-yielding bonds, you can significantly reduce unexplained P&L and make your hedges more effective by taking the actual LGD/recovery assumptions into account.