Bond Pricing: Spread Quoting

This is a series of short posts examining the bond markets and some of the key pricing, risk and quoting concepts (with EXAMPLES!) –
        The Yield Curve
        Duration/Convexity and DV01
        Spread Quoting
        Z-Spread
        Roll PnL

Corporate bonds give a higher yield than govvies, reflecting their increased credit risk – the chance that the company defaults before the investor receives – their payment on the bond. The difference between these two is called the ‘Credit Spread’ – and typically the lower the credit rating of the company, the higher the yield investors will demand to purchase the bonds, so this spread will be larger. Because of this, corporate bonds are sensitive to two risk factors – interest rates in the bond’s currency, and the credit risk of the issuer.

If govvie yields (and hence interest rates) in a given currency increase, existing fixed rate bonds will be less valuable and the price will fall in order to increase yields to reflect the new govvie yield. Similarly, if the credit rating of the issuer declines, bonds it has issued see price declines as the spread to govvie bonds increases to reflect the new, increased credit riskiness of the bonds.

Investors seeking exposure to interest rates will typically buy govvies – and some will go long corporate bonds to gain an additional yield pickup over the risk-free govvies. On the other hand, specialist credit investors often seek exposure only to the credit riskiness of corporate bonds, and for these investors the sensitivity to interest rate risk is unwanted. To hedge this risk out, they will often trade bond ‘switches’, going long a corporate bond and simultaneously short the govvie benchmark bond with the closest maturity to the corporate bond in question, to neutralise the interest rate risk.

An example corp curve showing the spread over govvies, which typically increases with maturity, and is steeper for lower-rated bonds

Because switches are traded so often, for most highly-rated investment grade bond, dealers will quote them not by price or by yield, but instead by the spread between a bond and its govvie benchmark. The investor typically transacts both legs of the switch simultaneously with the dealer. A practical advantage of this way of quoting is that even if there are interest rate movements between the time of quoting and the time the trade is transacted, the spread between the two bonds is highly insensitive to them and rarely needs requoting (interest rates typically move much more frequently than credit spreads).

An example corp curve is shown above with the corresponding govvie curve in the diagram. Note that no interpolation is performed – a govvie with a nearby maturity is chosen as a benchmark, which can lead to small maturity mismatch.




Once a deal is agreed, the investor and the dealer must still agree on the Spread-to-Price conversion. This is done in two steps – the spread between the corporate bond and the govvie bond, plus the yield of the govvie, gives the equivalent YtM r_y for the corporate bond. This is then converted into a price by discounting all of the bonds payments using r_y as a risky discount factor.

Example: an AAA-rated corporate bond with three remaining annual coupon payments of 4%, which also returns notional of $100 at maturity (assume the most recent coupon was paid recently and the price already reflects this), is quoted bid-offer at 65-60 bps spread to the govvie benchmark which is quoted at 2.2% YtM, expires in 2.75 years, and pays biannual coupons at 1.8%. What is the approximate cash price to buy the corporate bond?

The only relevant quantities here are the corp spread to govvie, the govvie YtM, and the payments remaining on the corp. Since the govvie has a YtM of 2.2%, and the corp ask-quote is 60 bps (we’re buying the bond*, so the ask price is the relevant spread), we pay a price that implies a YtM of 2.8%

    \[\text{Price} = \frac{\$4}{(1 + 0.028)} + \frac{\$4}{(1 + 0.028)^2} + \frac{\$104}{(1 + 0.028)^3}\]

Performing the calculation this way round doesn’t require a solver – plugging in the r_y value from the quotes, we get a price of $103.41.

Note that the govvie here has a YtM higher than its coupon payments so is trading below par – despite its credit riskiness, the corp bond is more valuable due to its higher coupon payments. In yield terms the relative price relationship is much clearer.

*An interesting point to note from this example is that we typically think of dealer bid prices being lower than offer prices. This is of course true with spread-priced bonds, but as a lower price corresponds to a larger yield/spread, the larger spread is actually the bid price (ie. the YtM/spread that the trader would receive if she buys the bond from you)