## 3. RVA of credit instruments: pricing bonds from CDS quotes

Bringing all previous ideas and concepts together we approach an arguable subject of bond trading based on several criteria:
1) derivation of hypothetical bond prices and 2) the spreads and basis comparison.

Survival probability curve can be used to perform respective adjustments to the bond cash flows. We employ the following formula:

Hypothetical price = [Cash Flow x (1 – PD)] x DF

PS – survival probability, PD – probability of default, RR – recovery rate, DF – discount factor derived from a zero-coupon curve (LIBOR or swaps).
All probabilities and discount factors must correspond to the period, when we expect the bond coupon to be paid. Making these adjustments allows us to build a better picture of the market’s perception of the risks related to the observed entities, particularly risks of default.
Although this procedure can be disputed, as biases can arise when we are dealing with prices quoted by market makers, who derive their own bond prices based on similar assumptions and thus include the default expectations into the figures.

How do these changes affect a bond’s price sensitivities and spread measures?
We provide an example of 6 senior secured bonds that are denominated in USD and have long-term issuer ratings from AA- to AA+ from S&P.
The information on market and adjusted data is displayed in the table below.

The results of the adjustment can be different for different bonds.
For example: Wal-Mart ’18 has a hypothetical price, which is less, than the one quoted by the market, whereas there is an opposite situation with the other bonds.
Such differences between actual and CDS-derived prices can suggest that we take long or short positions in these bonds, since we can expect that this deviation should eventually disappear.

But on the other hand, the ultimate goal of deriving these prices is to find relative value from spread and basis comparisons. The chart below provides us with visualization of how the ASW, Z- and the adjusted Z-spread (or C-spread) differ from one another and deviate from the benchmark “AA” USD curve. We provide linear interpolation and logarithmic approximation to get a grasp of the differences in trades that can occur based on this analysis.

RVA helps in determining the “richness” or “cheapness” of the bonds.
This is defined by a regression tool, which in our case is the chart containing the curve and bond spread scatter.
If a data point is located below the curve, we consider it to be trading “rich”, and if it is located above the curve, we assume that the bond is trading “cheap”.
Provided we handle our comparison using the logarithmic curve, there are 2 bonds that are trading rich judging by all 3 spread measures: IBM ‘15 and Wal-Mart ‘18; and 1 bond that is trading cheap – General Electric ’16.
The rest is up to the trader to decide, as the spread adjustment provides us with results that ultimately alter our view on the bonds.
For instance Coca-Cola ‘19 is trading cheap according to the Z-spread, but the adjustment that we derive from the CDS quotes tells us that the bond should be trading rich.

Another trading idea revolves around the CDS basis. The basis is simply defined as the difference between the ASW spread and the CDS spread.
The idea is that entering into an asset swap grants us exposure to floating rates, and we can calculate the amount of basis points that we will receive from the floating leg payments in exchange for the fixed leg (coupon) payments.
If this value exceed the default insurance (i.e. CDS spread), we have an opportunity to cover the CDS premium payments with the proceeds from the swap.
Let us refer to the above table once again and look at the results for Wal-Mart ‘18. The market CDS basis is negative -7 b.p., but the adjusted basis is +16 b.p., which means that hypothetically there should be no arbitrage opportunity in purchasing the insurance.

Hence we can see the various analytical techniques that spread analysis and default probability bootstrapping can offer for relative value analysis. We will continue with this topic in future articles.

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