Swap Spread example CFA Curriculum


I dont seem to get my head around the example given on pages 29 and 30 of the CFA Curriculum Vol 5.

The example illustrates the use of the swap spread in fixed income pricing and is used to price a corporate bond.

In the example the treasury yield for the maturity of the corporate bond is calculated by interpolation and is 0.586%. Then it is stated that the swap spread is 0.918%.
The yield of the corporate bond is calculated as Treasury yield + Swap Spread = 0.586% + 0.918% = 1.504% which is then used for discounting the cash flows and pricing the corporate bond.

I don’t get how the yield for the corporate bond calculated this way reflects the credit and liquditiy risk of the bond.

My understanding is that swap spread = swap rate - on the run Treasury yield

So Treasury yield + Swap Spread should be equal to Treasury yield + (swap rate - on the run Treasury yield) . Which basically just leaves me with the swap rate. However, disocunting the corporate bond with the swap rate doesen’t seem right.

Then it is also stated that the swap spread helps to identify time value, credit and liquditiy components of a bond’s YTM. The higher the swap spread, the higher the return that investors require for credit and/or liquidity risk.
How is this the case? If the swap spread increases for a given swap rate, the on the run treasury yield needs to decrease. But a decrease in yield would mean, that the investor is getting compensated less for the risks of the treasury bond.

If you discount corporate bonds at the swap rates then you assume that it has liquidity and credit risk similar to that of commercial banks. Note that you may need to use a rate that is higher than the swap rate if other risks are present.

For the second part of your question, the swap spread reflects liquidity and credit risk so an increase in spread is due to an increase in both types of risk (or either one of them). Your time value is reflected in your treasury yields. Also why does the treasury yield need to decrease for the swap spread to increase? The swap spread may increase while the treasury yield stays the same. This would reflect an increase in liquidity and/or credit risk. The treasury yields do not need to decrease for the swap spread to increase. Can you clarify as to why the treasury yield needs to decrease?

Thanks for your reply, cfageist.

Ok, if I assume that the swap rates adequately reflect all the risks in a bond, then I can use the swap spread for valuation of a specific corporate bond. I just have never seen anyone actually do this in the industry which is why I guess I had difficulties with the idea. I have only seen valuations with swap rate + x, where the x is a spread to relect the specific risks of the bond.

For the second part, you are absolutely right, for the swap spread to increase Treasury rates do not need to decrease. As you mentioned swap rates could increase (with constant Treasury rates) or there could be some combination of changes in Swap rates and Treasury rates that still result in a higher swap spread. My problem here again was the idea that the Swap spread, which reflects fairly general conditions (liquidity and credit risk) in the market (mainly the interbank market), can be used as a measure for the liquidity and credit risk of a specific corporate bond. But as with the valuation question, if it is assumed that the swap spread reflects all risk of a specific bond then it can also be used to measure its liqudity and credit risk.

Thanks for the clarification. Seems like the text uses the swap rates very broadly. As you said, adding additional risk premia over the swap rate is appropriate for most corporate bonds.