Question

Consider a zero-coupon bond maturing in 2 years with a face value of $1,000 and a yield to maturity of 2%. Assume the recovery rate is 40%, and that default can only happen exactly at the end of the 2-year period. There is a credit default swap (CDS) available for this bond, and the premium is 0.8%.

1. For both a bondholder and a CDS buyer (with notional value $1,000), compute the cash flows two years from today in the case where the bond defaults and the case where it doesn’t. Include only cash flows two years from today, and not the quarterly payments the CDS buyer makes to the CDS seller or the up-front cost of the bond.

Scenario	Bond cash flow	CDS cash flow
Default
No Default

2. Now consider a portfolio consisting of a bond with face value $1,000 and a CDS with notional value $1,000. Compute the cash flows two years from today in the case the bond defaults, and in the case it doesn’t. Include only cash flows two years from today, and not the quarterly payments the CDS buyer makes to the CDS seller or the up-front cost of the bond.

Scenario	Portfolio cash flow
Default
No Default

Answer 1

A. Scenerio 1 - In case of Default

Cash Flow for Bond Holder = Notional Amount * Recovery Rate

= 1000 * 40% = $400 (Inflow)

Cash flow for CDS Buyer = Notional Amount * (1- Recovery Rate)

= 1000 * (1-40%) = $600 (Inflow)

As per CDS Agreement, CDS buyer pays premium to CDS Seller ans in case of default , CDS seller makes on time payment to CDS Buyer of amount defaulted by reference Entity (i.e here Bond Issuer)

Scenerio 2 = In case of no Default

Cash Flow for Bond Holder = Notional Amount

= $1000 received as there is no default

Cash flow for CDS Buyer = 0 as there is no default , CDS seller is not liable to pay anything to CDS Buyer.

B. Portfolio Cash flows

In case of default = $400+ $600 = $1000

In case of no default = $1000 +0 = $1000

(Remember Bond is backed by CDS, CDS in the portfolio only has value if default occurs.

Also there is no need to do Weighted Average as both represents same asset, it is just that CDS is security here)