Spread Measures
What you'll learn
- LOS 23.fCalculate and interpret the swap spread for a given maturity.
- LOS 23.gDescribe short term interest rate spreads used to gauge economy wide credit risk and liquidity risk.
Swap spread refers to the amount by which the swap rate exceeds the yield of a government bond with the same maturity.
For example, if the fixed rate of a one year fixed for floating MRR swap is 0.57% and the one year Treasury is yielding 0.11%, the 1 year swap spread is 0.57% − 0.11% = 0.46%, or 46 bps.
Swap spreads are almost always positive, reflecting the lower credit risk of governments compared to the credit risk of surveyed banks that determines the swap rate.
The swap rate curve is arguably the most commonly used interest rate curve. This rate curve roughly reflects the default risk of a commercial bank with a credit rating of A1/A+.
The two year fixed for floating swap rate is 2.02% and the two year U.S. Treasury bond is yielding 1.61%. What is the swap spread?
Solution
I Spread
The I spread, or interpolated spread, for a credit risky bond is the amount by which the yield on the risky bond exceeds the swap rate for the same maturity. In a case where the swap rate for a specific maturity is not available, the missing swap rate can be estimated from the swap rate curve using linear interpolation.
6% Zinni, Inc., bonds are currently yielding 2.35% and mature in 1.6 years. From the provided swap curve, compute the I spread.
Swap curve:
| Tenor | Swap Rate |
|---|---|
| 0.5 | 1.00% |
| 1 | 1.25% |
| 1.5 | 1.35% |
| 2 | 1.50% |
Solution
Linear interpolation:
First, recognize that 1.6 years falls in the 1.5 to 2 year interval.
While a bond’s yield reflects time value as well as compensation for credit and liquidity risk, I spread only reflects compensation for credit and liquidity risks. The higher the I spread, the higher the compensation for liquidity and credit risk.
The Z Spread
The Z spread is the spread that, when added to each spot rate on the default free spot curve, makes the present value of a bond’s cash flows equal to the bond’s market price. Therefore, the Z spread is a spread over the entire spot rate curve.
For example, suppose the one year spot rate is 4% and the two year spot rate is 5%. The market price of a two year bond with annual coupon payments of 8% is $104.12. The Z spread is the spread that balances the following equality:
In this case, the Z spread is 0.008, or 80 basis points. (Plug Z = 0.008 into the right hand side of the equation just listed to reassure yourself that the present value of the bond’s cash flows equals $104.12).
The term zero volatility in the Z spread refers to the assumption of zero interest rate volatility. Z spread is not appropriate to use to value bonds with embedded options; without any interest rate volatility options are meaningless. If we ignore the embedded options for a bond and estimate the Z spread, the estimated Z spread will include the cost of the embedded option (i.e., it will reflect compensation for option risk as well as compensation for credit and liquidity risk).
A three year, 5% annual pay ABC, Inc., bond trades at a Z spread of 100 bps over the benchmark spot rate curve.
The benchmark one year spot rate, one year forward rate in one year and one year forward rate in year 2 are 3%, 5.051%, and 7.198%, respectively.
Compute the bond’s price.
Solution
First derive the spot rates:
value (with Z spread) =
TED Spread
The “TED” in “TED spread” is an acronym that combines the “T” in “T bill” with “ED” (the ticker symbol for the Eurodollar futures contract).
Conceptually, the TED spread is the amount by which the MRR exceeds the interest rate on short term U.S. government debt of the same maturity.
For example, if three month MRR is 0.33% and the three month T bill rate is 0.03%, then:
Because T bills are considered to be risk free while MRR reflects the risk of lending to commercial banks, the TED spread is seen as an indication of the credit and liquidity risk in the banking sector. A rising TED spread indicates that market participants believe banks are increasingly likely to default on loans and that risk free T bills are becoming more valuable in comparison. The TED spread captures the risk in the banking system more accurately than does the 10 year swap spread.
MRR OIS Spread
OIS stands for overnight indexed swap and represents interest rate on unsecured overnight lending between banks. The OIS rate roughly reflects the federal funds rate and includes minimal counterparty credit risk.
The MRR OIS spread (formerly the LIBOR OIS spread) is the amount by which the MRR (which includes some credit risk) exceeds the OIS rate (which includes only minimal credit risk) and also indicates the level of credit and liquidity risk in the banking system.