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Financial Essay

2261 words - 10 pages


Yield Spread is the difference between the yield-to-maturity of a risky bond and the yield-to-maturity of an on-the-run treasury benchmark bond with similar but not necessarily identical maturity.

YTM is the constant discount rate which, when applied to the bond’s cash flows, re-prices the bond.
* An investor who buys a bond can achieve a return equal to the YTM if the bond is held to maturity and if all coupons can be reinvested at the same rate as the YTM. In practice, this is difficult if not impossible to achieve since changes in the credit quality of the issuer may cause yields to change through time. As many ...view middle of the document...

However, the 5 year on-the-run treasury security would have changed multiple times in 5 years. As a result, yield spread is not a consistent measure through time.

* The YTM and yield-spread measures are only rough measures of return and therefore, credit risk. In no way do they actually measure the realized YTM of holding the asset.
* As a result, the yield spread should only be used strictly as a way to express the price of a bond relative to the benchmark, rather than a measure of credit risk. The only time when it may become useful is if the asset and Treasury are both trading at or very close to par. In this case, the YTM of the risky (defaultable) bond and treasury are close to their coupon values and the yield spread is a measure of the annualized carry from buying the defaultable bond and shorting the Treasury.

To overcome the issue of the maturity mismatch in the yield spread above, it is possible to use a benchmark yield where the correct maturity yield has been interpolated off the appropriate reference curve. Rather than choose a specific reference benchmark bond, the idea is to use a reference yield curve which can be interpolated.

The Interpolated Spread (I-spread): is the difference between the YTM of the risky bond and the linearly interpolated yield to the same maturity on an appropriate reference curve, such as the treasury yield curve.
The simplest way to interpolate the yield off the treasury curve is to find two treasury bonds which straddle the maturity of the defaultable (risky) bond. It is then simple to linearly interpolate the YTM of these two treasury bonds to find the yield corresponding to the maturity of the credit-risky bond.

* Viewed purely as a yield comparison, I-spread gets around the problem of mismatched maturity when calculating the yield spread, but it does not necessarily correspond to the YTM of a traded reference bond (the interpolated treasury security does not exist).
* In addition, it inherits all the drawbacks of the YTM measure, and so should be interpreted as a way to express the price of the defaultable bond relative to a curve.
* I-spread does take into account the shape of the term structure of interest rates, but only in a very crude way.

* If the reference curve is upward sloping and the benchmark has a shorter maturity, then the I-spread will be less than the yield spread.
* If the reference curve is downward sloping and the maturity is shorter than that of the benchmark, then the I-spread will be greater than the yield spread.

Z-SPREAD (Zero Volatility, Static Spread):
The Z-spread is the static spread that can be added to the zero-coupon (spot rate) treasury or the swap-rate yield curve that will make the present value of the future payments (coupon and face value) equal to the current price of the bond. As opposed to a single-point on the yield curve, the Z-spread uses the...

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