Definitions

The Z-spread (or ZSPRD) of a bond is the number of basis points one needs to apply to a series of zero rates such that the present value of the bond, accounting for accrued interest, equals the sum of all future cashflows discounted using the adjusted zero rate. The spread is calculated iteratively and provides a more accurate reflection of value than other measures as it uses the entire yield curve to value the cashflows.

If you calculate the present value all future cashflows for a bond using prevailing spot rates, you will discover that the price you calculate is greater than the price observed in the market. This difference arises because the market price incorporates additional factors such as liquidity and credit risk. The Z-spread quantifies the impact of these additional factors. It is the spread you need to add to the curve you are discounting with in order to generate a price that matches the market price.

Conventionally, the zero rates are determined from the Treasury curve, with semi-annual compounding.

## Example

Assume that a bond has three cashflows: \$5 on 1/1/1995; \$5 on 1/1/1996; and \$105 on 1/1/1997.

The corresponding zero rates (compounded semiannually) are 4.5% on 1/1/1995, 4.7% on 1/1/1996 and 5% on 1/1/1997.

Assuming that the accrued interest is 0, and the Z-spread is 50 basis points, the price of this bond on 1/1/1994, P, is given by:


begin{align} P & = frac{5}{(1 + frac{4.5% + 50 bp}{2})^{(2 times 1)}} + frac{5}{(1 + frac{4.7% + 50 bp}{2})^{(2 times 2)}} + frac{105}{(1 + frac{5.0% + 50 bp}{2})^{(2 times 3)}}
`     & = 98.49861 `
end{align}