Zero-Coupon Bond Yield Calculation

Article Quant Q&A · Author: david.t_92

Summary

The document addresses why a Chinese zero-coupon bond's quoted price may not rise toward face value as maturity approaches, and why a conventional compounded-yield calculation produces unusual results. The answer says this instrument uses a different convention from a typical zero-coupon bond: accrued interest is calculated linearly from the discount between face value and issue price, based on the portion of the issue-to-maturity period that has elapsed.

After adding accrued interest to the traded price, the answer derives a simple yield by comparing that adjusted price with face value and annualizing over the remaining time to maturity. It illustrates the calculation with a market observation and says the result matches the bond pricer. The response suggests that market documentation may confirm the convention, but it does not provide that source. Its formulas and example concern the stated bond convention; they should not be assumed to apply to all zero-coupon securities or markets.

Key ideas

The bond uses accrued interest tied to the elapsed portion of its issue-to-maturity period.
The accrued amount is added to the traded price before calculating yield.
The answer uses a simple yield convention rather than a compounded zero-coupon yield.
The calculation is presented as specific to this bond and its market convention.

Tags

Fixed income China markets Statistics

Full text

# Strange Market Data YTM for a Zero Coupon Bond


# Strange Market Data YTM for a Zero Coupon Bond












I am trying to compute the YTM of the following Zero-Coupon Bond:

The issue date was 13-01-2022 and the maturity date was 14-01-2023.

For me, it seems strange that the price remains "almost constant" when expiration approaches, I expect to tend to 100.

Also, I've manually computed the YTM using the following formula:

$$\text{YTM} = \left(\frac{Face Value}{Price}\right)^{(\frac{1}{n})} - 1 $$

And obtained the following results:

11/30/2022 -> YTM: 27.68%

10/31/2022 -> YTM: 21.46%

09/30/2022 -> YTM: 18.59%

04/30/2022 -> YTM: 15.82%

01/31/2022 -> YTM: 2.80%

Can anyone help me to understand why this happens? Could the BBG data be wrong as this comes from CHBE?

Thanks in advance.

## Answer by oronimbus (score 4, accepted)

https://quant.stackexchange.com/a/74919

This bond has a slightly different calculation logic to your average zero coupon bond. Denote $t$ the trade date, $t_0$ the issue date, $T$ the maturity date and $P$ the traded price.

You'll first need to calculate the accrued interest which is equal to: $$\text{AI} = \left(100-P_{\text{issue}}\right)\times \frac{t-t_0}{T-t_0}$$

Once you have the accrued, you can calculate the simple yield (not the compounded yield!) as: $$y_\text{simple}=\left(\frac{100}{P+\text{AI}}-1\right)\times \frac{T-t_0}{T-t}$$

To give you an example as of 31/10/22:

```
=(100/(97.5359+(100-97.3855)*290/365)-1)/(75/365)
```

Which matches exactly what the bond pricer is showing:

You can probably find confirmation for this somewhere on the CFETS website, although I haven't checked in detail.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.

Yield Calculation for an Amortizing-Discount Zero-Coupon Bond

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