Strange Market Data YTM for a Zero Coupon Bond

Question

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 1

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.