Reconstructed bond ETFs

Bonds are not reconstructed the way equities are. A bond ETF isn't a basket of returns to replicate with factors: it's a portfolio with a duration, exposed to the movements of a yield curve. So reconstruction starts there.

When UCITS quotes are too short, the past is rebuilt from a yield curve (Bund/Treasury, investment grade, aggregate). The proxy's monthly NAV follows the classic duration-and- convexity approximation; where possible it is then calibrated on real returns and spliced to the ETF's listed prices.

How it works

1. Choosing the curve driver

For each product, the yield series closest to its risk and duration profile is selected: 7–10 year government, investment grade corporate, aggregate. Euro-area curves come from the ECB; US Treasury curves come from public sources.

These are monthly observations of the curve, not prices of individual bonds.

2. From curve to NAV

Month by month, the yield change Δy is computed and the standard bond price approximation applied, accrued yield, minus duration effect, plus convexity, minus costs:

$r_t = y_t\,\Delta t - D\,\Delta y_t + \tfrac{1}{2}C\,(\Delta y_t)^2 - c_{\mathrm{TER}}\,\Delta t$

NAV starts at 100 and compounds multiplicatively:

$\mathrm{NAV}_t = \mathrm{NAV}_{t-1}\,(1 + r_t)$

Where:

• $\mathrm{NAV}_t$: cumulative value of the proxy; the first point is normalised to 100.
• $y_t$: annual curve yield in month $t$ (in decimals: 0.04 = 4%).
• $\Delta y_t = y_t - y_{t-1}$: yield change; $\Delta t$, years between observations, typically ≈ 1/12.
• $D$: the ETF's modified duration (years); $C$, the bond portfolio's convexity.
• $c_{\mathrm{TER}}$: annual product cost, subtracted proportionally to the period.

Where convexity isn't known a priori, the estimate $C \approx D(D+1)$ is used, typical of a plain-vanilla bond with duration $D$. For USD curves the NAV series is converted to euro at the historical end-of-month exchange rate.

3. Calibration against the listed ETF

If the UCITS ETF has enough history, simulated and real monthly returns are compared over the overlapping period. The average difference α (tracking residual) is added to each simulated period:

$r_t^{\mathrm{cal}} = r_t + \alpha$

where α is the mean of monthly returns (benchmark − simulated) over the common period.

Calibration recovers the systematic spreads a government curve alone doesn't capture, credit premium, roll-down, index tracking. It is not applied when benchmark history is insufficient.

4. Splicing with real quotes

At the first real monthly quote, the official NAV is anchored onto the synthetic proxy's level: reconstructed history covers only earlier dates, without duplicating the listed era. In the backtester the product appears as simfactor, with the synthetic track before listing and real prices after.

Which curves are used

Each row in the bond catalogue states the driver used. In general:

Reliability and limits

Replication via duration and yield curve gives a contained tracking error against reference bond indices, especially where credit risk is not material. On Treasuries, Bunds and government aggregates the track is accurate.

Where it degrades:

• High yield and stressed credit. When spreads blow out, high-yield behaviour is not described by duration and convexity. The α calibration helps on average, but it's a constant: it doesn't capture spread variation over time.
• Variable duration. The model uses a constant representative duration; the ETF's real duration moves with index composition.
• Estimated convexity. Where unknown, the $D(D+1)$ approximation is reasonable for a plain-vanilla bond, less so for portfolios with embedded optionality (callables, MBS).