Calculating Vault Performance

Overview

The rewards percentage is estimated on-the-fly using actual vault data. This takes the last five days or so of vault rewards and assumes they are representative of the next year.

The rewards shown exclude vault fees.

Technical Details

More concretely:

1. The TruMATIC / MATIC exchange rate as calculated by the vault is sampled periodically, on average every hour.

2. This time-series is then resampled, interpolating linearly in time between points in the price series to generate a new time-series with points precisely one hour apart.

3. The mean hourly return is taken over the last 120 share price readings.

4. This average is then compounded hourly to give an annual return.

Formally, denote by $\{(t_{i},s_{i})\}_{i=1,\dots,120}$ tuples representing successive times $t_{1} < \ldots < t_{120}$ and exchange rate prices originally sampled. This is converted into a time-series $\{(t^\prime_{j},s^\prime_{j})\}_{j = 1,\dots,n}$ where for each $j$

$$\begin{align*}t^\prime_{j+1} - t^\prime_{j} &= 1\text{ hour}\\ t^\prime_{n} &= t_{120} \\ s^\prime_{j} &= \frac{s_{i+1}(t_{i+1} - t^\prime_j) + s_{i}(t^\prime_{j} - t_{i})}{t_{i+1} - t_{i}}\end{align*}$$

where $i$ is such that $t_{i} \le t^\prime_{j} \le t_{i+1}$ and $n = \left\lfloor \frac{t_{120} - t_{1}}{\text{1 hour}} \right\rfloor$, i.e. the number of whole hours in the original sample. We then convert this into a list of hourly returns, adjusting for vault fees $r_{j} = (s_{j+1} / s_{j} - 1) / (1-\text{fee})$. To calculate the final rewards, we take the mean $\bar{r} = \frac{1}{n-1}\sum_{j=1}^{n-1}r_{j}$ of these hourly returns and compound this over a year to give an annual number:

$$\mathrm{APY} := \left(1+\bar{r}\right)^{24\times 365} - 1$$

Please note: the APY displayed on the front end is simply an estimate and can vary significantly depending on the performance of the network and of the validator to which we delegate.

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