🎯 Synthetic Benchmarks
LibreFolio can overlay synthetic benchmark curves on any FX chart. Unlike technical indicators (which are computed from market data), synthetic benchmarks are generated mathematically and serve as visual reference lines — "what if the price had followed this ideal trajectory?"
They are invaluable for:
- Comparing actual returns against a target growth rate.
- Visualising what a disciplined investment plan would look like.
- Adding oscillatory or cyclic references for seasonality analysis.
📈 Linear Growth
💡 Financial Meaning
A linear growth benchmark represents simple interest — the value increases by a fixed absolute amount each period. This models the scenario where you do not reinvest earnings (dividends, interest, coupons): cash payouts are received but kept aside, so only the original principal generates returns.
If instead you reinvest those earnings — either manually or automatically through accumulating instruments (e.g., accumulating ETFs, which reinvest dividends internally and benefit from tax deferral) — you should expect compound growth, where returns generate further returns.
In practice, the difference between linear and compound growth widens dramatically over long horizons. This is why the Linear benchmark appears as a straight line while the Compound benchmark curves upward exponentially.
Capital gains & losses
When selling an asset above its purchase price, the difference is a capital gain; below, a capital loss. Each jurisdiction has its own rules regarding tax rates, holding period thresholds, loss carry-forward duration, and matching methods (FIFO, LIFO, specific identification). For a theoretical overview, see Taxation & Tax Efficiency.
🔢 Mathematical Formula
where:
- \(y_0\) is the starting value (first data point of the chart),
- \(r\) is the annual growth rate (expressed as a decimal, e.g. 0.07 for 7%),
- \(t\) is time in years from the start.
This is equivalent to the simple interest formula \(A = P(1 + rt)\), where \(t\) is expressed in years using the applicable Day Count Convention.
⚙️ Parameters
| Parameter | Key | Default | Description |
|---|---|---|---|
| Annual Rate | annualRate |
5 | Growth rate in percent per year. |
| Offset | offset |
0 | Vertical shift as % of base value. |
🔍 Interpretation
The line is perfectly straight on a linear scale. Any point where the actual price is above the line means the asset has outperformed the target; any point below means underperformance. Because the growth is additive, the line curves downward on a logarithmic scale — making it easy to visually distinguish from compound growth.
📊 Compound Growth
💡 Financial Meaning
A compound growth benchmark represents compound interest — the value grows exponentially, meaning returns are reinvested. This is the natural growth model for most financial assets and the standard assumption in discounted cash flow (DCF) analysis.
🔢 Mathematical Formula
where:
- \(y_0\) is the starting value,
- \(r\) is the annual growth rate (decimal),
- \(t\) is time in years from the start.
This is equivalent to the compound interest formula \(A = P(1 + r)^t\) with annual compounding. The generalised formula with \(n\) compounding periods per year is:
LibreFolio's backend supports the following compounding frequencies: Annual (\(n=1\)), Semiannual (\(n=2\)), Quarterly (\(n=4\)), Monthly (\(n=12\)), Daily (\(n=365\)), and Continuous (\(n \to \infty\)).
When \(n \to \infty\) (continuous compounding):
🔄 Iterative Computation (Daily Stepping)
In LibreFolio the compound curve is computed iteratively rather than calling
pow() for each data point. This is both more efficient and instructive:
Then, for each successive day:
This is mathematically equivalent to the closed-form \(y_0(1+r)^t\) but replaces \(N\) expensive power operations with \(N\) simple multiplications — the same principle behind how banks actually accrue daily compound interest.
Rule of 72
A quick mental shortcut: an investment growing at \(r\)% per year will approximately double in \(72 / r\) years. At 7% → ~10.3 years.
⚙️ Parameters
| Parameter | Key | Default | Description |
|---|---|---|---|
| Annual Rate | annualRate |
7 | Compound growth rate in percent per year. |
| Offset | offset |
0 | Vertical shift as % of base value. |
🔍 Interpretation
The curve is straight on a logarithmic scale — this is the telltale sign of exponential growth. Overlaying a compound benchmark on a log-scale chart is the cleanest way to judge whether an asset is growing faster or slower than a target rate.
Compound Interest on Wikipedia
🌊 Sine Wave
💡 Financial Meaning
A sine wave benchmark represents periodic oscillation. It is useful for:
- Modelling seasonality (e.g. agricultural commodities, tourism-linked currencies).
- Providing a visual reference for cyclic patterns that traders suspect in the data.
- Testing the rendering pipeline with a known analytic waveform.
🔢 Mathematical Formula
where:
- \(A\) is the amplitude (peak-to-peak range as % of base value),
- \(T\) is the period in days,
- \(y_0\) is the base value (first data point),
- \(\text{offset}\) is a vertical shift.
⚙️ Parameters
| Parameter | Key | Default | Description |
|---|---|---|---|
| Amplitude | amplitude |
10 | Peak oscillation range as % of base value. |
| Period | period |
365 | Full cycle length in days. |
| Offset | offset |
0 | Vertical shift as % of base value. |
🔍 Interpretation
If the actual price roughly tracks the sine reference, the market exhibits a detectable cyclic component at that frequency. Deviations from the sine suggest non-periodic shocks or trend drift. Adjusting the period parameter lets you scan across different cycle lengths — effectively performing a manual version of spectral analysis.