Metrics Over Time
The Metrics
| Metric | Calculation | What it shows |
|---|---|---|
| Price Change % | changet = Pt − P0P0 × 100 A market's close against its first close, as a percentage. P0 is the first bar every market shares, not each market's own first bar, so the six are measured from one day. | What a unit bought at the start would be worth now. It is the context for the rows under it — the same movement is a different fact depending on whether a market was climbing or falling through it. |
| Annualized volatility | σt = sd(rt−N+1,…,rt) × √B The deviation of the last N log returns, scaled to a year by the root of the number of bars a year holds at that bar size. N is 720 bars and B follows the panel — 365 at a daily bar, 17,520 at 30 minutes. | How roughly a market moves, in the one unit that compares bar sizes and markets. A market at 50% is moving in a way that, kept up for a year, would put it half its own value from where it started. |
| Volatility of volatility | vovt = sd(|r|)mean(|r|) The deviation of the window's bar sizes over their own mean. A ratio rather than a size, so one axis carries every market and every bar size at once. | Whether a market's movement arrives evenly or in bursts. Near one the bars are spread the way an ordinary market spreads them; well above it, the window's whole move came from a handful of bars. |
| Return skew | skewt = mean((r − mean(r))3)sd(r)3 The standardized third moment of the window's returns. Zero is a symmetric window; the sign says which side the long tail is on. | Which direction a market's biggest bars go. Below zero it grinds up and falls hard, which is the usual shape; above zero it grinds down and jumps, which on this page is the meme pairs and almost nothing else. |
| Sideways % of window | ER = |rt−n+1 + … + rt||rt−n+1| + … + |rt| The efficiency ratio over 30 bars — net move against the sum of the moves that made it — then the share of the last 720 bars where it sat below 0.30. Two windows: a local reading of whether price is getting anywhere, and a long one saying how much of the time it was not. | How much of a market's life is spent going nowhere. The threshold is a choice rather than a standard, so the level is worth less than the shape — what matters is when a market leaves a range, not the exact percentage it sat at while inside one. |
| Uptrend % of window | upt = mean(ER > 0.30 and rnet > 0) × 100 The same 30-bar efficiency ratio as the row above, counted the other way: the share of the last 720 bars where it cleared 0.30 and the net move that got it there was positive. | How much of a market's life is spent climbing rather than ranging or falling. Read against the row above: what the two leave unaccounted for is the share spent trending down, so a flat sideways share with this one falling is a market turning over rather than calming. |
| Downtrend % of window | downt = mean(ER > 0.30 and rnet < 0) × 100 The same 30-bar efficiency ratio again, with the net move negative. With the two rows above it this accounts for the whole window: sideways, up and down add to a hundred at every bar. | How much of a market's life is spent falling with conviction, as opposed to drifting. Read as the third of a set — a market whose sideways share is steady while this one grows is not getting quieter, it is turning over. |
| Correlation to index | corrt = cov(r, rI)sd(r) sd(rI) Correlation of a market's log returns against the all-markets index's, over the same 720-bar window. Bounded between -1 and 1, so it needs no log axis and no room made for an outlier. | Whether these are six markets or one trade held six ways. Near 1 a market carries no risk the index does not already carry, so holding several of them is leverage rather than diversification. |
| Beta to index | betat = cov(r, rI)var(rI) The slope of a market's returns regressed on the index's, over the same window. One above means it moves further than the index; one below, less far. | The half of the picture correlation leaves out. Correlation says a market goes the same way as the index; beta says how far it goes when it does, and that is what decides what holding it does to a position. |
| Alpha % a year | αt = (mean(r) − beta · mean(rI)) × B The intercept of the same fit, annualized. What the market returned beyond what its beta to the index already accounts for. | Whether a market paid for itself or merely kept up. Over a window this short it is mostly noise at the fast end, which is itself the answer: alpha measured over a fortnight is not a fact about a market. |
| Turnover $M per bar | turnovert = mean(P V) Close times base-asset volume, averaged over the window and quoted in millions of dollars. In dollars rather than coins, since Dogecoin trades in billions of them and Bitcoin in thousands. | How much money actually moves through a market. The row below says what trading it costs; this one says whether there was anything to trade — and the two are not the same question. |
| Illiquidity % per $bn | illiqt = mean(|r|P V) × 109 Amihud illiquidity: each bar's move divided by the dollars that traded in it, averaged over the window and scaled to a percentage move per billion dollars of turnover. | What it costs to trade size. The only row here not made of price alone, and the one that says whether a backtest's fills were plausible — a rule working a thin market pays for the move it makes itself, on top of the fee. |
The Charts
Every metric, by bar size
Every market from August 2020 · one shared axis along each row · 720-bar window: 15d at 30m, 30d at 1h, 120d at 4h, 720d at 1d
What each market averages, by bar size
The mean of every line above, over its whole length · one panel per metric