Return-series statistics: arithmetic mean return, volatility (sample stdev), annualized Sharpe ratio, and max drawdown of an equity curve

returns_stats.cell

// Return-series statistics: arithmetic mean return, volatility (sample
// stdev), annualized Sharpe ratio, and max drawdown of an equity curve.
// sqrt/pow, sum() reductions, running peak tracking.

cell ReturnStats {
    face {
        signal mean_return(rets: List) -> Float
        signal volatility(rets: List) -> Float
        signal sharpe(rets: List, rf: Float) -> Float
        signal max_drawdown(equity: List) -> Float
    }

    on mean_return(rets: List) {
        return sum(rets) / len(rets)
    }

    // sample standard deviation (n-1 denominator)
    on volatility(rets: List) {
        let mu = mean_return(rets)
        let acc = 0.0
        for r in rets {
            acc = acc + (r - mu) * (r - mu)
        }
        return sqrt(acc / (len(rets) - 1))
    }

    // (mean - rf) / vol, annualized by sqrt(252)
    on sharpe(rets: List, rf: Float) {
        let excess = mean_return(rets) - rf
        let vol = volatility(rets)
        if vol == 0.0 { return 0.0 }
        return excess / vol * sqrt(252.0)
    }

    // largest peak-to-trough decline as a positive fraction
    on max_drawdown(equity: List) {
        let peak = equity[0]
        let worst = 0.0
        for v in equity {
            if v > peak { peak = v }
            let dd = (peak - v) / peak
            if dd > worst { worst = dd }
        }
        return worst
    }
}

cell test ReturnStatsTests {
    rules {
        // mean of [0.01, 0.02, 0.03] = 0.02
        assert abs(mean_return(list(0.01, 0.02, 0.03)) - 0.02) < 0.0001
        // volatility of that series: sample stdev = 0.01
        assert abs(volatility(list(0.01, 0.02, 0.03)) - 0.01) < 0.0001
        // positive returns vs zero rf → positive Sharpe
        assert sharpe(list(0.01, 0.02, 0.03), 0.0) > 0.0
        // equity 100 → 120 → 90 → 110: max drawdown = (120-90)/120 = 0.25
        assert abs(max_drawdown(list(100.0, 120.0, 90.0, 110.0)) - 0.25) < 0.0001
        // monotonically rising curve has zero drawdown
        assert abs(max_drawdown(list(100.0, 110.0, 120.0))) < 0.0001
    }
}