Low-Volatility Factor Score

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/** D17 reference algorithms. JSON boundary validation is deliberate and shared.
 * Arrays are copied before sorting; callers' inputs are never mutated.
 * QR solves least squares without forming normal equations.
 */
type Data = Record<string, any>;
type Result = Record<string, any>;
class ContractError extends Error {
}
const fail = (code: string): never => { throw new ContractError(code); };
const num = (x: unknown): number => typeof x === 'number' && Number.isFinite(x) ? x : fail('INVALID_NUMBER');
function integer(x: unknown, lo: number, hi: number): number { const v = num(x); return Number.isInteger(v) && v >= lo && v <= hi ? v : fail('INVALID_PARAMETER'); }
function vec(x: unknown, min = 1): number[] { if (!Array.isArray(x))
    fail('INVALID_SHAPE'); const a = x as unknown[]; if (a.length < min)
    fail('INSUFFICIENT_DATA'); return a.map(num); }
function mat(x: unknown, min = 1): number[][] { if (!Array.isArray(x) || x.length < min)
    fail('INSUFFICIENT_DATA'); const a = (x as unknown[]).map(v => vec(v)); if (new Set(a.map(r => r.length)).size !== 1)
    fail('LENGTH_MISMATCH'); return a; }
function same(...x: {
    length: number;
}[]): void { if (new Set(x.map(a => a.length)).size !== 1)
    fail('LENGTH_MISMATCH'); }
function ids(d: Data, n: number): string[] { required(d, ['ids']); if (!Array.isArray(d.ids) || d.ids.length !== n)
    fail('LENGTH_MISMATCH'); if (d.ids.some((v: unknown) => typeof v !== 'string' || !/^[A-Za-z0-9_.-]+$/.test(v)))
    fail('INVALID_ID'); if (new Set(d.ids).size !== n)
    fail('DUPLICATE_ID'); return [...d.ids]; }
function required(d: Data, keys: string[]): void { for (const key of keys)
    if (!Object.hasOwn(d, key))
        fail('MISSING_FIELD'); }
function validDate(v: unknown): boolean { if (typeof v !== 'string' || !/^\d{4}-\d{2}-\d{2}$/.test(v) || v.startsWith('0000'))
    return false; const date = new Date(v + 'T00:00:00Z'); return Number.isFinite(date.valueOf()) && date.toISOString().slice(0, 10) === v; }
function context(d: Data, op: string): void {
    const keys = ['as_of', 'formation_at', 'inputs_available_at'];
    const evaluation = ['ic', 'rank_ic', 'spread', 'decay'].includes(op);
    if (evaluation)
        keys.push('outcomes_start_at', 'outcomes_end_at', 'outcomes_available_at');
    required(d, keys);
    if (keys.some(k => !validDate(d[k])))
        fail('INVALID_DATE');
    if (d.formation_at > d.as_of || d.inputs_available_at > d.formation_at)
        fail('FUTURE_INPUT');
    if (evaluation) {
        if (d.outcomes_start_at < d.formation_at || d.outcomes_end_at < d.outcomes_start_at)
            fail('INVALID_OUTCOME_WINDOW');
        if (d.outcomes_available_at < d.outcomes_end_at)
            fail('INVALID_DATE_ORDER');
        if (d.outcomes_available_at > d.as_of)
            fail('IMMATURE_OUTCOME');
    }
}
const sum = (a: number[]): number => a.reduce((s, v) => s + v, 0);
const mean = (a: number[]): number => sum(a) / a.length;
const dot = (a: number[], b: number[]): number => sum(a.map((v, i) => v * b[i]));
const tr = (a: number[][]): number[][] => a[0].map((_, j) => a.map(r => r[j]));
const mm = (a: number[][], b: number[][]): number[][] => { const cols = tr(b); return a.map(row => cols.map(col => dot(row, col))); };
function sd(x: number[], ddof = 0): number { const m = mean(x); return Math.sqrt(sum(x.map(v => (v - m) ** 2)) / (x.length - ddof)); }
function standard(x: number[]): number[] { const m = mean(x), s = sd(x); if (s <= 1e-14 * Math.max(1, ...x.map(Math.abs)))
    fail('CONSTANT_CROSS_SECTION'); return x.map(v => (v - m) / s); }
function corr(x: number[], y: number[]): number | null { same(x, y); if (Math.max(...x) === Math.min(...x) || Math.max(...y) === Math.min(...y))
    return null; const xm = mean(x), ym = mean(y), a = x.map(v => v - xm), b = y.map(v => v - ym), den = Math.sqrt(dot(a, a) * dot(b, b)); return den <= 0 ? null : Math.max(-1, Math.min(1, dot(a, b) / den)); }
function ranks(x: number[]): number[] { const order = x.map((_, i) => i).sort((a, b) => x[a] - x[b]); const out = x.map(() => 0); let start = 0; while (start < x.length) {
    let end = start + 1;
    while (end < x.length && x[order[end]] === x[order[start]])
        end++;
    for (let j = start; j < end; j++)
        out[order[j]] = (start + 1 + end) / 2;
    start = end;
} return out; }
function quantile(x: number[], p: number): number { const y = [...x].sort((a, b) => a - b), h = (y.length - 1) * p, j = Math.floor(h), f = h - j; return y[j] * (1 - f) + y[Math.min(j + 1, y.length - 1)] * f; }
function compound(x: number[]): number { if (x.some(v => v <= -1))
    fail('INVALID_RETURN'); return Math.expm1(sum(x.map(Math.log1p))); }
/** erfc(|z|/sqrt(2)) via regularized Gamma(1/2,x); converged series/CF. */
function normalP(z: number): number {
    const x = z * z / 2, a = 0.5, lg = 0.5723649429247001;
    if (x === 0)
        return 1;
    const factor = Math.exp(-x + a * Math.log(x) - lg);
    if (x < a + 1) {
        let term = 1 / a, total = term, ap = a;
        for (let i = 1; i < 500; i++) {
            ap++;
            term *= x / ap;
            total += term;
            if (Math.abs(term) < Math.abs(total) * 1e-15)
                break;
        }
        return Math.max(0, 1 - total * factor);
    }
    let b = x + 1 - a, c = 1e300, d = 1 / b, h = d;
    for (let i = 1; i < 500; i++) {
        const an = -i * (i - a);
        b += 2;
        d = an * d + b;
        if (Math.abs(d) < 1e-300)
            d = 1e-300;
        c = b + an / c;
        if (Math.abs(c) < 1e-300)
            c = 1e-300;
        d = 1 / d;
        const delta = d * c;
        h *= delta;
        if (Math.abs(delta - 1) < 1e-15)
            break;
    }
    return Math.max(0, Math.min(1, factor * h));
}
export function ols(y: number[], x: number[][], lags = 0): Result {
    const n = y.length, p = x[0].length;
    same(y, x);
    if (n <= p)
        fail('INSUFFICIENT_DATA');
    integer(lags, 0, n - 1);
    const cols = tr(x), scales = cols.map(c => Math.sqrt(dot(c, c)));
    if (scales.some(s => s === 0))
        fail('SINGULAR_DESIGN');
    const q: number[][] = [], r = Array.from({ length: p }, () => Array(p).fill(0) as number[]);
    for (let j = 0; j < p; j++) {
        let v = cols[j].map(z => z / scales[j]);
        for (let pass = 0; pass < 2; pass++)
            for (let i = 0; i < j; i++) {
                const proj = dot(q[i], v);
                r[i][j] += proj;
                v = v.map((z, t) => z - proj * q[i][t]);
            }
        r[j][j] = Math.sqrt(dot(v, v));
        if (r[j][j] < 1e-10)
            fail('SINGULAR_DESIGN');
        q.push(v.map(z => z / r[j][j]));
    }
    const solve = (v: number[]): number[] => { const b = Array(p).fill(0) as number[]; for (let i = p - 1; i >= 0; i--) {
        let s = 0;
        for (let j = i + 1; j < p; j++)
            s += r[i][j] * b[j];
        b[i] = (v[i] - s) / r[i][i];
    } return b; };
    const beta = solve(q.map(c => dot(c, y))).map((b, i) => b / scales[i]), fitted = x.map(row => dot(row, beta)), residuals = y.map((v, i) => v - fitted[i]);
    const invr = tr(Array.from({ length: p }, (_, j) => solve(Array.from({ length: p }, (_, i) => Number(i === j)))));
    const bread = mm(invr, tr(invr)).map((row, i) => row.map((v, j) => v / scales[i] / scales[j]));
    const scores = x.map((row, t) => row.map(v => v * residuals[t])), meat = mm(tr(scores), scores);
    for (let lag = 1; lag <= lags; lag++) {
        const w = 1 - lag / (lags + 1);
        for (let t = lag; t < n; t++)
            for (let i = 0; i < p; i++)
                for (let j = 0; j < p; j++)
                    meat[i][j] += w * (scores[t][i] * scores[t - lag][j] + scores[t - lag][i] * scores[t][j]);
    }
    const cov = mm(mm(bread, meat), bread), se = cov.map((row, i) => Math.sqrt(Math.max(0, row[i]))), sse = dot(residuals, residuals), ym = mean(y), sst = sum(y.map(v => (v - ym) ** 2));
    return { coefficients: beta, standard_errors: se, fitted, residuals, r_squared: sst === 0 ? null : 1 - sse / sst, n, df_residual: n - p, hac_lags: lags, residual_sum_squares: sse, qr_min_diagonal: Math.min(...r.map((row, i) => row[i])) };
}
function score(d: Data, op: string): Result {
    let raw: number[];
    if (op === 'value') {
        required(d, ['book_equity', 'market_equity']);
        const b = vec(d.book_equity, 3), m = vec(d.market_equity, 3);
        same(b, m);
        if (Math.min(...b, ...m) <= 0)
            fail('INVALID_DENOMINATOR');
        raw = b.map((v, i) => v / m[i]);
    }
    else if (op === 'size') {
        required(d, ['market_equity']);
        const m = vec(d.market_equity, 3);
        if (Math.min(...m) <= 0)
            fail('INVALID_DENOMINATOR');
        raw = m.map(v => -Math.log(v));
    }
    else if (op === 'profitability') {
        required(d, ['revenue', 'cogs', 'assets']);
        const a = vec(d.revenue, 3), b = vec(d.cogs, 3), c = vec(d.assets, 3);
        same(a, b, c);
        if (Math.min(...c) <= 0 || Math.min(...a, ...b) < 0)
            fail('INVALID_DENOMINATOR');
        raw = a.map((v, i) => (v - b[i]) / c[i]);
    }
    else if (op === 'quality') {
        required(d, ['roe', 'debt_equity', 'earnings_variability']);
        const a = vec(d.roe, 3), b = vec(d.debt_equity, 3), c = vec(d.earnings_variability, 3);
        same(a, b, c);
        if (Math.min(...b, ...c) < 0)
            fail('INVALID_DENOMINATOR');
        const components = tr([standard(a), standard(b).map(v => -v), standard(c).map(v => -v)]);
        raw = components.map(mean);
        return { ids: ids(d, raw.length), raw, scores: raw, components, primary: raw[0] };
    }
    else {
        required(d, ['returns']);
        const histories = mat(d.returns, 3), lookback = integer(d.lookback ?? (op === 'momentum' ? 11 : 12), op === 'momentum' ? 1 : 2, histories[0].length), skip = op === 'momentum' ? integer(d.skip ?? 1, 0, histories[0].length - lookback) : 0;
        if (histories.some(row => row.some(v => v < -1 || (op === 'momentum' && v === -1))))
            fail('INVALID_RETURN');
        const end = histories[0].length - skip, included = histories.map(row => row.slice(end - lookback, end));
        if (op === 'momentum')
            raw = included.map(compound);
        else {
            const annual = num(d.annualization ?? 12);
            if (annual <= 0)
                fail('INVALID_PARAMETER');
            raw = included.map(row => -sd(row, 1) * Math.sqrt(annual));
        }
        const scores = standard(raw);
        return { ids: ids(d, raw.length), raw, scores, primary: scores[0], window_start: end - lookback, window_end_exclusive: end, lookback, skip };
    }
    const scores = standard(raw);
    return { ids: ids(d, raw.length), raw, scores, primary: scores[0] };
}
/** D17-F02-A05 public boundary. No mutation, implicit imputation or silent failure. */
export function compute(input: unknown): Result {
    const op = "lowvol";
    try {
        if (!input || typeof input !== 'object' || Array.isArray(input))
            fail('INVALID_SHAPE');
        const d = input as Data;
        if (Object.values(d).some(v => v === null))
            fail('INVALID_NUMBER');
        context(d, op);
        const result = score(d, op);
        const check = (v: unknown): void => { if (typeof v === 'number' && !Number.isFinite(v))
            fail('NUMERICAL_FAILURE'); if (Array.isArray(v))
            v.forEach(check);
        else if (v && typeof v === 'object')
            Object.values(v).forEach(check); };
        check(result);
        return { status: 'ok', method: op, ...result };
    }
    catch (error) {
        if (error instanceof ContractError)
            return { status: 'error', method: op, code: error.message };
        throw error;
    }
}