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+module fundit::indicatorCalculator
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+
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+/*
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+ * Annulized multiple
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+ */
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+def get_annulization_multiple(freq) {
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+
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+ ret = 1;
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+
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+ if (freq == 'd') {
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+ ret = 252; // We have differences here between Java and DolphinDB, Java uses 365.25 days
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+ } else if (freq == 'w') {
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+ ret = 52;
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+ } else if (freq == 'm') {
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+ ret = 12;
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+ } else if (freq == 'q') {
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+ ret = 4;
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+ } else if (freq == 's') {
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+ ret = 2;
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+ } else if (freq == 'a') {
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+ ret = 1;
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+ }
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+
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+ return ret;
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+}
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+
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+
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+/*
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+ * Trailing Return, Standard Deviation, Skewness, Kurtosis, Max Drawdown, VaR, CVaR
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+ * @param ret: 收益表,需要有 entity_id, price_dat, end_date, nav
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+ * @param freq: 数据频率,d, w, m, q, s, a
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+ *
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+ * Create: 20240904 Joey
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+ * TODO: var and cvar are silightly off compared with Java version
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+ *
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+ */
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+def cal_basic_performance(ret) {
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+
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+ t = SELECT entity_id, max(end_date) AS end_date, max(price_date) AS price_date, min(price_date) AS min_date,
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+ (nav.last() \ nav.first() - 1).round(6) AS trailing_ret,
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+ iif(price_date.max().month()-price_date.min().month()>12,
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+ (nav.last() \ nav.first()).pow(365 \(max(price_date) - min(price_date)))-1,
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+ (nav.last() \ nav.first() - 1)).round(6) AS trailing_ret_a,
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+ ret.std() AS std_dev,
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+ ret.skew(false) AS skewness,
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+ ret.kurtosis(false) - 3 AS kurtosis,
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+ ret.min() AS wrst_month,
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+ max( 1 - nav \ nav.cummax() ) AS drawdown
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+ FROM ret
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+ GROUP BY entity_id;
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+
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+ // var & cvar require return NOT NULL
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+ // NOTE: DolphinDB supports 4 different ways: normal, logNormal, historical, monteCarlo. we use historical
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+ t1 = SELECT entity_id, max(end_date) AS end_date, max(price_date) AS price_date,
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+ ret.VaR('historical', 0.95) AS var,
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+ ret.CVaR('historical', 0.95) AS cvar
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+ FROM ret
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+ WHERE ret.ret > - 1
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+ GROUP BY entity_id;
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+
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+ return (SELECT * FROM t LEFT JOIN t1 ON t.entity_id = t1.entity_id AND t.end_date = t1.end_date AND t.price_date = t1.price_date);
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+
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+}
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+
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+
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+/*
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+ * Lower Partial Moment
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+ * NOTE: risk free rate is used as Minimal Accepted Rate (MAR) here
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+ *
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+ */
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+def cal_LPM(ret, risk_free_rate) {
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+
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+ t = SELECT *, count(entity_id) AS cnt FROM ret WHERE ret > -1 CONTEXT BY entity_id;
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+
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+ lpm = SELECT t.entity_id, max(t.end_date) AS end_date,
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+ (sum (rfr.ret - t.ret) \ (t.cnt[0])).pow(1\1) AS lpm1,
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+ (sum2(rfr.ret - t.ret) \ (t.cnt[0])).pow(1\2) AS lpm2,
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+ (sum3(rfr.ret - t.ret) \ (t.cnt[0])).pow(1\3) AS lpm3
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+ FROM t
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+ INNER JOIN risk_free_rate rfr ON t.end_date = rfr.end_date
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+ WHERE t.ret < rfr.ret
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+ GROUP BY t.entity_id;
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+
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+ return lpm;
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+}
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+
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+/*
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+ * Downside Devision, Omega Ratio, Sortino Ratio, Kappa Ratio
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+ *
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+ * TODO: Java version of Downside Deviation (LPM2) uses cnt-1 as denominator to calculate mean excess return, which might be wrong
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+ * Java version of Omega could be wrong because Java uses annualized returns and cnt-1
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+ * Java'version of Kappa could be very wrong
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+ *
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+ */
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+def cal_omega_sortino_kappa(ret, risk_free_rate) {
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+
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+ lpm = cal_LPM(ret, risk_free_rate);
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+
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+ tb = SELECT t.entity_id,
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+ l.lpm2[0] AS ds_dev,
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+ (t.ret - rfr.ret ).mean() \ l.lpm1[0] + 1 AS omega,
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+ (t.ret - rfr.ret ).mean() \ l.lpm2[0] AS sortino,
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+ (t.ret - rfr.ret ).mean() \ l.lpm3[0] AS kappa
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+ FROM ret t
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+ INNER JOIN lpm l ON t.entity_id = l.entity_id
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+ INNER JOIN risk_free_rate rfr ON t.end_date = rfr.end_date
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+ GROUP BY t.entity_id;
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+
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+ return tb;
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+}
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+
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+
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+/*
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+ * Alpha & Beta
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+ *
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+ */
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+def cal_alpha_beta(ret, bmk_ret, risk_free) {
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+
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+ t = SELECT t.entity_id, t.end_date, t.ret, bmk.ret AS ret_bmk
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+ FROM ret t
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+ INNER JOIN bmk_ret bmk ON t.end_date = bmk.end_date
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+ WHERE t.ret > -1
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+ AND bmk.ret > -1;
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+
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+ beta = SELECT ret.beta(ret_bmk) AS beta FROM t GROUP BY entity_id;
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+
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+ alpha = SELECT t.entity_id, (t.ret - rfr.ret).mean() - beta.beta[0] * (t.ret_bmk - rfr.ret).mean() AS alpha
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+ FROM t
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+ INNER JOIN beta beta ON t.entity_id = beta.entity_id
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+ INNER JOIN risk_free_rate rfr ON t.end_date = rfr.end_date
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+ GROUP BY t.entity_id;
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+
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+ return ( SELECT * FROM beta AS b INNER JOIN alpha AS a ON a.entity_id = b.entity_id );
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+}
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+
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+/*
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+ * Winning Ratio, Tracking Error, Information Ratio
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+ * TODO: Information Ratio is way off!
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+ * Not sure how to describe a giant number("inf"), for now 999 is used
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+ */
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+def cal_benchmark_tracking(ret, bmk_ret) {
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+
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+ t0 = SELECT t.entity_id, t.end_date, t.ret, bmk.ret AS ret_bmk, count(entity_id) AS cnt, (t.ret - bmk.ret) AS exc_ret
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+ FROM ret t
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+ INNER JOIN bmk_ret bmk ON t.end_date = bmk.end_date
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+ WHERE t.ret > -1
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+ AND bmk.ret > -1
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+ CONTEXT BY t.entity_id;
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+
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+ t = SELECT entity_id,
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+ exc_ret.bucketCount(0:999, 1) \ cnt[0] AS winrate,
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+ exc_ret.std() AS track_error,
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+ exc_ret.mean() / exc_ret.std() AS info
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+ FROM t0 GROUP BY entity_id
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+
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+ return t;
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+}
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+
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+/*
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+ * Sharpe Ratio
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+ */
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+def cal_sharpe(ret, std_dev, risk_free_rate) {
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+
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+ sharpe = SELECT t.entity_id, (t.ret - rfr.ret).mean() / std.std_dev[0] AS sharpe
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+ FROM ret t
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+ INNER JOIN std_dev std ON t.entity_id = std.entity_id
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+ INNER JOIN risk_free_rate rfr ON t.end_date = rfr.end_date
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+ GROUP BY t.entity_id;
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+
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+ return sharpe;
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+}
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+
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+/*
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+ * Treynor Ratio
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+ */
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+def cal_treynor(ret, risk_free_rate, beta) {
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+
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+ t = SELECT *, count(entity_id) AS cnt
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+ FROM ret t
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+ INNER JOIN risk_free_rate rfr ON t.end_date = rfr.end_date
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+ WHERE t.ret > -1
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+ AND rfr.ret > -1
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+ CONTEXT BY t.entity_id;
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+
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+ treynor = SELECT t.entity_id, ((1 + t.ret).prod().pow(12\iif(t.cnt[0]<12, 12, t.cnt[0])) - (1 + t.rfr_ret).prod().pow(12\iif(t.cnt[0]<12, 12, t.cnt[0]))) / beta.beta[0] AS treynor
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+ FROM t
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+ INNER JOIN beta AS beta ON t.entity_id = beta.entity_id
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+ GROUP BY t.entity_id;
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+
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+ return treynor;
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+}
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+
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+/*
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+ * Jensen's Alpha
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+ * TODO: the result is slightly off
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+ */
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+def cal_jensen(ret, bmk_ret, risk_free_rate, beta) {
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+
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+ jensen = SELECT t.entity_id, t.ret.mean() - rfr.ret.mean() - beta.beta[0] * (bmk.ret.mean() - rfr.ret.mean()) AS jensen
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+ FROM ret t
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+ INNER JOIN bmk_ret bmk ON t.end_date = bmk.end_date
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+ INNER JOIN risk_free_rate rfr ON t.end_date = rfr.end_date
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+ INNER JOIN beta beta ON t.entity_id = beta.entity_id
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+ GROUP BY t.entity_id;
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+
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+ return jensen;
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+}
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+
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+/*
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+ * Calmar Ratio
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+ * TODO: the result is off
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+ *
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+ */
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+def cal_calmar(ret_a){
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+
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+ calmar = SELECT entity_id, trailing_ret_a \ drawdown AS calmar
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+ FROM ret_a;
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+
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+ return calmar;
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+}
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+
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+/*
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+ * Modigliani Modigliani Measure (M2)
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+ * NOTE: M2 = sharpe * std(benchmark) + risk_free_rate
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+ */
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+def cal_m2(ret, bmk_ret, risk_free_rate) {
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+
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+ m2 = SELECT t.entity_id, (t.ret - rfr.ret).mean() / t.ret.std() * bmk.ret.std() + rfr.ret.mean() AS m2
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+ FROM ret t
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+ INNER JOIN bmk_ret bmk ON t.end_date = bmk.end_date
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+ INNER JOIN risk_free_rate rfr ON t.end_date = rfr.end_date
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+ GROUP BY t.entity_id;
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+
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+ return m2;
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+}
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+
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+
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+/*
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+ * Monthly Since_inception_date Indicator Calculation
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+ * @param: ret: historical return table
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+ * index_ret: historical benchmark return table
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+ * risk_free: historical risk free rate table
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+ *
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+ * @return: indicators table
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+ *
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+ *
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+ * Create 20240904 模仿Java & python代码在Dolphin中实现,具体计算逻辑可能会有不同 Joey
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+ * TODO: some datapoints require more data, we need a way to disable calculation for them
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+ *
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+ */
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+def cal_indicators(mutable ret, index_ret, risk_free, freq) {
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+
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+ if (! freq IN ['d', 'w', 'm', 'q', 's', 'a']) return null;
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+
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+ // sorting for correct first() and last() value
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+ ret.sortBy!(['entity_id', 'price_date'], [1, 1]);
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+
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+ // 收益、标准差、偏度、峰度、最大回撤、VaR, CVaR
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+ rtn = cal_basic_performance(ret);
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+
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+ // alpha, beta
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+ alpha_beta = cal_alpha_beta(ret, index_ret, risk_free);
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+
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+ // 胜率、跟踪误差、信息比率
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+ bmk_tracking = cal_benchmark_tracking(ret, index_ret);
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+
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+ // 夏普
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+ sharpe = cal_sharpe(ret, rtn, risk_free);
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+
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+ // 特雷诺
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+ treynor = cal_treynor(ret, risk_free, alpha_beta);
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+
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+ // 詹森指数
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+ jensen = cal_jensen(ret, index_ret, risk_free, alpha_beta);
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+
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+ // 卡玛比率
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+ calmar = cal_calmar(rtn);
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+
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+ // 整合后的下行标准差、欧米伽、索提诺、卡帕
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+ lpms = cal_omega_sortino_kappa(ret, risk_free);
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+
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+ // M2
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+ m2 = cal_m2(ret, index_ret, risk_free);
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+
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+ r = SELECT * FROM rtn a1
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+ LEFT JOIN alpha_beta ON a1.entity_id = alpha_beta.entity_id
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+ LEFT JOIN bmk_tracking ON a1.entity_id = bmk_tracking.entity_id
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+ LEFT JOIN sharpe ON a1.entity_id = sharpe.entity_id
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+ LEFT JOIN treynor ON a1.entity_id = treynor.entity_id
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+ LEFT JOIN jensen ON a1.entity_id = jensen.entity_id
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+ LEFT JOIN calmar ON a1.entity_id = calmar.entity_id
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+ LEFT JOIN lpms ON a1.entity_id = lpms.entity_id
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+ LEFT JOIN m2 ON a1.entity_id = m2.entity_id
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+
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+ // 年化各数据点
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+ // GIPS RULE: NO annulization for data less than 1 year
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+ plainAnnu = get_annulization_multiple(freq);
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+ sqrtAnnu = sqrt(get_annulization_multiple(freq));
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+
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+ r.addColumn(['ds_dev_a', 'alpha_a', 'sharpe_a', 'sortino_a', 'jensen_a', 'track_error_a', 'info_a', 'm2_a'], [DOUBLE, DOUBLE, DOUBLE, DOUBLE, DOUBLE, DOUBLE, DOUBLE, DOUBLE]);
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+
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+ UPDATE r
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+ SET ds_dev_a = ds_dev * sqrtAnnu,
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+ alpha_a = alpha * plainAnnu,
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+ sharpe_a = sharpe * sqrtAnnu,
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+ sortino_a = sortino * sqrtAnnu,
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+ jensen_a = jensen * plainAnnu,
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+ track_error_a = track_error * sqrtAnnu,
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+ info_a = info * sqrtAnnu,
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+ m2_a = m2 * plainAnnu
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+ WHERE price_date.month() - min_date.month() >= 12;
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+
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+ return r;
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+}
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+
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+
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