Calmar 比率计算

Calmar Ratio Calc

专题: Finance / 金融
难度: L1
来源: MyntBit

个人笔记

题目详情

Calmar Ratio 通过比较复合年化增长率（CAGR）与最大回撤来评估投资策略的风险调整绩效。该指标在量化金融中评估每单位尾部风险产生的回报尤为重要，常用于对冲基金绩效分析。

任务：实现函数 solution(prices, periods_per_year)，计算 Calmar Ratio = CAGR / 最大回撤。CAGR = (最终价格/初始价格)^(periods_per_year/总周期数) - 1。

英文原题

The Calmar Ratio evaluates the risk-adjusted performance of an investment strategy by comparing its Compound Annual Growth Rate (CAGR) to its Maximum Drawdown. This metric is essential in quantitative finance for assessing the return generated per unit of tail risk, particularly in hedge fund performance analysis.
Task
Implement a function solution(prices, periods_per_year) that calculates the Calmar Ratio for a given sequence of portfolio prices. The calculation requires deriving the CAGR and HALF_OPEN (testing recovery).

解析

问题分析

Calmar 比率是年化收益率与最大回撤之比，广泛用于 CTA 和趋势跟踪策略评估。最大回撤衡量从峰值到谷底的最大损失，是投资者最直观的风险指标。

实现

double maxDrawdown(const std::vector<double>& equity_curve) {
    double peak = equity_curve[0], max_dd = 0;
    for (double v : equity_curve) {
        peak = std::max(peak, v);
        max_dd = std::max(max_dd, (peak - v) / peak);
    }
    return max_dd;
}
double calmarRatio(const std::vector<double>& monthly_returns) {
    double ann_return = std::accumulate(monthly_returns.begin(), monthly_returns.end(), 0.0) * 12.0 / monthly_returns.size();
    double dd = maxDrawdown(buildEquityCurve(monthly_returns));
    return dd > 0 ? ann_return / dd : 0.0;
}

复杂度与边界

时间复杂度：O(N)
空间复杂度：O(1)
边界条件：(1) 最大回撤为 0 时（无亏损）比率无限大——返回 0 (2) 仅基于月度收益估计年化收益可能偏误 (3) 受起始和结束时间点影响大

英文解析

Analysis

The Calmar ratio is the ratio of annualized return to maximum drawdown, widely used for CTA and trend-following strategy evaluation. Maximum drawdown measures the largest peak-to-trough loss, making it the most intuitive risk metric for investors.

Solution

double maxDrawdown(const std::vector<double>& equity_curve) {
    double peak = equity_curve[0], max_dd = 0;
    for (double v : equity_curve) {
        peak = std::max(peak, v);
        max_dd = std::max(max_dd, (peak - v) / peak);
    }
    return max_dd;
}
double calmarRatio(const std::vector<double>& monthly_returns) {
    double ann_return = std::accumulate(monthly_returns.begin(), monthly_returns.end(), 0.0) * 12.0 / monthly_returns.size();
    double dd = maxDrawdown(buildEquityCurve(monthly_returns));
    return dd > 0 ? ann_return / dd : 0.0;
}

Complexity & Edge Cases

Time complexity: O(N)
Space complexity: O(1)
Edge cases: (1) When max drawdown is 0 (no losses), ratio is infinite - return 0 (2) Annualized return estimated from monthly returns may be biased (3) Highly dependent on start and end timepoints

Verification

Calculate Calmar ratio for a strategy with known equity curve. Verify maximum drawdown is correctly identified. Benchmark annualized return calculation against geometric method.

Key Considerations

The Calmar ratio is the standard performance metric for managed futures and CTA strategies. A 3-year Calmar ratio (using 3-year annualized return divided by 3-year max drawdown) is the industry norm. Maximum drawdown is path-dependent - two strategies with identical returns can have vastly different drawdown profiles.