固收 Key Rate Duration

问题分析

You are evaluating the interest rate risk of a bond portfolio. You need to understand the difference between key rate duration and effective duration. Consider a scenario where the yield curve experiences a non-parallel shift. Specifically, the 5-year point on the yield curve increases by 25 basis p

解法

根据题目要求实现相应功能。核心逻辑需要：

// 核心数据结构和方法——根据题目 API 约定实现
// 1. 确定状态表示——选择支持所需操作的数据结构
// 2. 实现核心算法——确保 O(·) 时间复杂度和正确性
// 3. 处理边界条件——空输入、极值参数、并发访问

验证

用具体输入验证：构造已知输入的测试用例，确认输出匹配预期结果。

复杂度与边界

• 时间复杂度：取决于选用的算法
• 空间复杂度：取决于数据规模
• 关键边界条件：空输入、极值参数、并发场景下的正确性保证

英文解析

Analysis

Key rate duration measures a bond's (or portfolio's) sensitivity to shifts at specific maturity points on the yield curve, while effective duration measures overall sensitivity to a parallel shift. When the yield curve experiences a non-parallel shift (e.g., only the 5-year point moves), effective duration cannot capture the localized impact -- key rate duration specifically quantifies the price change from that isolated 5-year shift.

Key rate duration at maturity point k: KRD_k = (P0 - P_k) / (P0 * delta_y_k) where P_k is the price after shifting only the k-th key rate by delta_y_k, with other points unchanged.

Solution

def key_rate_duration(bond_pv_func, key_maturities, delta_y=0.001):
    """Compute key rate durations for each maturity point."""
    P0 = bond_pv_func(None)  # base price with current yield curve
    krd = {}
    for k in key_maturities:
        # Shift only the k-th maturity point by delta_y
        P_k = bond_pv_func({k: delta_y})  # price after isolated shift at k
        krd[k] = (P0 - P_k) / (P0 * delta_y)
    return krd

def effective_duration(bond_pv_func, parallel_shift=0.001):
    """Compute effective duration for parallel shift."""
    P_up = bond_pv_func({'all': -parallel_shift})
    P_down = bond_pv_func({'all': parallel_shift})
    P0 = bond_pv_func(None)
    return (P_down - P_up) / (2 * P0 * parallel_shift)

For the given scenario: 5Y key rate shifts by +25bps, all other points unchanged:

• The portfolio's price change approx KRD_5 * 25bps * P0
• Effective duration would estimate price change from a full parallel 25bps shift, overstating the actual impact

Complexity & Edge Cases

• Time complexity: O(K) for K key rate points, each requiring a PV calculation
• Space complexity: O(K) for key rate duration vector
• Edge cases: (1) Interpolation: shifting one key rate requires interpolating the shift to adjacent points (linear, quadratic). (2) Sum of all KRDs approx effective duration for small shifts. (3) Partial PV01: KRD * portfolio value = partial DV01 at that key rate. (4) Negative KRDs possible for bonds with embedded options or hedges.

Verification

Portfolio with effective duration = 6, KRDs: 2Y=0.5, 5Y=1.5, 10Y=3.0, 30Y=1.0 (sum = 6, matches)

• 5Y shift of +25bps: portfolio price change approx -1.5 * 0.25% * P0 = -0.375% * P0
• Full parallel 25bps shift: change approx -6 * 0.25% * P0 = -1.5% * P0
• KRD_5 captures the isolated impact; effective duration overstates by 4x in this scenario

Key Considerations

• Key rate durations decompose interest rate risk into curve shape components -- critical for hedging non-parallel shifts
• Common key rate buckets: 2Y, 5Y, 10Y, 30Y -- matching the most liquid swap/bond maturities
• Hedging: to neutralize KRD_5 exposure, trade instruments with offsetting KRD_5 (e.g., 5Y Treasury futures)
• Portfolio managers use KRD profiles to express curve shape views (steepening, flattening, butterfly)