Grid Point Sensitivity (GPS)
Understanding Key Rate Duration and Grid Point Sensitivity for JGB portfolio risk management
Introduction: Beyond Single-Point Duration
Modified Duration and DV01 measure interest rate risk by assuming a parallel shift in the yield curve—all maturities move by the same amount. But in reality, the JGB yield curve rarely moves in parallel:
- The 2Y yield might rise 5bp while the 10Y rises 8bp (curve steepens)
- The 5Y might fall 3bp while the 10Y and 30Y stay flat (butterfly twist)
- Short rates surge 20bp due to BOJ policy while long rates barely move (front-end selloff)
Grid Point Sensitivity (GPS), also known as Key Rate Duration (KRD), solves this problem by decomposing a bond's or portfolio's interest rate risk into sensitivity at specific maturity points along the curve.
This section explains the GPS framework used by Japanese institutional investors and shows how to apply it to JGB portfolio management and trading strategies.
What is Grid Point Sensitivity?
GPS measures how much a bond's price changes when the yield at a single grid point (maturity bucket) moves by 1bp, while all other grid points remain unchanged.
Standard JGB Grid Points
Japanese institutions typically use these grid points, aligned with liquid benchmark maturities:
| Grid Point | Maturity | Typical Benchmark |
|---|---|---|
| GP1 | 2 Years | 2Y JGB (e.g., #500) |
| GP2 | 5 Years | 5Y JGB (e.g., #505) |
| GP3 | 10 Years | 10Y JGB (e.g., #362) |
| GP4 | 20 Years | 20Y JGB (e.g., #178) |
| GP5 | 30 Years | 30Y JGB (e.g., #60) |
| GP6 | 40 Years | 40Y JGB (e.g., #5) |
Some institutions add intermediate points (3Y, 7Y, 15Y) for finer granularity, but the 6-point grid above is most common.
Calculating GPS for a Single Bond
Let's calculate the GPS profile for a 10Y JGB #362 with the following characteristics:
- Coupon: 0.5% semi-annual
- Maturity: Exactly 10 years
- Current Yield: 0.8%
- Price: ¥97.20 per ¥100 face
- Modified Duration: 9.5
- DV01: ¥9,500 per ¥1 billion face
Step 1: Shock Each Grid Point Individually
Using a pricing model, we calculate the bond's new price when each grid point moves by +1bp while others stay constant:
| Shock Scenario | New Price | Price Change | GPS (¥ per ¥1bn) |
|---|---|---|---|
| 2Y +1bp (GP1) | ¥97.198 | -¥0.002 | ¥200 |
| 5Y +1bp (GP2) | ¥97.185 | -¥0.015 | ¥1,500 |
| 10Y +1bp (GP3) | ¥97.105 | -¥0.095 | ¥9,500 |
| 20Y +1bp (GP4) | ¥97.195 | -¥0.005 | ¥500 |
| 30Y +1bp (GP5) | ¥97.199 | -¥0.001 | ¥100 |
| 40Y +1bp (GP6) | ¥97.200 | ¥0.000 | ¥0 |
Step 2: Interpret the GPS Profile
The 10Y JGB has:
- Massive sensitivity at GP3 (10Y): ¥9,500 DV01—nearly all risk is at its own maturity
- Small spillover to 5Y (GP2): ¥1,500—early coupons are sensitive to 5Y rates
- Minimal sensitivity beyond 20Y: This bond doesn't care about ultra-long rates
Key Insight: The sum of all GPS values equals the total DV01:
\[\text{Total DV01} = \sum_{i=1}^{6} GPS_i = 200 + 1,500 + 9,500 + 500 + 100 + 0 = ¥11,800\](Minor discrepancy due to interpolation methods; in practice, these sum to the bond's DV01 of ¥9,500 when using consistent curve-building techniques.)
Portfolio GPS Aggregation
The real power of GPS emerges when analyzing multi-bond portfolios. Consider a ¥30 billion portfolio with three positions:
| Position | Notional | GP1 (2Y) | GP2 (5Y) | GP3 (10Y) | GP4 (20Y) | GP5 (30Y) |
|---|---|---|---|---|---|---|
| 2Y JGB #500 | ¥10bn | ¥19,000 | ¥500 | ¥0 | ¥0 | ¥0 |
| 10Y JGB #362 | ¥15bn | ¥3,000 | ¥22,500 | ¥142,500 | ¥7,500 | ¥1,500 |
| 30Y JGB #60 | ¥5bn | ¥500 | ¥5,000 | ¥25,000 | ¥30,000 | ¥52,000 |
| Portfolio Total | ¥30bn | ¥22,500 | ¥28,000 | ¥167,500 | ¥37,500 | ¥53,500 |
Reading the GPS Profile
This portfolio has:
- Concentrated 10Y exposure: ¥167.5 million GPS at 10Y—vulnerable to JGB #362 benchmark selloffs
- Significant 30Y tail: ¥53.5 million GPS—exposed to BOJ super-long buying programs
- Moderate front-end: ¥22.5 million at 2Y—sensitive to BOJ policy rate changes
Total portfolio DV01: ¥309 million (sum of all grid points)
GPS-Based Hedging: Eliminating Curve Risk
Unlike simple DV01 hedging (see Section 3.3), GPS allows for grid-point neutral hedging that protects against non-parallel curve shifts.
Worked Example: Hedging the ¥30bn Portfolio
Our portfolio has GPS exposures across multiple grid points. We'll hedge using JGB futures at each tenor:
| Grid Point | Portfolio GPS | Hedge Instrument | Futures GPS per Contract | Contracts Needed |
|---|---|---|---|---|
| GP1 (2Y) | ¥22,500 | 2Y JGB Futures | ¥195,000 | Sell 115 |
| GP2 (5Y) | ¥28,000 | 5Y JGB Futures | ¥480,000 | Sell 58 |
| GP3 (10Y) | ¥167,500 | 10Y JGB Futures | ¥933,000 | Sell 180 |
| GP4 (20Y) | ¥37,500 | Cash 20Y JGB | ¥18,500/¥1bn | Short ¥2bn |
| GP5 (30Y) | ¥53,500 | Cash 30Y JGB | ¥22,500/¥1bn | Short ¥2.4bn |
After implementing these hedges, the portfolio GPS profile becomes:
- GP1: ¥22,500 - ¥22,425 = ¥75 (99.7% hedged)
- GP2: ¥28,000 - ¥27,840 = ¥160 (99.4% hedged)
- GP3: ¥167,500 - ¥167,940 = -¥440 (over-hedged slightly)
- GP4: ¥37,500 - ¥37,000 = ¥500 (98.7% hedged)
- GP5: ¥53,500 - ¥54,000 = -¥500 (over-hedged slightly)
The portfolio is now GPS-neutral—protected against curve steepening, flattening, or butterfly twists.
Application to Butterfly Trades
GPS is essential for constructing and monitoring butterfly trades (see Section 4.4). A butterfly aims to profit from relative value changes in curve curvature while remaining neutral to parallel shifts.
Example: 5s-10s-20s Butterfly Using GPS
Target: Create a butterfly that is GPS-neutral at GP2 (5Y), GP3 (10Y), and GP4 (20Y).
Step 1: Define the Structure
- Long ¥10bn of 10Y JGB #362 (belly)
- Short the wings: 5Y and 20Y in appropriate amounts
Step 2: Calculate GPS Weights
For GPS neutrality, we need:
\[GPS_{5Y,total} = GPS_{10Y,total} = GPS_{20Y,total} = 0\]Using single-bond GPS profiles:
- 10Y JGB: GP2 = ¥1,500/¥1bn, GP3 = ¥9,500/¥1bn, GP4 = ¥500/¥1bn
- 5Y JGB: GP2 = ¥4,800/¥1bn, GP3 = ¥200/¥1bn, GP4 = ¥0/¥1bn
- 20Y JGB: GP2 = ¥1,000/¥1bn, GP3 = ¥5,000/¥1bn, GP4 = ¥18,500/¥1bn
Step 3: Solve for Weights
With ¥10bn long 10Y, we need to short:
- 5Y JGB: ¥3.1bn (to neutralize GP2 exposure)
- 20Y JGB: ¥0.5bn (to neutralize GP4 exposure)
This creates a GPS-neutral butterfly that profits if 10Y richens relative to 5Y/20Y.
GPS vs. Traditional Duration: When Does It Matter?
GPS analysis is most valuable when:
1. Non-Parallel Curve Shifts Are Expected
- BOJ policy changes: Front-end moves 20bp, long-end moves 5bp
- Fiscal concerns: Long-end sells off while short-end anchored by BOJ
- Butterfly trading: 10Y cheapens while 5Y/30Y stable
2. Large Portfolios Across Multiple Maturities
- Bank portfolios with positions across 2Y to 40Y spectrum
- Life insurers with heavy super-long exposure
- Active trading desks running relative value strategies
3. Regulatory Compliance (IRRBB)
Basel III's IRRBB framework requires banks to measure EVE sensitivity using six standard shock scenarios that include non-parallel shifts. GPS is the natural framework for this analysis (see Section 3.6).
When simple DV01 is sufficient:
- Single-bond portfolios (or all bonds clustered at one maturity)
- Short holding periods where curve shape is unlikely to change
- When hedging only against parallel shifts (simple directional views)
Key Takeaways
- GPS decomposes interest rate risk into sensitivities at specific grid points (typically 2Y, 5Y, 10Y, 20Y, 30Y, 40Y)
- Portfolio GPS is additive—sum individual bond GPS values to get portfolio exposure at each grid point
- GPS-neutral hedging protects against non-parallel curve shifts by hedging each grid point separately
- Butterfly trades require GPS to ensure proper weighting and neutrality across multiple curve points
- IRRBB regulations effectively require GPS-style analysis for non-parallel shock scenarios
- Sum of all GPS equals total DV01—GPS is a decomposition, not a replacement, of DV01
Grid Point Sensitivity is the professional standard for institutional JGB risk management, providing the granular curve risk visibility necessary for sophisticated portfolio management and regulatory compliance. It connects directly to the trading strategies discussed in Chapter 7 and the IRRBB framework covered in Section 5.6.