Chapter 5 5.3

DV01 - Dollar Value of a Basis Point

Understanding DV01 as a practical risk metric for portfolio management

DV01: The Portfolio Manager’s Metric

While Modified Duration gives risk as a percentage, portfolio managers and traders need a more practical, absolute measure of risk: How much money (in Yen) do I make or lose if yields move by one basis point (0.01%)?

This is the DV01, or "Dollar Value of a Basis Point." For JGBs, this is more accurately called the Yen Value of a Basis Point (YV01), but the term "DV01" is used globally.

DV01 is the absolute change in a bond's price (in currency) for a 1 basis point (0.0001) change in yield.

Calculation Formulas

There are two common ways to calculate DV01. Both give nearly identical results.

Method 1: Using Modified Duration (The Estimate)

This is the quickest way. You simply take the Modified Duration percentage risk and apply it to the bond's full market value, scaled down to 1 basis point.

\[\text{DV01} = D_{mod} \times \text{Market Value} \times 0.0001\]

Where:

  • $D_{mod}$ = Modified Duration (e.g., 2.9513)
  • $\text{Market Value}$ = The bond's full price (Price per ¥100 × Face Value / 100)
  • $0.0001$ = 1 Basis Point

Method 2: “Bumping” the Yield (The Precise Way)

This is the "pure" calculation. You price the bond twice, 1 basis point apart, and find the difference. This is what professional trading systems do.

$$\text{DV01} = P(y) - P(y + 0.0001)$$

Where:

  • $P(y)$ = The bond's price at the current yield $y$
  • $P(y + 0.0001)$ = The bond's price at the current yield *plus* 1 basis point

Worked JGB Example

Let's use our 3-year JGB from the previous sections.

  • Modified Duration ($D_{mod}$): 2.9513
  • Market Value (Price): ¥1,005,903.53
  • Yield (y): 0.8%

Step 1: Calculate DV01 using Method 1

$$\text{DV01} = 2.9513 \times ¥1,005,903.53 \times 0.0001$$ $$\text{DV01} = \textbf{¥296.87}$$

Step 2: Calculate DV01 using Method 2 (for comparison)

  • $P(0.8000\% \text{ yield})$ = ¥1,005,903.53
  • $P(0.8001\% \text{ yield})$ = ¥1,005,900.56 (Recalculated with the new yield)

$$\text{DV01} = ¥1,005,903.53 - ¥1,005,900.56$$ $$\text{DV01} = \textbf{¥296.97}$$

As you can see, the results are extremely close. We will use ¥297 for simplicity.

Interpretation

A DV01 of ¥297 means that for every 1 basis point (0.01%) that the bond's yield rises, its market value will fall by approximately ¥297. Conversely, if its yield falls by 1 bp, its value will rise by ¥297.

Portfolio DV01 & Hedging

The true power of DV01 is its additivity. You cannot sum the durations of different bonds, but you can (and must) sum their DV01s.

Portfolio DV01: The total DV01 of a portfolio is the simple sum of the DV01s of every bond in it.

\[\text{DV01}_{\text{Portfolio}} = \text{DV01}_{\text{Bond A}} + \text{DV01}_{\text{Bond B}} + ...\]

Risk Management: A portfolio manager knows their total DV01 at all times. If their portfolio has a DV01 of +¥15,000,000, they know they will lose ¥15 million for every 1 basis point yields rise.

Hedging: This “DV01-neutral” hedging is the core of bond trading.

  • The Position: A portfolio with +¥15M DV01 (this is a “long” risk position).
  • The Hedge: The manager needs to add a short position with a matching -¥15M DV01.
  • The Tool: They will short JGB futures. If the 10-year JGB future has a DV01 of ¥12,000 per contract, they can calculate their hedge:
\[\begin{align} \text{Hedge Ratio} &= \frac{\text{DV01}_{\text{Portfolio}}}{\text{DV01}_{\text{Futures}}} \\ &= \frac{¥15,000,000}{¥12,000} \\ &= \textbf{1,250 \text{ contracts}} \end{align}\]

By shorting 1,250 JGB futures contracts, the manager’s portfolio is now “DV01-neutral,” or “duration-hedged.”

Advanced Topic: Portfolio DV01 Aggregation

While the basic principle of summing DV01s is straightforward, professional JGB portfolio management requires deeper understanding of how to aggregate DV01 across complex portfolios and implement effective hedging strategies.

Multi-Bond Portfolio DV01 Calculation

Consider a realistic institutional portfolio with ¥50 billion in JGBs across multiple maturities:

Position Notional (¥bn) DV01 per ¥1bn Total DV01 (¥)
2Y JGB #500 ¥10 ¥1,950 ¥19,500,000
5Y JGB #505 ¥15 ¥4,800 ¥72,000,000
10Y JGB #362 ¥20 ¥9,200 ¥184,000,000
30Y JGB #60 ¥5 ¥22,500 ¥112,500,000
Total Portfolio ¥50 — ¥388,000,000

Portfolio DV01 = ¥388 million

This means:

  • A 1bp parallel rise in yields → Portfolio loses ¥388 million
  • A 1bp parallel fall in yields → Portfolio gains ¥388 million
  • A 10bp rise → Portfolio loses ¥3.88 billion

Weighted vs. Aggregate DV01

Some institutions track both:

1. Aggregate DV01 (shown above)

Total yen exposure to 1bp yield change. This is the most important metric for risk limits and hedging.

2. Weighted Average Duration

For reporting and benchmarking purposes, some calculate a portfolio-weighted duration:

\[\text{Portfolio Duration} = \frac{\text{Portfolio DV01}}{\text{Portfolio Market Value} \times 0.0001}\]

For our ¥50 billion portfolio trading near par with DV01 of ¥388 million:

\[\text{Portfolio Duration} = \frac{¥388,000,000}{¥50,000,000,000 \times 0.0001} = 7.76 \text{ years}\]

This 7.76-year figure is useful for comparing against benchmarks (e.g., "Are we shorter or longer duration than the NOMURA-BPI index?").

Hedging a Multi-Maturity Portfolio with JGB Futures

Now let's hedge this ¥388 million DV01 portfolio using 10-year JGB futures.

Step 1: Determine Futures DV01

Assume 10Y JGB futures have:

  • Contract size: ¥100 million face value
  • Futures price: 142.50
  • CTD bond DV01: ¥9,200 per ¥1bn (approximately duration 9.2)
  • Conversion factor: 0.985

The DV01 per futures contract is approximately:

\[\text{Futures DV01} = \frac{\text{CTD DV01} \times \text{Contract Size}}{\text{Conversion Factor}}\] \[\text{Futures DV01} = \frac{¥9,200 \times 100}{0.985} = ¥933,000 \text{ per contract}\]

(Note: In practice, you'd use the precise conversion factor-adjusted DV01 provided by your trading system.)

Step 2: Calculate Hedge Ratio

\[\text{Number of Contracts} = \frac{\text{Portfolio DV01}}{\text{Futures DV01}}\] \[\text{Number of Contracts} = \frac{¥388,000,000}{¥933,000} = 415.8 \approx \textbf{416 contracts}\]

By selling 416 contracts of 10Y JGB futures, the portfolio becomes approximately duration-neutral.

Step 3: Verify the Hedge

  • Cash portfolio DV01: +¥388 million (long)
  • Futures position DV01: -416 × ¥933,000 = -¥388 million (short)
  • Net DV01: ≈ ¥0 (hedged)

✓ The portfolio is now protected against parallel shifts in the yield curve.

Basis Risk in Cross-Maturity Hedging

An important subtlety: We're hedging a portfolio containing 2Y, 5Y, 10Y, and 30Y bonds using only 10Y futures. This creates basis risk:

  • If the curve steepens (2Y falls, 30Y rises), the hedge performs poorly
  • If the curve flattens (2Y rises, 30Y falls), the hedge performs poorly
  • If the curve shifts in parallel, the hedge works well

This is where Key Rate Duration (see Section 3.2 advanced topic) and Grid Point Sensitivity (see Section 3.5) become critical. A more sophisticated hedge would:

  1. Calculate DV01 exposure at each grid point (2Y, 5Y, 10Y, 30Y)
  2. Hedge each grid point separately using:
    • 2Y futures for 2Y exposure
    • 5Y futures for 5Y exposure
    • 10Y futures for 10Y exposure
    • 20Y or 30Y bonds for long-end exposure (fewer liquid futures)
  3. This creates a "grid-point neutral" hedge that protects against non-parallel shifts

Worked Example: Selective Grid Point Hedging

Let's say the portfolio manager analyzes the DV01 by maturity bucket and finds:

Maturity Bucket DV01 Exposure Hedge Instrument Hedge Ratio
2Y exposure ¥19.5 million 2Y JGB futures Sell 100 contracts (¥195k DV01 each)
5Y exposure ¥72 million 5Y JGB futures Sell 150 contracts (¥480k DV01 each)
10Y exposure ¥184 million 10Y JGB futures Sell 197 contracts (¥933k DV01 each)
30Y exposure ¥112.5 million Cash 20Y JGB short Short ¥5bn (¥22.5m DV01 per ¥1bn)

This targeted hedging approach eliminates basis risk from curve twists, but requires:

  • More sophisticated risk systems
  • Access to multiple futures contracts
  • Higher transaction costs (more legs to execute)
  • Careful monitoring and rebalancing

Dynamic Rebalancing

DV01-based hedges are not static. They require periodic rebalancing because:

1. Duration Drift

As time passes, bonds age and their DV01 changes (usually decreases). A 10Y bond becomes a 9.75Y bond after 3 months, with slightly lower DV01.

2. Yield Changes

When yields move, DV01 changes (this is related to convexity). A bond with DV01 of ¥9,200 at 1% yield might have DV01 of ¥9,500 at 0.5% yield.

3. Portfolio Transactions

Any trades (buying or selling bonds) change the portfolio DV01 and require hedge adjustment.

Best Practice: Recalculate portfolio DV01 and hedge ratios:

  • Daily for actively traded portfolios
  • Weekly for stable buy-and-hold portfolios
  • Immediately after large trades or significant market moves (>10bp)

DV01 Limits and Risk Management

Institutional risk management frameworks typically impose DV01 limits:

Example: Regional Bank Trading Desk Limits

  • Maximum Net DV01: ¥500 million (unhedged directional exposure)
  • Maximum Gross DV01: ¥5 billion (total long + short positions)
  • Grid Point Limits: Maximum ¥200 million DV01 at any single grid point

Traders must stay within these limits or obtain special approval. Breaches trigger alerts and potential position reduction.

Key Takeaways

  1. Portfolio DV01 is simply the sum of individual bond DV01s—no complex weighting needed
  2. Hedge ratios use DV01, not duration: Contracts = Portfolio DV01 ÷ Futures DV01
  3. Single-tenor hedges create basis risk when portfolios span multiple maturities
  4. Grid-point hedging eliminates curve risk but requires more instruments and complexity
  5. Dynamic rebalancing is essential as DV01s drift over time and with yield changes
  6. Risk limits expressed in DV01 are standard in institutional fixed income management

Understanding portfolio DV01 aggregation and hedging is fundamental to professional JGB portfolio management and forms the basis for implementing the trading strategies covered in Chapter 7.