How do risk factor sensitivities like DV01, delta, and vega help a risk manager understand portfolio exposures?

Question

AcadiFi · Accepted Answer

Risk factor sensitivities measure how much a portfolio's value changes for a small move in a single underlying risk factor, holding everything else constant. They are the **first-order building blocks** of risk management and are essential for both hedging and risk reporting.

**Key Sensitivities by Asset Class**

| Sensitivity | Definition | Asset Class |
|---|---|---|
| **DV01 (Dollar Value of a Basis Point)** | Change in value for a 1 bp parallel shift in yields | Fixed income |
| **Delta** | Change in value for a $1 move in the underlying | Equities, commodities, FX |
| **Vega** | Change in value for a 1% move in implied volatility | Options |
| **Theta** | Change in value for one day's time decay | Options |
| **Rho** | Change in value for a 1% move in interest rates | Options, swaps |
| **CR01** | Change in value for a 1 bp move in credit spreads | Credit instruments |

**Aggregation Example**

Waverly Asset Management runs a multi-strategy portfolio:

| Strategy | Position | Key Sensitivity | Value |
|---|---|---|---|
| US Treasuries | $500M 10-year bonds | DV01 | +$425,000/bp |
| Interest rate swaps | Pay fixed, receive float | DV01 | -$380,000/bp |
| S&P 500 options | Long calls, delta-hedged | Vega | +$180,000/vol pt |
| Corporate bonds | $200M IG portfolio | CR01 | -$95,000/bp |

**Net interest rate sensitivity:** +$425,000 - $380,000 = **+$45,000/bp** (small residual long duration)

```mermaid
flowchart TD
    A["Portfolio Risk Dashboard"] --> B["Interest Rate: DV01 = +$45K/bp"]
    A --> C["Equity Vol: Vega = +$180K/vol pt"]
    A --> D["Credit Spread: CR01 = -$95K/bp"]
    B --> E["Rates up 50bp: -$2.25M"]
    C --> F["Vol up 5 pts: +$900K"]
    D --> G["Spreads widen 20bp: -$1.9M"]
```

**Why Sensitivities Beat VaR for Day-to-Day Management**

1. **Actionable** — DV01 tells you exactly how many futures contracts to sell to hedge duration; VaR does not
2. **Decomposable** — you can attribute risk to individual factors and positions
3. **Real-time** — sensitivities update instantly with market moves; full VaR recalculation may take hours
4. **Transparent** — regulators and senior management can understand "we have +$45K DV01" more easily than "our VaR is $3.2M"

**Limitations:**
- Sensitivities are **linear approximations** — they break down for large moves (need gamma/convexity)
- They don't capture cross-factor correlations (rates and spreads moving together)
- Aggregation assumes risk factors are independent unless you build a covariance model

For more on sensitivity analysis, explore our FRM Part I course.

How do risk factor sensitivities like DV01, delta, and vega help a risk manager understand portfolio exposures?

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