> For the complete documentation index, see [llms.txt](https://docs.force.xyz/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.force.xyz/asset-directory/dv01-and-cross-hedging.md).

# DV01 and Cross-Hedging

**DV01** is the money a position makes or loses when the rate moves by one basis point. On a real bond it is a messy quantity: it depends on the coupon, the maturity, and the current level of rates, and it changes as rates move. That last property is **convexity**.

Force markets have none of that.

## Why DV01 is constant here

Both Force markets are cash-settled on a **rate index quoted in percent**. One basis point is 0.01 index points, always, whatever the level of rates. There is no bond to discount and no cash flows to reprice, so the value of a basis point does not change as rates move.

$$
\text{PnL} = \Delta\text{rate (bp)} \times \text{contracts} \times \text{DV01 per contract}
$$

PnL is exactly linear in the rate move. A move from 4.00% to 4.10% is worth precisely as much as a move from 6.00% to 6.10%, and a 10 basis point gain and a 10 basis point loss are the same size.

This is a property of an index-settled contract, not a claim about bonds. A real 10-year note has convexity; a perp on the 10-year *yield* does not.

## Why the cross-hedge is one for one

DV01 per contract is **the same in both markets**. A basis point is 0.01 index points in FORCE-US10Y and 0.01 index points in FORCE-MORT30, and both settle in the same currency.

So one contract of one market offsets the rate exposure of one contract of the other, and a position long one and short the other is left holding the **spread** between them rather than the level of rates.

$$
\text{Spread} = \text{Mortgage rate} - \text{10-year yield}
$$

This is deliberate, and it is why the mortgage index is built with a coefficient of exactly one on the Treasury leg rather than a fitted sensitivity. A fitted coefficient would track the historical relationship slightly more closely and would break the clean hedge. Keeping it at one means the two markets net exactly, and the residual is the thing a rates trader actually wants to express a view on.

{% hint style="info" %}
One for one nets the **rate** exposure, not the **risk**. The mortgage spread moves on its own, driven by mortgage-backed securities and lender behaviour rather than by Treasuries. A hedged position is a position in that spread, and the spread has ranged from roughly 1.5 to 3.1 percentage points over the last several years.
{% endhint %}

The [Cross-Hedge Calculator](/trader-tools/cross-hedge-calculator.md) sizes this for you.


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