Basis Point Value (BPV)

Basis point value (BPV) is the amount by which the value of a fixed-income position changes when the relevant interest rate or yield moves by one basis point, or 0.01 percentage points. It is expressed in currency, such as "$6,370 per basis point", which makes it easy to compare and add up the rate sensitivity of bonds, loans, interest rate swaps and futures. Traders, treasurers, portfolio managers and bank risk teams use it to set limits and size hedges.

BPV goes by several names. Market practitioners often say DV01 (dollar value of an 01) or PV01 (present value of an 01), and some firms draw technical distinctions between these labels. BPV is the money counterpart of portfolio duration, which measures sensitivity as a percentage, and it assumes a parallel move, so it is supplemented by measures of yield curve risk.

A bathroom scale tells you your weight, but a nutrition label tells you how much one extra biscuit adds. BPV is the nutrition label for interest rates. It answers a simple question: if rates go up by the smallest unit the market normally quotes, how much money does this position gain or lose?

Because the answer is in pounds, dollars or euros, it is easy to talk about. A desk with a limit of "$50,000 per basis point" knows that a move of ten basis points against it would cost roughly half a million. A treasurer hedging a loan can match the amount the loan moves with an opposite position that moves by the same amount.

For a bond or portfolio, BPV can be estimated from modified duration:

• $D_{\text{mod}}$ is the modified duration of the position, in years.
• $P$ is the market value of the position, including accrued interest.
• $0.0001$ is one basis point written as a decimal.

Suppose a fund holds $10 million face value of a bond priced at 98 per 100, so the market value is $9.8 million, with a modified duration of 6.5. The BPV is 6.5 × $9,800,000 × 0.0001 = $6,370. If yields rise by 8 basis points, the position loses about 8 × $6,370 = $50,960.

BPV can also be found directly by revaluing the position with all yields shifted up by one basis point and comparing the result with the current value. Banks and dealers usually compute it this way for swaps and complex portfolios, often shifting the interest rate swap curve rather than a single yield.

BPV makes hedging a matter of matching numbers. The hedge ratio is:

Continuing the example, if one bond futures contract has a BPV of $85, the fund would sell about $6,370 ÷ $85 ≈ 75 contracts to neutralise its sensitivity to a parallel move. A company that has borrowed at a floating rate can likewise compare the BPV of its debt with that of a pay-fixed swap to decide the swap's notional amount. Because BPVs are additive, a risk manager can sum them across positions to see the net exposure of a whole book.

• Trading limits. Fixed-income and swap desks are commonly given limits in BPV terms, by currency and by maturity bucket.
• Bank balance sheet risk. Asset-liability teams measure the BPV of the banking book as part of managing interest rate risk, alongside earnings and economic value of equity measures.
• Corporate treasury. Treasurers use BPV to explain how much a debt portfolio or investment portfolio of fixed-income securities will change in value for a given rate move.
• Bucketed risk. Splitting BPV by maturity, sometimes called key rate BPV, shows where on the yield curve the exposure sits.

BPV is a linear, first-order measure. For large rate moves it misstates the change in value because bond prices are curved in yield, an effect called convexity. A single BPV figure assumes every rate moves by the same amount, which rarely happens, so two positions with equal and opposite BPVs can still lose money if the curve twists. BPV also ignores credit spread changes, changes in the timing of cash flows for callable bonds or mortgages, and volatility, so it is used together with scenario analysis and measures such as value at risk.