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# CALCULATING THE DOLLAR VALUE OF A BASIS POINT

The objective of hedging a fixed income position with futures contracts is to insure that as the underlying security loses value, the futures hedge compensates for this loss by gaining a comparable amount. While many may make the mistake of matching notional values or tick increments, the best way to hedge is to match the dollar value of a one- basis point change (DV01) in the yield of the underlying security and that of the hedging vehicle.

In the case of U.S. Treasury futures, you have a hedging vehicle that derives its DV01 from the underlying Treasury security. Although Treasury futures have a notional coupon of 6 percent, they are not coupon bearing instruments since they do not have cash flows. Treasury futures track the price of the most economical security to deliver, and derive their DV01 from the cash instrument they track. In most cases, this instrument is the issue that is cheapest-to-deliver (CTD) into the futures contract.

## Price-Yield Relationship of a Treasury Security

A common misconception is that the DV01 of a Treasury security remains fixed as the yield of the instrument changes. In truth, the price-yield relationship of a Treasury security is nonlinear. As yields fluctuate, the DV01 of a Treasury security changes.

Exhibit 1 shows the price-yield relationship of a Treasury security as depicted by the curved line. As yields increase, a Treasury security’s price falls by decreasing dollar amounts. As yields decrease, a Treasury security’s price rises by increasing dollar amounts. The line tangent to the curve represents the DV01 of a Treasury security. As yields increase, the slope of this line flattens. As yields decrease, the slope of this line steepens. This flattening and steepening of the line tangent to the curve illustrates the

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