The recent decision by the Chicago Board of Trade to change the "notional coupon" on its Treasury Complex will alter Treasury contracts in several important ways outlined in this article.

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Conversion Factors Conversion factors are multiplicative grade adjustments that equilibrate the differences in coupon and maturity of issues eligible for delivery. In reality, they simply represent the present value of the bond under consideration given the following assumptions:

The coupon of the bond or note is discounted by a 6% yield to maturity.
Settlement occurs on the first day of the delivery month (e.g., March 1, June 1, September 1, or December 1).
The maturity date is rounded to the nearest whole quarter for bonds and 10-year notes and rounded to the nearest month for 5-year and 2-year notes.
A one dollar par amount.
Conversion factors will be higher because of the lower rate at which coupons will be discounted.

Futures Prices The price of the March 2000 T-bond futures contract will be significantly lower than the December 1999 contract for several reasons.

The contract will "track" cash securities priced closer to par than the old cheapest-to-deliver issuethe 11 1/4 of 2/15/15. On March 29, 1999, the 11 1/4 traded at 155-15. On this date, the CTD issue of the March 2000 bond contract was the 81/2 of 2/15/20, trading at 130-15. Pricing the contract forward based upon this issue results in a much lower futures price.

Also, the shift to a 6% pricing convention results in higher conversion factors. Because conversion factors figure in the futures pricing formula, they affect the price of the contract. The following equation presents a simplified version of the theoretical pricing formula for Treasury futures:

Futures Price =
CTD Cash Price- Carry- Strategic Delivery Option Value

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Conversion Factor (of the cheapest to deliver)
Because the conversion factor is in the denominator, a higher conversion factor, all else being equal, will result in a lower futures price.

Strategic Delivery Option Values The contract specifications give shorts the option to choose which issue to deliver and when to deliver it. These options can be valuable in certain yield curve environments. During the past several years, the 11 1/4 of 2/15/15 was entrenched as CTD due to its short duration and the low level of yields. As a result, the likelihood of a shift in the CTD was small, and the value of the strategic delivery options was low. The change to a 6% notional coupon increases the probability of switches in CTD and increases the optionality of the contracts. The equation above shows that increased strategic delivery option values will reduce futures prices.

The increase in the value of the strategic delivery options offers basis traders renewed opportunities. A good way to compare the likelihood of a switch in the CTD is to calculate the implied repo rate for each issue within the deliverable set. In late March, Bloomberg showed 10 issues within seven basis points of the highest implied repo rate and, so, in the running for CTD status.

Volatility Several factors interact to make the volatility analysis interesting. First, shifting to a 6% coupon will cause the contract to track a higher duration issue. The table compares the modified durations of the CTD issues for the December 1999 and the March 2000 contracts.

Contract Coupon Maturity Duration DV01
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December 1999 11 1/4 2/15/15 9.0 $140.25
March 2000 8 1/8 8/15/19 11.0 $138.70


If both of these issues were trading at par (100) then the DV01 of the 8 1/8 % issue would be greater than that of the 11 1/4 %. However, the 11 1/4 issue was trading at a much higher premium, resulting in a higher DV01. So for a given change in yields, the dollar price change is greater for the lower duration instrument. Here, the price level effect dominates the duration increase effect. To obtain the DV01 of the futures contract, divide the DV01 of the cash instrument by its conversion factor.

DV01 Dec 1999 = $140.25/1.2810 = $109.48
DV01 Mar 2000 = $138.70/1.2405 = $111.81
The DV01 of the March 2000 futures contract is $111.81 for each $100,000 par. This is not significantly different from the DV01 of the December contract. It should be noted that the DV01s were not "option adjusted." That is, the probability of a switch in the CTD occurring was not factored into the value. This simplification isnt as significant for the December contract as it is for the March 2000 contract, because switches in CTD are more likely with the latter.

Positive and Negative Convexity Unlike individual Treasury bonds and notes, the CBOT futures contract exhibits "negative convexity." Recall that positive convexity describes the case where the price change predicted by duration is always less than the true price change for a given yield change. When yields fall, the price of an option-free bond rises by more than the duration measure predicts. When yields rise, the price falls by less than duration predicts. This "positive convexity" is a favorable characteristic of being long fixed-income instruments.

In addition, duration varies inversely with changes in yields. Another measure of price sensitivity related to duration is basis point value (BPV), or the dollar value of a basis point (DV01), which predicts how the dollar value of the cash security or futures contract changes given a one basis point yield change.

Since the CBOT Treasury futures contracts contain "embedded options," they exhibit "negative convexity." With Treasury futures, when yields change, the CTD may also change. The likelihood of a switch occurring is greater for the 6% coupon futures contract than with the 8% contract, given current yields. Therefore, the price sensitivity of a futures contract differs from that of a contract where this probability is zero.

DV01 of June 8% DV01 of June 6%
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100 $99.5 $113.7
75 $102.7 $119.4
60 $102.0 $112.9
50 $103.1 $113.4
40 $104.5 $115.4
25 $106.5 $113.7
10 $112.1 $111.5
0 $109.7 $112.5
-10 $112.6 $111.1
-25 $113.4 $100.3
-40 $115.5 $102.1
-50 $116.8 $103.5
-60 $118.5 $102.5
-75 $120.8 $104.5
-100 $124.5 $108.0

The table and chart provide useful illustrations of that phenomenon. Analyzing the June 1999 8% coupon futures contract, notice that as yields change, the futures BPV varies rather smoothly, consistent with the presence of positive convexity. This happens because the futures contract is tracking one particular cash issuethe 11 1/4 of 2/2015. However, in the case of the theoretical June 1999 futures contract, assuming a 6% conversion factor, as yields fall, the CTD switches. As a result, the BPV of the futures contract declines rather than increases. The BPV falls from $112.5 to $108.0 if yields fall by 100 basis points. In addition, as yields rise, the DV01 increases. This is because the risk characteristics of the futures contract are a function of the CTD security, and the futures contract is now tracking different CTD issues at different yield levels. The chart highlights the contrasts in a dramatic way.

It is important for both hedgers and speculators to be aware of how both the 6% and 8% coupon futures contracts respond to changes in yields. Given the different sensitivities of the two contracts, hedge ratios need to be monitored and adjusted when necessary.