These substantial correlations suggest that investors can significantly reduce the risk of a Brady holding with a well-designed hedge of the bond's exposure to U.S. interest rates. This paper examines how to accurately quantify and offset this U.S. interest rate component and, due to cost and convenience considerations, illustrates that Chicago Board of Trade T-bond futures are frequently the most efficient hedge vehicles available.
Brady Par Bonds: A Combination of Sovereign and U.S. Credits
U.S. corporate paper is priced at a spread over the appropriate U.S. Treasury rate, the most important valuation factor for high-grade, fixed-income markets. Based on monthly prices since 1982, changes in Treasury rates explained 88 percent of the variation in investment grade corporate bond prices.
During this same period, Treasury rates accounted for approximately 70 percent of the variation in BBB bond prices. In the case of U.S. high-yield markets, however, the spread over Treasuries comprises an even greater portion of the total yield, and U.S. Treasury rates can account for as little as 30 percent of the price variation.
A Brady par bond, in effect, joins U.S. interest rate risk to an exposure to sovereign credit risk. As with other emerging debt issues, one rationale for investing in a Brady bond derives from the investor's expectation that the issuing country's creditworthiness will improve. As that happens, with all other factors constant, the spread of the Brady yield over the U.S. Treasury yield will fall, and the Brady bond will gain value, assuming relatively stable U.S. bond yields and values.
However, problems arise when U.S. interest rates rise and bond values fall. Unhedged, rising U.S. Treasury yields can offset the price increase in the Brady bond due to a s, though, the on-the-run Treasury goes ,on special" in the repo market because of strong demand for that particular instrument. That will result in a lower repo rate relative to other cash Treasuries, and increase the carry
While investors could choose to hedge with another less liquid cash Treasury bond that has a more attractive repo rate, that advantage would likely be offset by the higher transaction costs associated with less liquid bonds. Using futures to hedge allows investors to minimize the combined costs associated with transaction spreads and financing rates.
Table 2 shows how several potential hedge vehicles relate to Argentine pars during two time periods and suggests hedging alternatives.
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Table 2: Correlating Hedge Alternatives
Daily Five Day Daily Five Day
Changes Changes Changes Changes
6.25% August '23 .37 .46 .58 .70
11.25% February'15 .39 .45 .66 .70
CBOT 10-year T-note futures .35 .39 .69 .68
CBOT T-bond futures .34 .41 .58 .73
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Notice that correlations are highest in the more recent period, especially for five-day changes. A correlation close to 0.70 indicates that approximately half of the variance in Argentine par bond price changes results from changes in Treasury yield rates. The four possibilities shown all meet that standard. It follows that a well- constructed hedge can significantly reduce the price variability of a Brady bond investment.
Modified Adjusted Duration: Managing a Brady Bond's Compound Credit Components
As effective as a standard duration hedge may be, the unique structure of Brady bonds suggests a better approach to hedging.
Partially collateralized fixed-coupon Brady bonds are compound credits- part high-quality U.S. Treasury risk and part sovereign risk. The market prices the risky stream of coupon payments in terms of a spread over a U.S. Treasury. Thus, both the collateralized, non-risky principal payment and the coupon payments are sensitive to movements in U.S. Treasury rates.
This means that managing the exposure of a Brady par bond to U.S. interest rate risk requires more than hedging the collateralized principal payment.
The fact that the value of the coupon stream of a Brady par issue is derived from a spread over the U.S. rate suggests that the discount rate for the risky coupon component should be higher than the discount rate for the safe principal component. Discounting each cash flow at its appropriate risk factor results in an adjustment to a modified duration measure that captures this structure.
The Stripped Yield Spread: A "Truer" Measure of Creditworthiness
One possible way to define the appropriate discount rates, and, ultimately, the most effective hedge ratio for these bonds, involves a three-step process:
1. price the principal component of the Brady bond in terms of the value of a U.S. zero coupon with a similar maturity
2. subtract that price from the total Brady bond price, and
3. find the yield of that remainder.
That derived yield, often called the 'stripped yield" of a Brady par issue, provides the discount rate for the coupon stream.
Subtracting the stripped yield from the U.S. Treasury yield generates the 'stripped yield spread" of the Brady issue in question. That stripped yield spread may provide a better indicator of the creditworthiness of the Brady issuer than the yield-to-maturity spread commonly used in contrasting U.S. corporate issues with Treasuries.
If the stripped yield spread measures a country's creditworthiness better than the yield-to-maturity spread, then the stripped yield spread should remain constant if U.S. interest rates change while the country's credit risk remains stable. However, if the stripped yield spread is independent of Treasury rates, the yield-to-maturity spread is not. Table 3 shows how the yield-to-maturity spread for Argentine par bonds changes in response to stripped yield spread and U.S. Treasury rate changes.
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Table 3: Changes in Yield-to-Maturity Spread for Argentine Par Bonds
Change
in Treasury Change in stripped yield spreads (bp)
yields (bp) -20 -10 0 10 20
-25 (15.73) (9.87) (4.02) 1.80 7.61
-20 (14.97) (9.08) (3.22) 2.63 8.46
-15 (14.20) (8.30) (2.41) 3.46 9.31
-10 (13.44) (7.52) (1.61) 4.28 10.16
-5 (12.68) (6.73) (0.80) 5.11 11.01
0 (11.92) (5.95) 0.00 5.93 11.85
5 (11.16) (5.17) 0.80 6.76 12.70
10 (10.40) (4.39) 1.61 7.59 13.55
15 (9.64) (3.61) 2.41 8.41 14.39
20 (8.88) (2.82) 3.21 9.23 15.24
25 (8.12) (2.04) 4.01 10.06 16.08
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As the table indicates, with no change in the Argentine stripped yield spread, a five-basis-point decrease in U.S. Treasury yields will decrease the yield-to-maturity spread by 0.80 basis points. This analysis suggests that investors will find themselves about 16 percent underhedged if they assume that the yield-to-maturity spread fully captures sovereign credit risk and will remain constant as Treasury rates change.
The stripped yield allows hedgers to adjust the traditional duration measure so that they can more precisely account for the impact of changing U.S. interest rates on the value of both the coupon stream and principal components of a Brady bond. A modified adjusted duration calculation adjusts standard duration to compensate for the dependence of the yield-to-maturity spread itself on U.S. Treasury rates. [For information on how to calculate the stripped yield and modified adjusted duration, please contact Kenneth L. Telljohann of Lehman Brothers at (212) 528-9624.]
Since the modified adjusted duration assigns more of the bond's present value to the principal payment (the longest cash flow) than modified duration does, it follows that the modified adjusted duration will be longer than modified duration. Table 4 compares the modified durations and modified adjusted durations for the four major fixed rate Brady bond issues. Notice that the modified adjusted duration diverges anywhere from 10 percent to 50 percent from modified duration.
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Table 4: Comparing Durations
Modified
Modified Adjusted
Duration Duration Difference
Argentine pars 9.98 11.74 17.6%
Brazil pars 8.30 12.41 49.5%
Mexico pars 10.04 11.03 9.8%
Venezuela pars 7.84 10.65 35.9%
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Investors could extend this analysis another step to account for the rolling interest guarantee. Its effect on modified adjusted duration depends on the way in which one models the guarantee, but the impact of that effect on hedge performance is small, in any event, and can be omitted here.
As a practical matter, a hedge based on the longer modified adjusted duration will require a larger short hedge position and, as a result, it is slightly more expensive to carry than a standard duration hedge.
Empirical Duration Can Improve Short-Term Hedging
Modified adjusted duration hedging relies on the assumption that par bond stripped yield spreads move independently of Treasury yields over the term of the investment. Recent market behavior suggests that this assumption doesn't hold at all times. Brady bond dependence on U.S. Treasuries can differ significantly from calculated relationships.
It is possible to derive an empirical duration by regressing changes in Brady bond prices on changes in U.S. Treasury yields. For relatively short investment horizons, basing a hedge on this measure may more effectively neutralize the impact of U.S. interest rate changes.
Table 5 shows empirical durations for each of the major fixed-rate Brady bonds. These were determined by comparing daily changes in Brady bond prices with changes in the Treasury long bond yield over the prior three-month period.
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Table 5: Empirical Durations
Times
Empirical Adjusted
Duration Duration
Argentina pars 18.66 yrs 1.59
Brazil pars 18.34 1.49
Mexico pars 12.40 1.14
Venezuela pars 13.60 1.31
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If stripped yield spread changes were independent of Treasury rate changes, empirical duration would remain close to modified adjusted duration. Yet empirical durations for the bonds shown here range from 14 percent to 60 percent higher than modified adjusted duration, and have varied significantly over time.
Choosing the Most Appropriate Hedge Ratio
How investors approach hedging out the U.S. interest rate component of Brady bond risk depends on their assumptions about the nature of the credit spread.
These assumptions will determine the appropriate duration measure and, therefore, the most effective hedge ratio. If the yield-tomaturity spread is assumed to accurately describe the creditworthiness of the Brady issuer, then that spread should remain constant when creditworthiness remains constant, even if U.S. interest rates change. In that case, the appropriate hedge ratio is the standard modified duration-based tool used in hedging U.S. Treasuries.
If hedgers assume instead that the stripped yield spread quantifies the creditworthiness of the Brady country, they will further assume that it will be the stripped yield spread that will remain stable as U.S. rates change. In that case, the appropriate hedge ratio is based on modified adjusted duration.
Finally, investors may assume that while spreads are a function of the creditworthiness of the Brady issuer, the spreads themselves may also be a function of U.S. rates. In that case, an empirical duration based on a regression of recent changes of Brady prices on U.S. prices can lead to the most effective hedge ratio.
While empirical duration may provide the most sensitive measure in the short term, it also can vary a great deal from week to week. Accordingly, investors must be able to perform the necessary calculations to rebalance the hedge. The resultant gains should at least offset the costs and effort of that activity. As with any strategy that requires frequent rebalancing, these costs can be minimized by using futures contracts as the hedge vehicle.
Further, with the passage of time, the empirical and modified adjusted duration measures tend to converge. As a result, even if investors believe that the empirical approach would otherwise be best, they may opt to base their hedge ratios on modified adjusted duration if the hedge position is to be held for a long period of time.
Hedging Brady Bonds: A Recent Application
A hedge based on modified adjusted duration would have helped investors during the major market downdraft of the first quarter of 1994. During that period, the entire Brady market was hit hard.
Suppose an investor held $10 million face of the Mexican par on December 31, 1993, and decided to hedge out the U.S. interest rate component with T-bond futures for the first quarter of 1994. On that day, the Mexican bond was priced at 85.08 (includes accrued interest) to yield 7.70 percent, and its modified adjusted duration was 11.75.
Hedgers would typically establish an initial position in the nearby futures contract and then roll the hedge forward to the next expiration before the delivery cycle begins. Therefore, the hedger sells CBOT March T-bond futures and holds that short position from December 31, 1993, through February 28, 1994. He then buys those contracts back and sells the appropriate number of June contracts. Finally, he lifts the hedge entirely on March 31.
At the end of December, the cheapest-to-deliver Treasury bond was the 12.5% of August 'l4--one of the last callable issues in the delivery window. It was priced at 166.29 (includes accrued interest) to yield 6.27 percent, with a conversion factor of 1.3921. The March T-bond futures price was 114.50 and the modified duration of the futures contract (to the call date) was 8.71. The modified adjusted duration- based hedge ratio on December 31, 1993 is calculated in Table 6.
[For an in-depth examination of the principles underlying CBOT U.S. Treasury futures contracts, please consult the CBOT pulication entitled "Treasury Futures for Institutional Investors," available free of charge from the CBOT Pulications Services Bookstore.]
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Table 6: Hedge Ratio (Modified Adjusted Duration) 12-31-93
11.75 85.08 10,000,000
------ x ------ x 1.3921 x ---------- = 96.08
8.71 166.29 100,000
Initial Market Conditions
12/31/93 2/28/94
Mexican Par
Price (full) 85.08 77.59
YTM 7.70% 8.66%
Modified adjusted duration 11.75 11.22
US T-Bond Futures
CTD: 12.5 of Aug '14
Cash price (full 166.29
March futures price 114.50 112.41
YTM (futures) 6.38 6.57
Modified duration (futures) 8.71
Conversion factor 1.3921
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By February 28, 1994, the March futures price had fallen to 112.41. Accordingly, each contract in the short futures position had gained $2,094, and the gain for the entire futures position was $201,024.
As Table 7 illustrates, although the 12.5 percent T-bonds of August '14 remained the cheapest-todeliver bond, everything else changed. The full price of the Mexican par bond had dropped to 77.59, its modified adjusted duration had dropped to 11.22, and the June futures duration (again, to the call date) was 8.37. Given that data, the hedge ratio for the last month of the hedge was 92 futures contracts.
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Table 7: Hedge Ratio for Roll 2-28-94
11.22 77.59 10,000,000
----- x 1.3891 x ------ x ------------ = 91.66
8.37 157.62 100,000
Market on Roll Date
2/28/93 3/31/94
Mexican Par
Price (full) 77.59 69.27
YTM 8.66% 9.42%
Modified adjusted duration 11.22
US T-bond Futures
CTD: 12.5 of Aug'14
Cash price (full) 157.62
June futures price 111.34 106.25
YTM (futures) 6.70
Modified duration (futures) 8.37
Conversion factor 1.3891
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Assessing the Results
By March 31, the Mexican par price had declined to 69.27 from a December 31 price of 85.08. The value of the $10 million face had declined from $8,508,000 to $6,927,000 for a loss of $1,581,000.
During the last month of the hedge period, the price of June T-bond futures dropped from 111.34 to 106.25. Each short futures contract gained $5,093 for a total futures gain of $468,629. Added to the $201,024 futures gain of the first two months of the hedge, that amounts to a $669,653 total futures gain from the hedge. The hedge results can be seen in Table 8.
As a result of the hedge, the capital loss on the Mexican par position was reduced from 18.58 percent to 10.71 percent. The 7.87 percentage points saved by the futures hedge amounts to slightly more than 40 percent of the price change during that three-month period.
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Table 8: Hedge Results
12/31/93 3/31/94
Mexican par value $8,508,000 $6,927,000
March coupon payment 312,500
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$7,239,500
Futures gain 669,653
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Net result $7,909,153
Results comparison
% capital return without futures -18.58%
% capital return with futures -10.71%
-------
Advantage of futures hedge 7.87%
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Hedging Limitations
Any long-term static hedge like this is subject to a number of market factors that hedgers often omit from consideration.
One of the most significant of these factors is carry. During the holding period of this hedge, the cost of carrying the short futures position amounted to approximately 2.5 percent of the actual value of the Mexican par bond. Absent that, the aggregate position would have suffered a smaller loss.
In addition, duration hedges are effective only for small, parallel shifts in the yield curve. Hedge performance may not be noticeably affected by slight changes in the shape of the yield curve, given a very short hedging horizon. Over a period as long as three months, however, nonparallel yield curve changes can become significant.
As previously stated, hedgers must rebalance their positions as market conditions change. In this example of the Mexican par, a hedger could have considered rebalancing at several different points.
Finally, a widening of sovereign spreads during the hedging period can create the appearance of a malfunctioning hedge. Certainly, the sovereign spreads of all the Brady issues changed significantly during the period in question. The Mexican stripped yield spread widened from 254 basis points on December 31 to 452 basis points on March 31. Because a modified adjusted duration does not account for changes in price due to changes in the stripped yield spread, this effect could not have been hedged with a modified adjusted duration hedge ratio.
Conclusion
Brady bond investors purchase these securities for the enhanced yields associated with emerging market sovereign debt. The overriding goal in hedging the U.S. interest rate component of Brady bonds is to factor out the negative effects of these interest rate changes. CBOT Treasury bond futures allow hedgers to preserve, or even maximize, the performance of Brady bonds.
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