When analyzing the risk/return profile of a proposed trade, it is important to take both parallel and slope risk into account. To illustrate this, consider the following 10-, 20- and 30-year Treasury bonds:

CUSIP	coupon	maturity	yield
912810DU	9.375%	2/15/06	6.775%
912810DV	9.25%	2/15/16	7.067%
912810EW	6%	2/15/26	6.976%

The parallel durations, non-parallel durations, and convexities of these bonds are shown in the following table:

bond	parallel duration	non-parallel duration	convexity
10-year	6.32	1.01	0.27
20-year	9.63	0.45	0.73
30-year	12.39	0.00	1.32

Suppose an investor owns $10m of the 20-year bonds and wishes to enhance the convexity of the portfolio. One alternative is to execute a duration-matched trade: sell $10m 20-year bonds and purchase $7.8m 30-year bonds. This increases portfolio convexity by 0.78 1.32 - 0.73 = 0.30.

Assuming the remainder of the sale proceeds is held in cash, this trade involves giving up approximately 30 bp in yield. So, for example, over a 6-month horizon yields would have to move by only 50 bp for the gain from convexity to offset the loss in income.

This may appear an attractive risk/return tradeoff. However, the duration-matched analysis ignores yield curve slope risk. The above trade is not slope neutral: it changes non-parallel duration from 1.01 to 0.00. An overall steepening in the yield curve will cause significant underperformance.

In terms of absolute risk, the change in non-parallel duration is over three times as significant as the change in convexity. The above trade is therefore not a neutral way to enhance convexity; it implies a view on the direction of the 20-year/30-year yield spread.

A more valid convexity enhancement trade would be neutral with respect to both parallel and slope risk. Thus the investor should sell $10m 20-year bonds and buy $5.5m 30-year bonds and $4.5m 10-year bonds, to match both parallel and non-parallel duration.

This trade increases portfolio convexity by only 0.10; i.e. a 100 bp shift in yields will result in price outperformance of $0.10. It also involves giving up approximately 18 bp in yield. So in this case, over a 6-month horizon yields would have to move by 90 bp for the convexity gain to offset the loss in income.

It is clear that when both parallel and slope risk are taken into account, the convexity enhancement strategy appears less attractive from a risk/return point of view. If the approximate breakeven calculations described above are replaced by detailed analysis using BondEdge's "Specified Scenario" capability, similar results are be obtained.

The simple breakeven analysis used here is not applicable to bonds with embedded options. In this case convexity does not fully describe the price-yield relationship for wide fluctuations in yields, and proposed trades must therefore be analyzed in detail using BondEdge's portfolio simulation tools. But yield curve slope risk is still relevant. (Note that BondEdge's non-parallel duration, like effective duration, is "option adjusted".)

For option-embedded bonds, other risks - such as volatility risk - also come into play. These can be monitored separately using BondEdge; see the Interactive Data Fixed Income Analytics research papers Risk Measures and Interpreting and Using Advanced Risk Measures for further details.