Market Risk Management: What Risk Really Means in Fixed Income
This is Part 1 of our retelling of Chapter 3 from “Trading the Fixed Income, Inflation and Credit Markets: A Relative Value Guide” by Neil C. Schofield and Troy Bowler (Wiley, 2011, ISBN: 978-0-470-74229-7).
Previous: Swaps, Options and the Forward Connection
What Does Risk Actually Mean?
Every day, analysts call trades “high risk” or “low risk” like that alone tells you something. The assumption is that high risk is bad and low risk is good. But the authors push back on this.
Think about it differently. A high-risk trade with massive potential return? That might be high quality. A low-risk trade with tiny returns? That’s arguably low quality. Hedge fund investors routinely buy out-of-the-money options where the expected payoff is 10 times the premium. They’ll probably lose the premium. But when the unexpected happens, the returns are enormous.
There’s another layer too. A trade that looks bad in isolation might be brilliant inside a portfolio. Buying puts when you’re long equities looks like a losing bet on its own. But as portfolio insurance? Very smart.
The takeaway: never judge a trade in isolation. What matters is its marginal contribution to the overall portfolio’s risk and reward. A well-diversified portfolio might hold both bullish and bearish positions, even if the manager is overall bullish.
Defining Market Risk
The book focuses on two types of financial risk: credit risk (will the borrower pay you back?) and market risk. Market risk is simpler to define: the risk that an asset or liability changes value because some market price moved. That’s it. FX risk, equity risk, interest rate risk are all just flavors of market risk.
Spot Market Risk: Duration and Its Friends
Macaulay Duration
The oldest risk measure still in use. Its technical definition is “the present value-weighted time to receipt of cash flows.” Measured in years. Not very intuitive.
Here’s the logic. A bond’s maturity doesn’t tell you when you’ll actually get your money back. A high-coupon bond pays out more during its life, while a zero-coupon bond pays everything at the end. Duration gives you a weighted average of when you receive cash flows, where the weights are present values.
For a 5-year bond with a 6% coupon and 4% yield, Macaulay duration works out to 4.49 years. Not a number that makes your heart sing with understanding. But the bigger the duration, the more sensitive the bond is to interest rate changes. That’s the useful part.
What drives duration:
- Longer maturity = higher duration (but the increase slows down)
- Lower coupon = higher duration
- More frequent coupons = lower duration
- Lower yield = higher duration
Modified Duration
This is the practical version. Modified duration tells you: for a 1% change in yield, how much does the bond’s price change in percentage terms?
Take our example bond. Modified duration is 4.32 years. Meaning: if yields drop by 1%, the price goes up by about 4.32%. If yields rise by 1%, the price drops by about 4.32%.
In dollar terms, that’s a 4.70 point move on a bond priced at 108.90. Much easier to work with than “4.49 years.”
The Convexity Problem
Modified duration assumes a straight-line relationship between price and yield. But the actual relationship is curved. For small yield changes, the linear approximation works fine. For large moves, it breaks down.
Duration overestimates how much prices fall when yields rise and underestimates how much prices rise when yields fall. This curvature is called convexity, and it’s actually good for bond investors.
When you own a bond with positive convexity: prices rise at an accelerating rate when yields fall, and fall at a decelerating rate when yields rise. You win more on the upside than you lose on the downside. That’s a nice property.
Convexity is a second-order correction. Add the convexity adjustment to the duration estimate, and your price predictions become much more accurate. For our example bond, the duration-only estimate for a 1% yield increase predicts a price of 104.20. Adding convexity gives 104.33, which matches the actual calculated price almost exactly.
What drives convexity:
- Lower coupon = higher convexity
- Longer maturity = higher convexity
- Lower yield = higher convexity
- More frequent coupons = higher convexity
DV01: The Trader’s Favorite
Modified duration measures a 1% move. In normal markets, yields don’t jump 1% in a day. Traders want something tied to realistic moves. That’s the DV01 (dollar value of an 01): how much the clean price changes for a single basis point (0.01%) move in yield.
For our bond: DV01 is about 0.047 per 100 face value. On a $10 million position, that’s $4,705 per basis point. Now you’re talking real money and real risk.
DV01 is linear, so it shares duration’s predictive limits for big moves. But as a rule of thumb, it works well for moves up to about 10 basis points.
FRNs and Credit Instruments
Floating-rate notes have minimal interest rate risk. Their duration maxes out at the time until the next coupon reset (typically 3 months) and drops to zero on the reset date. They’re mainly exposed to credit risk, not rate risk.
For credit default swaps, the market uses risky PV01: the value today of receiving one basis point per year for the life of the contract, adjusted for both the time value of money and the probability of default. It incorporates survival probabilities and hazard rates. The risky DV01 (or delta) measures the P&L impact of a one basis point parallel shift in the credit curve.
Forward Risk
The risk of a forward position comes from the forward pricing formula:
Forward price = Spot price + Net carry
So forward prices move when either spot prices or carry costs change.
Fixed Income Forward Risk
For a bond forward, a decrease in repo rates lowers the forward price (bad for a long position). A decrease in the spot bond price also lowers the forward price. The forward risk is really an exposure to the yield curve shape: repo rates represent the short end, bond prices represent the long end. A long forward position loses money if the curve steepens.
Credit Forward Risk
A forward CDS position is essentially long one maturity and short another. The risk is about changes in the credit curve shape. Buying protection forward loses money if the credit curve flattens.
Carry and Roll Down
These two concepts are essential for swap traders.
Carry is the income from the fixed leg minus the LIBOR cost of the floating leg. It’s based on observed market prices today.
Roll down is the gain (or loss) from a swap aging into a different point on the yield curve, assuming the curve doesn’t move. If you receive fixed at 6.92% on a 5-year swap, and one year later the 4-year rate is 6.90%, you could close out at a profit of 2 basis points. The steeper the curve, the bigger the roll down effect.
Traders look at both carry and roll down when sizing up potential trades.
That covers the first half of Chapter 3. We’ve gone from the philosophical question of what risk means, through the practical tools of duration, convexity, and DV01, to the forward risk framework and the carry-and-roll-down concepts that traders use every day.