Pricing Relationships: The Relative Value Triangle and Spot Pricing
This is Part 1 of our retelling of Chapter 2 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).
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What Is Relative Value, Really?
Most people hear “relative value” and think: is this thing cheap or expensive compared to something else? That’s fair. Like comparing two pairs of sneakers and picking the better deal.
But Schofield and Bowler push the definition further. For them, relative value means: what is the best way to express a particular view on the market?
Here’s a simple example. Say you want to earn a return in euros with minimal credit risk. You could buy AAA-rated euro sovereign bonds. Fine. But you could also:
- Buy a bond future
- Receive fixed in an interest rate swap
- Execute an option trade that profits if rates move the way you expect
Same view. Four different ways to play it. That’s the wider meaning of relative value. It’s not just about finding the cheapest bond. It’s about finding the smartest structure.
One thing the authors want to be clear about: they’re not talking about arbitrage. True arbitrage is when you find the same asset at two different prices and pocket a risk-free profit. That’s a separate concept entirely.
The Relative Value Triangle
At the center of all this sits what the authors call the “relative value triangle.” Picture a triangle with four components: spot, forward, swap, and options. The triangle shows mathematical links between all of them.
Here’s the quick version:
- The spot price of a bond connects to its forward price through something called “net carry” (basically, the cost of holding the asset).
- A swap can be valued as if it were a pair of bonds, one fixed-rate and one floating.
- Forward rates can be derived from spot rates of different maturities.
- A swap rate is essentially a weighted average of forward rates.
- Options connect to the rest through volatility and put-call parity.
This triangle is the roadmap for the entire chapter. Everything connects to everything else.
Spot Pricing: How Do You Value a Bond?
There are two ways to think about the value of any asset. Either it’s worth whatever someone will pay for it, or it’s worth the cash flows it will generate. The book focuses on the second approach.
The Basics of Bond Pricing
Take a bond with no default risk, 4-year maturity, and a 5% annual coupon. Per 100 face value, the cash flows look like this:
- Year 1: 5
- Year 2: 5
- Year 3: 5
- Year 4: 105
To figure out today’s price, you need to discount those future payments back to the present. Why? Because 5 received today is worth more than 5 received next year. You could invest that 5 now and earn interest. This is the “time value of money,” and it’s the foundation of everything in finance.
If you use a single rate of 4.5% to discount all cash flows, you get a price of about 101.79. This single discount rate is called the yield to maturity (YTM). It’s a one-number summary of your expected return if you buy the bond and hold it until it matures.
But here’s the catch: YTM only works perfectly if you can reinvest every coupon you receive at that same 4.5% rate. If rates change, your actual return will differ. That’s called reinvestment risk, and it’s the main weakness of YTM.
Clean Price vs. Dirty Price
The 101.79 is the “dirty price.” It includes accrued interest. But bonds trade on a “clean” basis, which strips out the daily interest buildup. This avoids a misleading upward drift in quoted prices just from interest accruing day after day.
If the market price is below the calculated fair value, the bond is “cheap.” If it’s above, it’s “rich.”
Beyond YTM: Zero-Coupon Rates
Using one rate for all cash flows feels a bit lazy, right? Rates for different time periods are different. So it makes sense to use a different rate for each cash flow. That’s where zero-coupon rates come in.
A zero-coupon rate applies to a structure with only two cash flows: one at the start, one at maturity. No coupons in between. No reinvestment risk. The rate you see is the rate you get.
You can break a coupon-paying bond into a series of zero-coupon cash flows, discount each one separately, and add them up. The result should match the YTM approach (since YTM is basically an average of the zero-coupon rates).
Bootstrapping
Most zero-coupon rates for longer maturities aren’t directly observable. So you derive them from par yields using a process called “bootstrapping.” You start with the 1-year rate (which is already zero-coupon since there’s only one payment), then use it to solve for the 2-year zero rate, then use both to get the 3-year rate, and so on.
Key pattern: when the par yield curve slopes upward, zero-coupon rates sit above the par curve. When it slopes down, they sit below.
Forward Rates: The Misunderstood Curve
Forward rates are rates known today that apply to future periods. Like: what’s the 1-year rate going to be in 1 year? You can calculate this from two zero-coupon rates using the “no arbitrage” principle.
The logic works like this. A bank needs to lock in a lending rate for a future period. They hedge by borrowing long and lending short today. The forward rate falls out of the math.
Forwards as Breakevens
Here’s where it gets interesting. Say you’re choosing between a 1-year bond at 5% and a 2-year bond at 6%. The forward rate for the second year works out to about 7.01%.
If the actual 1-year rate next year ends up below 7.01%, the 2-year bond wins. If it lands above 7.01%, the 1-year bond wins. If it’s exactly 7.01%, you’re indifferent. The choice isn’t about whether rates go up or down. It’s about whether they go up more or less than the forward rate implies.
Are Forwards Forecasts?
Nope. The authors are firm on this. Forward rates are math, not predictions. They’re calculated from no-arbitrage principles, with no subjective belief built in. Empirically, forward rates have been terrible predictors of actual future rates. They usually overpredict.
Floating-Rate Notes and Inflation Pricing
FRNs are bonds where the coupon resets periodically (usually quarterly) at LIBOR plus a spread. You can’t calculate a traditional yield because future coupons are unknown. Instead, the market uses a “discount margin” as the yield measure. FRNs are mostly immune to interest rate changes and are primarily sensitive to changes in the issuer’s credit quality.
Inflation-linked bonds use the Canadian model (also adopted by the UK after 2005). The key concept is the “index ratio,” which scales cash flows by inflation to preserve purchasing power. These bonds are quoted in real terms, meaning a change in inflation alone won’t affect their price. Only changes in real yields matter.
Credit Pricing Basics
When there’s default risk, investors demand a credit spread over the sovereign rate. The spread can be estimated with a simple formula:
Credit spread = Probability of default x (1 - Recovery rate)
If the probability of default is 1% and recovery is 40%, the spread is roughly 0.60%. Simple but useful for a ballpark number.
The market typically assumes a 40% recovery rate for senior unsecured investment-grade debt and 20% for subordinated debt. Default probabilities can be backed out from observed CDS spreads, giving market-implied views that traders compare against their own opinions.
That wraps up the first half of Chapter 2. We’ve covered how relative value thinking goes beyond simple cheap-vs-rich comparisons, how the RV triangle connects spot, forward, swap, and option markets, and how bonds, FRNs, linkers, and credit instruments are priced in the spot market.