Welcome to Yield and Yield Spread Measures!

Welcome, future charterholders! Today, we are diving into one of the most critical parts of Fixed Income: Yield and Yield Spreads. Think of "Yield" as the heart rate of a bond—it tells you how much "life" (return) you are getting out of your investment. "Spreads" are like comparing your heart rate to an athlete's; they tell us how much extra return we get for taking on more risk than a "safe" government bond.

Don’t worry if these terms sound a bit technical at first. We’re going to break them down step-by-step using simple logic and real-world examples.

1. Yield-to-Maturity (YTM): The "Gold Standard"

The Yield-to-Maturity (YTM) is the most common way to talk about a bond's return. It is the internal rate of return (IRR) of a bond's cash flows. In simple terms: it’s the annual return you’ll earn if you hold the bond until it matures and reinvest all your coupons at that same rate.

How to Calculate YTM

To find the YTM, we use the bond pricing formula. The price of the bond (\(PV\)) is the sum of the present values of all future coupons (\(PMT\)) and the face value (\(FV\)):

\(PV = \frac{PMT}{(1+r)^1} + \frac{PMT}{(1+r)^2} + ... + \frac{PMT + FV}{(1+r)^n}\)

Where \(r\) is the YTM per period.

Important Assumptions of YTM

For you to actually realize the YTM, two things must happen:

1. The issuer must make all payments on time (no default).
2. You must be able to reinvest all coupon payments at the same YTM rate.

Quick Review: If a bond's price goes UP, its YTM goes DOWN. They have an inverse relationship. Think of it like a seesaw!

2. Specific Yield Conventions

Not all yields are calculated the same way. The CFA curriculum highlights a few specific "conventions" you need to know:

Street Convention vs. True Yield

Street Convention: This ignores weekends and holidays. It assumes every payment happens exactly on the scheduled day, even if that day is a Sunday when banks are closed.
True Yield: This accounts for the fact that if a payment date falls on a weekend, you won't get paid until Monday. Because of this slight delay in receiving cash, the True Yield is usually slightly lower than the Street Convention yield.

Current Yield

This is a "quick and dirty" measure. It only looks at the annual coupon income relative to the current price. It ignores capital gains or losses and the time value of money.

\(Current \ Yield = \frac{\text{Annual Coupon Payment}}{\text{Current Bond Price}}\)

Yield to Call (YTC)

Some bonds are "callable," meaning the issuer can pay you back early. If the bond is likely to be called, investors look at the Yield to Call instead of YTM. You calculate it the same way as YTM, but you use the call date as the maturity and the call price as the face value.

Key Takeaway: Yield to Worst (YTW) is the lowest of all possible yields (YTM and all various YTCs). It represents the "conservative" estimate of your return.

3. Matrix Pricing: Estimating the Price of Illiquid Bonds

What if a bond doesn't trade often? We can't see its market price, so we use Matrix Pricing. This is just a fancy term for "estimation based on similar bonds."

Steps for Matrix Pricing:

1. Find yields of active bonds with similar credit ratings and similar maturities.
2. Use linear interpolation to estimate the yield for our specific maturity.
3. For example: If a 2-year bond yields 4% and a 4-year bond yields 6%, we can estimate a 3-year bond yields 5% (right in the middle!).

Did you know? Matrix pricing is also used to estimate the Spread for new bonds that haven't been issued yet.

4. Money Market Yields

Money market instruments (like T-bills) are short-term (less than a year). They use different math than long-term bonds. There are two main types:

Discount Basis (DR)

Used for T-bills. The "interest" is the difference between what you pay and the face value. It uses a 360-day year and the face value as the denominator.

\(r_{BD} = \frac{D}{F} \times \frac{360}{t}\)

Where \(D\) = dollar discount, \(F\) = face value, and \(t\) = days to maturity.

Add-on Yield (AOR)

Used for bank CDs and Libor-style rates. It uses the purchase price as the denominator.

\(r_{AOR} = \frac{D}{P} \times \frac{360}{t}\)

Common Mistake: Forgetting which day count to use. Always look for whether the question asks for a 360-day or 365-day year!

5. Yield Spreads: Measuring Risk

A "spread" is the difference between the yield on a risky bond and a benchmark (usually a "risk-free" government bond).

G-Spread and I-Spread

G-Spread: The "G" stands for Government. It is the yield of a bond minus the yield of a Government bond with the same maturity.
I-Spread: The "I" stands for Interbank (or Interpolated). It is the yield of a bond minus the Swap rate (the rate banks charge each other).

Z-Spread (Zero-Volatility Spread)

The Z-spread is more advanced. Instead of using one single benchmark rate, it looks at the entire spot rate curve. It is the constant spread you add to every spot rate to make the present value of the bond's cash flows equal to its market price.

Option-Adjusted Spread (OAS)

This is crucial for bonds with "embedded options" (like callable bonds).
OAS = Z-spread - Option Value (in basis points)

Think of it this way: If a bond is callable, the issuer has a "right" that hurts you. The Z-spread includes the compensation for that "hurt." If you strip away the value of that option, you are left with the OAS, which represents just the credit and liquidity risk.

Memory Aid: OAS is the Only spread that removes the "noise" of the option to show you the true credit risk.

Summary Table: Spread Quick Review

G-Spread: Spread over Government bonds.
I-Spread: Spread over Swap rates.
Z-Spread: Constant spread over the entire Spot Curve.
OAS: Z-Spread minus the value of the embedded option.

Final Encouragement

You've made it through the basics of Bond Yields and Spreads! If the math feels heavy, just remember: Yield is return, and Spread is the "extra" for taking risk. Keep practicing the formulas for Money Market yields, as those are high-probability exam topics. You’ve got this!