Latest / VoraPrep Audio — Professional Licensure & Certification Exam Prep / [CFA Level I] CFAFI: Fixed-Income Valuation: Yields and Spreads
Transcript
- Hey, welcome to VoraPrep Audio. Thanks for tuning in. Imagine this scenario. You're the fixed-income analyst at your firm. A portfolio manager walks over with a few questions. She needs to know the value of a bond portfolio, and she needs to know why it's valued that way. She wants you to explain the current yield curve. And she needs a price for a specific corporate bond that almost never trades. This is exactly the kind of thing the exam throws at you. It’s not about just memorizing formulas. It's about knowing which tool to use for which job. And that’s what we’re going to get straight today: yields and spreads. The absolute foundation for all of this is the spot rate. A spot rate is the purest interest rate you can find. It’s the yield on a zero-coupon bond. That means it’s the rate for one single payment at one single point in the future. There are no coupons to worry about, and no reinvestment risk. Just: you pay this today, you get that back in exactly two years. That two-year rate is the two-year spot rate. The whole collection of these rates for different maturities—one year, two year, ten year, and so on—forms the spot rate curve. It's the DNA of interest rates. In theory, this is how you should value a regular coupon bond. You discount each individual cash flow. That means every coupon, and the final principal. And you use the specific spot rate that matches the timing of each payment. Now, if spot rates are what rates are today, forward rates are what the market thinks rates will be in the future. They're implied rates, baked right into the current spot rate curve. They aren’t a crystal ball, but they show the market's expectation. Let’s make that real with a quick calculation, because you’ll definitely see this. Imagine the one-year spot rate is 3% and the two-year spot rate is 4%. What does that imply the one-year rate will be, starting one year from now? The logic is that you should be indifferent between two options. Option one: invest for two years straight at the two-year rate. Option two: invest for one year, then reinvest for another year at the future rate. So we set them equal. The formula is: one plus the two-year spot rate, squared, equals... one plus the one-year spot rate... times... one plus our forward rate. Let's plug in the numbers. One point oh four squared is one point oh eight one six. That has to equal one point oh three, times one plus our forward rate. So we just divide one point oh eight one six by one point oh three. We get about one point oh five oh one. That means the implied one-year forward rate, one year from now, is about 5.01%. It’s the rate that makes the math work, with no arbitrage. Okay, so we have spot rates and forward rates. But the number you hear about most is the Yield-to-Maturity, or YTM. YTM is the workhorse of bond yields. It’s the single discount rate that connects a bond's future cash flows to its current market price. It accounts for all the coupons and the final principal payment. It’s like an average rate over the bond's whole life. But it comes with some big assumptions. It assumes you hold the bond to maturity, the issuer never defaults, and—this is the big one—that you reinvest every single coupon payment at that exact same YTM. In the real world, that's pretty unlikely. So what do you do when you have a bond that doesn't have a price? The one that rarely trades? You can't calculate a YTM if you don't have a price. This is where matrix pricing comes in. It’s an estimate of the bond's value based on its peers. You look for other bonds that are trading actively. You find bonds from issuers with a similar credit rating. They should also have similar maturities and similar coupon rates. You see their YTM.s, and you interpolate to find a reasonable YTM for your illiquid bond. It’s an estimate, but it’s a structured and defensible one. Alright, the last big piece of the puzzle is yield spreads. This is huge on the exam. A spread is just the extra yield you get for taking on extra risk compared to a benchmark. That benchmark is usually a super-safe government bond. The most basic one is the G-spread. The 'G' stands for government. It’s just the bond’s YTM minus the YTM of a government bond with the same maturity. Simple. It tells you a bit about the credit and liquidity risk. A slightly better version is the I-spread. The 'I' is for interpolated. This compares the bond’s yield to a swap rate instead of a government bond yield. Swap rates are often seen as a purer reflection of interest rates. They're less affected by the unique supply and demand quirks of the government bond market. So, it's a cleaner comparison for corporate bonds. But the G-spread and I-spread are limited. They rely on a single yield comparison for a given maturity. A more precise measure is the Z-spread, or Zero-volatility spread. The Z-spread asks a different question. It asks: what single, constant spread do I need to add to every single spot rate along the entire Treasury spot curve? A spread that makes the present value of the bond's cash flows equal its market price. It’s more precise because it uses the entire spot curve to value the bond. But even the Z-spread isn't perfect, because it ignores embedded options. This brings us to the Option-Adjusted Spread, or OAS. Many corporate bonds are callable, meaning the issuer can buy them back early. That’s a risk for you, the investor. The OAS takes the Z-spread and adjusts for the value of that embedded option. It strips it out. So the OAS tells you the spread you are earning for only the credit and liquidity risk, with the option effect removed. It’s the cleanest measure. And here’s a key relationship to remember. Think about a callable bond. That call option benefits the issuer, not you. So its value is subtracted from the spread. This means the OAS will be less than the Z-spread. The difference between them is the value of that call option. Now think about a putable bond. You have the right to sell it back early, so the option benefits you. In this case, the OAS will be greater than the Z-spread. So, when you see a question, don't just grab a formula. Think about what you're being asked to do. Are you valuing cash flows with the purest rates? Use spot rates. Are you trying to figure out what the market expects? Calculate the forward rate. Are you pricing an illiquid bond? You’re probably using matrix pricing. And if you’re comparing relative value, especially for a bond with an option, you need to get to the Option-Adjusted Spread. That shows what you’re really getting paid for the risk. One of the biggest traps is just using YTM for everything. The exam might give you a bond's price and a spot rate curve and ask for its value. If you just calculate the YTM and use that, you've missed the point. You have to discount each cash flow by its corresponding spot rate. It’s a more precise valuation. To recap it all one more time: Spot rates are the pure, foundational rates for single payments. Forward rates are the market's implied guess about future spot rates. YTM is the common, single-rate average, but it has flaws. When it comes to spreads, think of it as getting a clearer picture of risk. The G-spread is a quick look. The I-spread is a bit better. The Z-spread is a much sharper picture using the whole spot curve. And the OAS is the perfectly clear, high-definition photo. It adjusts for options to show you the pure compensation for credit and liquidity risk. VoraPrep is a full exam-prep app — lessons, practice questions, and an AI tutor in one place. Get started at Vora Prep dot com.