Fixed Income is a central topic in finance, and it increases in importance (topic weight wise) as you advance to CFA Level 3. With so many key concepts to cover, we decided to create our Cheat Sheet series of articles, which focuses on one specific topic area for one specific CFA Level.
This cheat sheet is basically a CFA Level 1 Fixed Income notes and formula sheet. ☕ CFA Fixed Income is one of the more quantitatively intensive topics in the exams and getting your fixed income basics right would build you a good base for the subsequent levels as well.
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By referring to the CFA Learning Outcome Statements (LOS), we prioritize and highlight the absolute key concepts and formula you need to know for each topic. With some topic-specific tips at the end too!
Use the Cheat Sheets during your practice sessions to refresh your memory on important concepts. Don’t forget to bookmark this page and revert back often as it’s a big topic to go through 🙂
The Fixed Income CFA Level 1 topic area constitutes one of the largest segments of the broader capital market. It mostly covers any investments where investors are loaning the money for a fixed, scheduled repayment: hence the name ‘fixed income’. For Level 1, Fixed Income is third largest topic (sharing the title with Equity Investments) after FRA and Ethics. It is crucial to get a solid foundation on fixed income fundamentals from Level 1 as its topic weight increases throughout the 3 levels.
CFA Level 1 Fixed Income’s topic weighting is 10%-12%, which means 18-22 questions of the 180 questions of CFA Level 1 exam is centered around this topic. It is covered in 2023’s Topic 6 which contains 6 Learning Modules (LMs).Here’s the summary of CFA Level 1 Fixed Income’s chapter readings:
| Learning Module | Sub-topic | Description |
|---|---|---|
| 1 | Fixed Income Securities: Defining Elements | Understanding what a fixed income security is, and what’s its basic structure like. |
| 2 | Fixed Income Markets: Issuance, Trading & Funding | Understanding the structure and norms of the fixed income market. |
| 3 | Introduction to Fixed Income Valuation | Highlights the nuances of valuing and pricing fixed income securities. The most important chapter really. |
| 4 | Introduction to Asset Backed Securities | Dives into the detail of asset-backed securities and sub-products, such as residential and commercial mortgage-backed securities. |
| 5 | Understanding Fixed Income Risk and Return | Outlines the types of risks associated with typical fixed income securities. A topic to focus on with lots of testable concepts. |
| 6 | Fundamentals of Credit Analysis | Focuses on credit risk, a type of risk especially relevant to fixed income. |
This CFA topic area aims to introduce readers to fixed income basics, how they are priced and valued. The concepts discussed are especially important for those who aspire to be in Fixed Income Portfolio Management – credit, macro or otherwise. Even for those who do not plan to pursue a career in Fixed Income, these topics will be an inalienable part of their skill repertoire. This is because the various markets are often related and great investors (e.g. Warren Buffet, Peter Lynch, George Soros) often possess knowledge of different kinds of markets – not just the market they are investing in.
In short, CFA Level 1 Fixed Income teaches you: – about the various fixed income products available in the market and how these markets operate;
– how to price these securities: what are the risk factors to pricing a fixed income security and how to hedge any associated risks?
Negative (restrictive) covenants are what bond issues must not do. Some examples:
A callable bond gives the issuer the right to redeem all or part of the bond before maturity.
This embedded option benefits the issuer as it protects the issuer when the interest rates drop (i.e. when it does, issuer can call/redeem the bond, and reissue a new bond at a lower rate).
To compensate investors of a higher reinvestment risk, issuers offer a higher yield for callable bonds.
Therefore, the price of callable bond (Vcallable bond) is always lower than the price of a straight (non-callable) bond because the call option adds value to an issuer.
Vcallable bond = Vnon-callable bond – Vcall option
A putable bond gives the bondholder the right to sell the bond back to the issuer at a pre-determined price on a specified date(s).
This embedded option benefits the bondholder as it protects the bondholder when the interest rates rise (i.e. when it does, bond price falls, bondholder can sell the bond back to issuer at a pre-determind price, and reinvest their cash at a higher rate).
Putable bonds offer a lower yield and is worth more than a non-putable bond.
Vputable bond = Vnon-putable bond + Vput option
Convertible bonds gives the bondholder the right to exchange the bond for a specified number of common shares in issuing company.
With debt and equity features, convertible bonds provide benefits to both:
Contingent convertible bonds (CoCos) automatically converts to equity upon a pre-specified event.
Yield to maturity (YTM) is the constant discount rate that equates the sum of present value of future cashflows to the current price of the bond. In this specific case, all the spot rates are the same: z1 = z2 = zN = r.
| Coupon rate vs Yield to Maturity (YTM) | Bond price |
|---|---|
| Coupon rate = YTM | Price = Par value |
| Coupon rate < YTM | Price < Par value, a discount |
| Coupon rate > YTM | Price > Par value, a premium |
| Inverse effect | Bond price is inversely related to YTM, the higher the YTM the lower the price, and vice versa. |
| Convexity effect | Bond price is more sensitive to discount rate reduction than discount rate increases. |
| Coupon effect | If all else constant, bonds with lower coupon rates are more sensitive to discount rate changes. |
| Maturity effect | If all else constant, bonds with longer maturity are more sensitive to discount rate changes. |
PV=FV \times \Big (1-\frac\times DR \Big)
DR=\Big (\frac \times \frac\Big)
PV=\frac<\Big(1+\frac\times AOR\Big)>
AOR=\Big(\frac \times \frac\Big)
The main difference between DR and AOR is that interest is included in the face value for DR, but it is added to the principal for AOR.
Forward rate is an interest rate in the future. The Implied Forward Rate (IFR) can be calculated from n-period spot rates (zn):
(1+z_A)^A \times (1+IFR_)^=(1+z_B)^B
This is a loan a buyer takes on to buy real estate (house, flat, land etc.) whereby the property bought is used as collateral.
Characteristics of residential mortgage loans:
| Maturity | Number of years to maturity varies by country. In US, it is typically 15-30 years. |
| Interest rate | A few types: fixed, adjustable (variable), initial period fixed rate, convertible. |
| Amortization schedule | Full, partial, interest only. |
| Prepayment | Prepayment is a payment made in excess of the scheduled amount of principal repayment. Some mortgages have prepayment penalty, some don’t. |
| Foreclosure | Recourse loans means in the event of default, lender can claim the shortfall (outstanding mortgage amount less sale proceeds from property) from the borrower. |
Mortgage pass-through securities are created when shares or participation certificates are sold in a pool of mortgage loans.
| Pass-through rate | This is the coupon rate on the MBS, which takes into account the annual servicing fee. |
| Prepayment risks | Risk due to uncertain future cash flows due to principal repayment. This has 2 components: |
1) Contraction risk: Risk of faster than expected prepayments due to interest rate decline. Borrowers are more inclined to prepay in full and refinance at the lower rate.
2 measures of prepayment rate are:
a) Single monthly mortality rate (SMM) is a monthly measure of prepayment rate.
\scriptsize SMM=\fracb) Conditional repayment rate (CPR) is an annualized version of SMM.
CMOs are securities backed by a pool of mortgage pass-through securities, structured with tranches of varying exposures to prepayment risks.
Types of CMO tranches:
Duration of a bond – expressed in years – shows the % change in bond price to a 1% change in interest rate. The higher the duration, the more sensitive the bond is to changes in interest rates.
Macaulay duration (MacDur) is a weighted average time it would take to receive all of a bond’s cashflow.
Modified duration (ModDur) is an estimated % price change for a bond given a change in its yield to maturity.
Modified \space duration=\fracIf Macaulay duration is unknown, annual modified duration can be estimated with:
ApproxModDur= \frac=\fracBonds with embedded option and MBS don’t have a well defined YTM as they may be prepaid before maturity.
Hence, effective duration may be a better measure for these instruments, as it measures the sensitivity of a bond price change to a change in benchmark yield curve (instead of its own YTM).
EffDur=\fracKey rate duration measures a bond’s price sensitivity to a change in the shape of a benchmark yield curve for a given maturity.
This is used to assess yield curve risk, i.e. non-parallel shifts in yield curve.
| Change in a variable (all else constant) | Effect on bond duration |
|---|---|
| Higher coupon rate | Lower |
| Higher yield to maturity (YTM) | Lower |
| Longer time-to-maturity | Usually positively correlated with Macaulay and Modified duration: |
Money duration measures the price change in units of currency in which the bond is dominated, given a change in annual yield to maturity.
Money Duration = AnnModDur x PV full
PVBP estimates the change in the full price of the bond in response to 1 bp change in its YTM.
PVBP=\frac=Money \space duration \times 0.0001
The % change in a bond’s full price for a given change in yield with convexity-adjustment is:
\footnotesize \%\triangle PV^=(-AnnModDur \times \triangle Yield)+(0.5 \times AnnConvexity \times (\triangle Yield)^2)
\small Return \space impact \approx -(ModDur \times \triangle Spread)+ 0.5(Convenxity + \triangle Spread^2)
| Capacity | Evaluate if the ability of borrower to make principal and interest payments over the debt term. |
| Collateral | Quality and value of the assets pledged as collateral. |
| Covenants | Terms and conditions that the issuer must comply with. |
| Character | Quality of management team, company’s financial history, whether there have been late payments or bankruptcy in the past. |
If you are quantitatively inclined, I suggest you do look at this topic early in your CFA studies. However, it is useful to first familiarize yourself with the concepts of Time Value of Money and the Discounted Cash flow approach.
In fact, we have a detailed recommended CFA Level 1 study topic order that covers all these points to maximize your study efficiency.
This depends wholly on where you currently stand:
I would recommend using prep provider notes – you can see what’s on offer here. If you find some of the concepts hard to get, move up a notch and consult the CFA Institute curriculum, which is useful for occasional deep-dives but may be too dry and lengthy to function well as your main study material.
What is it? The Handbook of Fixed Income Securities has been the most trusted resource in the world for fixed income investing for decades.
About the Author: Frank J. Fabozzi is professor of finance at EDHEC Business School, a member of the EDHEC Risk Institute and on the board of BlackRock.
If you want to ace this section (and you do), your CFA calculator is your best friend.
Fixed Income Investments is a topic area that is especially calculator-heavy, and CFA exam calculations are not your regular multiplications and divisions that you can do using a paper and a pen.
So you’ll need to know your calculator’s functions and operations like the back of your hand. Practice regularly with practice exams and given examples, and consider having a look at our calculator guides for extra handy tips:
As the saying goes – practice makes perfect. It is not different with this topic.
If you are new to finance and Fixed Income, make sure you go through enough numerical problems before you sit for the actual exam from study notes.
Then try and attempt the questions that you may find in the CFA Institute’s curriculum. Finally, attempt your practice exams, and that should form a pretty solid preparation.
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Hi, I think the return impact formula is incorrect. Rather than: Return impact≈−(ModDur×△Spread)+0.5(Convexity+△Spread^2 )
It should be Return impact≈−(ModDur×△Spread)+0.5(Convexity x△Spread 2 ) Reply
