CFA Fixed Income Level 1: Our Cheat Sheet – 300 hours (2023)

Note: This cheat sheet will be updated for the latest 2022 syllabus.

Fixed income is a central issue in the financial sector and is becoming increasingly important (weight problemwisely) advancing to CFA level 3. With so many key concepts covered, we decided to create our series of tips articles that focus on a specific subject area for a specific CFA level.

This cheat sheet is basically a CFA Tier 1 Fixed Income Grading and Formula Sheet.☕CFA Fixed Income is one of the most quantitatively intensive topics on the exams, and getting the fixed income fundamentals right can also provide a good foundation for the levels below.

More cheat sheets will be posted in the coming weeks,Sign up for our member listbe notified first.

By referencing the CFA Learning Outcomes Statements (LOS), we have prioritized and highlighted key concepts and formulas you need to know for each topic. With some topic specific tips at the end!

Use the cheat sheets during your practice sessions torefresh your memoryin important terms. Don't forget to bookmark this page and come back often, it's a great thread to check out 🙂

We will!

CFA Fixed Income Level 1: An Overview

The CFA Tier 1 Fixed Income subject area represents one of the largest segments of the broader capital market and primarily covers all investments where investors borrow money for a fixed, scheduled payment - hence the name "Annuities".

For Tier 1, Fixed Income is the third biggest theme (sharing the title with Equity Investments).FORAyethic🇧🇷 Maintaining a strong foundation of Tier 1 fixed income fundamentals is critical as a thematic weightingincreaseon all 3 levels.

The weighting of the CFA Tier 1 Fixed Income topic is 10% to 12%, which means that 18 to 22 questions out of the 180 questions on the CFA Tier 1 exam are about this topic.

It is coveredStudy Sessions 13-14, which contains reading 39-44.

Here is the summary of readings for the CFA Tier 1 Fixed Income chapters:

This CFA topic is intended to introduce readers to the fundamentals of fixed income securities, as well as their pricing and valuation. The concepts discussed are especially relevant for those who want to participate in the management of fixed income portfolios: credit, macro or not.

Even for those not aspiring to a career in Fixed Income, these topics will become an integral part of their skill repertoire. This is because different markets are often interconnected and great investors (eg Warren Buffet, Peter Lynch, George Soros) are often knowledgeable about different types of markets, not just the market they invest in.

In summary, CFA Fixed Income Level 1 teaches:

– the various fixed income products available on the market and how these markets work;
– How are these values ​​valued? What are the risk factors for valuing a fixed income security and how can the associated risks be hedged?

Reading 39: Fixed Income Securities: Definitive Elements

Types of Bond Contracts

Affirmative (positive) covenants are what bond issuers must do. Some examples:

• make timely interest and principal payments;
• comply with all laws and regulations;
• Protecting and preserving assets.

Negative (restrictive) covenants are what bond issues must haveNoDoes. Some examples:

• Debt Restrictions: Restrictions on maximum acceptable leverage ratios and minimum acceptable interest coverage ratios.
• Negative Promises: Additional Debt Instruments may not be issued with a higher rating than the existing Debt Instruments.
• Limits on Distributions to Shareholders: Limiting the amount of money that can be spent on dividends and share buybacks.
• Restrictions on Mergers and Acquisitions.

Structure of a security's cash flows

• bullet bonus: The full principal amount of the bond is paid at maturity.
• Depreciation (total or partial):
  • A fully amortized bond pays equal interest and principal repayments periodically throughout the life of the bond, so that the bond is paid in full when it matures.
  • A partial amortization bond is a bond in which only a small portion of the principal is paid during the life of the bond, with a larger payment at maturity. Essentially, it's a mix of bullet and full call titles.
• sinking fund: The issuer pays a specified portion of the principal each year during the life of the bond or after a specified date. A declining fund deal has lower credit risk but higher reinvestment risk for investors.

Securities with contingent provisions

redeemable bonds

A callable bond gives the issuer the right to redeem all or part of the bond before maturity.

This built-in option benefits the issueras it protects the issuer if interest rates drop (ie if they do, the issuer can call/redeem the bond and reissue a new bond at a lower interest rate).

To compensate investors for the higher reinvestment risk, issuers offer a higher yield on callable bonds.

Therefore, the price of the callable security (v_{enforceable title}) is always lower than the price of a plain (non-callable) bond because the call option creates value for an issuer.

v_{enforceable title}= V_{non-redeemable bond}–v_{call option}

redeemable bonds

A callable bond gives the bondholder the right to sell the bond to the issuer at a predetermined price on a specified date or dates.

This integrated option benefits the bondholderSince it protects the bondholder if interest rates rise (i.e., if they do, the price of the bond falls), the bondholder can sell the bond back to the issuer at a predetermined price and reinvest their money at a predetermined rate of the highest. interest).

Callable bonds offer a lower yield and are worth more than a non-callable bond.

v_{enforceable title}= V_{non-redeemable bond}+v_{put option}

convertible bonds

Convertible bonds give the bondholder the right to exchange the bond for a specified number of shares of common stock in the issuing company.

With foreign and equity features, convertible bonds offer advantages for both:

• Investors, as they have the opportunity to convert it into shares and participate in more gains if the share price goes up, but are protected against losses if the share price goes down.
• Issuers because they have reduced interest expense because convertible bonds have lower yields and when debt is converted there is no debt to pay. It can also be a chargeable convertible.

Contingent Convertible Bonds (CoCos) are automatically converted into shares at a predetermined event.

• conversion price= Price per share at which the security can be converted into shares
• conversion rate= Number of shares of common stock into which each security can be converted
• conversion value= current share price x exchange rate
• conversion premium= convertible bond price – conversion value

Reading 40: Fixed Income Markets: Issuance, Trading and Financing

4 mechanisms for public offering of securities

• guaranteed offer: An investment bank agrees an offer price with the issuer and buys the entire bond issue at that price, assuming the risk of reselling it to other investors.
• Best Effort Offer: Unlike a written offer, the investment bank acts only as an intermediary and sells as many securities as possible without taking on the underwriting risk. Unsold securities are returned to the issuer.
• shelf record: It is a type of public offering in which the issuer can sell the entire issue of securities in tranches. You only need to file a single document with the regulator to describe the potential future bond issue, saving registration and administration fees.
• the auction: Government bonds are usually sold to investors at auctions.

Types of corporate debt

• bank first: bilateral (single loan) and syndicated (group of creditors)
• Commercial Paper (CP): A flexible, low-cost, short-term loan with terms ranging from 15 days to 1 year. It is issued on the market and usually costs less than bank loans.
• corporate bonds and bonds: Called Promissory Note if the term is less than 12 years, Bond if the term is equal to or greater than 12 years.

Short-term financing alternatives from banks

• retail warehouses: Current accounts, savings and money market
• short term wholesale funds: central bank money, interbank money, certificates of deposit (CD).
• repurchase agreements(“Repos”): are purchase and sale operations, secured loan modality.
  • Repo – The seller borrows money from the buyer and provides collateral as collateral.
  • Reverse Buyback: Buyer borrows securities to cover a short position.
  • The repo or haircut margin is the percentage difference between the market value of the bond (collateral) and the loan amount. The repurchase margin level depends on the quality of the collateral, the length of the repurchase term, the merchant's credit risk, and collateral supply and demand.
  • The repurchase rate is the annualized interest rate on the loan.

Reading 41: Introduction to Valuing Fixed Income Bonds

Pricing of bonds with spot rates

PV=\frac{PMT}{(1+z_1)^1}+\frac{PMT}{(1+z_2)^2}+...+\frac{PMT+FV}{(1+z_N)^ NORTE}

Yield to maturity (YTM) is the constant discount rate that makes the sum of the present value of future cash flows equal to the current price of the bond. In this particular case, all spot rates are the same: e.g.₁= z₂= z_norte= r.

Parity, discount, and premium bonds

Relationship between bond price, coupon rate, term, YTM

Total price, fixed rate and accrued interest

• Full/dirty price = Fixed/clean/noted price + Marchzinsen (AI)

\begin{align*}PV^{completo}&=PV^{plano} + AI=PV(1+r)^{\frac{t}{T}}\\AI&= \frac{t}{T} \veces PMT\end{align*}

• where t = number of days since last coupon payment,
• T= number of days in the coupon period (real/real for government bonds, 30/360 for corporate bonds),
• PMT = interest payment per period

Performance Measures for Fixed Income Securities

• Semester equivalent yield of the security= income per semester x 2
• Current Performance= annual cash coupon payment divided by bond price
• Yield on call (YTC)= Bond yield callable if the bond is held through the first call date.
• Worst Yield (YTW)= the smallest among all YTC and YTM scenarios.

Measures of Return on Money Market Instruments

Basis of discount rate (DR)

PV=FV \times \Big (1-\frac{Tage}{Jahr}\times DR \Big)

DR=\Large (\frac{year}{days} \times \frac{FV-PV}{FV}\Large)

Additional fee base (AOR)

PV=\frac{FV}{\Large(1+\frac{days}{year} \times AOR\Large)}

AOR=\Great(\frac{Jahr}{Tage} \times \frac{FV-PV}{PV}\Great)

The main difference between DR and AOR is that in DR interest is included in the face value, but in AOR it is added to the principal.

Implicit forward rates (IFR)

The forward rate is an interest rate in the future. The implicit forward rate (IFR) can be calculated from n-period spot rates (e.g._norte):

(1+z_A)^A \ves (1+IFR_{A,B-A})^{B-A}=(1+z_B)^B

Differential Income Measures

• to spread= Differential of yield on a bond relative to the benchmark yield on a government bond
• I spread= Yield differential of a security in relation to the standard exchange rate for the same maturity and currency.
• Z-spread(Zero Volatility Spread or Static Spread) is the constant spread over the reference government spot curve, such that the present value of the cash flows is equal to the bond price.
• Spread adjusted to the option(OAS) = Z-Spread – Answer Options
  • If it is a callable bond, the option benefits the issuer (since it can call it if interest rates fall, i.e. the bond price rises), so option cost > 0 and OAS < Z -spread for bonds redeemable.
  • If the bond is callable, the option benefits the bondholder (as he can sell the bond back to the issuer at a pre-agreed price if interest rates rise, i.e. the bond price falls), so option cost < 0 and OAS > Z - Spread for callable securities.
  • One way to think of it is that the cost of the option is the additional return the writer has to pay for the option.
  • With a callable bond, the issuer buys the call option, which means it has to pay at a higher yield; option costs are positive.
  • With a callable bond, the writer sells the put option and is paid a lower yield: the cost of the option is negative.

Reading 42: Introduction to asset-backed securities

Mortgage loans for residential properties

It is a loan that a buyer takes to buy a property (house, apartment, land, etc.), with the property acquired as collateral.

Features of mortgage loans:

Residential Mortgage Backed Securities (RMBS)

• Agency RMBS, which are guaranteed by the government or quasi-government, must have credit accordingly.
• Non-brokered RMBS are issued by private companies and may feature non-compliant loans. Requires credit enhancements to reduce credit risk.

mortgage transfer bonds

Mortgage transfer bonds are created when shares or participation certificates in a pool of mortgage loans are sold.

2 measures of the prepaid tariff are:

a) Single Monthly Mortality Rate (MMR)is a monthly measure of the prepaid rate.

\scriptsize SMM=\frac{Prepaid \space en \space month \space t}{Start of \space Mortgage \space Balance \space for \space month \space t - Planned \space Main \space Refunds \space for \space month \ space t }

b) Conditional Reimbursement Rate (CPR)is an annualized version of SMM.

Collateralized Mortgage Obligations (CMOs)

CMOs are securities backed by a pool of tranche-structured mortgage transfer securities with varying prepayment risks.

CMO leg types:

Commercial Mortgage Backed Securities (CMBS)

• The CMBS are backed by a suite of high-yield commercial real estate mortgage loans.
• Interest will be paid on the outstanding principal of all tranches.
• The highest rated bonds are paid first, credit default losses are offset against the principal of the lowest rated CMBS tranche, ie h Principal/Residual Tranche.
• CMBS investors enjoy significant termination protection(prepayment risk coverage) integrated into the CMBS structure,but try the risk of the balloon(a type of rollover risk) as most of CMBS' underlying credit investments are global loans that require significant repayments of principal at maturity.

Secured Debt Obligations (CDOs)

• CDOs are securities backed by a diversified pool of one or more debt securities, eg Corporate bonds, bank loans, ABS, CMBS, RMBS, credit default swaps on securities.
• Structured in senior, mezzanine and junior/equity tranches with different risk-return expectations.
• Unlike an ABS, a CDO requires an escrow agent to actively buy and sell debt securities to generate enough cash flow to meet the CDO's obligations and excess margin to pay shareholder and asset management fees.
• If the underlying assets default, there is a risk that investors in the junior/equity tranche may lose their original investment and cash flow will be insufficient to pay interest to senior/mezzanine tranche bondholders.

Reading 43: Understanding Fixed Income Risk and Return

duration

The duration of a bond, expressed in years, shows the percentage change in the bond's price given a 1% change in interest rates. The longer the duration, the more sensitive the bond is to changes in interest rates.

Duration

The Macaulay duration (MacDur) is a weighted average time it would take to realize all of a bond's cash flow.

modified duration

Modified duration (ModDur) is an estimated percentage change in a bond's price given a change in its yield to maturity.

Modified \space duration=\frac{Macaulay \space duration}{1+r}

Approximate Modified Duration

If the Macaulay duration is unknown, the modified annual duration can be estimated using:

ApproxModDur= \frac{(PV_-)-(PV_+)}{2 \times (\triangle Yield) \times (PV_0)}=\frac{ApproxMacDur}{1+r}

effective duration

Bonds with a built-in option and MBS do not have a well-defined YTM, as they can be prepaid before maturity.

As such, effective duration may be a better measure for these instruments, as it measures the sensitivity of a change in a bond's price to a shift in the benchmark yield curve (rather than its own YTM).

EffDur=\frac{(PV_-)-(PV_+)}{2 \times (\triangular curve) \times (PV_0)}

Key rate duration

Key interest rate duration measures the sensitivity of a bond's price to ashape shifta benchmark yield curve for a specified time frame.

This is used to assess yield curve risk, i.e. h Non-parallel shifts in the yield curve.

Influence of bond maturity, coupon and yield on interest rate risk

duration of money

Duration of money measures the change in price in currency units in which the security is dominant, given a change in the annual yield to maturity.

Gelddauer = AnnModDur x PV^complete

One Basis Point Price (PVBP)

PVBP estimates the change in total security price in response to a 1bp change in YTM.

PVBP=\frac{(PV_-)-(PV_+)}{2}=Geld \gap duration \times 0.0001

convexity

approximate convexity

ApproxCon=\frac{(PV_-)+(PV_+)-(2 \times PV_0)}{(\Yield triangle)^2 \times (PV_0)}

The percentage change in the total price of a bond given a change in convexity-adjusted yield is:

\footnotesize \%\triangle PV^{full}=(-AnnModDur \times \triangle Yield)+(0,5 \times AnnConvexity \times (\triangle Yield)^2)

effective convexity

EffCon=\frac{(PV_-)+(PV_+)-(2 \times PV_0)}{(\triangle curve)^2 \times (PV_0)}

Reading 44: Basics of Credit Analysis

Credit risk

• 2 components of credit risk: risk of default (or probability of default) and value of loss (or loss upon default).
• expected loss= probability of default x severity of loss given default
• severity of loss= 1 - recovery rate
• Impact on profitability due to credit spread change (with convexity adjustment):

\retorno pequeño \impacto espacial \approx -(ModDur \times \triangle Spread)+ 0.5(Convenxity + \triangle Spread^2)

The Four C's of Credit Analysis

CFA levell 1 Fixed Income Tips

Deal with the subject of fixed income from the beginning of your studies

If you are quantitatively inclined, I suggest you study this topic early on in your CFA studies. However, it makes sense to familiarize yourself with the firstTime value of money concepts and discounted cash flow approach.

In fact, we have a detailed recommendationOrder of Study Topics for CFA Level 1It covers all these points to maximize your learning efficiency.

What learning materials should I use?

It all depends on where you are:

• When you have experience in fixed income, it's like a fish in water.
• If you are new to finance, certain concepts can be very strange.

I recommend using the preparation provider notes; I cansee what's on offer here🇧🇷 If you find some of the concepts difficult to grasp, take it a step further and check out the CFA Institute syllabus, which is useful for the occasional dig but can be too dry and time-consuming to work well as basic study material.

If you wantmore reading materialI always recommendFrank J. Fabozzi Fixed Income Securities Handbook.

Which is?The Fixed Income Securities Handbook has been the world's most trusted resource on fixed income investing for decades.

About the author:Frank J. Fabozzi is Professor of Finance at EDHEC Business School, member of the EDHEC Risk Institute and member of the BlackRock Board of Directors.

Master your calculator for this topic

If you want to pass this section with flying colors (and you do), then this is the place for you.CFA Calculatoris your best friend.

Fixed income investing is a particularly computer-intensive subject, and the calculations on the CFA exam are not your usual pencil-and-paper multiplication and division.

Therefore, you should know your calculator's functions and operations like the back of your hand. practice regularlypractice testsand given examples, and consider checking out our calculator guides for additional helpful tips:

• The 300 Hour Guide to the Texas Instruments BA II Plus Calculator
• The Ultimate List of BA II Plus Calculator Tips for CFA Exams

What do I do to practice?

As the saying goes, practice makes perfect. This topic is no different.

If you are new to finance and fixed income, make sure you solve enough numbers problems before taking the actual study notes test.

Then try the questions found in the CFA Institute program. finally try yourpractice tests, and that should be pretty solid prep.

More tips articles will be posted in the coming weeks. Stay one step ahead of other CFA candidatesSubscribe to our member list to be notified.

In the meantime, here are other related articles that might be of interest to you:

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• CFA Level 1: How to Prepare for and Pass the CFA in 18 Months
• CFA Tier 1 Tips: Top 10 Tips From Past Candidates
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• How to Learn Effectively: Best Practices That Work for CFA, FRM, and CAIA
• The Definitive Guide to CFA Practice Questions