Exam FRM Level 1 Ultimate Guide (Book 3)

Estimated reading time: 35 minutes



We now discuss our extensive summary for book 3 in the FRM Level 1 syllabus.

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FRM Level 1 Book 3 – Financial Markets and Products



Commercial banking involves the traditional activities of receiving deposits and making loans

These activities can be categorized as either retail or wholesale


Retail banking

Retail banking involves transacting with private individuals and small businesses


Wholesale banking

Wholesale banking involves transacting with large corporations

Loans and deposits are much larger in wholesale banking than in retail banking


Investment banking

Investment banking involves a variety of activities such as:

  • Raising debt or equity capital for companies
  • Providing advice to companies on mergers, acquisitions, and financing decisions
  • Acting as a broker–dealer for trading debt, equity, and other securities



A major activity of a bank’s investment banking arm is raising capital for companies in the form of debt, equity, or more complicated securities (e.g., convertible debt)

This process is referred to as underwriting


Banking Risks

The three major risks that banks face:

  1. Market Risks
  2. Credit Risks
  3. Operational Risks


Market risk

Market risks are the risks arising from a bank’s exposure to movements in market variables (e.g., exchange rates, interest rates, commodity prices, and equity prices)


Credit risk

Credit risk arises from the possibility that borrowers will fail to repay their debts


Operational risk

Operational risk is defined by bank regulators as: The risk of loss resulting from inadequate or failed internal processes, people, and systems or from external events

It is important for banks to keep sufficient capital for the risks they are taking


Equity capital

The most important capital is equity capital

When calculating regulatory capital, it is important to distinguish between the trading book and the banking book

  • The trading book consists of assets and liabilities that are held to trade
  • The banking book consists of assets and liabilities that are expected to be held until maturity

Many of the problems experienced during the financial crisis were a result of a lack of liquidity, rather than a shortage of capital


The Basel Committee for Banking Supervision

The Basel Committee for Banking Supervision was established in 1974 to provide a forum where the bank regulators from different countries could exchange ideas

As a result of the liquidity problems encountered during the crisis, the Basel Committee has (as part of Basel III) developed two liquidity ratios to which banks are required to adhere:

  • The Liquidity Coverage Ratio is a requirement designed to ensure that banks have sufficient sources of funding to survive a 30-day period of acute stress
  • The Net Stable Funding Ratio is a requirement that limits the size of mismatches between the maturity of assets and the maturity of liabilities

Traditionally, banks have originated loans and kept them on their balance sheet

An alternative to this is what has become known as the originate-to-distribute model

Under this model, banks use their expertise to originate loans and then sell them (directly or indirectly) to investors


Insurance Companies and Pension Plans

Insurance provides protection against specific adverse events

  • The company or individual obtaining protection is known as the policyholder
  • Typically, the policyholder must make regular payments known as premiums

Most insurance contracts can be categorized as either life insurance or property and casualty insurance

There are similarities between pension plans and the contracts offered by life insurance companies

  • In an employer-sponsored pension plan, it is typically the case that both the employee and the employer make regular contributions to the plan
  • The contributions are used to fund a lifetime pension for the employee following the employee’s retirement

Pension plans are like annuity contracts in that they are designed to produce income for an individual for the remainder of his or her life following retirement


Defined Contribution and Defined Benefit

There are two types of pension plans: defined contribution and defined benefit

In a defined contribution plan, the funds are invested by the employer

In a defined benefit plan, funds are also usually contributed by the employer and employee. In this case, however, the contributions are pooled, and a formula is used to determine the pension received by the employee on retirement

A defined benefit plan is much riskier for an employer than a defined contribution plan

In a defined contribution plan, the company is merely acting as an agent investing the pension plan contributions on behalf of its employees


Catastrophe bonds

When a company does not want to keep catastrophe risks, it can pay a reinsurance company to take them on

It can also use derivatives known as CAT (catastrophe) bonds

A CAT bond is a bond issued by an insurance company that pays a higher-than-normal rate of interest


Moral hazard

Moral hazard is the risk that the behavior of the policyholder will change as a result of the insurance


Adverse selection

Adverse selection is the risk that insurance will be purchased only by high-risk policy holders

Solvency II specifies a minimum capital requirement (MCR) and a solvency capital requirement (SCR)

If capital falls below the SCR, an insurance company is required to formulate a plan to bring it back up above the SCR level

If it falls below the MCR level, the insurance company may be prevented from taking new business


Fund Management

Fund managers invest money on behalf of individuals and companies

Funds from different clients are pooled, and the fund managers choose investments in accordance with stated investment goals and risk appetites

There are several advantages to this approach:

  1. Fund managers may have more investment expertise
  2. Transaction costs are usually lower for large trades
  3. Smaller investors can achieve better diversification


Mutual Funds

Mutual funds (called unit trusts in some countries) have been a popular investment vehicle for small investors

  • There are two types of mutual funds: open-end and closed-end
  • Open-end funds are by far the most popular and account for over 98% of mutual fund assets in the U.S.

The key feature of open-end funds is that the number of shares (and the size of the fund) expand and contract as investors choose to buy and sell shares

Open-end funds can be categorized as follows:

  • Money market funds
  • Bond funds, and
  • Equity funds


Hybrid funds

Funds that invest in more than one type of security are referred to as hybrid funds (or multi-asset funds)


Closed-end funds

Closed-end funds are funds where the number of shares remains constant through time

A closed-end fund is basically a regular company whose business is to invest in other companies

Whereas open-end funds are bought and sold at their NAV, share prices for closed-end funds are typically lower than their NAV


Advantages of Closed-End Funds

  • Unlike open-end fund shares, shares of closed-end funds can be bought and sold at any time of day; they can even be shorted
  • Unlike open-end funds, closed-end funds do not need to keep enough liquid assets to handle possible redemptions
  • This is because closed-end fund investors trade with each other, whereas open-end fund investors trade with the fund itself


Exchange-traded funds (ETFs) combine features of open-end mutual funds with features of closed-end mutual funds

Hedge funds (a form of alternative investments) are subject to less regulation than mutual funds and ETFs

While mutual funds and ETFs cater to the needs of small investors, hedge funds usually accept only large investments from wealthy private individuals or institutions


Hedge Funds and Mutual Funds

Differences between hedge funds and mutual funds/ETFs:

A mutual fund or ETF allows investors to redeem their shares on any day. A hedge fund may have a lock-up period during which time funds cannot be withdrawn

The NAV of a mutual fund or ETF must be calculated and reported at least once a day. Hedge funds have no such requirements, and their NAVs are reported much less frequently

Mutual funds and ETFs must disclose their investment strategies. Hedge funds generally follow proprietary strategies but do not disclose everything

Mutual funds and ETFs may be restricted in their use of leverage. A hedge fund is only restricted by the amount banks are willing to lend to it

Hedge funds charge both an incentive fee as well as a management fee


Introduction to Derivatives

Derivatives are contracts whose values depend on (or derive from) the values of one or more financial variables (e.g., equity prices and interest rates)

  • These variables are referred to as underlyings

Derivatives can be categorized into linear and non-linear products


Linear derivatives

Linear derivatives provide a payoff that is linearly related to the value of the underlying asset

Forward contracts are an example of linear derivatives

The value and payoff of a forward contract prior to maturity is linearly dependent on the value of the underlying asset


Non-linear derivatives

Options, on the other hand, are non-linear derivatives

  • Their payoff is a non-linear function of the value of their underlying asset
  • They are contracts where the holder has the right (but not the obligation) to buy or sell an asset for a specified price at a future time


Derivative trading

Derivatives trade on exchanges as well as in over-the-counter markets

Advantages of over-the-counter (OTC) markets:

  • The contracts traded do not have to be the standard contracts defined by exchanges
  • Market participants can trade any contracts they like


Contracts and Options

A forward contract is an over-the-counter contract where two parties agree to buy and sell an asset for a predetermined price at a future time

Spot contracts are agreements to buy or sell an asset almost immediately

A futures contract provides a similar payoff to a forward contract, but it trades on an exchange

Options are derivatives that give the holder the right (but not the obligation) to buy or sell an asset at a predetermined price in the future

They trade on exchanges as well as in the over-the-counter market


Types of traders

There are three main categories of traders in derivatives markets:

  1. Hedgers
  2. Speculators
  3. Arbitrageurs



Hedgers use derivatives to reduce risk exposure



Speculators use derivatives to take risks with a relatively small upfront payment



Arbitrage involves taking advantage of inconsistent pricing across two or more markets


Exchanges and OTC Markets

An exchange is an organization with members who trade with each other

Netting is a procedure where short positions and long positions in a particular contract offset each other

Exchanges operate what are known as central counterparties (CCPs) to clear all transactions between members

An advantage of CCPs is that it is much easier for exchange members to close out positions

Once an exchange has decided to establish a CCP, it must find a way of managing the associated credit risk. It can do this with a combination of the following:

  • Netting
  • Variation margin and daily settlement
  • Initial margin
  • Default fund contributions



“Shorting” a stock involves borrowing shares and selling them in the usual manner

At some later date, the shares are repurchased and returned to the account from which they were borrowed



Buying on margin refers to the practice of borrowing funds from a broker to buy shares or other assets



Special Purpose Vehicles (SPV) or Special Purpose Entities (SPE), are companies created by another company in such a way that the credit risks are kept legally separate

SPVs and SPEs are sometimes created to manage a large project without the organization setting it up being put at risk


Central Clearing

Central counterparties (CCPs) have been used for trading derivatives in exchange-traded markets for many years

The rules developed by CCPs for members posting margin allow the exchanges to handle credit risks efficiently

As a result, failures of CCPs handling exchange-traded products have been rare

While exchange-traded futures contracts trade continuously, OTC contracts trade only intermittently

As a result, OTC contracts are less liquid than exchange-traded contracts

CCPs clearing trades in the OTC markets operate in much the same way as CCPs clearing trades on exchanges

Members are required to post initial margin and variation margin as well as make contributions to the default fund


Advantages of the Central Clearing Model

It is much easier for market participants to exit a CCP transaction

They manage the margining, netting, settlement, and default resolution that would typically be handled by each market participant in the case of bilateral clearing

They can also improve liquidity in the OTC market by making it much easier for market participants to net and exit from transactions

They are much simpler organizations than banks and are therefore much easier to regulate


CCP Disadvantage

A disadvantage of CCPs is that they tend to increase the severity of adverse economic events

That is, they are pro-cyclical

Very few futures contracts lead to the delivery of an underlying asset

This is because traders prefer to close out contracts before the delivery period


Forward vs. Futures

Forward and futures contracts are similar in that both are agreements to buy or sell an asset in the future. However, there are key differences:

Most forward contracts are on foreign exchange or interest rates

In contrast, futures contracts are on a wide range of financial and non-financial assets

A futures contract is traded on an exchange but a forward contract is an over-the-counter product

A forward contract is subject to more credit risk

A futures contract is settled daily but a forward contract is settled at the end of its life

Closing out a forward is not as easy as it is for a futures contract

A company with a forward contract must approach its counterparty and negotiate a close out

Forward contracts usually specify a single delivery date. In contrast, futures contracts specify a period (sometimes a month)

Because futures contracts are traded on an exchange, they are standardized financial products

Forward contracts have the advantage in that the delivery date can be chosen to meet the precise needs of the client


Using Futures for Hedging

Like other derivatives, futures can be used for either speculation or hedging

A position in a futures contract can reduce exposure to exchange rates, interest rates, equity indices, or commodity prices

Eliminating all risk exposures using futures is usually impossible

It is therefore important to develop a way of calculating an optimal hedge


An optimal hedge

An optimal hedge is a hedge that reduces risk as much as possible


A short futures position

A short futures position is appropriate in the following situations:

A company owns a certain quantity of an asset and knows that it will sell it at a certain time in the future

A company knows that it will receive a certain quantity of an asset in the future and plans to sell it


A long hedge

A long hedge is the opposite of a short hedge

It can be used when a company knows it will have to buy a certain asset quantity in the future


Basis Risk

Basis risk is the risk associated with the basis at the time a hedge is closed

Basis risk arises from the difference between the spot price of the hedged asset and the futures price for the contract used for hedging at the time the hedge is closed out


Portfolio beta

The beta of a portfolio is the sensitivity of its return to the return of the market portfolio

If a portfolio has a beta of 1.0, it mirrors what the market does

If the portfolio has a beta of 0.5, it is half as volatile as the market

When the beta is 2.0, it is twice as volatile as the market

Hedging using stock index futures is quite popular

Stock index futures are a way of reducing or increasing an investor’s exposure to the market for a period of time


Foreign Exchange Markets

The foreign exchange market (Forex, FX, or currency market) is the market where participants exchange one currency for another

Note the following:

Spot trades – where there is an agreement for the immediate or almost immediate exchange of currencies

Forward trades – where there is an agreement to exchange currencies at a future time

The Forex market attracts both hedgers and speculators

In terms of notional trading volume, the foreign exchange market is by far the largest market in the world

The most common exchange rate quotes are between USD and another currency

Spot exchange rates are typically quoted with four decimal places

The bid-ask spread in large trade amounts of a currency is typically quite small


FX Swaps

A forward foreign exchange transaction, where two parties agree on an exchange at some future date, is termed an out-right transaction or a forward outright transaction

  • It can be contrasted with an FX swap transaction, where currency is exchanged on two different dates

Typically, an FX swap involves a foreign currency being bought (sold) in the spot market and then sold (bought) in the forward market

An FX swap is a way of funding an asset denominated in a foreign currency by paying interest in the domestic currency


Transaction risk

Transaction risk is the risk related to receivables and payables


Translation risk

Translation risk arises from assets and liabilities denominated in a foreign currency


Economic risk

Economic risk is the risk that a company’s future cash flows will be affected by exchange rate movements


Nominal and Real interest rates

Nominal interest rates are usually quoted in the market and indicate the return that will be earned on a currency

Real interest rates are adjusted for inflation

There is a no-arbitrage relationship between forward exchange rates and spot exchange rates that involves interest rates


Pricing Financial Forwards and Futures

A financial asset is an asset whose value derives from a claim of some sort

An investment asset is an asset held by market participants for investment purposes

All financial assets (and a small number of non-financial assets) are investment assets

Non-investment assets are sometimes referred to as consumption assets

In theory futures prices and forward prices for contracts with the same maturity on the same asset should be approximately equal


Index Arbitrage

Both of the following trading strategies can be categorized as index arbitrage

If an index futures price is greater than its theoretical value, an arbitrageur can buy the portfolio of stocks underlying the index and sell the futures

If the futures price is less than the theoretical price, the arbitrageur can short the stocks underlying the index and take a long futures position

The no-arbitrage forward/futures price of a financial asset can be computed from risk-free interest rates and the income generated by the asset


Commodity Forwards and Futures

Most commodities are consumption assets

This means that they are rarely held for purely investment reasons

Metals such as gold and silver are exceptions

Commodity owners usually intend to use the commodity in some way, after which it ceases to be available for sale


Commodities and Financial Assets

There are several important differences between commodities and financial assets. Some differences in particular are as follows:

The storage costs associated with financial assets (e.g., stocks and bonds) are negligible

The storage costs for commodities can be quite substantial (e.g. insurance cost)

Commodities can be costly to transport and thus their prices can depend on their location

By contrast, financial assets are usually transported electronically at virtually no cost

A commodity held for investment purposes (e.g., gold or silver) can be borrowed for shorting

A financial asset provides investors with an expected financial return that reflects its risk. Most commodities do not have this property

The prices of most commodities are mean reverting. This means it tends to get pulled back toward some central value, even in the face of volatility


Commodity Types

Agricultural commodities with futures contracts include products that are grown (e.g., corn, wheat and sugar) as well as livestock (e.g., cattle and hogs)

It is expensive to store agricultural commodities

Commodity metals include gold, silver, platinum, palladium, copper, tin, lead, zinc, nickel, and aluminum

Their storage costs are typically lower than those of agricultural products

Energy products are another important category of commodities. There are futures contracts on crude oil and crude oil extracts (e.g., petroleum and heating oil)

Futures also trade on natural gas and electricity

Derivative contracts on weather are available in both the exchange-traded and over-the-counter markets

The most popular contracts are those with payoffs contingent on temperature (which are used by energy companies as hedges)

Some precious metals are held for investment purposes (Gold and silver are in this category)

The lease rate for an investment commodity is the interest rate charged to borrow the underlying asset

The cost of carry for an asset reflects the impact of:

  • Storage costs
  • Financing costs
  • Income earned on the asset


The Options Market

A European call (or put) option gives the buyer the right to buy (or sell) an asset at a certain price on a specific date

An American call (or put) option gives the buyer the right to buy (or sell) an asset at a certain price at any time before and during the specified date

The date specified in the option is known as the expiration date (or maturity date)

Most (not all) exchange-traded options are American

By contrast, many of the options traded in the over-the-counter market are European

The price at which an asset can be bought or sold using an option is referred to as the strike price (or exercise price)

American options are more difficult to analyze than European options because they can be exercised at any time before maturity

European options can be valued using the Black-Scholes Merton model

American options can only be valued by using numerical procedures such as binomial trees

Cash dividends usually do not affect the terms of a stock option


Option Properties

The price of stock option can depend on:

  • The price of the underlying stock
  • The strike price
  • The risk-free rate
  • The volatility of the stock price
  • The time to maturity
  • The dividends to be paid during the life of the option

Many exchanged-traded options (including options on individual stocks) are American

Put-call parity describes the relationship between the price of a European call option and that of a European put option with the same strike price and time to maturity


Trading Strategies

Options can be arranged to form a wide spectrum of payoff patterns

In theory, an investor with access to European options with all strike prices for a given maturity could achieve any continuous payoff function of the underlying asset price at expiry

The option trading strategies considered in this segment can be divided into four groups:

  • Strategies involving an option and the underlying asset
  • Strategies involving two or more call options
  • Strategies involving two or more put options
  • Strategies involving both call and put options



Strategies involving only call options or only put options are termed spreads



Strategies involving both call and put options are termed combinations


Put-Call parity

The put-call parity describes the relationship between the price of a European put option and that of a European call option with the same strike price and time to maturity


Principal Protected Notes

A principal protected note (PPN) is a security created from a single option such that the investor benefits from any gain in the value of a specified portfolio without the risk of losses



A package is a portfolio consisting of plain vanilla options on an asset

Examples of packages include: bull spreads, bear spreads, butterfly spreads, calendar spreads, straddles, and strangles

Packages are sometimes regarded as exotic options

This, as they are positions built to reflect a specific market view and risk tolerance


A bull spread

A bull spread is a position appropriate for an investor expecting an increase in the price of an asset


A bear spread

A bear spread is a position where the trader buys a European put option with strike price K2 and sells a European put option with strike price K1

Like a bull spread, a bear spread has a small probability of attaining a large return if both options begin out-of-the-money and a high probability of attaining a modest return if both options begin in-the-money


A box spread

A box spread is a portfolio created from a bull spread (using call options) and a bear spread (using put options)

The strike prices and times to maturity used for the bull spread are the same as those used for the bear spread


A butterfly spread

A butterfly spread involves positions in three options. It can be created from either call or put options



A straddle is a position created from a long call and a long put with the same strike price and time to maturity. The strike price is usually close to the current asset price

The cost of a straddle can be reduced by making the strike price of the call greater than the strike price of the put. The position is then called a strangle


A diagonal spread

A diagonal spread is created from a long call (or put) and a short call (or put) where both the strike prices and the times to maturity are different.

It can be considered as a cross between a bull/bear spread and a calendar spread



A strip is like a straddle except that two puts are purchased for every call. It is appropriate when a trader anticipates a big move in the asset price and a downward movement is considered more likely than an upward movement



A strap is like a straddle except that two calls are purchased for every put. It is appropriate when a trader anticipates a big move in the asset price and an upward movement is considered more likely than a downward movement


Exotic Options

Standard European and American options which usually trade on exchanges are termed plain vanilla options

Options with non-standard properties are termed exotic options

Exotic options are designed by derivatives dealers to meet the specific needs of their clients and are usually traded in the over-the-counter markets

Exotic options can be very profitable for derivatives dealers because they have relatively large bid-offer spreads

Recall: A package is a portfolio consisting of plain vanilla options on an asset

Examples of packages include: bull spreads, bear spreads, butterfly spreads, calendar spreads, straddles, and strangles

Packages are sometimes regarded as exotic options because they are positions built to reflect a specific market view and risk tolerance

Any derivative product can be converted into a zero-cost product by arranging for it to be paid for in arrears

Exchange-traded American options can be exercised at any time at the pre-determined fixed strike price


A forward start option

A forward start option is an option that will begin at a future time. It is usually stated that the option will be at-the-money at the time it starts


A gap option

A gap option is a European call or put option where the price triggering a payoff is different from the price used in calculating the payoff


A cliquet option

A cliquet option is a series of forward start options with certain rules for determining the strike prices


A chooser option

With a chooser option, the holder has a period of time (after purchasing the option) where he or she can choose whether it is a put option or a call option


Binary Options

There are four types of binary options:

  1. Cash-or-nothing call
  2. Cash-or-nothing put
  3. Asset-or-nothing call
  4. Asset-or-nothing put


Traditional European options

Traditional European options can be thought of as combinations of binary options

A long position in a European call option is a combination of:

  • A long position in an asset-or-nothing call, and
  • A short position in a cash-or-nothing call with a payoff equal to the strike price

Similarly, a long position in a European put option is:

  • A short position in an asset-or-nothing put, and
  • A long position in a cash-or-nothing put with a payoff equal to the strike price


Cash-or-nothing options

Cash-or-nothing options are sometimes referred to as digital options


Asian options

Asian options provide a payoff dependent on an arithmetic average of the underlying asset price during the life of the option

The payoff from a lookback option depends on the maximum or minimum asset price reached during the life of the option.


Barrier options

Barrier options have payoffs that depend on whether the asset price reaches a particular barrier


Compound options

A compound option is an option on another option. Thus, there are two strike prices and two maturity dates

In an asset-exchange option, the holder has the right to exchange one asset for another


Basket options

A basket option is an option on a portfolio of assets. These portfolios can contain assets such as stocks, stock indices, and currencies


Volatility swaps

A volatility swap is a forward contract on the realized volatility of an asset during a certain period

The payoff from a variance swap is calculated analogously to the payoff from a volatility swap

The variance rate for an asset is the square of its volatility


Properties of Interest Rates

The interest rate term structure describes how interest rates vary depending on their maturity

In an upward-sloping term structure, long-term interest rates are higher than short-term interest rates

A major factor in determining an interest rate is the risk that the borrower will default and not repay the lender in full. This risk is called credit risk

As credit risk increases, the interest rate required by the lender from the borrower also increases

Another factor in determining interest rates is liquidity. In this context, liquidity refers to the ease with which an interest-bearing instrument can be sold from one investor to another at a competitive price


The London Interbank Offered Rate

The London Interbank Offered Rate (Libor) has historically been an important reference rate in financial markets

Libor interest rates are compiled from the estimated unsecured borrowing costs of 18 highly rated global banks

In a repo agreement, securities are sold by Party A to Party B for a certain price with the intention of being repurchased at a later time at higher price

The risk-free rates used to value derivatives are determined from overnight interbank rates using overnight indexed swaps

Treasury rates are not used because they are considered to be artificially low


Bond valuation

The valuation of a bond involves identifying its cash flows and discounting them at the interest rates corresponding to their maturities

The return earned by an investor on a bond is often described by what is termed the bond yield. This is the discount rate that equates the present value of all the cash flows to the market price

The par yield of a bond is the coupon rate that would cause the value of the bond to equal its par value


Yield duration

Yield duration measures the sensitivity of a bond’s price to a change in its yield

Forward rates are the future interest rates implied by today’s zero-coupon interest rates


Forward rate agreements

A forward rate agreement (FRA) can be thought of as an agreement to apply a certain interest rate to a certain principal for a certain period in the future


Corporate Bonds

A bond is a debt instrument sold by the bond issuer (the borrower) to bondholders (the lenders)

  • The bond issuer agrees to make payments of interest and principal to bondholders
  • The principal of a bond (also called its face value or par value) is the amount the issuer has promised to repay at maturity
  • Bonds perceived to be riskier than others available require higher interest rates to attract investors
  • The interest rate on a bond is termed the coupon rate. In the U.S., coupons are usually paid every six months

The face value of a bond in the U.S. is usually USD 1,000 and bond prices are typically quoted per USD 100 of principal

Corporate bond issuances are typically arrangement by investment banks

The issuing corporation can choose between a private placement and a public issue


Private Placements

In a private placement, bonds are placed with a small number of large institutions (e.g., pension funds)

A private placement has several advantages to the issuer:

  • There are fewer registration requirements
  • Rating agencies are not involved because they don’t usually rate non-public issuances
  • The issuance cost is lower
  • The issuance can be completed quickly
  • The issuance can be relatively small

Interest rates for private placement bonds are generally higher than those for equivalent publicly issued bonds

The issuer must therefore weigh the benefits of private placement against the payment of a higher interest rate

Bonds issued via private placements are often not traded. Instead, they are typically held by the original purchasers until maturity


Bond Indentures

A bond indenture is a legal contract between a bond issuer and the bondholder(s) defining the important features of a bond issue. These features include:

  • The maturity dates
  • The amount and timing of interest payments
  • Callable and convertible features (if any)
  • The rights of bondholders in the event of contract violations


Ratings Agencies

Ratings agencies such as Moody’s, S&P, and Fitch provide opinions on the creditworthiness of bond issuers

Bonds rated above a certain threshold are referred to as investment grade

Bonds below this threshold are given various names: high-yield, non-investment grade, speculative grade, or simply junk

Two important statistics published by rating agencies are:

  • The default rates
  • The recovery rates


Mortgages and Mortgage-Backed Securities

Mortgages are used to finance residential and commercial property

Mortgage-backed securities (MBSs) are investments created from the cash flows provided by portfolios of mortgages

Variable-rate mortgages are termed adjustable-rate mortgages (ARMs)

In an ARM, the interest rate is typically fixed for several years and is then tied to an interest rate index

ARMs are less risky than fixed-rate mortgages for lenders and riskier than fixed-rate mortgages for borrowers

For this reason, ARMs typically have lower initial interest rates than comparable fixed-rate mortgages

An interesting aspect of fixed-rate mortgages in the U.S. is that borrowers have an American-style option to pay off their outstanding mortgage balances. This is referred to as the borrower’s prepayment option

An amortization table shows the monthly principal and interest payments on a mortgage

Mortgage portfolios (or mortgage pools) can be created for investment purposes

The mortgages in a pool are usually similar in terms of loan type, interest rate, and origination date


The weighted-average coupon

The weighted-average coupon (WAC) is the weighted-average interest rate on the mortgages in the pool

With the weight assigned to each mortgage being proportional to its outstanding principal



Pass-throughs are characterized by:

  • Their issuers
  • Their coupons
  • Their maturities


The dollar roll

A trade known as a dollar roll involves selling a TBA for one settlement month and buying a similar TBA for the following settlement month



Refinancing arises when a borrower prepays a mortgage in order to refinance the underlying property

The most likely reason for this is a decline in interest rates



Curtailments are partial prepayments. These tend to occur when loans are relatively old and balances are relatively low


Turnover prepayments

Turnover prepayments arise when a borrower sells the property in question


Option-adjusted spreads

The option-adjusted spread (OAS) is the excess of the expected return provided by a fixed-income instrument over the risk-free return adjusted to account for embedded options


Interest Rate Futures

The bonds issued by the U.S. government with original maturities of ten years or less are referred to as Treasury notes

Bonds with longer maturities are referred to as Treasury bonds

However, Treasury notes and bonds are collectively referred to as bonds

Eurodollar futures contracts provide payoffs dependent on movements in short-term interest rates

Treasury note and bond futures contracts provide payoffs dependent on movements in longer-term rates

Final settlement for Eurodollar futures contracts is in cash and happens on the Monday before the third Wednesday of the delivery month

The payout equals USD 100 minus the Libor fixing on that day

In contrast, Treasury note/bond futures are settled by delivering a particular bond/note

The party with the short position can choose which bond/note to deliver and decide when the delivery will take place



Swaps are over-the-counter (OTC) derivatives contracts where the parties agree to exchange certain cash flows in the future

These exchanges of cash flows depend in part on the future values of variables such as interest rates, exchange rates, equity prices, and commodity prices

As a result, there is always some uncertainty associated with swaps

Forward contracts can be treated as swaps where there will be a cash-flow exchange on just one future date

However, swaps often feature exchanges on many future dates

While the value of a swap is normally zero (or very close to zero) when it is initiated, the value of each exchange made in the swap is typically not zero

It is usually the case that some exchanges have positive values while others have negative values at the time the swap is initiated

The most common interest rate swap involves Libor being exchanged for a pre-determined fixed rate for several years

Interest rate swaps are popular products because they can be used to transform assets and liabilities

That is, a company with a floating-rate loan can use a swap to convert it to a fixed-rate liability

Swaps where Libor is exchanged for a fixed interest rate can be used to estimate Libor forward rates

The procedure used is a bootstrap method where progressively longer maturity swaps are considered

Swaps exchanges can be defined in many ways


Equity Swaps

An equity swap is a swap where a fixed return is exchanged for the return generated when the notional principal is invested in pre-specified equity

Swaps have the potential to give rise to credit risk



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