CFA - Study

Swaps versus futures

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· Swaps can be customized and do not require any margin payments, but they do create a lot of credit risk.
· Futures are more liquid and so cheaper. They do require margin but do not create any credit risk.
· Swaps are mainly used by large firms and institutional investors for hedging. Futures are used for both hedging and speculation by individuals as well as institutional investors.

Advantages and Limitations of swaps over capital markets

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Advanateges:
· Low financing cost due to lower transaction costs
· Quick and anonymous execution in OTC markets with no regulations, and anonymity.
· Allow to hedge over longer time horizons.
· Allow custom designed contract (historically , exploit perceived market inefficient is not possible today as the market is getting matured and offered few arbitrage apportunities)
· Comparative advantage

Limitations:
· difficult to find counterparties
· difficult tohttp://cfa-studynotes.blogspot.com/2009/01/characteristics-of-swaps.html alter or terminate once initiated
· other counterparties exposes to default risk (most important among the limitations)
· Swaps usually limited to small no of firms , financial institutions, swap facilitator.

Interest Rate Swap (plain vanilla) and Currency Swap

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Interest rate swap (plain vanilla):
· One party pays interest coupons based on a fixed rate and the other pays coupons based on LIBOR that sets for the period.
· Payments are exchanged on a net basis and there is no exchange of notional value.
· At least one of the sequence of cash flow is uncertain.

Currency swap:

· Notional amounts and payments on the two sides are denominated in different currencies. The most common type involves the exchange of LIBOR-based payments in US dollars and fixed rate payments in a foreign currency
· A borrower who has floating rate liabilities and is concerned about a rise in interest rates should enter into a pay-fixed swap to fix its cost of debt.A borrower who has fixed rate liabilities and is concerned about a fall in interest rates should enter into a receive-fixed swap to convert its debt into floating rate.
· The notional principal change hands at the beginning of the swap; Interest payment are made without netting (A pays interest in USD to B, D pays in AUD to B at the settlement date)
· The notional principal is swapped again at the termination of the agreement;
· Generally, the variable interest rate for USD determined at the beginning and pay at the end of the settlement period.

Terminating a Swap Contract

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The easiest way to terminate the contract is to hold it to maturity. However, if one or both parties in a swap contract wish to terminate, there are several methods:
· Enter into a separate and offsetting swap
· Cash settlement based on market value.
· Sell the swap to another party, usually requires permission from the other party and not commonly used in the market place.
· Use a swaption. A swaption gives the owner the right to enter into another swap at terms that are set in advance. By executing the swaption, the party can offset its current swap.

Characteristics of Swaps

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· Non-standardized contracts that are traded over the counter (OTC), allow to deal with much longer horizons than exchange-traded instruments, but subject to credit risk
· give greater privacy & escape regulation.
· Swaps are contracts that exchange assets, liabilities, currencies, securities, equity participations and commodities.
· Generally used for risk management by institutions
· Most involve multiple payments as a series of forward contracts, although one-payment contracts are possible
· When initiated, neither party exchanges any cash, a swap has zero value at the beginning.

Interest Rate Changes and Option Prices

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· Options are priced on a risk-neutral basis, so a long call (for example) would be paired with a short stock.
· A short-stock position generates interest revenue, which makes the call option more valuable. If interest rates go up, the interest revenue from the short stock position increases, which makes the call worth even more. For put options and dividends, it works in the opposite direction.
· When interest rates are high, the prices of calls are higher and the prices of puts are lower. When rates are high, the option itself is more attractive than the underlying asset. By purchasing an option instead of the underlying asset, an investor saves cash.
· Puts are adversely affected by higher rates because investors lose interest while waiting to sell their underlying assets. This works for all underlying assets except when dealing with bonds or interest rates.
· Interest rate volatility has a huge effect on option prices. When volatility increases, call and put prices both increase because of the increased possibility that a downside or upside event could occur concerning the option. The upside helps call price and has no effect on puts, while downside helps puts with no effect on calls and is especially true when options are out of the money. Downside does begin to matter when options become in the money.

Lower bounds of Option Prices and the possibility of early exercise.

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Lower bounds for American and European Option Prices

E_C0 ≥ Max{0, [S₀ – PV (CF,o,T)] – X/(1+r)^T}
E_P0 ≥ Max {0, X/(1+r)^T – {S₀-PV(CF,0,T)}

Where: C = Call, S = Strike price, PV = Present value, CF = Cash Flow, r = interest rate, T= Time to expiration of the option

Cash flows for underlying assets are as follows:
· Stocks pay dividends - in formula terms FV (D,O,T) or PV (D,O,T)
· Bonds pay interest - in formula terms FV (CI,O,T) or PV (CI,O,T)
· Currency pays interest
· The underlying price is reduced by the PV of the cash flows of the underlying; therefore, the put-call parity relationship is calculated as:

E_C0 +X/(1+r)^T = E_P0 +{S₀ – PV(CF,0,T)}

The Relationship between American and European Options
· At any given point in time, the value of a call option or a put option cannot exceed a particular price.
· A call option can never be worth more than the stock price; therefore, the value of a call option should be lower or equal to the stock price.
· In the case of a put option, the upper bound is the strike price at which the contract has been entered. The value of a put will be lower than or (at most) equal to the strike price of the option. If this condition is violated, an investor can make use of the arbitrage opportunity by writing the option and investing the proceeds at the risk-free rate of interest.
· The lower bounds for an American call option are the same as the lower bounds for a European call option. Prices of American and European options differ mainly in whether they can be exercised before expiration, as is the case with American calls. As such, in most cases American calls and puts will be worth more than European calls and puts and their lower bounds will also differ.
· When the underlying asset does not make cash payments such as dividends or interest payments, the value of an American call option is equal to a European call option.
· When cash payments are involved, the value of an American call option tends to be higher than a European call option.
· American put options are almost always worth more than European put options.
· Cash flows on the underlying security and their effect on the put-call parity and the lowers bounds of options prices

Notes:
· Currency pays interest
· Commodities have carrying costs

Protective Put

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· aka portfolio insurance or hedged port
· buy a long position in underlying securities + buy a put
· protects the downside risk at a cost
· Appropriate for limiting downside risk when upside potential is still present
· Think stock may go down in near future, want to preserve upside potential

Profit = max(0,X-S_T)+S_T-S₀-P₀
Max Profit = S_T-S₀-P₀ (no upside limit)
Max loss = -X+S₀+P₀
Breakeven price = X+P₀

Covered Call

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· buy underlying security + sell a call
· earns income at the expense of upside potential
· appropriate if asset’s price is not expected to move up over ST

Profit = -max(0,S_T-X)+S_T-S₀+C₀
Max proft = X-S_o+C_o
Max loss = C₀-S₀

Synthetic strategies

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S0=C0 - P0 + Xe-rT
P₀=C₀ - S₀ + Xe^-rT
C₀= P₀+ S₀ - Xe^-rT
Xe^-rT = P₀+ S₀ - C₀

The right hand sied is the synthetic equivalents of the securities of the left.

Put-Call Parity

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· no arbitrage relationship for European-style put & call options that have same characteristics
· a port consisting of a call & a zero coupon bond (earning risk free return) with face value equal to strike = portfolio consisting of a put & a stock
· true only for European options
· the relationship must hold, otherwise arbitrage profit will be produced.

P₀+S₀=C₀+X_e^-rT

Put Option

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Payoff
PT=max(0,X-S_T)
Breakeven at X-P₀

Notes:
Both Call & put, payoffs & profits is linear function of S_T
Call, infinite payoff -> no upper limit
Put, upper limit to the profit is X-P₀

Call option

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Call option gives owner the right, not obligation, buyer or the holder of long position
seller, writer, holder of short position

Payoff
C_T=S_T-X if ST▷X, C_T=0 if S_T≦X
=> C_T=max(0,S_T-X)
Profit = max (0, X_T-X)-C₀ = C_T-C_o
If S_T◁X+C_o, call buyer profit ◁0◁call seller profit
If S_T=X+C_o, call buyer profit =0=call seller profit
If S_T▷X+C_o, call buyer profit ▷0▷call seller profit
Breakeven at X+C₀, or X+premium

Where:
◁ - smaller than
▷ - greater than
C_o - premium

How are the Prices of Options are Affected by the Time to Expiration?

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The price of an option has two components, the intrinsic value and the time value. The intrinsic value of an option is the difference between the actual price of the underlying security and the strike price of the option. The time value is determined by the remaining lifespan of the option, the volatility and the cost of refinancing the underlying asset (interest rates).

Longer term call, both American and European, typically values more than short term call because there is more time to have an event that can occur to make them go in the money. For American put, same as call.

European puts can only be exercised on the maturity date. If the put were to go into the money, one could exercise that option and receive the funds before the maturity date - that money could then be invested in another asset. Consequently, with the European put an investor has to wait to receive the funds and loses those extra days to earn additional income.

Option Payoffs

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Payoffs for interest rate options function are similar to other options. The main difference is that the interest rate options take the days to maturity attached to the agreement into account. Also, the payoff from the option is not made until the end of the number of days attached to the rate. For example, if an interest rate option expires in 60 days and is based on 180-day LIBOR, the holder will not be paid for 180 days.

Interest rate option payoffs
Interest rate call option payoffs are determined by the following formula:

Max {(underlying asset – exercise rate) (days in rate/360) , 0 }

Interest rate put option payoffs are determined by the following formula:

Max {( Exercise rate - underlying asset –) (days in rate/360) , 0 }

Intrinsic Value - Intrinsic value in options is the in-the-money portion of the option's premium. It is the value that any given option would have if it were exercised today.

Intrinsic value of a call = Min {0, CP –X}
Where CP - stock's current price (CP), X - option's strike price (X)

Intrinsic value of a put = Min {0, X-CP}

Time Value - The time value is any value of an option other than its intrinsic value, basically as the risk premium. Fundamentally, time value is related to a stock's beta or volatility. If the market does not expect the stock to move much (if it has a low beta), then the option's time value will be relatively low. Conversely, the option's time value will be high if the stock is expected to fluctuate significantly.

Option	Min. Value	Max. Value
European call	ct ³ Max{0, St-X/(1+RFR)^T-t}	St
American call	Ct ³ Max{St-X/(1+RFR)^T-t}	St
European put	pt ³ Max{0, X/(1+RFR) ^T-t - St}	X/(1+RFR) ^T-t
American put	Pt ³ Max{0, X - St}	X

Interest Rate Options vs. FRAs

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Forward rate agreement (FRA)
· an agreement between two parties to exchange a fixed interest payment for a floating interest payment.
· FRAs are OTC derivatives - forward contracts in which one party (which is referred to as the borrow or buyer) pays a fixed interest rate, and another party receives a floating interest rate equal to a reference rate (the underlying rate). The receiver is also referred to as the lender or seller.
· The payments are calculated over a notional amount over a certain period and netted - in other words, only the differential is paid on the termination date.

Interest rate options
· Give buyers the right, but not the obligation, to synthetically pay (in the case of a cap) or receive (in the case of a floor) a predetermined interest rate (the strike price) over an agreed period.

Similarities
· Both Interest rate options and FRAs have interest rates as their underlyer.
· Both use put or call formats.
· Both use a notional amount to define the size of the trade.
· Neither requires an exchange of principal.

Differences
· An FRA is a commitment to make one interest rate payment and receive another one at a future date while an option is the right to make one interest rate payment and receive another one.
· Interest rate options have exercise rate or strike rate instead of an exercise price like an FRA.

Types of options in terms of the underlying instruments

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Financial Options:
Financial options have financial assets, such as an interest rate or a currency, as their underlying assets. There are several types of financial options:

Stock Option
Also known as equity options, these are a privileges sold by one party to another. Stock options give the buyer the right, but not the obligation, to buy (call) or sell (put) a stock at an agreed-upon price during a certain period of time or on a specific date.

Index Option
A call or put option on a financial index, such as the Nasdaq or S&P 500. Investors trading index options are essentially betting on the overall movement of the stock market as represented by a basket of stocks.

Bond Option
An option contract in which the underlying asset is a bond. Other than the different characteristics of the underlying assets, there is no significant difference between stock and bond options. Just as with other options, a bond option allows investors to hedge the risk of their bond portfolios or speculate on the direction of bond prices with limited risk.

A buyer of a bond call option is expecting a decline in interest rates and an increase in bond prices. The buyer of a put bond option is expecting an increase in interest rates and a decrease in bond prices.

Interest Rate Option
Option in which the underlying asset is related to the change in an interest rate. In general, the call buyer of an interest rate option expects interest rates will go up, while the put buyer hopes rates will go down.

Currency Option
A contract that grants the holder the right, but not the obligation, to buy or sell currency at a specified price during a specified period of time. Investors can hedge against foreign currency risk by purchasing a currency option put or call.

Options on Futures
Like other options, an option on a futures contract is the right but not the obligation, to buy or sell a particular futures contract at a specific price on or before a certain expiration date. A call option gives the holder (buyer) the right to buy (go long) a futures contract at a specific price on or before an expiration date. The holder of a put option has the right to sell (go short) a futures contract at a specific price on or before the expiration date.

Commodity Options
These are options in which the underlying asset is a commodity such as wheat, gold, oil and soybeans.

Basic Options Concept

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Option buyer has the right to buy or to sell the underlying asset but no obligation to do so.

Option seller (writer) has no right, but an obligation to complete the trade required by the option contract.

Call option: Gives its holder the right to purchase an asset at the strike price.
Put option: Gives its holder the right to sell an asset at the strike price.

American vs. European:
· American-style options can be exercised at any time up to the expiration date.
· European-style options can only be exercised on the expiration date.
· Since American-style gives more flexibility, it can be more expensive than European-style in some (but not all) cases.
· Both options have the same value on the expiration date.
· Most of the options throughout the world are A. options

Moneyness
The concept of moneyness describes whether an option is in-, out-, at-, or in-the-money by examining the position of strike vs. existing market price of the option's underlying security.

Call option is in-the-money if current asset price is greater than strike price, and out-of-themoney if current asset price is smaller than strike price.

Put option is in-the-money if current asset price is smaller than strike price, and out-of-the-money if current asset price is greater than strike price. If current asset price equals strike price, both are at the money

Over the Counter Options
Many derivative instruments such as forwards, swaps and most exotic derivatives are traded OTC.

· unregulated
· Dealers offer to take either a long or short position in option and then hedge that risk with transactions in other options derivatives.
· Buyer faces credit risk because there is no clearing house and no guarantee that the seller will perform
· Price, exercise price, time to expiration, identification of the underlying, settlement or delivery terms, size of contract, etc. are customized

Exchange-Traded Options
· traded on a regulated exchange
· All terms are standardized except price.
· The exchange establishes expiration date and expiration prices as well as minimum price quotation unit.
· The exchange also establishes whether the option is American or European, its contract size and whether settlement is in cash or in the underlying security.
· Usually trade in lots in which 100 shares of stock = 1 option
· The most active options are the ones that trade at the money
· Can be bought and sold with ease and holder decides whether or not to exercise. When options are in the money or at the money they are typically exercised.
· Most have to deliver the underlying security.
· Regulated at the federal level

Closing futures positions:

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· Offset {buy a contract to close a short position and sell a contract to close a long position, most common}.
· Delivery {any contract outstanding at expiration settled by physical delivery of asset, less than 1% of settlement use this method.
· Cash settlement {many financial futures do not allow physical delivery and instead require cash settlement}.
· Exchange for physicals (EFP) {two traders with opposite side of a contract conduct the transaction and ask exchange to cancel their positions, different from delivery:

actually exchange goods
contract not closed
2 traders privately negotiated

Future markets

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· Futures buyer has a long position on underlying asset.
· Futures seller has a short position.
· Futures buyer profits if asset price rises, while futures seller profits if asset price falls.

Futures contracts is standardized by the quality of the underlying asset, notional amount, tick size {smallest unit by which futures price can change}, tick value {dollar value of one tick}, expiration, delivery terms, and margin requirements.

---- standardized contract terms => uniformity promote market liquidity
---- Clearing house =>never default, split all trades & acts as counterparties.

Benefits of futures:
· Price discovery (by creating a highly liquid and transparent market)
· Hedging. Regulation and speculation are required for smooth functioning of futures market, but are not considered to be benefits.

Hedging:
· To reduce a long exposure {e.g. investor holding a stock portfolio, firm mining gold, farmer with wheat in the field}, you would sell futures.
· To reduce a short exposure {e.g. airline that needs to buy oil, importer who needs to buy foreign currency}, you would buy futures.

Speculation:
· If you believe prices will rise buy futures. If you think they will fall, sell futures.

Open interest = Outstanding long positions + Outstanding short positions
· open interest refers to the no. of contracts that currently in existence
eg. open interest of 100-> 100 short positions & 100 long positions.

Trading volume
· Activity measured by trading volume:
· Number of contracts executed in a given day.
· When a party buys a future it generates one unit of trading volume.
· If the party then closes out by selling the contract, it generates another unit of trading volume.

Margin & Daily settlement
· can be posted in cash, bank letter of credit, or treasury bills

Initial margin:
· Amount that must be deposited at the time of opening a futures position.

Maintenance margin:
· Level to which a margin account may fall before a request for additional funds (a margin call) is made.

Variation margin = Initial margin - Equity balance in margin account
· Must be deposited upon the receipt of a margin call to bring the margin account back to the required level.

Types of contract:
· agricultural & metallurgical contracts
· interest bearing assets (interest rate future)
· foreign exchange, Indexes

In physical,metal is most active contract; In all contract types, financial instruments is most spectacular groth, more than 50% of all trading volume.

Futures versus forwards

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Forwards:
· Negotiated privately in the OTC market,
· Customized
· Do not have any margin requirements
· Expose the parties to credit risk.
· Require no cash transaction until delivery date, usually not regulated

Futures:
· Standardized, exchange-traded contracts
· More liquid and so cheaper than forwards
· Buyers and sellers must deposit a margin with the exchange/clearing house
· Near-zero credit risk
· Regulated

Characteristics of Currency Forward

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Used as a foreign currency hedge when an investor has an obligation to either make or take a foreign currency payment at some point in the future.

Foreign currency futures contracts have standard contract sizes, time periods, settlement procedures and are traded on regulated exchanges throughout the world.

Foreign currency forwards contracts may have different contract sizes, time periods and settlement procedures than futures contracts, considered as over-the-counter (OTC).

Forward rate agreements (FRAs)

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· A forward rate agreement is a forward contact on a short-term interest rate, usually LIBOR.
· It is a forward contract to borrow / lend money at a certain rate at some future date,
· the potential borrower can lock in borrowing rate with FRA, a contract to enter into a loan at a future date.
· Usually settled with cash payment, the amount of settlement makes the total interest rate (actual interest cost + FRA settlement) equal to the contracted interest cost in FRA

If market rate greater than the rate in FRA, bank pay borrower
If market rate smaller than the rate in FRA, borrower pay bank

Settlement
[(notional principal)[(floating rate at settlement – forward rate) (days/360)] / [(1+floating rate at settlement) (days /360)]

Numerator - the difference between the actual rate that exists in the marketplace on the expiration date and the agreed-upon rate at the beginning of the contract.

The divisor - Discounting the payment at the current LIBOR, based on the assumption that they will accrue interest.

Eurodollar Time Deposit Markets,LIBOR and Euribor

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Eurodollar Time Deposit Markets
Eurodollar time deposits are demoniated in U.S. dollars on deposit outside the United Statest.

London Interbank Offer Rate (LIBOR )
The interest rate paid on interbank deposits in the international money markets (also called the Eurocurrency markets), commonly used as a benchmark for short-term interest rates in setting loan and deposit rates and as the floating rate on an interest rate swap.

Euro Interbank Offered Rate (Euribor)
Similar to LIBOR except it uses euros and euro deposits in the lending and borrowing between banks, instead of dollars. Euribor is the rate at which euro interbank term deposits are offered by one prime bank to another prime bank. Euribor is the benchmark rate of the large euro money market.

Forward Contracts on Bonds

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The basic characteristics of a forward contract on a bond are very much like those of equity. A bond pays a coupon similar to an equity paying a dividend. The differences are:

· Bonds mature
· Bonds can have calls and convertibility.
· Bonds have a default risk

Forward contracts can be on an individual issue as well as on a portfolio of bonds or on a bond index.

Zero-coupon bond forward contract
Agreeing to buy the bond at a later date, but before its maturity, at specified price.
sold at a discount to par and are quoted in terms of the discount rate.

Coupon-paying bond forward contract
Interest payments of the bond are typically semi-annual and can sell at a premium or discount to the bond's par value.

Equity Forward Contracts

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An equity forward is a contract for the purchase of an individual stock, a stock portfolio or a stock index at some future date at a specified price.

Most forwards do not pay dividends except for forwards that are "total return" forwards.

End Users vs Dealers

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End Users
End-users have specific risk management concerns that can be mitigated by an appropriate forward contract,

Dealer
A dealer helps facilitate the trading and structure of these transactions based on the end user's specific needs and goals.

Early termination

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By entering into a new forward contract with opposite position, i.e. one long and one short.

Default Risk and Early Termination
For forward contracts, without a formal exchange and clearing house to guarantee delivery and payment, there is always a chance that either the buyer or the seller will default on an obligation. If one of these counterparties fails, the other is still responsible for performing under the contract.

Reversing trade prior to the expiration date will effectively increase the default risk exposure because two counterparties are involved. To extinguish default risk on a forward contract, a trader must place the reversing position with the same counterparty and under the same terms as in the originally contract.

Unlike forward contract, there is no default risk on futures as the clearing house acts as a counterparty, guaranteeing delivery and payment.

Settling a Forward Contract at Expiration

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Physical Delivery
· It requires the actual underlying asset to be delivered on the specified delivery date, most common with commodities and other financial instruments
· Most derivatives are not actually exercised, but are traded out before their delivery dates.
· Settlement by physical delivery is carried out by clearing brokers or their agents.

Cash Settlement
It requires the counterparties to the contract to net out the cash difference in the value of their positions. The appropriate party receives the cash difference.

Differences between long and short positions in forward markets

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Long position holder: buyer of the contract
The long position will take the delivery of the asset and pay the seller of the asset the contract value

Short position holder: seller of the contract.
The seller is obligated to deliver the asset versus the cash value of the contract at the origination date of this transaction.

When it comes to default, both parties are at risk because typically no cash is exchanged at the beginning of the transaction. However, some transactions do require that one or both sides put up some form of collateral to protect them from the defaulted party.

Purposes and Criticism of Derivative markets

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Purposes and Benefits
· Speculation - derive profit from changes in interest rates, equity markets, currency exchange rate, global supply and demand for commodities.
· Price Discovery
· Risk Management - help hedge against inflation and deflation, and generate returns that are not correlated with more traditional investments
· Improve market efficiency for the underlying asset
· Help reduce market transaction costs

Criticisms
· Sophistication - potential for huge gains and huge losses, appropriate for only sophisticated investors with a high tolerance for risk.
· Lifespan - as each day passes and the expiration date approaches, more and more "time" premium lose and the option's value decreases.
· Direction and market timing - investors must accurately predict the direction in which the market or index will move during a set period of time. A mistake here almost guarantees a substantial investment loss.
· Costs - The bid/ask spreads of more common derivatives such as options can be daunting.

Futures, forwards, Options, Swap

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Forwards
· negotiated privately in the OTC market, customized,
· do not have any margin requirements
· do expose the parties to credit risk.
· Have uniqure contract, have default risk.
· Require no cash transaction until delivery date, usually not regulated

Futures
· Standardized
· exchange-traded contracts that are more liquid and so cheaper than forwards.
· Futures buyers and sellers must deposit a margin with the exchange/clearing house.
· Futures have near-zero credit risk. Regulated.

Options
Contracts that give their owners the right, but not the obligation, to conduct a transaction in the future, whose terms are set in the option contract.

Call option - provide the holder the right (but not the obligation) to purchase an underlying asset at a specified price (the strike price), for a certain period of time.

Put option - give the holder the right to sell an underlying asset at a specified price (the strike price).

Swaps
· Contracts for the exchange of two or more sets of cash flows between two parties.

Forward Commitments vs. Contingent claim

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A forward commitment is a contract between two (or more) parties who agree to engage in a transaction at a later date and at a specific price.

Two major types of forward commitments:

Forward contracts, or forwards - OTC-traded derivatives with customized terms and features.

Futures contract, or futures - exchange-traded derivatives with standardized terms.

Exchange-traded vs. over-the-counter derivatives

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Derivatives
Derivatives are financial contracts or securities whose payoff depends on underlying assets or indices.
Exchange-traded derivatives
· Traded on established exchanges (the New York Stock Exchange, the French CAC or the Chicago Board of Trade).
· Highly standardized terms and features.
· The regulated exchanges provide clearing and regulatory safeguards to investors

Over-the-counter or OTC-traded derivative
· Traded outside of the formal, established exchanges, including forwards, swaps and exotic derivatives
· Can be created by any two counterparties with highly flexible terms and a nearly infinite number of underlying assets or asset combinations
· Large financial institutions serve as derivatives dealers to customize derivatives for the specific needs of clients

Price Volatility for bonds

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Properties concerning the price volatility of an option free bond:
· Price is inversely related to yield.
· Price sensitivity depends on maturity and coupon.
· For small changes in yield, the price change is same whether yield moves up or down.
· For large changes in yield, the price increase for a fall in yield is greater than the price decrease for a similar rise in yield, i.e. the price yield curve is convex.
· The lower the coupon, the longer the term to maturity, the lower the initial yield -> the greater the bond price volatility
· Yield/price relationship for option free bonds is not linear but convex, referred to as positive Convexity.

Positive convexity:
· The decrease in an option-free bond’s price due to a rise in yield is lower than the increase for an equal fall in yield. This results a positive adjustment to the duration-based estimate of price change whether yield goes up or down.

Price-Volatility Characteristics of Callable and Prepayable Securities
· Embedded options can dramatically change the price-yield profile.
· At high yields the profiles of these bonds are similar, but at low yields price of callable/prepayable securities grows slower with a fall in yield than the price of option-free bonds {price compression}.

Negative convexity:
· For callable and prepayable securities, at low levels of yield, the price increase for a given fall in yield is less than the price decrease for an equal rise in yield. ie, Prices rise at a decreasing rate. The point where the curve starts to flatten is at ( or near a yield level of y’

Price Volatility Characteristics of Putable Bonds
· The advantage of these bonds to an investor is that if market yields rise and the value of the bond falls below the put price, the investor can exercise the put option and stem his losses to the put price.
· The price of a puttable bond will react same way as an option-free bond at low yield levels. As rates rise, the puttable bond’s price will decrease at the same rate as an option-free bond, but the decline will be lessened because of the value of the put option.

Value of puttable bond = value of option free bond + the option.

Convexity

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Convexity is a measure of the degree of curvature of the price/yield relationship, to indicate the error in the estimated change in bond's price based on duration.

Effective convexity = (V_ + V+ - 2 x Vo) / (2 x Vo x dy²).

It is the 2nd derivative of price function wrt yield. For callable bond, V is capped at call price.

Contribution of convexity = Convexity x dy².

For noncallable bond, convexity effect is always +ve no matter which direction interest rate move but it can be –ve if the bond has embedded options.
Thus, approximate bond price change (using duration and convexity), i.e.

Approx. price change = -1 x Duration x dy + Convexity x dy²

Modified Convexity vs. Effective Convexity
With modified convexity the cash flows do not change due to a change in interest rates.

Effective Convexity, on the other hand, assumes that cash flow does change due to a change in interest rates.

When bonds have options, it is best to use effective convexity just like you should use effective duration. For option-free bonds, either convexity measure will be a positive value, whereas when it comes to bonds with options, the effective convexity could be negative even if the modified convexity is positive.

Price value of a basis point (PVBP)

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A measure of bond price volatility that shows the extent to which the price of a bond will change when the required yield changes by one basis point. That is, the difference between the initial price and the price if yield is changed by 1bp, a variation of dollar duration.

PVBP = Duration x Price / 10,000

Approximate % change in bond price

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Approximate % change in bond price = (-) (duration)(dy)

Duration tends to:
· underestimate the increase in price that occurs with a drecrease in yield; overestimate the decrease in price that comes with an increse in yield.
· The difference is due to the curvature of the actual price path.
· The larger the change in yield, the larger the error.
· For small changes, estimated and actual price changes are equal or very close.

Duration

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Duration is a measure of the slope of the price-yield function, steeper at low interest rate and flatter at high interest rate for non-callable bonds. It represents the percentage change in price for a 100 basis point change in yield.

Effective Duration
Duration is the approximate percentage change in price for a 100 basis point change in rates.
Effective Duration = (V_- V+) / (2 x Vo x dy in decimal).

Note:
· go down or up by same no. of basis points

Modified Duration
Modified duration is the approximate percentage change in a bond’s price for a 100 basis points change in yield, assuming that the bond’s expected cash flow does not change when the yield changes. This works for option-free bonds such as Treasuries but not with option-embedded bonds because the cash flows may change due to a call or prepayment.

Macaulay duration
Macaulay’s duration is the weighted average number of years remaining to receive the present value of a bond.

It gives the analysis a short cut to measure modified duration. But because modified duration is flawed by not incorporating the change in cash flows due to an embedded option, so are Macaulay durations.

Modified duration = Macaulay’s Duration/ (1 + yield/k)
Macaulay duration = Modified duration x (1 + BEY/2).

Notes:
· The duration of zero coupon bond = its maturity;
· Duration of a floater coupon bond = the time to the next reset date

When is Effective Duration a Better Measure?

When a bond has an embedded option, the cash flows can change when interest rates change because of prepayments and the exercise of calls and puts. Effective duration takes into consideration the changes in cash flows and values that can occur from these embedded options.

Duration of a portfolio
Duration of a portfolio equals the weighted average of the durations of the bonds in the portfolio.

Duration/convexity approach

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To provide an approximation of the actual interest rate sensitivity of a bond or bond portfolio, simplier than full valuation approach.

Full Valuation Approach

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To measure the interest rate risk by re-valuing the bond or portfolio for a given interest-rate change scenario, referred to as a scenario analysis. Work well for periodic reports but impractical for managing risk of large portfolio.

Steps:
1. Start with current market yield and price
2. Estimate chagnes in yields
3. Revalue bonds
4. Compare new value to current value

It take the changes in cash flows into account.

Nominal spread, Static spread, Zero-volatility spread, Option-adjusted spread

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Nominal spread – simpliest

Nominal spread = (YTM of the bond – YTM of a Treasury security of similar maturity)

Limitations of nominal spread:
· Does not account for term structure of interest rates (no arbitrage pricing).
· Ignores affect of embedded options.

Static spread (Z-spread)
· Spread not over the treasury’s YTM but over each of the spot rates in a given treasury term structure, ie. same spread is added to all risk-free spot rates.
· more accurate than nominal spread as it is based upon the arbitrage free spot rates.
· Equal to nominal spread if yield curve is perfectly flat.

PV = CF1/(1+Z1 +SS) +CF2/(1+Z2 +SS)³+ CF3/(1+Z3+SS)³ , by trial & error to find SS (Z-spread)

Zero-volatility spread (Z-spread):
· Spread over the entire Treasury spot rate curve.
· Accounts for the term structure of interest rates, but ignores the affect of embedded options.
· Difference between Z-spread and nominal spread is greatest for amortizing bonds, for longterm high-coupon bonds, and for steep yield curves.

Option-adjusted spread (OAS):
· Spread over entire Treasury spot rate curve after accounting for embedded options.
· OAS is highly dependent on the model used to calculate the spread and the assumption for interest rate volatility.
· Higher interest rate volatility assumed » Lower OAS.

Option cost = Z-spread - OAS.

For option-free bonds OAS = Z-spread.
For option value greater than 0( call), OAS smaller than Z-spread;
For option value smaller than 0 (put), OAS greater than Z-spreadNominal spread may be misleading in the case of securities with embedded options. Buy securities with largest OAS for a given duration.

Forward Rate

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A forward rate is the borrowing / lending rate in the future. The logic is that the return from investing in a 2-year bond is the same as that from investing in a 1-year bond and then rolling the proceeds into a second 1-year bond one year from now.

Forward rate from period 1 to period 2 = (1 +Z2)² / (1 + Z1) – 1

Where:
Z1 is the spot rate for 1-year
Z2 is the spot rate for 2-year.

Given the forward rates, calculate spot rate
(1+Z3)³ = (1+ f1)(1+f2)(1+f3)

Calculate N-period spot rate (SN)
ZN)3 = [(1+ f1)(1+f2)…..(1+fN)]^1/(N+1) –1

Bootstrapping Spot Rate

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Bootstrapping is the process of calculating spot rates from coupon bond yields.

Example:
Given a 2-year bond price (P) with annual coupon (C) and 1-year spot rate Z1,
You can calculate 2-year spot rate in the following formula:

P = C/(1+Z1) + (C+PAR)/ (1+Z2)²

Given Z1,Z2 and the price of a 3-year bond, you can calculate Z3 in the same manner.

Annual pay, semi-annual pay, Reinvestment income

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Annual pay versus semi-annual pay:
Many non-US governments and corporate bonds that pay annual coupons.

Annual pay yield = (1 + BEY/2)² - 1.

BEY = [(1 + Annual-pay yield)^1/2 - 1] x 2.

Total Dollar Return = coupons + principal + reinvestment income, i.e. to calculate the FV of the reinvestment coupon + principal at maturity

Reinvestment income
Reinvestment income can make up a large portion of the return for a bond due to its compounding effect.

Factors That Affect Reinvestment Risk
There are two characteristics that affect reinvestment risk:
· The longer the maturity, the more the total dollar return depends on reinvestment income to realize the yield to maturity at the purchase time. Longer maturity = greater reinvestment risk.
· The higher the coupon rate, the more the total dollar return depends on the reinvestment of the coupon payments. Higher coupon rate = greater reinvestment risk

Yield Measurements

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Current yield
= Annual coupon / Price

Problem: do NOT consider capital gain/ loss or reinvestment income

Yield to maturity (YTM)
IRR of an investment in the bond that equates the PV of all expected cash flows from bond to its full price.

At par, nominal yield(coupon) = current yield = YTM
At discount, nominal yield(coupon) smaller than current yield smaller than YTM
At premium, nominal yield(coupon) greater than current yield greater than YTM

Note:
· for semiannual bond, IRR is not YTM which is equal to BEY

Assumptions and limitations of YTM:
· Security will be held to maturity
· All intermediate cash flows will be reinvested at the same rate as yield. Higher term to maturity leads to higher reinvestment risk. Higher coupon rate implies higher reinvestment risk.
· All coupon payment are received promptly & timely fashion, ie no credit risk. So YTM is also referred to as promise yield.
· A flat yield curve (rarely exist)

Bond-equivalent yield (BEY)
· Discount rate calculated using six-monthly periods and annualized by multiplying by two.

Realized return (annualized basis) = YTM =BEY

Equivalent annual yield (EAY) = (1+YTM/2)² for semiannually paid bond

Yield to call
Value bond on the basis that it will be called on first call date. Market conversion is to use the lower /more convervative measure of yield (YTM or YTC) as the appropariate indicator of value.

For premium bond, YTC smaller than YTM
For discount bond, YTM smaller than YTC

Yield to put

Yield to worst(YTW)
The lowest expected return among YTC, YTP, YTM etc.

Cash flow yield (CFY)
Based on the cash flows that include an assumption regarding prepayment rate. Useful for MBS that have monthly payments. The estimated rate of principal repayment may be different from the actual rate of prepayment.

EAY= (1 + Monthly CFY)¹² - 1

Sources of return for a bond

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Sources of return includes:
· Coupon
· Capital gain or loss
· Income from reinvestment of interim cash flows

Total return = Coupon interest payments + Reinvestment income + Capital gain/loss.

Stripping, Reconstitution

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Stripping
If a dealer finds Treasury coupon bonds trading at a lower price than Treasury strips, he can make a riskless (arbitrage) profit by buying coupon bond and selling strips.

Reconstitution
If a dealer finds Treasury coupon bonds trading at a higher price than Treasury strips, he can make an arbitrage profit by buying strips and selling coupon bonds.

Appropriate discount rate

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· The minimum interest rate that an investor should accept is the yield that is available in the market place for a risk-free bond.
· The on-the-run Treasury security is most often used as they reflect the latest yields and are the most liquid securities.
· For corporate bonds, a risk premium can be added to the risk free rate.

Ideally, each cash flow should be valued using the spot rate corresponding to its maturity. Bond price is inversely related to discount rate. Can add risk premium to the risk free rate or series of risk free sport rates

Computation of Bond Price

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Bond prices can be expressed as a percentage of par value or as a yield.

Yield to Maturity (YTM)
· A single discount rate that makes the present value of a bond’s cash flows equal to the market price.
· YTM for a semiannual-pay bond is twice the semiannual discount rate and so called as bond equivalent yield.

YTM_annual-pay = (1+YTM _{semianual-pay}/2)²-1
YTM_{semiannual-pay} = [(1+YTM_annual-pay)^1/2-1]x2 = BEY

Bond price of a bond with semi-annual coupon payment:

P = CPN1 / (1-YTM/2) + CPN2 / (1-YTM/2)² +.+ (CPN2N + PAR) / (1-YTM/2)^2N

Where: YTM is BEY

Bond price for a zero-coupon bond
P = Par / (1 + YTM/2)^{2 N}

Where: YTM is BEY

Full price of a bond between coupon payments

P= Σ[Cash flow in period t/(1 + Discount rate)^(t-1+w)]

Where:
w is the no. of days remaining until next coupon (i.e. between settlement date (exclusive) and next copon date(inclusive)/ Total days in coupon period)

Accrued interest = Coupon x (1 - w)

Clean price = Full price - Accrued coupon.

Day count conventions:
· Actual/Actual (US governmentt bond);
· Actual/365 (Bristish government bond),
· 30E/360 (German government bond, Eurobond, most corporate bond, most munis)

Price-Yield Relationship
Inversely related, convex ( bond prices go up faster than they go down)

Pull to par
As time passes, the price of a bond trading at a premium will fall back to par and the price of a bond trading at a discount will rise to par.

Deficiency of traditional approach to valuation:
Each cash flow is unique. Valuing all cash flows of a security using a single discount rate is incorrect unless for a flat term structure. YTM is only a an approximate or weighted average of a set of spot rates.

Arbitrage-free valuation
Each individual cash flow is valued by discounting it at a spot rate corresponding to its maturity.

P = CPN1 / (1-S1) + CPN2 / (1-S2)² +.+ (CPNN + PAR) / (1-SN)^N

Where Si is the corresponding spot rate.
Arbitrage: If the sum of the PVs of cash flows is more than the price of the security, then buy the security and sell the cash flows individually, and vice versa.
Cash flows are valued using the spot rate corresponding to their maturity. It is more accurate than the traditional approach.

Difficulty in estimating expected cash flow

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· Bonds with embedded option - uncertain timing of principal repayment
· Bonds with variable coupon - uncertain coupon payment rate as it will be reset occasionally
· Bonds with conversion or exchange privilege

Bond Valuation Process

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1. Estimate the expected cash flows
2. Determine the appropriate discount rates.(either the bond’s yield to maturity or a series of spot rates
3. Calculate sum of present values {= ΣCash Flow_t/(1 +Discount rate)^t}

LIBOR

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LIBOR is:
· the interest rate at which banks can borrow funds from other banks in the London interbank market.
· fixed on a daily basis and derived from a filtered average of the world's most creditworthy banks' interbank deposit rates for larger loans with maturities between overnight and one full year.
· the world's most widely used benchmark for short-term interest rates.

Factors that affect the yield spreads

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Impact of embedded options
Call option increases reinvestment risk and yield spread must be higher to compensate.
Option adjusted spread < nominal spread

Put option is favorable towards investors and thus reduces yield spread
Option adjusted spread > nominal spread

The yield spread of Agency MBS is primarily due to prepayment risk. Option-adjusted spread excludes the risk due to the embedded option, while the nominal spread does not, making an option-adjusted spread a superior measure to compare returns.

Impact of Liquidity
Lack of liquidity can increase yield spread, even of off-the-run Treasuries.

Impact of tax-exemption:
Munis trade at low yields (even negative yield spread) because their income is tax exempt.
After-tax yield = Pre-tax yield x (1 - Marginal tax rate of investor)

Impact of technical factors:
Imbalance between supply and demand for securities drives temporarily distorted. Yield spreads rise if there is a glut in supply of bonds. The yields spreads of sovereign bonds over US Treasuries are “nominal” since the currencies may be different and the spreads are simply differences in two yields.

Credit spread

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· The difference in yield between two identical issues except credit rating
· Credit spread tends to widen when the economy enters a recession and narrow when economy is booming, as a funcation of the state of economy.

Intermarket vs. Intramarket Spread

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Intermarket spread:
· Yield spread for same maturity and different sectors. For example, treasuries vs corporate bond

Intramarket spread:
· Yield spread for different maturities and same sector. For example, Long Treasuries vs. Short treasuries or AA corporate bond vs. BBB corporate bond

Yield Spread

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Yield spread is caused by differences in credit quality, call features, tax treatment or maturity.

Absolute yield spread
= Yield of bond - Yield of reference bond.(in basis point)

Problem: may stay same even if interest rate are rising or falling and cause misleading as spread is changing if in %

Relative yield spread
= Absolute yield spread / Yield of the reference bond

As a % of the reference bond, better basis for comparison over time than absolute spread & of the reference yield

Yield ratio
= Yield of bond / Yield of reference bond.= relative yield spread +1

Theories for the shape of yield curve

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Expectations hypothesis:
· Term structure of interest rates results from the market’s expectations of future interest rates. If the market expects inflation and consequently interest rates to be higher in future periods, it will expect higher forward rates leading to an upward sloping yield curve.

Problem: fail to account for why term structure of interest rates is upward sloping more often than downward sloping.

Liquidity preference theory:
· Investors demand a premium for investing in long-term bonds to compensate for higher risk. Borrowers are willing to pay the extra yield since short-term debt that needs to be rolled over exposes them to refinancing risk.

Problem: upward basis

Market segmentation theory:
· Various borrowers and lenders have preferred maturity ranges based on their objectives. These preferences are fixed. Thus the market is divided into distinct maturity segments, in which interest rates are determined by the demand and supply of loanable funds. If there is a shortage of loanable funds in the short term and excess in the long term, then short-term rates will be high and long-term rates will be low.

Term structure of interest rate

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Graph of zero coupon yields (strip) (spot rates) versus maturity. Solves problem of Treasury yield curve.

Treasury yield curve

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Treasury yield curve is the graph of yields of on-the-run Treasuries versus maturity.

Yield curve can be used as benchmark for bonds (off-the-run treasury yield is considered as appropriate for non-US government bonds), but two problems exist:
· Yields of on-the-run Treasuries are lowered by demand in repo market
· Different coupons and reinvestment risk makes yields non-comparable.(greater duration or interest rate risk for new lower coupon on-the-run securities in comparison with off-the-run.)

Yields for missing maturities can use linear approximation:
Yield_n = Yield(lower) + {Yield(higher)-Yield(lower)}(n-lower) / (higher – lower)

Shapes of yield curve
Upward or Normal Yield Curve
· short-term rates are lower than long-term rates
Inverted Yield Curve
· short-term rates are higher than the longer part of the curve, occurs during economic contraction
Flat Yield Curve
· little or no change between short-term and long-term rates.

International bonds

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Foreign bonds
e.g. Yankees are issued by non-US firms in the US, Samuai bond issed by non-Japanese but traded in Japan, bulldog bonds in London.

Eurobonds
· Unsecured
· issued outside the legal system of any one country
· not usually registered through a regulatory agency
· offered simultaneously to investors in several countries by a group of int’l investment and merchant bankers
· Straight fixed-rate coupon bond- Euro Straights, others called plain vanilla bonds.

Global bonds
· sold in Yankee and Eurobond market

Sovereign debt
· issued by various governments.
· Ideal for investors diversifying abroad.
· Withholding tax is a key concern}, borrow directly from banks.

Collateralized Debt Obligations

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An investment-grade security backed by a pool of bonds, loans and other assets. CDOs do not specialize in one type of debt but are often non-mortgage loans or bonds.

Similar in structure to a collateralized mortgage obligation (CMO) or collateralized bond obligation (CBO), CDOs are unique in that they represent different types of debt and credit risk. In the case of CDOs, these different types of debt are often referred to as 'tranches' or 'slices'. Each slice has a different maturity and risk associated with it. The higher the risk, the more the CDO pays.

Asset-backed securities

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A security that is backed by a pool of loans or receivables, including auto loans, consumer loans, commercial assets (planes, receivables), credit cards, home equity loans, and manufactured housing loans.

Enhancement of credit quality:
External:
· corporate guarantee
· letter of credit
· bond insurance (insur co)

Internal
· ABS
· over-collateralization
· securities with different priorities.

Commercial Paper

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· A short term unsecured promissory note, shorter than 270 days to maturity and Issue as a zero-coupon security.
· Companies continue to "roll over" or pay off the holders by issuing new commercial paper in the market. The risk to investors is that the issuing company will not be able to place the new commercial paper to pay off their older debt.

Ways to issue commercial paper
Directly Placed
· The issuing company sells the paper directly to the investing public without the help of an agent or intermediary. An example would include GE Capital.

Dealer-Placed
· The issuing company uses an agent to help sell its paper in the marketplace.

Commercial paper has its own credit rating and can de divided into financial and non-financial companies.

Negotiable CDs
· A savings certificate entitling the bearer to receive interest. A CD bears a maturity date, a specified fixed interest rate and can be issued in any denomination. CDs are generally issued by commercial banks and are insured by the Federal Deposit Insurance Corporation (FDIC). The term of a CD generally ranges from one month to five years.

A certificate of deposit
· A promissory note issued by a bank. It is a time deposit that restricts holders from withdrawing funds on demand. Although it is still possible to withdraw the money, this action will often incur a penalty.

Bankers Acceptances
· A short-term credit investment created by a non-financial firm and guaranteed by a bank. Acceptances are traded at a discount from face value on the secondary market. Banker's acceptances are very similar to T-bills and are often used in money market funds.

Medium-term Notes (MTNs)

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· Offer to investors by the issuer's agent instead of being underwritten by investment banks and then sold to the public in one shot.
· help to cover the funding gap between commercial paper and long-term bonds
· can also come in different structures such as step up notes, inverse floaters, deleveraged floaters, range notes and index amortizing notes.
· 9 months to 30 years.

MTNs are sold in small quantities on a continuous basis whereas corporate bonds sold lump sum in large quantities at greater time intervals.

Unlike corporate bonds, investors can choose the maturity and coupon of MTN. With the help of a derivative wrapper, they can embed options, change currency, link the return to equity index, etc. MTN + Derivatives = Structured notes. Structure note a aka ule busters as it enalble institutions to bypass rules governing the use of derivatives as hedging instruments.

Shelf-registered rule
Once registered, can sell in market at discretion of the issuer. Sold at “ best effort” basis- underwriter not guarantee the price to the issuer (opposite to firm commitment underwriting arrangement).

Structured Note
A synthetic medium-term debt obligation with embedded components and characteristics that adjust the risk/return profile of the security., e.g. 5 year bond tied with an option contract for increasing the returns

Corporate bonds

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Senior secured bonds
· backed by all of the issuer’s assets and highest priority in bankruptcy eg mortgage bonds

Collateral trust bonds
· backed by financial assets eg stocks or bonds
· Equipment trust certificate - backed by specific of transportation equipment).
· Mortgage bonds - backed by specific assets
· Debentures -backed only by issuer’s promise to pay
· Subordinate bonds -lowest ranking bonds, claim after senior bonds and debentures, aka as junior bonds

Secured debt backed by assets or collaterals classified as personal property, financial assets, real property.

Unsecured debt is debenture bonds. Subordinated debentures ranked below debenture bonds

If a firm goes bankrupt, bondholders have priority over stockholders. Secured debt holders have the highest chance of recovering their investment. Corporates are rated by rating agencies for risk of default.

Default rates (issuer default rate - equal rate of all issues)
· Dollar default rate ( par value of issue defaulted in a year divided by total par value outstanding
· Cumulative dollar default rate measures the default probability over the bond lifetime.

Credit enhancements:
Third party guarantees and letter of credit (LOC) issued by banks.

Four C’s of credit analysis
Character
Capacity
Collateral
Covenants

Corporate bonds bells and whistles:
· Sinking fund bonds
· issuer sets aside funds to redeem some bonds before scheduled maturity

Callable bonds
· issuer can redeem before scheduled maturity.

Putable bonds
· bondholders can sell bonds back to issuer before scheduled maturity

Convertible bonds
· bondholders can exchange into issuer’s stock

Debenture bonds with warrants attached

Zero coupon bonds
· pay no coupons, issued at steep discount to par
· Income bonds - interest paid only if issuer makes a profit, else accumulated and paid later

Securities issued by State and Local Government

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Municipal securities (or munis):
Issued by state and local governments in the US but NOT free of credit risk.
Not all munis are tax-exempt but some taxable. Income is tax-exempt but capital gains are taxed.

Two types of munis
General obligations (Tax-backed debt obligations)
· backed by the full taxing power of the issuing authority and so is safer

Revenue bonds
· backed only by the cash flow of the project with no recourse to the issuing authority
· pay P & S only if sufficient revenue generated and usually higher yields than General obligations.

Tax exempt rate = Equivalent rate for taxable bond x (1 - Tax rate)

Special structures for munis:
· Insured bonds- insured by third party, commonly for revenue market
· Prerefunded bond-refunded prior to their rist date of call, used to buy treasury products, little or no credit risk, safest type of munis.

Types of the loans that act as collateral for the bonds

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Mortgage Pass through Securities
· Simply channel the cash flows from underlying mortgages to the holders of securities. The shares are in form of participation certificates and the prepayment risk is similar to callable risk. Underlying mortgags that met underwriting criteria are conforming loans and the mortgages in the pool are securitized.

Collateralized Mortgage Obligations (CMOs)
· Subdivide the mortgage pool into several tranches with different cash flows and prepayment risk profiles {junior tranches bear more}. The tranches offer investors different payment rules and par values. For example Tranche A might receive all principal payments until the balance is zero then the payments would flow to Tranche B and so on.

Stripped Mortgage-Backed Securities

Note:
· Home mortgages- Consist of equal monthly payments {interest plus principal} and allow borrowers to prepay all or a part of the loan.
· Prepayment & curtailment - Mortgage backed security receive principle & interrest payments after administrative costs deducted, ie net interest for MBS investors. Prepayment rfer to early retirement of whole balance, Curtailment- refer to partial prepayment

Treasurys under Federal agencies

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Treasurys under Federal agencies referred to as semi-government bonds or government agency bonds and can be further broken down into two categories:

Federally Related Institutions
Arms of the federal government including Government National Mortgage Association (Ginnie Mae), backed by the full faith and credit of the U.S. Government.

Government Sponsored Enterprises (GSEs)
Privately owned, publicly chartered entities to help lower the cost of funding in certain sectors of the marketplace such as:
· Federal National Mortgage Association (Fannie Mae) - provides credit for the residential housing sector.
· Federal Home Loan Mortgage Corporation (Freddie Mac) - provides credit for the residential housing sector.
· Federal Home Loan Bank - provides credit for the residential housing sector.
· Federal Agriculture Mortgage Corporation - provide credit for farm proprieties
· Federal Farm Credit System - provide credit for agricultural part of the economy
· Student Loan Marketing Association (Sallie Mae) -provides support for higher education.

Secondary market for treasuries

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Mostly traded in OTC market. Most recently issued Treasury becomes on-the-run and trades at a higher price relative to off-the-run issues due to higher liquidity. Price quotes as a percent of par value. The quotes are in fraction of 1/32.

Treasury auction process

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· Competitive {yield and quantity- broker/dealers, institutions, money management firms}and non-competitive {quantity only, individual investors} bids.
· Single-Price Auction (with the help of competitive bids, ranked from lowest to highest yield demanded, identify the stop yield where quantity offered equals quantity demanded, then fill
· competitive and noncompetitive bids at the price implied by the stop yield.
· Multiple-price or “ Dutch” Auction(ranked and each group of bidders paid a different price . Dutch auctions held by Fed NY.

Treasury STRIPS Program

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Treasury STRIPS Program (Separate Trading of Registered Interest and Principal Securities)
The U.S. government does not issue zero coupon notes and bonds and there is a strong demand for an instrument with no credit risk and a maturity of greater than one year.

These securities come in two different forms:

Coupon Strips
Coupon strips come from the coupon payment part of the security.

Principal Strips
Principal strips come from the principal payment.

Coupon strips accrue interest and are taxed each year even though interest is not paid until maturity. This causes negative cash flows for a taxable entity. Foreign investors often like principal strips because of the preferred tax treatments they can receive in their home countries.

On-the-run vs. Off-the-run Government Securities

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On-the-run Securities
· most current security issued by the U.S.Treasury Department, tend to be more liquid in the marketplace.

Off-the-run Securities
· the securities that are replaced by the on-the-run securities,tend to be less liquid in the marketplace

Note:
· Price quotes as a percent of par value. The quotes are in fraction of 1/32.

US Treasury securities

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T-bills
· maturity of less than 12 months, no coupon rate, issued at a discount to par value, mature at par value.

T-notes
· maturity of 1 to 10 years, semi-annual coupon

T-bonds
· maturity of greater than 10 years, semi-annual coupon.

Treasury Inflation Protected Securities (TIPS)
· Issued as notes or bonds and help to protect the investor against inflation risk
· The inflation reflected through upward adjustments to the principal value of the bond. At maturity, get greater of initial par or the inflation adjusted principal. But due to the IRS taxes, TIPS fail to povide perfect inflation protection

Adjusted principal = Principal x (1 + Annual inflation / 2)

Coupon = Adjusted principal at end of period x Coupon rate / 2

Political risk

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With governments and municipalities, investors must evaluate the willingness(desire) of the issuer to pay as well as the ability to pay.

Regulatory risk

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Bond price changes due to changes in regulations.

Event risk

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Natural and corporate events can affect the issuer’s ability to pay. For example: disasters, corporate restructurings

Event risk

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Natural and corporate events can affect the issuer’s ability to pay. For example: disasters, corporate restructurings

Inflation risk

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Unexpected rise in inflation raises yields and lowers the price of all bonds except TIPS. Reduce the puchasing power of bond payments.

Yield volatility risk

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· Rise in yield volatility increases value of embedded options
· When expected yeild volatility increase, the value of call option increase-> decrease value of callable bond;
· If yield volatility increase ,value of put option increase -> increse value of putable bond. They move in opposite ways

Exchange rate risk

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Exchange rate risk exists with bonds denominated in foreign currencies.

Liquidity risk

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· Investors will not be able to realize the true value of their investments due to a widening of the bid-ask spread and a lack of buyers or sellers.
· Estimate through bid-ask spread which is also considered be a type of transaction cost.
· Increases in extreme events or if one or more dealers leave the market.
· Instintutional investors need to mark their holdings to market (using bid price or use evaluation model if no active bids-> if illiquid, prevailing market price not true

Bid-ask spread: Highest Bid - Lowest Ask

Credit risk, Downgrade risk, Default risk

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Credit risk
The loss due to a debtor’s inability to meet its bond obligations. Credit spread risk {aka risk premium, widening of bond spread over the benchmark - happens before ratings downgrade, yield on a risky bond = yield on a defalut free bond + risk premiun, increase risk-> increase spread->decrease price}.

Downgrade risk
Fall in the bond price due to a ratings downgrade.

Default risk
Issuer fails to make interest and principal payments

The highest – prime grade, below BBB- or Baa3-noninvestment grade (junk bonds)

Examples:
Moody’s: Aaa, Aa2 etc
Standard & Poor’s: AAA, AA+ etc
Fitch: use similar system to S&P

Reinvestment risk

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The proceeds from an investment may have to be reinvested at a lower rate than the rate available from the investment itself.

The reinvestment risk for callable bonds and amortizing bonds is higher than bullet bonds. Zero coupon bonds have no reinvestment risk.

It is required to balance reivestment risk against price risk - if interest rate decline, price rise which helps to offset the losses in reinvesting coupon payments at lower market int rate.

Yield curve risk

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The graph showing the relationship between term to maturity and yield to maturity is Yield Curve. Bonds with different maturity change by different amount due to the change in the shape of yield curve.

As Economic circumstance change, curve shift up or down, either in

Parallel shift
· interest rate change by same no. of basis points for all maturities

Non-parallel shift
· different maturities undergo different changes in yield. Bond with shorter maturity will not be affected to the same extent as the one with longer maturity when interest rise.
· If LT rate rise, bond value rapidly drop due to the compounding effect on distant cash flows.
· Longer-term bond has greater price sensitivity and higher bond duration.

Call and prepayment risk:

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Call provision makes the bond’s cash flows unpredictable, increases reinvestment risk, and limits the potential for price appreciation. Prepayment risk is similar.

Measurement of interest rate risk

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Duration of a bond (D)
· Percentage change in price for a 100 basis point change in yield
· aka bond’s effective duration, go down or up by same no. of basis points
· Duration of zero coupon rate equals its maturity
· Duration of a floater coupon bond equals the time to the next reset date

D = (V_- V+) / (2 x Vo x dy in decimal)

Approximate bond price change = -1 x Duration x Price x dy

Dollar duration = -1 x Duration x Price / 100

Effect of yield level :
· Price volatility inversely related to the level of market yields. As yields increase, bond prices fall
· The price curve gets flatter and is referred to as positive convexity. The bond prices go up faster than they go down.

Factors affect bond price sensitivity

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Maturity - bond with longer maturity is more sensitive to interest rate movements as more cash flows will be affected over a longer period of time.

Coupon Rate - bond with lower coupon rate is more sensitive to interest rate movement. Zero bond has the greatest interest rate risk

Yield - bond with higher yield is less sensitive to interest rate movement due to the nature of positive convexity

Embedded options -can increase or decrease sensitivity depending on the features of the options

Eixstence of embedded options make future cash flows of the bond harder to predict and thus affect the sensitivity

Callable bond value = value of the straight bond components – value of the ebedded call option

In the formula, negative sign is used because call option is of value to the issuer not the bondholder.

Straight bond has inverse relationship between yield and prices. However, if with call options, investors will be unwilling to pay more than the call price or at least not much more so that call price acts as a ceiling on the callable bond value. When yield fall, the call option becomes more valuable to the issurer up to the ceiling value; When yields rise, the value of a callable bond may not fall as much as that of a similar straight bond

Note:
Interest rate risk of FRN is lower than that of a fixed-coupon bond. Still, it exists due to: fixed coupon until the next reset period( time lag), fixed margin, change in credit quality, or the presence of a cap on the floating rate.

Interest rate risk

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Refer to how the bond price changes in response to the interest rate movement. The risk not only depends on direction of change in market interest rate but also its magnitude. When interest rates go up, investors’ bond prices fall. When interest rates go down, bond prices rise

Coupon rate < yield =""> Price < Par value {bond trades at a discount}
Coupon rate = Yield => Price = Par value {bond trades at par}
Coupon rate > Yield => Price > Par value {bond trades at a premium}

Financing the purchase of the bonds

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Repurchase agreements (a.k.a. repo):
One party (seller or security lender) sells a security to another (buyer or security borrower) with an agreement to buy it back at a specified price on a later date. Security lender does a repo, security borrower does a reverse repo.

Reverse repo:
Used by institutional investors in bond markets where it allows to finance a larger portion of the purchase price than margin buying.

If 1 day =>overnight repo
If >1 day => term repo

Margin buying:
· As a collateral loan by buying stock partly with cash and partly with a loan. It is more common for individual than institution.
· The Fed sets the cash component, or the margin, at 50%.

In equity markets, it is used by individual and institutional borrowers.

Cost of loan = Call money rate + service charge
where:
Call money rate is the rate the broker borrowed from bank & investor borrow from broker in turn at call money rate plus service charge

Embedded options

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Give the issuer or bondholder rights to dispose of or redeem a bond and can have a dramatic effect on the price of a security’s cash flow as well as its total return.

Options that Benefit the Issuer
Call options - allows the issuer to call the bonds prior to maturity if prevailing rates decrease enough to replace the existing issue with lower coupon bonds.

Prepayments - similar to call features and gives the issuer the right to repay principal ahead of scheduled repayment, in whole or in part.

Caps – A cap puts a maximum amount that an issuer has to pay in the face of rising interest rates for bond with floating interest rate.

Options that Benefit the Holder
Puts - give the bond bolder the right to receive principal repayment before maturity and help them dump their holdings and reinvest their proceeds at a higher rate as rates rise.

Floor - set a limit on the interest payment at a certain level even as market rates decline below the floor level.

Conversion option - give the right to bondholder to exchange for the issuer’s stock when the equity of the firm is outperforming the bonds.

Notes:
· If the option benefit the issuer, the yield increase.
· If the option benefit the bondhodler, the yield decrease.

Early retirement provisions

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Call provision
· state whether issuer can retire the bond before maturity date
o noncallable
o freely callable
o deferred call provision- initially noncallable but after which time it becomes callable.

Call schedule
· Call price represents a premium above par usually. If not being called, the call price will decline over price according to a schedule until reach par at maturity.

Refunding provision
· state whether issuer can call the bond using proceeds of a new debt issue

Nonrefundable bond
· typically freely callable but nonrefundable, prohibit premature retirement from proceeds of a lower coupon bond

Note:
· A bond can be callable with or without being refundable. But a refundable bond must be callable.
· A callable, refundable bond is the easiest one to call.
· A no-call provision in early years gives the investor some protection.

Scheduled retirement provisions

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Bullet maturity
· most common, pay entire principle in one lump sum at maturity.

Serial bonds
· bond maturity varies with serial numbers, very common in municipal market, actually made of a series of smaller bond with its own coupon & maturity

Amortizing bond
· principal repaid in installments e.g. mortgage backed/asset-backed securities

Sinking fund provision
· issuer required to retire bond issue according to a schedule, with two methods:
· Cash - issuer deposit required cash annually with the trustee who will retire the applicable proportion of bonds by using random bond selection method;
· Delivery – issuer purchase bond with total par value to be retired in the market and delivery them to trustee.

Accelerated sinking fund provision
· permit issuer to retire more than the annual stipulated sinking fund amount

Basic Features of Bonds

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Maturity:
Short Term - 1-5 years
Intermediate term - 5-12 years
Long term - over 12 years

Par Value
Dollar amount the holder will receive at the bond's maturity, usually $100 or $1,000

Coupon Rate
the interest rate the bond will pay the holders each year, paid in 2 semi-annual installments in the US, outside US mostly paid annually

Currency Denomination
The currency that the interest and principle will be paid in.

Yield
Refer to the actual return of the bond, on BEY basis

Price
Usually quoted as % of par value

Accrued interest
Interest earned since the last coupon payment date. It will be paid by the buyer to the seller along with the clean price of the bond.

Full price(dirty) = Clean price + Accrued interest

Bond Indenture

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A contract between a bondholder and the issuer stating the obligations and restrictions of the issuer and also the rights of bondholders.

Affirmative covenants
Refer to what the issuer promises to do for the investor, e.g pay interest and principle in a timely manner; paying taxes and other expenses.

Negative covenants
Refer to the restriction on on the borrower, e.g.. issue additional securities or taking on additional debt that may harm the current bondholders.

Price-to- Cash Flow (P/CF)

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P/CF = market value of equity / cash flow = market value per share / cash flow per share
Where: cash flow = CF, adjusted CFO, FCFE, or EBITDA

Advantages:
· Less manipulated than earnings
· Tend to be less volatile
· Studies have indicated that it is a reliable metric over the longer-term.

Disadvantages:
· Some items are not included, such as non-cash revenue.

Different cash flow measures are used for different purposes.
Earning plus non cash charges
= net income + depreciation + amortization

Cash flow from operations (CFO)

Adjusted CFO

As CFO includes the items relating to financing and investing activities, need to adjust by adding back the after-tax interest cost
Adjusted CFO = CFO – {net cash interest (1-tax rate)}

Free Cash Flow to Equity (FCFE)

Defined as cash available to shareholders after funding capital required, working capital needs, debt financing requirements. It is more volatile than straight cash flow.

FCFE = (net income + depreciation + new debt issues) – (Capital Spending + additions to working capital + principal repayments)

EBITDA
Represent a flow to both equity and debt.

Price-to-Sales (P/S)

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P/S = market value of equity / total sales = market price per share / sales per share

Advantages:
· Always positive, even for distressed firms
· Less manipulated
· Less volatile than P/E
· Useful for start ups and in mature or cyclical industries
· Studies has indicated low ratio outperform high ratio

Disadvantage:
· High sales growth does not guarantee high profit growth
· Does not reflect differing cost structures
· Revenue recognition can distort sales.

Price-to-Book Value (P/BV)

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P/BV = Market value of equity / book value of equity = market price per share / book value per share

Advantages:
· Usually positive
· More stable than P/E
· useful for finance and commodity firms and for firms that have negative earnings
· Studies have indicated low ratio outperform low ratio

Disadvantages:
· high P/BV can result from high amount of fixed assets at historic cost
· low P/BV can occur when assets (bad debts) with less than bookvalues
· BV does not include non-physical assets e.g. patents
· May not be comparable between companies
· Accounting conventions cause differing BVs
· Book value is not an accurate measure of actual market value.

Note:
· Book value is commonly adjusted to tangible book value and balance sheets are adjusted for significant off-balance-sheet assets and liabilities.

Price-to-Earnings (P/E)

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Trailing P/E = Market price per share / EPS over previous 12 months
Leading P/E = Market price per share / forecasted EPS over next 12 months

Advantages:
· Earning is a key determinant of value
· Easy to use
· Most commonly measure
· Studies have indicated a strong correlation to long-term average returns

Disadvantages:
· Not useful with negative earnings
· Earnings can be volatile
· Earnings are more easily manipulated

Earnings multiplier model

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P0/E1 - based on expected earnings, leading P/E ratio
P0/E0 - trailing P/E ratio

Leading P/E = Trailing P/E x[ 1/(1+g)]

Given the growth rate is constant, use DDM to determine P/E ratio as:
P0/E1 = (D1/E1) / (k - g)

P0= D1 / (k - g)
E1 = (1+g) E0
ROE = (net income /sales) (Sales / total assets) (total assets / equity)

P/E ratio increase if
· Increase dividend payout D1/E1
· Increase growth rate g
· Decrease k
· Increase ROE, g=ROE x retention ratio

Problem of using P/E analysis
· Earnings are based on historical caosst and with different quality
· Business cycle
· The model cannot be used if k is smaller than g