Fixed Income Securities

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Fixed Income Securities and their Derivatives
2
Money Markets
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Objectives for Session 2

• To understand the scope of the money market
• To understand differences between the money and
  bond markets
• To understand the various concepts of yield
  employed in the money markets
• To understand money market quotes
• To understand the main features of the Fed funds
  and RP markets

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The Money Market

• Securities traded in the money market are
• Short-term
• Rated investment grade or better
• Actively traded
• Less volatile than bonds

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The Money Market

• Examples
• Short term governments
• Bankers acceptances
• Domestic and Eurodollar CDs
• Fed funds
• RPs

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Concepts of Yield

• Measurement issues
• Basis
• Days
• Interest accrual
• Three conventions
• Discount basis
• Simple interest basis
• Compound interest

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Some Notation
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Discount Basis

• The discount yield on a single payment security
  is defined as
• The difference between the amount payable at
  maturity and the price of the security now
• Divided by the amount payable at maturity

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Example
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Annualized Discount Yield

• To annualize, multiply the raw discount yield by
  the number of investment periods in a year
• Convention 1 year 360 days

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Example
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For Example
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Price of a Discount Security

• Given a quoted discount yield of d, the price of
  a security with face value F is

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For Example
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The Value of an 01

• The value of an 01 measures the price change
  caused by a .01 (one basis point) change in the
  discount yield
• The value of an 01 indexes risk
• For 1,000,000 face value of a 90-day security,
  the value of an 01 is 25

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Quick Check

• What would be the value of an 01 for 1,000,000
  face value of a 180-day security?
• Of 1,000,000 face value of a 360-day security?
• Which of the three securities (90-day, 180-day,
  360-day) is most sensitive to changes in interest
  rates?
• How is this sensitivity related to risk?

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Simple Interest Yield

• The simple interest yield is defined as
• The difference between the amount payable at
  maturity and the price of the security now
• Divided by the price of the security now
• Annualized using either 360-day or 365-day year

When the simple yield is annualized using a
360-day year, it is called a money market yield
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Example
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Relation to Discount Yield

• The simple yield on a security having a discount
  yield of d is

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Quick Check

• Would you prefer an investment offering
• A simple yield (365-day year) of 8, or
• A money market yield of 8?
• For given F, P, settlement date and maturity
  date, which is greater
• The discount yield
• The simple yield
• The money market yield

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Simple Interest

• If you invest P at the simple yield y for a
  period of tsm days, how much will you receive at
  the end of the period?
• From the formula for simple yield

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Simple Interest

• Similarly, if you invest P at the simple yield y
  for a fraction 1/n of a year, how much will you
  receive at the end of the period?
• From the formula for simple yield

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Example
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Compound Interest

• If you invest P at the simple yield y for a
  fraction 1/n of a year,
• And then reinvest the result at the same yield
  for another 1/n years, how much will you receive
  at the end of the period?

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Compound Interest

• If you continue reinvesting for a whole year, at
  the end of the year you will receive

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Effective Interest

• The effective yield on a compounded investment is
  the amount the investor ends up with at the end
  of the year less the amount he invested at the
  beginning of the year divided by the amount
  invested at the beginning of the year

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Example
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Effective Interest

• The more frequent the compounding, the higher the
  effective yield

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Effective Interest

• The effect of compounding is greater the higher
  the simple yield

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Short Investment Period

• Occasionally, we want the effective yield on an
  investment held for less than a full year.
• If there are n compounding periods during a full
  year and m compounding periods during the
  investment period, we use the formula

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Bond Equivalent Yield

• In the US, bonds pay interest semi-annually, but
  bond yields are quoted as simple interest.
• For example, a bond paying 8 actually pays
  interest of 4 (8/2) twice yearly.
• The effective yield on this bond would be

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Quick Check

• Would you rather have a one-year investment that
  pays 8.15 simple interest or one that pays 8
  compounded monthly? Explain.
• Why are effective yield greater than simple
  yields?
• Is a bond equivalent yield an effective yield?

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Application Treasury Bills

• Review
• What are T-bills?
• When are they issued?
• How are they sold in the primary market?
• How are they traded in the secondary market?
• Inside and outside markets
• WI trading
• On the run and off the run issues

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T-Bill Rates

• T-bills are quoted as bid and asked discount
  yields to two decimal places
• Bid what dealers are offering to pay for bills
• Ask what dealers are willing to sell bills for
• The quoted discount yields imply prices

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Example
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T-Bill Ask Yields

• The ask yield quoted for T-bills is a bond
  equivalent yield.
• BEQs understate effective yields for investments
  with more than 1/2 year to maturity
• For T-bills with less than 182.5 days to
  maturity, the ask yield is the simple yield

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T-Bill Ask Yields

• But the simple yield is bigger than the BEQ for
  bills with more than 182.5 days to maturity
• The simple yield is an effective yield for the
  life of the T-bill the BEQ understates the
  effective yield
• The correct formula introduces the right amount
  of understatement

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Application Repo

• A repurchase agreement, or repo, is a single
  transaction consisting of
• A spot portion in which a security is sold for
  cash and
• A forward portion in which the security is
  repurchased for later settlement
• Repo can be for overnight, term or open

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Repo
Collateral
Securities Dealer

• Investor

Day 1
Cash (Principal)
Collateral
Securities Dealer
Investor
Day 2
Cash (Principal Interest)
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Repo
Collateral
Securities Dealer

• Investor

Day 1
Cash (Principal)
At settlement, the collateral is sold for cash to
the investor.
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Repo
Collateral
Securities Dealer

• Investor

Day 2
Cash (Principal Interest)
At maturity, the dealer repurchases the
collateral for cash. The extra cash paid at
maturity is interest and is determined by the
repo rate.
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Example
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Repo Mechanics

• Margin
• Margin is collateral in excess of the principal
  amount of the transaction
• Demanded to limit credit exposure
• Typically 1 to 3 (5 to 10 for riskier
  collateral)
• Example If margin is 2, a dealer would deliver
  10.2 million (market value) of collateral
  against a principal amount of 10 million.

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Example T-bill Margin
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Repo Mechanics

• Marking to Market
• Collateral may be marked to market and the trade
  adjusted
• Margin call If collateral value declines
  additional collateral may be required to restore
  the original margin. (Dealer delivers more
  collateral to investor.)
• Repricing If collateral value declines, the
  principal amount of the transaction can be
  reduced to restore the original margin. (Dealer
  wires cash back to investor.)

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Repo Mechanics

• Collateral
• Substitution
• Dealer may request the investor to return the
  original collateral in exchange for different
  collateral having the same market value
• If collateral cannot be substituted, it is
  special
• Cash flows
• The repo seller is entitled to receive any
  interest or principal payments off the collateral

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Repo Mechanics

• Collateral
• Delivery
• Outright Seller delivers the collateral to the
  buyer. Buyer returns the collateral at maturity.
• Safekeeping Seller holds the collateral for the
  buyer. Also known as letter repo or held in
  custody repo.
• Third party Seller delivers collateral to
  purchasers custodial account at sellers
  clearing bank.

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Reverses

• A reverse is a repo viewed from the perspective
  of the counterparty lending cash
• There are two reasons for doing reverses
• Investors seeking short-term relatively safe
  investments may invest in repo.
• Traders seeking to cover a short position in a
  security may borrow the needed securities by
  doing a reverse for specific collateral

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Repo Rates

• General collateral rates
• Relation to the Fed funds rate
• Specials
• Rates can go special when there is strong demand
  for specific collateral
• Example Traders as a group build up a sizeable
  short position in a particular issue.

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Repo Books

• Dealers often work both sides of the market,
  doing repo with one group of investors and
  reverses with another.
• In a matched book, a dealer reverses in
  securities from one party, repos them out to
  another party, and profits from the spread.

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For Example

• A Brazilian bank finances some of its Brazilian
  Brady holdings by doing a repo with a dealer in
  New York for LIBOR 1
• The repo dealer in New York uses the collateral
  to do a repo with an American investor for LIBOR
• The dealer pockets the spread (1)

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Application Tailing

• If you buy a 90-day T-bill and hold it for 30
  days, it becomes a 60-day bill.
• To create a T-bill tail
• Buy a T-bill with t1 days to maturity
• Finance it for t2 days with term repo
• Inherit a T-bill with t1 - t2 days to maturity
  when the financing comes off.
• Dealers use this strategy to buy T-bills forward

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For Example
A dealer creates an 83-day bill tail
In effect, the dealer purchases the 83-day bill
for a rate of 4.41
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Quick Check

• The 91-day T-bill is quoted at bid 6.06 and ask
  6.05. How much would a customer have to pay to
  acquire 1,000,000 face value of the bill?
• Explain the mechanics of a repo transaction.
• What is margin in the repo market? Why is it
  needed? How does it vary by collateral?
• How do repo rates go special?

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Review

• Scope of the money market and relation to bond
  market
• Three bases for measuring yield
• Effective yield
• Details of the T-bill market
• Mechanics of the RP market

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Next
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Bonds, Bonds, Bonds