Functions of a Banks Security Portfolio

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Functions of a Banks Security Portfolio

• Stabilize the Banks Income
• Offset Credit Risk Exposure
• Provide Geographic Diversification
• Provide Backup Source of Liquidity
• Reduce Tax Exposure
• Serve as Collateral
• Hedge Against Interest Rate Risk
• Provide Flexibility
• Dress Up a Banks Balance Sheet

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Written Investment PolicyRegulator Guidelines

• The Quality or Degree of Default Risk Exposure
  the Institution is Willing to Accept
• The Desired Maturity Range and Degree of
  Marketability Sought for All Securities
• The Goals Sought for its Investment Portfolio
• The Degree of Portfolio Diversification the
  Institution Wishes to Achieve with its Investment
  Portfolio

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Money Market Instruments Used by a Bank

• Treasury Bills
• Short-Term Treasury Notes and Bonds
• Federal Agency Securities
• Certificates of Deposit
• Eurocurrency Deposits
• Bankers Acceptances
• Commercial Paper
• Short-Term Municipal Obligations

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Capital Market Instruments Used by a Bank

• Treasury Notes and Bonds Over One Year to
  Maturity
• Municipal Notes and Bonds
• Corporate Notes and Bonds
• Asset Backed Securities

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Other More Recent Investment Instruments

• Structured Notes
• Securitized Assets
• Stripped Securities

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Factors Affecting the Choice of Securities

• Expected Rate of Return
• Tax Exposure
• Interest Rate Risk
• Credit Risk
• Business Risk

• Liquidity Risk
• Call Risk
• Prepayment Risk
• Inflation Risk
• Pledging Requirements

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Default Risk

• Investment Grade
• Moodys SP
• Aaa AAA
• Aa AA
• A A
• Baa BBB

• Speculative Grade
• Moodys SP
• Ba BB
• B B
• Caa CCC
• Ca CC
• C C

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Interest Rate Risk

• Rising Interest Rates Lowers the Value of
  Previously Issued Bonds
• Longest Term Bonds Suffer the Greatest Losses
• Many Interest Rate Risk Tools Including Futures,
  Options, and Swaps Exist Today

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Bond valuation

• The value (or price) of a bond is the present
  value of the cash flows to be received form this
  security.

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Example

• What is the price of a 5 year 7 coupon bond with
  a face value of 1000 if the market yield on
  similar bonds is 6 and the bond pays semiannual
  coupons?
• Coupon 70 so two 35 semiannual coupons
• Pm 298.56 744.09 1042.65 or 104.26
  percent of par

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Bond yields

• A bond yield is a measure of the return on a bond
• There are several different yield measures that
  bond traders use. Each serves a different purpose

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Bond yields

• Nominal Yield
• This is simply the coupon rate of a particular
  issue. If a bond has a coupon rate of 9 its
  nominal yield is 9
• Current yield (CY)
• The current yield is the current percent of the
  market price the bonds coupon represents
• CY Ci/Pm
• Example A 7 coupon bond priced at 970 has a
  curent yield of CY 70/970 7.22

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Bond yields

• Promised yield to maturity (YTM)
• This is the most common yield figure quoted for
  bonds
• The YTM is the total return an investor can
  expect to earn if two assumptions hold
• The bond is held until maturity
• All coupons are reinvested at the YTM

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Bond yields

• Promised yield to maturity (YTM)
• To calculate the YTM use the valuation formula
  from before
• Instead of determining the proper i and solving
  for Pm we use the quoted market price and solve
  for i. The i found in this manner gives you the
  YTM
• The procedure described above gives an exact
  measure of the YTM
• This procedure requires an iterative process, you
  must plug in different values of i until you
  equate the cash flows and the market price

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Bond Yields

• Approximating the YTM

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Example

• What is the APY for a 9 coupon bond with 10
  years until maturity selling for 925?
• APY 97.5/987.5 9.87
• YTM (actual) 10.21
• The APY generally gives a lower than actual yield
  but ranks bonds in the same order as the YTM.

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Bond Yields

• YTM for a zero coupon bond
• Pzero Par/(1i)n

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Bond Yields

• Promised yield to call (YTC)
• The YTM might give a misleading measure for bonds
  that have a call feature
• Bonds that are likely to be called will have
  shortened maturity and a lower yield then a
  similar bond that is not called.
• For this reason, the promised yield to call is
  often determined for bonds whose price is above
  par (premium bonds).

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Bond Yields

• Promised yield to call (YTC)
• The promised YTC is determined exactly as the YTM
  except the call price of the bond is substituted
  for par and the time until the bond is callable
  is substituted for maturity.

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Bond Yields

• Promised yield to call (YTC)
• Example What is the YTC for a 11 bond that is
  callable in 5 years at a price of 1110 and is
  currently selling for 1050?
• AYC 122/1080 11.3
• Actual YTC 11.356

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Bond Yields

• Realized Yield (Horizon yield)
• The realized yield measures the return an
  investor can expect to earn for an investment
  held to less than the maturity date of the bond
• The realized yield also measures actual returns
  to a bond position after the bond is sold.

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Bond Yields

• Realized Yield (Horizon yield)
• The realized yield is a good measure but requires
  us to estimate
• The selling price of the bond
• The reinvestment rate for coupons
• We can calculate an approximate realized yield in
  the same way we calculated the approximate YTM
  and YTC
• The difference is we replace the par value with
  the expected selling price and the maturity with
  the expected investment horizon.

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Bond Yields

• Example
• What is the approximate realized yield on a 8
  bond with an expected selling price in five years
  of 1050 a current price of 930?
• ARY 104/990 10.50
• RY 10.624

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Bond Yields

• Realized Yield (Horizon Yield)
• Both the ARY and the actual realized yield
  calculated using the present value formula assume
  coupons can be invested at the realized yield.
• If we are calculating actual returns or want to
  estimate RY with more reasonable assumptions we
  can use an alternative method.
• The alternative method compares ending wealth to
  beginning wealth to measure returns.
• This method allows for differing assumptions
  about coupon reinvestment rates

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Example

• What is the realized yield on a 10 bond that we
  bought for 1030 two years ago and sold for 1100
  if we reinvested all coupons at a 6 annual rate?
  Assume the coupon is paid semiannually.
• First determine the ending wealth
• Coupon one 35 (1.03)3 38.245
• Coupon two 35 (1.03)2 37.13
• Coupon three 35 (1.03) 36.05
• Coupon Four 35
• Selling price 1100
• Ending wealth 38.24 37.13 36.05 35 1100
  1246.42

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Example

• RY ((EW/Pm)1/2n 1) 2
• RY ((1246.42/1030)1/4 1) 2 9.767

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Interest rate risk

• Remember bond yields and prices are inversely
  related.
• Because of this the largest risk to bond
  investors is the risk associated with changes in
  interest rates.
• The amount of exposure a bond has to interest
  rate changes is called interest rate risk

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Interest rate risk

• Since interest rate risk is so important to bond
  returns, it is important to have an accurate
  measure of interest rate risk.
• The true measure of bond price volatility is to
  measure the percentage change in a bonds price
  for a given change in interest rates.

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Interest rate risk

• The relationship between price and yields
• Price and yields are inversely related for all
  bonds
• Price volatility is directly related to term to
  maturity
• Price volatility increases at a decreasing rate
  as term to maturity increases

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Interest rate risk

• The relationship between price and yields
• Bond price volatility is inversely related to
  coupon payments
• Price movements due to changes in yields are not
  symmetric
• Decreases in yields raise prices more than
  increases in yields drop prices

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Trading strategies if interest rate movements are
known

• If we know interest rates will increase we would
• Know prices will decrease
• Want to buy bonds with the least sensitivity to
  interest rate movements
• If interest rates will decrease we would
• Know prices will increase
• Want to buy bonds that are most sensitive to
  interest rate movements

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Duration measures

• Duration is a measure of the interest rate
  sensitivity of a bonds price
• It is a composite measure of the timing of a
  bonds cash flow characteristics taking into
  consideration its coupon and term to maturity

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Duration measures

• Macaulay Duration (MD)
• Basically, MD comes from taking the first
  derivative of the bond price with respect to the
  yield
• MD is a time weighted measure of when cash flows
  are received for a bond

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Duration measures

• MD
• The denominator of the formula is simply the
  price of the bond
• The numerator weights the cash flows received by
  the year in which they are received to give you
  duration

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Example

• What is the duration of a 3 year, 9 bond with a
  YTM of 6?
• MD 2928.54/1081.26 2.71

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Duration measures

• Relationship between MD and bond characteristics
• 1. Duration is inversely related to the coupon
  rate
• 2. There is generally a positive relationship
  between duration and the term to maturity
• 3. Duration is always less than or equal to
  maturity
• 4. There is an inverse relationship between YTM
  and duration

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Duration measures

• Modified duration
• Modified duration Dmod MD/(1i/2)

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Example

• The modified duration for a bond with a YTM of
  10, a duration of 6 that pays semiannual
  interest is
• Dmod 6/(1.05) 5.714

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Duration measures

• Modified duration
• Modified duration can be used to approximate the
  change in the price of a bond for a small change
  in interest rates
• Specifically ?P/P x 100 -Dmod x ?i
• This means the percentage change in price is
  equal to the change in interest time the modified
  duration

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Example

• Assume we expect interest rates to fall 45 basis
  points (i.e. the YTM falls form 10 to 9.55),
  what is the approximate percentage change in the
  price of the bond in the previous example whose
  modified duration was 5.714?
• ?P/P x 100 -Dmod x ?i
• change in P -5.714 x 45/100 2.571
• The bond price will increase approximately 2.5
  when interest rates fall by 45 basis points

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Duration measures

• Trading strategies based on modified duration
• If a bond portfolio manager expects interest
  rates to fall then he or she should lengthen the
  average duration of the bonds in the portfolio as
  much as possible.
• If interest rates are expected to increase, the
  average duration should be lowered as much as
  possible.

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Bond Convexity

• The relationship between modified duration and
  interest rate changes only holds for small
  changes in interest rates
• The formula for changes in price using the
  modified duration approach assumes price changes
  are linearly related to interest rate changes
• The actual relationship between price changes and
  interest rate changes is curvilinear.

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Bond Convexity

• The amount of curve in the relationship between
  interest rate changes and price changes is called
  the convexity of a bond and determines how badly
  the modified duration approach misestimates bond
  price changes.

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Bond Convexity

• Mathematically, convexity amounts to finding the
  second derivative of the bond pricing formula
  with respect to the yield

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Bond Convexity

• Equation

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Example

• What is the convexity of a 3 year, 9 bond with a
  YTM of 6?
• Con 11353.62/1081.26 10.50

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Bond Convexity

• Determinants of convexity
• There is an inverse relationship between coupon
  and convexity
• There is a direct relationship between maturity
  and convexity
• There is an inverse relationship between yield
  and convexity.

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Bond convexity

• Summary of price effects when interest rates
  change
• For small interest rate changes, the modified
  duration explains almost the entire change in a
  bonds price
• For large changes in interest rates and very
  convex bonds it is important to realize the bond
  price change will be effected by both its
  duration and its convexity.

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Bond convexity

• The change in price attributable to convexity can
  be written as
• P change due to convexity ½ x Price x Convexity
  x (? in yield)2

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Investment Maturity Strategies

• The Ladder or Spaced-Maturity Policy
• The Front-End Load Maturity Policy
• The Back-End Load Maturity Policy
• The Barbell Strategy
• The Rate Expectation Approach

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