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• Money market instruments
– Basic features: Short-term debt obligations
of large corporations and governments that
mature in a year or less. Highly liquid and
relatively low-risk debt instruments.
– Examples
• T-bills: short-term (91 days, 182 days, and
52 weeks) highly liquid US government
securities issued at a discount from the
face value and returning the face amount
at maturity. Minimum denominations of
$10,000
• Commercial paper: short-term unsecured
debt issued by large corporations.
Fixed-income securities: longer-term (at least
1 year) debt obligations of corporations and
governments that promise to make
semiannual coupons and returning the face
value at maturity.
Ex)
• Treasury bonds or notes:
T-note maturities range up to 10 years
(currently 2, 5, and 10 years), while T-bonds
have 10 to 30 years. Minimum
denominations of $1,000.
Treasury Inflation Protected Securities (TIPS)
In Jan. of 1997, the US Treasury started selling
securities (both notes and bonds) whose coupon
rate adjusted periodically with the change in
the rate of inflation.
Changes in inflation rate are reflected in the
principal and not the coupon rate. The
inflation-adjusted principal is multiplied with
the coupon rate to computed the interest
payments to investors. These adjustments are
made semi-annually.
e.g) Suppose that a TIPS purchased July 1 has a
coupon rate of 3%. The par value of the
principal is $100,000. Assume that annualized
inflation is 4% for the next six months.
The inflation-adjusted principal:
The semi-annual inflation rate is 4%*0.5 = 2%.
This is applied to the principal of $100,000
which gives the inflation adjusted principal of
$100,000 (1+0.02) = $102,000
Semiannual coupon payment:
102,000*0.015 = $1,530
• Municipal securities (Munis)
Debt issuances by state and local governments in
the U.S.
Interest income from these securities is exempt
from U.S. Federal taxes but capital gains are
not.
General obligation munis (GOs) are backed by
the “full faith and credit” of the taxing
governmental unit
Revenue bonds are supported through revenues
generated from projects that are funded with the
help of the original bond issue.
• Investment securities are defined as
those securities with maturities greater
than one year
Q) Why are Treasury bills not considered
to be investment securities?
ANSWER: Because they are short-term
money market instruments with maturities
less than one year. They are held more for
liquidity purposes than for investment
income.
•
The composition of the securities portfolio of
all U.S. commercial banks in 1998
1. U.S. government agency securities (that are not
direct obligations of the U.S. Treasury but
nonetheless are federally sponsored or
guaranteed): about 10% of total assets
2. U.S. Treasury (2.2%) Other (2.5%)
3. State and local government (0.9%)
Evaluating Investment Risk
1. Credit risk
Default risk: The possibility that the issuer will fail
to meet its obligations under the indenture.
While the bond market views default as the
lack of timely payment of interest and
principal, technical default may occur due to
the issuer’s violation of other terms of the
indenture.
Downgrade risk: the risk that a bond is reclassified
as a riskier security by a credit rating agency.
When an issue is downgraded, the yield adjusts
immediately to reflect the new rating.
2. Reinvestment risk
When bond investors receive coupon payments, they bear
the risk of reinvesting them at a rate of return or yield
that is lower then the promised yield on the bond. This
is known as reinvestment risk. The risk is present to a
greater extent for those investors who depend on a
bond’s coupon for most of their return. Reinvestment
risk becomes more problematic with longer time
horizons and when the current coupons being reinvested
are relatively larger. Reinvestment is minimized with
low or zero-coupon bond issues or when time horizons
are short.
– Call risk
Bonds that can be redeemed by the borrowing
firm prior to maturity.
Call deferment period must expire.
Also, bond’s price must be greater than or
equal to the call price.
Call risk related to reinvestment risk, as
bonds are typically called during low interest
rate periods.
Call premium paid as compensation for
reinvestment risk.
3. Liquidity risk
It represents the likelihood that an investor will be unable
to sell the security quickly and at a fair price.
If the price fluctuates widely from transaction to
transaction in the absence of interest rate and other
changes, the security is said to trade in a market that is
not liquid.
Quantitatively, liquidity risk can be estimated through the
Bid-ask spread. High spreads signal an illiquid market.
Investors like liquid markets so that they can buy and
sell securities quickly and at a fair price.
4. Yield curve risk
A bond is made up of several coupon payments
over its term. Each coupon payment can be
viewed as a separate zero coupon bond. A
different discount rate or yield applies for each
cash flow payment date.
Usually these individual discount rates do not
change by the same amount. Shifts in the yield
curve of any kind are of concern to bond
investors and present a source of uncertainty.
The risk associated with the yield curve is known
as yield curve risk.
The U.S. Treasury Yield Curve
When the yields on different Treasuries are
plotted against their corresponding maturities,
the resulting graph is known as the Treasury
yield curve.
U.S. Treasuries are used as a benchmark for
computing yields on risky bonds. For a given
maturity, a risk premium is added to the
corresponding maturity Treasury security to
arrive at the yield for a risky bond.
Under the normal economic conditions, this curve
is upward sloping and is also called the normal
yield curve.
An inverted or downward sloping yield curve (i.e.
shorter term interest rates exceeding longer
term interest rates) is sometimes observed
during economic contractions.
The term structure of interest rates is a graphic
representation of yields to maturity versus time
until maturity using zero-coupon Treasury
strips instead of Treasury coupon securities as a
basis for comparison.
Treasury strips are created by investment bakers
who strip off payments and sell them separately
from the rest of the bond. This process creates
a series of “zero coupon” securities. Zeros do
not suffer from reinvestment rate risk since
there is no cash flow until maturity. This
method provides a better relationship between
yields and different maturities.
Yield spread
Although the yield spread has been defined as the
difference between the yield on a non-treasury
security and a benchmark Treasury security of
the same maturity, it can also be defined for
any two bonds, even if both are non-treasury
issues.
Yield spread = yield on bond 1 of maturity t –
yield on bond 2 of maturity t
There are three ways in which yield spread can be
quantified.
a. Absolute yield spread
b. Relative yield spread
This quantifies the absolute yield spread as a
percentage of the reference yield
c. Yield ratio = yield on bond 1 / yield on bond 2
= relative yield spread + 1
Consider two bonds X and Y. Their respective
yields are 6.5% and 6.75%. Using bond X as
the reference bond, compute the absolute yield
spread, the relative yield spread and the yield
ratio.
Absolute yield spread = 6.75% -6.5% = 0.25% or
25 basis points
Relative yield spread = 0.25%/0.65% = 0.038
Yield ratio = 6.75% / 6.5% = 1.038 = 0.038 +1
Absolute yield spread may stay the same even if
interest rates are rising or falling.
This could be misleading, since as a percentage of
the benchmark rate, the spread is declining.
This effect can only be captured by the relative
yield spread or the yield ratio.
As verification of this, suppose the absolute
spread stayed constant at 25 basis points, but
the reference rate rose to 7.5%. The relative
spread would fall to 25/750 = 0.0333.
Theoretical spot rates
The use of a single discount factor (i.e. YTM) to
value all bond cash flows assumes that interest
rates do not vary with term to maturity of the
cash flow.
In practice, this is usually not the case - interest
rates exhibit a term structure, meaning that
they vary according to time to receipt of the
cash flow.
Consequently, YTM is really an approximation or
weighted average of a set of spot rates (a spot
rate is an interest rate used to discount a single
cash flow to be received in the future).
Forward rates
Spot interest rates are the result of market participant’s
tolerance for risk and their collective view regarding
he future path of interest rates. If we assume that
these results are purely a function of expectations
(called the expectations theory of the term structure
of interest rates) we can use spot rates to estimate the
market’s consensus on future interest rates.
Based on the expectations theory, investors earn the
same return regardless of their holding period. So,
investor would earn the same amount by either
purchasing a two-year bond and holding it for two
years or purchasing a one-year bond now and another
one-year bond next year.
e.g) Suppose that you have a two-year time
horizon and are offered the choice between
locking in a 2-year spot rate of 8.167 percent or
investing at the 1-year spot rate of 4% and
rolling over your investment at the end of the
year into another 1-year security.
5. Price Risk/Interest Rate Risk
Duration
• Modified duration
• Using modified duration to estimate a price
change
• Effective duration
• Portfolio duration
• Convexity
• Estimating the convexity effect
Investment strategies
• Passive investment strategies
Space-maturity approach (or ladder
approach)
Spread available investment funds
evenly across a specified number of
periods within the bank’s investment
horizon.
Simple and low transactions costs, but
passive with respect to interest rate
conditions and liquidity is sacrificed to
some extent.
Split-maturity approach (or barbell approach)
Greater quantities of short-term and
long-term securities are held.
This strategy balances liquidity and
higher income.
Can adapt to front-end loaded and backend loaded approaches.
Investment strategies
• Passive investment strategies
Ladder Approach
$10 $10
$10
$10
$10
Barbell Approach
$20
1 yr
$10
$20
2 yrs 3 yrs 4 yrs 5 yrs
Maturities of Securities
10.16 Why might the split-maturity approach to
investment management be preferred to the
spaced-maturity approach?
ANSWER: The spaced-maturity approach evenly
spreads the investments of the bank over time into
different maturity ranges. This approach to
investment management sacrifices higher yields
on longer-term securities as well as liquidity in
terms of holding shorter-term liquid securities.
The split-maturity approach overcomes these
drawbacks by allocating larger proportions of the
investment portfolio to both shorter-term and
longer-term securities. This balances both earnings
and liquidity goals of the bank.
Investment strategies
• Aggressive investment strategies
– Yield curve strategies
"Playing the yield curve" involves changing the
maturity structure of the investment portfolio as
interest rates change.
When interest rate levels are relatively low, the bank
will purchase shorter-term securities. These securities
are gradually rolled over into higher-yielding
securities as interest rates rise in the future.
When interest rate levels are peaking out,
maturing securities are rolled over into longerterm securities to lock in high yields as well as
to possibly earn a sizable capital gain as interest
rates fall in the near future.
Riding the yield curve -- assumes that the
yield curve will not move in the near
future. Example: assume that the yield
curve is upward sloped. Buy securities
and hold them so that their maturity
decreases and (due to the shape of the
yield curve) their yields decline (prices
rise). Sell for a capital gain.