The market for bond and loans - measuring interest rates and returns

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The market for bond and loans - measuring
interest rates and returns

• Mishkin, Chap 4

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• Chap 4 discusses
• Measuring interest rate step I - concept of
  present value (PV)
• Measuring interest rate step II - classifying
  debt instruments according to timing and nature
  of payments and defining yield to maturity (YTM)
• Calculating YTM for different kinds of bonds and
  loans, relationship between YTM and other
  characteristics of an asset
• Simpler approximations of YTM current yield,
  yield on a discount basis concepts of nominal
  vs. real interest rates
• Interest rate vs. rate of return on bonds
  Interest rate risk

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• Measuring interest rate step I - Concept of
  Present value (PV)
• What is present value and why do we need it?
• Q Suppose you are promised a payment of 100 a
  year from now. Will you be as happy as if you
  were given 100 today? Why or why not?
• Most people have ______________. They value the
  future ________________, that is they ________
  the future.
• present value or PV of 100 received a year later
  
• Say you are as happy receiving 1 today as
  receiving 1.05 a year later.
• PV or value today of 100 received a year later
  
• General formula for PV

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Interest rates on debt assets are
. The
is one factor influencing
interest rates. Others are Say, the annual
interest rate on a Savings Account 10. 1
invested in SA today becomes, at the end of 1
year at the end of 2 years at the end of
n years If 1 invested today becomes
__________ n years later, the amount that we
need to invest today to get 1, n years later
is ___________. If interest rate i, the
amount we need to invest today to get 1, n
years later is ______________. PV of a cash
inflow of x, n years later, if the interest
rate today is i The PV is the amount you need
to
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• II . Measuring interest rate step II -
  defining yield to maturity (YTM)
• A debt asset pays unequal amounts at different
  points of time through out their terms.
• a 10-year US savings bond pays
• a 10-year US T-note pays
• a consol pays
• All payments need to be considered when
  determining an interest rate.
• Present Value of an asset
• Some numerical examples

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• Classifying debt assets
• 4 major types depending on the timing and broad
  nature of their payments
• Simple loans
• Fixed payment loans
• Coupon bonds
• Discount bonds

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• Major difference between loans and bonds
• interest rate on a loan or Yield To Maturity
  (YTM) is
• Formula
• interest rate on a bond or Yield To Maturity
  (YTM) is
• Formula

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• III. Calculating YTM on different types of
  debt assets
• 1. A simple loan pay 110 in a years time at a
  cost of 100 today.
• YTM
• A commercial borrower gets a loan of 1m today
  and pays back 2m, 5 years later.
• The annual interest rate he pays (YTM)
• 2. Suppose a car loan offers to pay 3000 every
  year for 5 years, at a cost of 10,000 today.
• The YTM or annual interest rate

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3. A coupon bond costing 850 (market price),
pays 100 yearly for 10 years, 1000 on
maturity (its face value). Its YTM 4.
A T-bill maturing a year from now, has a face
value of 1000 and a market price of 950
today. Its YTM The YTM on a
US-Savings bond which matures in15 years from
today, pays a face value of 1000 and costs
800 today
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Why do we choose to measure the interest rates on
debt assets as their yield to maturity? Fundament
al theorem (FT) of finance An asset is worth no
more or no less (to a rational investor) than its
present value in a competitive financial market.
In a competitive market therefore, the market
price of an asset PV You have 3000 to
invest with two options open a savings account
at 10 annually or lend to a (honest) friend who
promises to pay 1100 the first year, 1210 the
second year, 1331 the third year. Which is
better? Suppose the interest rate on the SA is
15. Your friend cannot change the payments but
is willing to accept a smaller or larger loan.
What would you do?
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The PV of an asset is what it takes to
____________________________ ____________________
______________________________________ The PV of
an asset is often described as the fundamental
worth of the asset. Suppose your friend has a
history of default. What would you do if the rate
on SA is 10 and the size of the loan is
negotiable? What is the fundamental worth of the
loan? FT in essence If the price of an asset
(P) is determined by market forces of demand and
supply, it settles at its fundamental value.
Why? Hence YTM assuming PPV, is the rate it
takes __________________________
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• Relationship between YTM and other
  characteristics of an asset
• C annual coupon payments, FV face value, P
  market price of a bond
• coupon rate for a coupon bond, r C/FV
• LV loan value or principal amount, FP annual
  fixed payment on a loan
• n term to maturity
• Given C, FV and n, as P increases, the YTM of a
  coupon bond
• Given FV and n, as P increase, the YTM of a
  discount bond
• Given LV, and n, as FP increases the YTM for a
  fixed payment loan
• Given FP and n, as LV increases, the YTM for a
  fixed payment loan

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• The following relationships can be proved
• When P FV, yield to maturity
  _______________.
• When P lt FV, yield to maturity
  __________________.
• When P gt FV, yield to maturity ___________________
  .
• Note The other way implications are also true.
• a consol or a perpetuity is a ____________________
  ________________.
• The YTM for a consol

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IV. Simpler approximations to YTM the Current
Yield on coupon bonds xc Obsv. 1. For a
consol _____________________________. In general
the longer the term to maturity of a bond
__________________________________________.
2. If P FV for a coupon bond
_________________________________. The closer P
is to FV, ________________________________________
______.
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• the nominal interest rate is the interest rate
  calculated
• the real interest rate is the
• Relationship between the two ir
  ________________, where
• The equation is known as _________________________
  .
• Real interest rates are more relevant for
  decision making because

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• V. Difference between YTM and the rate of return
  
• Most buyers dont hold on to their assets
  throughout their term to maturity, but carry them
  for shorter periods.
• Rate of return on a bond held for one period from
  date t to date t1
• where

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• Calculating the one period rate of return on a
  bond at date t
• If Pt 1 is known at date t, use formula on
  previous slide
• Pt 1 may not be known at date t it has to be
  calculated using the present value formula.
• Pt 1 present value of the asset over its
  remaining term to maturity starting at date t
  1, at the interest rate at date t 1.
• Example An asset pays 1000 at the end of year
  1, 1000 at the end of year 2, and 1000 at the
  end of year 3. Market interest rate is 5
  currently. At the end of year 1, it increases to
  8 and remains at that level for the next two
  years.
• P year 1
• Pyear 2
• If an investor buys the asset at the beginning of
  year 1 and sells it off at the beginning of year
  2, the one year rate of return is equal to

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• Properties of the rate of return on a bond
• RET differs from xc if __________________________
  _______________
• A rise in interest rates is accompanied by a
  ______ in bond prices for bonds whose terms to
  maturity are _______ than the holding period
• The ______ the term to maturity, the _______ the
  percentage ______.
• Prices and rates of return for longer term bonds
  are _______ volatile compared to prices and rates
  of return for shorter term bonds.
• interest rate risk is