Seminar in Finance

2. Type of Rates
Zero Rates
Measuring Interest Rates
01
04
02
03 Risk - free rate
Table of Contents
Bond Pricing
05

3. Forward Rates
Theories of the term
structure Interest rate
Duration
06
09
07
08 Convexity
Table of Contents

4. TYPES OF RATES

5. • The rates an investor earns on
Treasury bills and Treasury
bonds.
• The instruments used by the
government to borrow in its
own currency.
• Usually assumed that there is
no chance that a government
default on an obligation.
Treasury rates

6. • The rates at which banks lend
funds to each other at the end of
the day.
• To ensure the maintenance of
federally-mandated reserve
requirements.
• It is only available to the most
creditworthy institutions.
Overnight rates

7. • The difference between the price
at which securities are sold and
the (higher) price at which they
are repurchased.
• They are secured borrowing rates.
Repo rates

8. The most common type: overnight
repo (rolled over day to day)
• the borrower does not honor
the agreement => the lending
company simply keeps the
securities.
• the lender does not keep to its
side of the agreement => the
original owner keeps the cash.
Repo rates

9. • The benchmark interest rate at which major global banks lend to one
another for short-term loans.
• Compiled by asking banks to provide quotes estimating the rate of
interest at which they could borrow funds from other banks just before
11:00 a.m. (U.K. time).
• The banks submitting quotes typically had good credit ratings.
• LIBOR submissions by banks involved judgment and could be subject
to manipulation.
LIBOR rates

10. Question 1:
A. It is the same as the Treasury rate
B. It is an overnight interbank rate
C. It is a rate for which collateral is posted
D. It is a type of repo rate
Which of the following is true of the fed funds
rate?

11. Question 1:
A. It is the same as the Treasury rate
B. It is an overnight interbank rate
C. It is a rate for which collateral is posted
D. It is a type of repo rate
Which of the following is true of the fed funds
rate?

12. MEASURING
INTERES RATES

13. how interest rates are
measured
how to change the
compounding frequency
of interest rates

14. Daily Weekly Quarterly Annually
The compounding frequency used
for an interest rate is the unit of
measurement.
MEASURING INTEREST
RATES

15. MEASURING INTEREST
RATES
Suppose that an
amount A is invested for
n years at an interest
rate of R per annum.
If the rate is compounded once
per annum, the terminal value of
the investment is:

16. MEASURING INTEREST
RATES
Suppose that an
amount A is invested for
n years at an interest
rate of R per annum.
If the rate is compounded m
times per annum, the terminal
value of the investment is:

17. Compounding Frequency
Annual (m = 1)
Semiannually (m=2)
Quartely (m=4)
Monthly (m = 12)
Value of $100 at end of year (S)
110.00
Weekly (m = 52)
Daily (m = 365)
110.25
110.38
110.47
110.51
110.52
Effect of the compounding frequency on the value of $100 at
the end of 1 year when the interest rate is 10% per annum

18. CONTINUOUS COMPOUNDING
• The limit as the compounding frequency, tends to infinity is
known as continuous compounding.

19. CONTINUOUS COMPOUNDING
With continuous compounding, an amount A invested for n years at rate
R grows to:

20. • Compounding a sum of money at a
continuously compounded rate R for
n years involves multiplying it by:
• Discounting at a continuously
compounded rate R for n years
involves multiplying by:
CONTINUOUS COMPOUNDING

21. THE RISK - FREE RATE

22. THE RISK - FREE RATE
The risk - free rate is the rate of
return on an investment that has
a zero chance of loss.
01
02
It means the investment is so safe that
there is no risk associated with it.

23. U.S. Treasuries, which are
backed by a guarantee from
the U.S. government.

24. • Different countries and economic zones
use different benchmarks as their risk-
free rate.
• The rates on Treasury bills and Treasury
bonds are the correct benchmark risk-
free rates for derivative traders working
for financial institutions.
THE RISK - FREE RATE

25. Derivative traders usually
use LIBOR rates as short-
term risk-free rates.
This is because they regard
LIBOR as their opportunity
cost of capital.

26. • Treasury bills and Treasury bonds must be purchased by financial
institutions to fulfil a variety of regulatory requirements.
• The amount of capital a bank is required to hold to support an
investment in Treasury bills and bonds is substantially smaller
than the capital required to support a similar investment in other
very low-risk instruments.
• Treasury instruments are given a favourable tax treatment
compared with most other fixed-income investments because
they are not taxed at the state level.
TREASURY RATES ARE TOO LOW TO
BE USED AS RISK-FREE RATES

27. Question 2:
What does the risk-free rate represent in
finance?
A. The rate of return on a completely risk-free
investment
B. The highest possible return on an investment
C. The average return in the market
D. The rate of return on a high-risk investment

28. Question 2:
What does the risk-free rate represent in
finance?
A. The rate of return on a completely risk-free
investment
B. The highest possible return on an investment
C. The average return in the market
D. The rate of return on a high-risk investment

29. ZERO RATES

30. ZERO
RATES
• A zero rate (or spot rate), for maturity T is the rate of interest
earned on an investment that provides a payoff only at time T.
• Zero Rates are determined by bootstrapping, using market
price on Treasury Securities with different maturities

31. ZERO RATES
The outcome is a
Zero-Coupon Yield
Curve.

32. ZERO-COUPON
YIELD CURVE
Zero-Coupon
Treasury Yield
Curve
Zero-LIBOR
Zero-OIS Swap
Rate Yield
Curve

33. DETERMINING ZERO
RATES

34. The 1.5-year rate can be calculated by solvingRx0.25=> R=1.603% (per annum) => R=2.225% (per annum)
+ 2e => R=2.010% (per annum)
Bond
Principal
Time to
Maturity
(yrs)
Annual
Coupon
Bond price
($)
100 0.25 0 99.6
100 0.50 0 99.0
100 1.00 0 97.8
100 1.50 4 102.5
100 2.00 5 105.0
Using bootstrap method to determine zero rated
• The 3-month rate with
continuously compounded:
=> R=1.603% (per annum)
=> R=2.225% (per annum)
• The 1-year rate with
continuously compounded
• The 6-month rate with
continuously compounded:
=> R=2.010% (per annum)
Data for bootstrap method
• The 2-year zero rate
=> R=2.416% (per annum)
• The 1.5-year rate
=> R=2.416% (per annum)

35. DETERMINING ZERO
RATES
Using bootstrap
method to determine
zero rated.

36. BOND PRICING

37. BOND PRICING
• Most bonds pay coupons to the holder periodically.
• The bond's principal (which is also known as its par value or
face value) is paid at the end of its life.

38. BOND PRICING
The theoretical price of a
bond can be calculated
as the present value of all
the cash flows that will
be received by the owner
of the bond.

39. BOND PRICING
A more accurate approach
is to use the appropriate
zero rate for each cash
flow.

40. BOND YIELD
The bond yield is the discount rate
that makes the present value of the
cash flows on the bond equal to
the market price of the bond.

41. The par yield for a certain maturity is the coupon rate that causes
the bond price to equal its par value.
If m is the number of coupon payments per year, d is the present
value of $1 received at maturity and A is the present value of an
annuity of $1 on each coupon date
PAR YIELD

42. Question 3:
What is the relationship between bond prices and bond
yields?
A. Inverse: As prices rise, yields rise.
B. Direct: As prices rise, yields fall.
C. No relationship: Bond prices and yields move independently

43. Question 3:
What is the relationship between bond prices and bond
yields?
A. Inverse: As prices rise, yields fall.
B. Direct: As prices rise, yields rise.
C. No relationship: Bond prices and yields move independently

44. FORWARD RATES

45. FORWARD RATES
Forward interest rates are
the rates of interest implied
by current zero rates for
periods of time in the
future.

46. FORWARD RATES
Only approximately true
when rates are not
expressed with
continuous
compounding

47. INSTANTANEOUS
FORWARD RATE
The forward rate that
is applicable to a very
short future time
period that begins at
time T.

48. The 1-year and 2-year zero interest rate of a 10-year investment
is 3% per annum and 4% per annum respectively.
The forward rate for year 2:
EXAMPLE

49. FORWARD RATE
AGREEMENTS

50. FRA
An agreement to
exchange a
predetermined fixed rate
for a reference rate in the
market at a future time.

51. An FRA entered into sometime ago ensures that a company will
receive 4% (s.a.) on $100 million for six months starting in 1 year.
Forward LIBOR for the period is 5% (s.a.) The 1.5 year zero rate is
4.5% with continuous compounding.
The FRA is
EXAMPLE

52. DURATION

53. DURATION
A measure of how long
the holder of the bond
has to wait before being
repaid a bond’s price by
the bond’s total cash
flows.

54. Which one of the following statements regarding bond duration is
correct?
Question 4:
A. The duration of a coupon bond is simply the remaining term
to maturity of the bond.
B. The duration measures how long the holder of the bond has to
wait before being repaid a bond’s price by the bond’s total cash
flows
C. The yield duration of a bond measures the sensitivity of the
bond price to changes in yield to maturity on the bond.
D. B and C

55. Which one of the following statements regarding bond duration is correct?
Question 4:
A. The duration of a coupon bond is simply the remaining term
to maturity of the bond.
B. The duration measures how long the holder of the bond has to
wait before being repaid a bond’s price by the bond’s total cash
flows
C. The yield duration of a bond measures the sensitivity of the
bond price to changes in yield to maturity on the bond.
D. B and C

56. KEY DURATION
RELATIONSHIP
The approximate
relationship between
percentage changes
in a bond price and
changes in yield

57. KEY DURATION
RELATIONSHIP
If bond yields (y) is
expressed with
annual compounding

58. KEY DURATION
RELATIONSHIP
If bond yields (y) is
expressed with a
compounding
frequency of m times
per year

59. • The duration of a bond portfolio can be defined
as a weighted average of the durations of the
individual bonds in the portfolio, with the
weights being proportional to the bond prices.
• The key duration relationship for a bond
portfolio describes the effect of small parallel
shifts in the yield curve.
• By choosing a portfolio so that the duration of
assets equals the duration of liabilities, a
financial institution eliminates its exposure to
small parallel shifts in the yield curve.
BOND PORTFOLIOS

60. CONVEXITY

61. CONVEXITY
• The duration relationship applies
only to small changes in yields.
• For large changes in yields, the
percentage change in the price of
the bond depends on duration and
convexity.

62. CONVEXITY
The convexity of a bond
measures the curvature
of the relationship
between the price and
yield of the bond.

63. THEORIES OF THE TERM
STRUCTURE OF
INTEREST RATES

64. Expectations Theory Market Segmentation
Theory
Liquidity Preference
Theory
THEORIES TO DETERMINE THE SHAPE OF CURVE

65. EXPECTATIONS THEORY
long-term rates reflect expected future short-term rates.
MARKET SEGMENTATION THEORY
no necessary relationship between short, medium, and long-term rates.
LIQUIDITY PREFERENCE THEORY
investors prioritize short-term liquidity, leading to upward-sloping yield curves.

66. • Net interest income, the surplus of received interest overpaid
interest, requires careful management.
• As banks collectively adjust rates to address asset/liability
mismatches, liquidity preference theory becomes evident in their
strategic responses.
MANAGEMENT OF NET INTEREST INCOME

67. • Asset/liability mismatches present a significant liquidity risk for financial
institutions.
• A portfolio with mismatched maturities may encounter difficulties in
meeting short-term obligations, especially when faced with rising
interest rates.
• To address this risk, financial institutions utilize tools such as interest rate
swaps and strategic rate adjustments through derivatives, providing
crucial mechanisms for effective liquidity risk management.
LIQUIDITY AND THE RISKS

68. Question 5:
Which of the following is NOT a theory of the term
structure?
A. Expectations theory
B. Market segmentation
theory
C. Liquidity preference theory
D. Maturity preference theory

69. Question 5:
Which of the following is NOT a theory of the term
structure?
A. Expectations theory
B. Market segmentation
theory
C. Liquidity preference theory
D. Maturity preference theory

70. SUMMARY

71. SUMMARY
Traders frequently use continuous compounding when analyzing the
value of options and more complex derivatives.
Types of interest rates are quoted in financial markets
• The n-year zero or spot rate: is applicable to an investment lasting for
n years when all of the return is realized at the end.
• The par yield: the coupon rate that causes the bond to sell for its par
value.
• Forward rates: are applicable to future periods of time implied by
today's zero rates.

72. SUMMARY
The method most commonly used to calculate zero rates is known as the
bootstrap method.
A forward rate agreement (FRA) is an over-the-counter agreement where
an interest rate (usually LIBOR) will be exchanged for a specified interest
rate with both rates being applied to a predetermined principal over a
predetermined period.

73. SUMMARY
Duration measures the sensitivity of the value of a bond portfolio to a
small parallel shift in the zero-coupon yield curve.
Liquidity preference theory can be used to explain the interest rate term
structures that are observed in practice.

74. REVISION

75. WORD
SEARCH

76. Hint:
In a ..., a financial institution
that owns securities agrees to
sell the securities for a certain
price and buy them back at a
later time for a slightly higher
price.
WORD
SEARCH
1

77. Hint:
In a ..., a financial institution
that owns securities agrees to
sell the securities for a certain
price and buy them back at a
later time for a slightly higher
price.
WORD
SEARCH
1

78. WORD
SEARCH
Hint:
The rate of interest implied by
current zero rate for periods of
time in the future.
2

79. WORD
SEARCH
Hint:
The rate of interest implied by
current zero rate for periods of
time in the future.
2

80. WORD
SEARCH
Hint:
The measure of how long the
holder of the bond has to wait
before being repaid a bond’s
price by the bond’s total cash
flows
3

81. WORD
SEARCH
Hint:
The measure of how long the
holder of the bond has to wait
before being repaid a bond’s
price by the bond’s total cash
flows
3

82. WORD
SEARCH
Hint:
The ... theory indicates that
long-term interest rates should
reflect expected future short-
term interest rates.
4

83. WORD
SEARCH
Hint:
The ... theory indicates that
long-term interest rates should
reflect expected future short-
term interest rates.
4

84. WORD
SEARCH
Hint:
The benchmark interest rate at
which major global banks lend
to one another for short-term
loans
5

85. WORD
SEARCH
Hint:
The benchmark interest rate at
which major global banks lend
to one another for short-term
loans
5

86. WORD
SEARCH
Hint:
A ... ... for maturity T is the rate
of interest earned on an
investment that provides a
payoff only at time T.
6

87. WORD
SEARCH
Hint:
A ... ... for maturity T is the rate
of interest earned on an
investment that provides a
payoff only at time T.
6

88. WORD
SEARCH
Hint:
The method used to determine
zero rates.
7

89. WORD
SEARCH
Hint:
The method used to determine
zero rates.
7

90. THANK YOU!
- FROM GROUP 4 -