1. THE VALUATION OF RISKLESS SECURITIES
CHAPTER FIVE
THE VALUATION OF RISKLESS SECURITIES

2. INTEREST RATES NOMINAL V. REAL INTEREST RATES Nominal interest rates:
represent the rate at which consumer can trade present money for future money

3. INTEREST RATES NOMINAL V. REAL INTEREST RATES real interest rate
the rate of return from a financial asset expressed in terms of its purchasing power (adjusted for price changes).

4. YIELD TO MATURITY CALCULATING YIELD TO MATURITY : AN EXAMPLE
Suppose three risk free returns based on three Treasury bonds:
Bond A,B are pure discount types;
mature in one year
Bond C coupon pays $50/year;
matures in two years

5. YIELD TO MATURITY Bond Market Prices: Bond A $934.58 Bond B $857.34
Bond C $946.93
WHAT IS THE YIELD-TO-MATURIYTY OF THE THREE BONDS ?

6. YIELD TO MATURITY YIELD-TO-MATURITY (YTM)
Definition: the single interest rate* that would enable investor to obtain all payments promised by the security.
very similar to the internal rate of return (IRR) measure
* with interest compounded at some specified interval

7. YIELD TO MATURITY (1 + rA) x $934.58 = $1000 rA = 7% CALCULATING YTM:
BOND A
Solving for rA
(1 + rA) x $ = $1000
rA = 7%

8. YIELD TO MATURITY (1 + rB) x $857.34 = $1000 rB = 8% CALCULATING YTM:
BOND B
Solving for rB
(1 + rB) x $ = $1000
rB = 8%

9. YIELD TO MATURITY (1 + rC)+{[(1+ rC)x$946.93]-$50 = $1000 rC = 7.975%
CALCULATING YTM:
BOND C
Solving for rC
(1 + rC)+{[(1+ rC)x$946.93]-$50 = $1000
rC = %

10. SPOT RATE
DEFINITION: Measured at a given point in time as the YTM on a pure discount security

11. SPOT RATE SPOT RATE EQUATION: where Pt = the current market price of a
pure discount bond maturing in t years;
Mt = the maturity value
st = the spot rate

12. DISCOUNT FACTORS
EQUATION:
Let dt = the discount factor

13. DISCOUNT FACTORS EVALUATING A RISK FREE BOND: EQUATION
where ct = the promised cash payments
n = the number of payments

14. FORWARD RATE
DEFINITION: the interest rate today that will be paid on money to be
borrowed at some specific future date and
to be repaid at a specific more distant future date

15. FORWARD RATE EXAMPLE OF A FORWARD RATE
Let us assume that $1 paid in one year at a spot rate of 7% has

16. FORWARD RATE EXAMPLE OF A FORWARD RATE
Let us assume that $1 paid in TWO yearS at a spot rate of 7% has a

17. FORWARD RATE
f1,2 is the forward rate from year 1 to year 2

18. FORWARD RATE
To show the link between the spot rate in year 1 and the spot rate in year 2 and the forward rate from year 1 to year 2

19. FORWARD RATE
such that or

20. FORWARD RATE
More generally for the link between years t-1 and t: or

21. FORWARD RATES AND DISCOUNT FACTORS
ASSUMPTION:
given a set of spot rates, it is possible to determine a market discount function
equation

22. YIELD CURVES
DEFINITION: a graph that shows the YTM for Treasury securities of various terms (maturities) on a particular date

23. YIELD CURVES TREASURY SECURITIES PRICES
priced in accord with the existing set of spot rates and
associated discount factors

24. YIELD CURVES SPOT RATES FOR TREASURIES One year is less that two year;
Two year is less than three-year, etc.

25. YIELD CURVES YIELD CURVES AND TERM STRUCTURE
yield curve provides an estimate of
the current TERM STRUCTURE OF INTEREST RATES
yields change daily as YTM change

26. TERM STRUCTURE THEORIES
THE FOUR THEORIES
1. THE UNBIASED EXPECTATION THEORY
2. THE LIQUIDITY PREFERENCE THEORY
3. MARKET SEGMENTATION THEORY
4. PREFERRED HABITAT THEORY

27. TERM STRUCTURE THEORIES
THEORY 1: UNBIASED EXPECTATIONS
Basic Theory: the forward rate represents the average opinion of the expected future spot rate for the period in question
in other words, the forward rate is an unbiased estimate of the future spot rate.

28. TERM STRUCTURE THEORY: Unbiased Expectations
A Set of Rising Spot Rates
the market believes spot rates will rise in the future
the expected future spot rate equals the forward rate
in equilibrium
es1,2 = f1,2
where es1,2 = the expected future spot
f1,2 = the forward rate

29. TERM STRUCTURE THEORY: Unbiased Expectations
THE THEORY STATES:
The longer the term, the higher the spot rate, and
If investors expect higher rates ,
then the yield curve is upward sloping
and vice-versa

30. TERM STRUCTURE THEORY: Unbiased Expectations
CHANGING SPOT RATES AND INFLATION
Why do investors expect rates to rise or fall in the future?
spot rates = nominal rates
because we know that the nominal rate is the real rate plus the expected rate of inflation

31. TERM STRUCTURE THEORY: Unbiased Expectations
CHANGING SPOT RATES AND INFLATION
Why do investors expect rates to rise or fall in the future?
if either the spot or the nominal rate is expected to change in the future, the spot rate will change

32. TERM STRUCTURE THEORY: Unbiased Expectations
CHANGING SPOT RATES AND INFLATION
Why do investors expect rates to rise or fall in the future?
the future spot rate is greater than current rates due to expectations of inflation

33. TERM STRUCTURE THEORY: Unbiased Expectations
Current conditions influence the shape of the yield curve, such that
if deflation expected, the term structure and yield curve are downward sloping
if inflation expected, the term structure and yield curve are upward sloping

34. TERM STRUCTURE THEORY: Unbiased Expectations
PROBLEMS WITH THIS THEORY:
upward-sloping yield curves occur more frequently
the majority of the time, investors expect spot rates to rise
not realistic position

35. TERM STRUCTURE THEORY: Liquidity Preference
BASIC NOTION OF THE THEORY
investors primarily interested in purchasing short-term securities to reduce interest rate risk

36. TERM STRUCTURE THEORY: Liquidity Preference
BASIC NOTION OF THE THEORY
Price Risk
maturity strategy is more risky than a rollover strategy
to convince investors to buy longer-term securities, borrowers must pay a risk premium to the investor

37. TERM STRUCTURE THEORY: Liquidity Preference
BASIC NOTION OF THE THEORY
Liquidity Premium
DEFINITION: the difference between the forward rate and the expected future rate

38. TERM STRUCTURE THEORY: Liquidity Preference
BASIC NOTION OF THE THEORY
Liquidity Premium Equation
L = es1,2 - f1,2
where L is the liquidity premium

39. TERM STRUCTURE THEORY: Liquidity Preference
How does this theory explain the shape of the yield curve?
rollover strategy
at the end of 2 years $1 has an expected value of
$1 x (1 + s1 ) (1 + es1,2 )

40. TERM STRUCTURE THEORY: Liquidity Preference
How does this theory explain the shape of the yield curve?
whereas a maturity strategy holds that
$1 x (1 + s2 )2
which implies with a maturity strategy, you must have a higher rate of return

41. TERM STRUCTURE THEORY: Liquidity Preference
How does this theory explain the shape of the yield curve?
Key Idea to the theory: The Inequality holds
$1(1+s1)(1 +es1,2)<$1(1 + s2)2

42. TERM STRUCTURE THEORY: Liquidity Preference
SHAPES OF THE YIELD CURVE:
a downward-sloping curve
means the market believes interest rates are going to decline

43. TERM STRUCTURE THEORY: Liquidity Preference
SHAPES OF THE YIELD CURVE:
a flat yield curve means the market expects interest rates to decline

44. TERM STRUCTURE THEORY: Liquidity Preference
SHAPES OF THE YIELD CURVE:
an upward-sloping curve means rates are expected to increase

45. TERM STRUCTURE THEORY: Market Segmentation
BASIC NOTION OF THE THEORY
various investors and borrowers are restricted by law, preference or custom to certain securities

46. TERM STRUCTURE THEORY: Liquidity Preference
WHAT EXPLAINS THE SHAPE OF THE YIELD CURVE?
Upward-sloping curves mean that supply and demand intersect for short-term is at a lower rate than longer-term funds
cause: relatively greater demand for longer-term funds or a relative greater supply of shorter-term funds

47. TERM STRUCTURE THEORY: Preferred Habitat
BASIC NOTION OF THE THEORY:
Investors and borrowers have segments of the market in which they prefer to operate

48. TERM STRUCTURE THEORY: Preferred Habitat
When significant differences in yields exist between market segments, investors are willing to leave their desired maturity segment

49. TERM STRUCTURE THEORY: Preferred Habitat
Yield differences determined by the supply and demand conditions within the segment

50. TERM STRUCTURE THEORY: Preferred Habitat
This theory reflects both
expectations of future spot rates
expectations of a liquidity premium

51. END OF CHAPTER 5