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Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
Fundamentals Of Bond Valuation
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Fundamentals Of Bond Valuation

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  • 1. FUNDAMENTALS OF BOND VALUATION 1
  • 2. YIELD TO MATURITY • CALCULATING YIELD TO MATURITY EXAMPLE – Imagine three risk-free returns based on three Treasury bonds: Bond A,B are pure discount types; mature in one year 2
  • 3. Bond C coupon pays $50/year; matures in two years 3
  • 4. YIELD TO MATURITY Bond Market Prices: Bond A $934.58 Bond B $857.34 Bond C $946.93 WHAT IS THE YIELD-TO-MATURITY OF THE THREE BONDS? 4
  • 5. 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 5
  • 6. YIELD TO MATURITY • CALCULATING YTM: – BOND A – Solving for rA (1 + rA) x $934.58 = $1000 rA = 7% 6
  • 7. YIELD TO MATURITY • CALCULATING YTM: – BOND B – Solving for rB (1 + rB) x $857.34 = $1000 rB = 8% 7
  • 8. YIELD TO MATURITY • CALCULATING YTM: – BOND C – Solving for rC (1 + rC)+{[(1+ rC)x$946.93]-$50 = $1000 rC = 7.975% 8
  • 9. SPOT RATE • DEFINITION: Measured at a given point in time as the YTM on a pure discount security 9
  • 10. SPOT RATE • SPOT RATE EQUATION: Mt Pt 1 st where Pt = the current market price of a pure discount bond maturing in t years; Mt = the maturity value st = the spot rate 10
  • 11. DISCOUNT FACTORS • EQUATION: Let dt = the discount factor 1 dt 1 st 11
  • 12. DISCOUNT FACTORS • EVALUATING A RISK FREE BOND: – EQUATION n PV d t ct t 1 where ct = the promised cash payments n = the number of payments 12
  • 13. 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 13
  • 14. FORWARD RATE • EXAMPLE OF A FORWARD RATE Let us assume that $1 paid in one year at a spot rate of 7% has 1 PV $.9346 1.07 14
  • 15. FORWARD RATE • EXAMPLE OF A FORWARD RATE Let us assume that $1 paid in two years at a spot rate of 7% has a 1 (1 f1, 2 ) PV $.8573 (1 .07) f1, 2 9.01% 15
  • 16. FORWARD RATE f1,2 is the forward rate from year 1 to year 2 16
  • 17. 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 $1 1 f1, 2 $1 (1 s1 ) (1 s2 ) 2 17
  • 18. FORWARD RATE such that (1 s1 ) 1 f1, 2 (1 s2 ) or 2 (1 s1 )(1 f1, 2 ) (1 s2 ) 18
  • 19. FORWARD RATE • More generally for the link between years t- 1 and t: t (1 st ) (1 f1, 2 ) t 1 (1 st ,1 ) • or t 1 t (1 st 1 ) (1 ft 1,t ) (1 st ) 19
  • 20. FORWARD RATES AND DISCOUNT FACTORS • ASSUMPTION: – given a set of spot rates, it is possible to determine a market discount function – equation 1 dt (1 st 1 )t 1 (1 ft 1,t ) 20
  • 21. YIELD CURVES • DEFINITION: a graph that shows the YTM for Treasury securities of various terms (maturities) on a particular date 21
  • 22. YIELD CURVES • TREASURY SECURITIES PRICES – priced in accord with the existing set of spot rates and – associated discount factors 22
  • 23. YIELD CURVES • SPOT RATES FOR TREASURIES – One year is less than two year; – Two year is less than three-year, etc. 23
  • 24. 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 changes 24
  • 25. TERM STRUCTURE THEORIES • THE FOUR THEORIES 1.THE UNBIASED EXPECTATION THEORY 2. THE LIQUIDITY PREFERENCE THEORY 3. MARKET SEGMENTATION THEORY 4. PREFERRED HABITAT THEORY 25
  • 26. 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. 26
  • 27. TERM STRUCTURE THEORY: Unbiased Expectations • THEORY 1: 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 27
  • 28. 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 28
  • 29. 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 29
  • 30. 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 30
  • 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 31
  • 32. 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 32
  • 33. 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 33
  • 34. TERM STRUCTURE THEORY: Liquidity Preference • BASIC NOTION OF THE THEORY – investors primarily interested in purchasing short-term securities to reduce interest rate risk 34
  • 35. 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 35
  • 36. TERM STRUCTURE THEORY: Liquidity Preference • BASIC NOTION OF THE THEORY – Liquidity Premium • DEFINITION: the difference between the forward rate and the expected future rate 36
  • 37. TERM STRUCTURE THEORY: Liquidity Preference • BASIC NOTION OF THE THEORY – Liquidity Premium Equation L = es1,2 - f1,2 where L is the liquidity premium 37
  • 38. 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 ) 38
  • 39. 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 39
  • 40. 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 40
  • 41. TERM STRUCTURE THEORY: Liquidity Preference • SHAPES OF THE YIELD CURVE: – a downward-sloping curve • means the market believes interest rates are going to decline 41
  • 42. TERM STRUCTURE THEORY: Liquidity Preference • SHAPES OF THE YIELD CURVE: – a flat yield curve means the market expects interest rates to decline 42
  • 43. TERM STRUCTURE THEORY: Liquidity Preference • SHAPES OF THE YIELD CURVE: – an upward-sloping curve means rates are expected to increase 43
  • 44. TERM STRUCTURE THEORY: Market Segmentation • BASIC NOTION OF THE THEORY – various investors and borrowers are restricted by law, preference or custom to certain securities 44
  • 45. 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 45
  • 46. TERM STRUCTURE THEORY: Preferred Habitat • BASIC NOTION OF THE THEORY: – Investors and borrowers have segments of the market in which they prefer to operate 46
  • 47. TERM STRUCTURE THEORY: Preferred Habitat – When significant differences in yields exist between market segments, investors are willing to leave their desired maturity segment 47
  • 48. TERM STRUCTURE THEORY: Preferred Habitat – Yield differences determined by the supply and demand conditions within the segment 48
  • 49. TERM STRUCTURE THEORY: Preferred Habitat – This theory reflects both • expectations of future spot rates • expectations of a liquidity premium 49

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