Chapter4. Term Structure of Interest Rate || Part.1

4.1 The Yield Curve

Variation in Bond Yields

• Yield to maturity(YTM) of any bond is strongly tied to general conditions in the fixed income securitied market
  채권의 만기 수익률 (YTM)은 fixed income securities 시장의 일반적인 조건과 밀접한 관련이 있습니다.
• All yields tend to move together in this market
• But all bond yields are not exactly the same
• Two major factors : quality ratings and time to maturity
  신용등급과 만기일이 중요한 factor이다.

Variation in Yields : Quality Ratings

• Variations in yields across bonds is explained in part by the fact that bonds have various quality ratings

• Only natural that high quality is more expensive than low quality

Variation in Yields : Maturity

• “Long” bonds (bonds with very distant maturity dates) tend to offer higher yields than “short” bonds of the same quality

• Effect of time to maturity is shown by a yield curve

Yield Curves

• Yield curve displays yield as a function of time to maturity

• Rising curve is a “normally shaped” yield curve (this shape occurs the most often)

• Inverted yield curve: Long bonds happen to have lower yields than short bonds

 

• Inverted shape tends to occur when short-term rates increase rapidly – Investors believe that the rise is temporary, so that long-term rates remain near their previous levels
• Predictor of economic recession – Predicts lower interests in the future as long-term bonds are demanded

 

 

4.2 The Term Structure

 

 

Term Structure

• Term structure : the relationship between interest rates(yield를 보는 게 아니다.) and maturities

• Term structure theory focuses on pure interest rates
• Theory is based on the observation that the interest rate charged for money depends on the length of time that the money is held
  • Example: Your local bank will offer you a higher rate of interest for deposits committed for 3 years than for shorter deposits
• 시간에 따라서 돈을 빌리거나 빌려줄 때 이자는 달라야 하고, 그런 부분들을 어떻게 표현할 수 있는지 보자. => Spot rates, forward rates, short rates

Spot Rates

• Spot rates are the basic interest rates defining the term structure

• Spot rate (s_t): Rate of interest, expressed in yearly terms, charged for money held from the present time (t=0) until time t

Spot Rates : Compounding

• Definition of spot rates implicitly assumes a compounding convention

• Convention might vary with the purpose at hand
  Convention은 현재의 목적에 따라 다를 수 있다. 

• In all cases, the rates are still quoted as yearly rates
  모든 경우에, 요금은 여전히 ​​연간 요금으로 인용됩니다

• Yearly compounding convention is the most convenient

Spot Rates : Discount Factors

 

• Discount factors : Factors by which future cash flows must be multiplied to obtain an equivalent present value

 

Spot Rates from Zero-Coupon Bonds

• In theory, spot rates can be measured by the yields of zero-coupon bonds (best to use Treasuries to eliminate default risk)

• Since a zero-coupon bond promises to pay a fixed amount at a fixed date in the future, the ratio of the payment amount to the current price defines the spot rate for the maturity date of the bond
  제로 쿠폰 채권은 미래에 정해진 날짜에 고정 금액을 지불 할 것을 약속하기 때문에, 현재 가격에 대한 지불 금액의 비율은 채권의 만기일에 대한 스팟 비율을 정의합니다
• Unfortunately, the set of available zero-coupon bonds is typically sparse

• Thus, it is not always practical to determine a complete set of spot rates this way

Determining Spot Rates

• Spot rate curve can be determined from the prices of coupon-bearing bonds by beginning with short maturities and working forward toward longer maturities
  Spot rate curve(현물 만기일)는 단기 만기부터 시작하여 장기 만기일을 앞당겨 쿠폰 보유 채권의 가격에서 결정될 수 있습니다
  • 1) s1을 구한다
  • 2) p를 알고 s1을 알면 s2를 알 수 있다. 

 

 

• 이런 식으로 반복하면 s1, s2...s5 등 다 구할 수 있는데, 귀찮잖아
• 만약 s5만 궁금하다면 어떻게 할 수 있을까? 예제를 가져와봄

• Zero coupon bonds를 만들어서 연산한다.