4-16
Yield on a Discount Basis（贴现基础上的 收益率
Less accurate but less difficult to calculate idb = F-P 360 X F days to maturity
idb = yield on a discount basis F = face value of the Treasury bill (discount bond) P = purchase price of the discount bond Uses the percentage gain on the face value Puts the yield on an annual basis using 360 instead of 365 days Always understates the yield to maturity The understatement becomes more severe the longer the maturity
4-17
Question:wich would you rather own?
• You are offered two bonds,a one-year u.s. treasury bond with a yield to maturity of 9% and a one-year u.s. treasury bill with a yield on a discount basis of 8.9%.
Simple Loan—Yield to Maturity
PV = amount borrowed = $100 CF = cash flow in one year = $110 n = number of years = 1 $110 $100 = (1 + i )1 (1 + i ) $100 = $110 $110 (1 + i ) = $100 i = 0.10 = 10% For simple loans, the simple interest rate equals the yield to maturity
4-9
Coupon Bond—Yield to Maturity
Using the same strategy used for the fixed-payment loan: P = price of coupon bond C = yearly coupon payment F = face value of the bond n = years to maturity date C C C C F P= . . . + 2 3 n 1+i (1+i) (1+i) (1+i) (1+i)n
（对于到期期限长于持有期的债券而言，利率上升与债券的价格负相关，进而引起投资该 债券的资本损失）
• The more distant a bond’s maturity, the greater the size of the perceninterest-rate change
4-11
Consol or Perpetuity（统一公债；永续债券）
• A bond with no maturity date that does not repay principal but pays fixed coupon payments forever
Pc C / ic Pc price of the consol C yearly interest payment ic yield to maturity of the consol Can rewrite above equation as ic C / Pc For coupon bonds, this equation gives current yieldŃ an easy-to-calculate approximation of yield to maturity
• The interest rate that equates the present value of cash flow payments received from a debt instrument with its value today
（使债务工具所有未来回报的现值与其今天 的价值相等的利率）
Chapter 4
Understanding Interest Rates
利率的重要性
• 与我们的生活息息相关：挣还是赚？
• 在世界所有流通的总市值中，有2/3被归 为固定收益证券。
4-2
Present Value（现值）
• A dollar paid to you one year from now is less valuable than a dollar paid to you today (一年后你收入的1美元不如你现在收入的1 美元值钱）
4-8
Fixed Payment Loan— Yield to Maturity
The same cash flow payment every period throughout the life of the loan LV = loan value FP = fixed yearly payment n = number of years until maturity FP FP FP FP LV = ...+ 2 3 1 + i (1 + i) (1 + i) (1 + i) n
4-18
Following the Financial News: Bond Prices and Interest Rates
4-19
Rate of Return(回报率）
The payments to the owner plus the change in value expressed as a fraction of the purchase price Pt 1 - Pt C RET = + Pt Pt RET = return from holding the bond from time t to time t + 1 Pt = price of bond at time t Pt 1 = price of the bond at time t + 1 C = coupon payment C = current yield = ic Pt Pt 1 - Pt = rate of capital gain = g Pt
• A rise in interest rates is associated with a fall in bond prices, resulting in a capital loss if time to maturity is longer than the holding period
n
• 其中， D表示持续期， Ct为第t 期的现金流或利息， F为资产或负债面值（到期日的价值），n为该项资 产或负债的期限，i为市场利率,P为金融工具的现值。
多次性偿付类资产
P0 C1 /(1 r) C2 /(1 r) ...... Cn /(1 r)
4-12
Discount Bond—Yield to Maturity
For any one year discount bond F-P i= P F = Face value of the discount bond P = current price of the discount bond The yield to maturity equals the increase in price over the year divided by the initial price. As with a coupon bond, the yield to maturity is negatively related to the current bond price.
4-13
思考：债券合成
• 用零息债券复制息票债券。
• 用息票债券复制零息债券。
4-14
到期收益率的缺陷分析
1. 投资者持有债券至偿还期。
2. 再投资收益率等于到期收益率。 3. 到期收益率难以计算。
4-15
Current Yield(当期收益率）
It is an approximation of the yield to maturity on coupon bonds which defined as the yearly coupon payment divided by the price of the security ic=C/P Where ic=current yield P=price of coupon bond C=yearly coupon payment
（债券的到期日越远，利率变动引起债券价格变动的比率就越大）
4-21
16.3.1 “持续期”概念
• 持续期：
• 是固定收入金融工具的所有预期现金流入量的加权 平均时间，也可以理解为金融工具各期现金流抵补 最初投入的平均时间。有效持续期实际上是加权的 现金流量现值与未加权的现值之比。
tC t nF t t 1 (1 i ) n 1 i D P
4-20
• The return equals the yield to maturity only if the holding period equals the time to maturity
（只有持有期与到期期限一致的债券回报率才与最初的到期收益率相等）
Rate of Return and Interest Rates