Understanding Interest Rates Chapter 4 Understanding Interest Rates

Present Value （現值） A dollar paid to you one year from now is less valuable than a dollar paid to you today Why? A dollar deposited today can earn interest and become $1 x (1+i) one year from today.

Discounting the Future (未來值折現)

Simple Present Value (簡單現值)

Time Line Cannot directly compare payments scheduled in different points in the time line $100 $100 $100 $100 Year 1 2 n PV 100 100/(1+i) 100/(1+i)2 100/(1+i)n

Four Types of Credit Market Instruments Simple Loan(簡單放款) Fixed Payment Loan(固定償還放款) Coupon Bond(附息債券) Discount Bond(貼現債券)(零息債券)

Yield to Maturity (到期收(殖)益率) 由於債券的付息方式、有無付息、期限等並不相同，故收益率的計算有許多不同方式。 三種不同付息方式的債券： 附息債券 折價債券 永久債券 The interest rate(利率) that equates the present value of cash flow(現金流量現值) payments received from a debt instrument with its value today

Simple Loan(簡單貸款)

Fixed Payment Loan(固定支付貸款)

Coupon Bond(附息債券) 與fixed payment loan 有何差別？

Consol or Perpetuity (永續債券or永久公債) A bond with no maturity date(無到期日) that does not repay principal(本金) but pays fixed coupon(固定票息) payments forever 永久公債的價格可表示如下： 永久公債的收益率 = 利息收益除以公債的價格： For coupon bonds, this equation gives the current yield(當期收益率), an easy to calculate approximation to the yield to maturity

Discount Bond (貼現債券，又稱零息債券-zero-coupon bond、折價債券)

折價債券(Discount Bond)的收益率 1年期折價債券的收益率 n年期折價債券的收益率 1年期以內折價債券的收益率 貨幣銀行學 Ch4 利率的行為

附息債券(Coupon Bond)收益率 到期收益率 持有期間收益率 貨幣銀行學 Ch4 利率的行為

貳‧債券的種類 政府公債 中央政府公債 地方政府公債 公司債 擔保與無擔保公司債 固定、變動與固定加變動利率公司債 可轉換與不可轉換公司債 可贖回與不可贖回公司債 參加與不參加公司債 附息票、到期一次還本付息與零息公司債 記名與無記名公司債 金融債券 外國債券

公司債 可分為普通公司債與轉換公司債。前者發行者須為股票公開發行公司，而轉換公司債發行者須為上市或上櫃公司，另公司債可視擔保有無分為有擔保公司債及無擔保公司債，如經金融機購保證可視為有擔保。 《圖片資料來源大眾銀行http://www.tcbank.com.tw/》

公債

That’s table can calculates by function of IRR in EXCEL Table 1 Yields to Maturity on a 10%-Coupon-Rate(票面利率) Bond Maturing in Ten Years (Face Value = $1,000) When the coupon bond (附息債券) is priced at its face value (票面價值), the yield to maturity equals the coupon rate (票面利率) The price of a coupon bond and the yield to maturity are negatively related The yield to maturity（市場殖利率） is greater than the coupon rate (票面利率) when the bond price (債券價格) is below its face value (面值) That’s table can calculates by function of IRR in EXCEL That’s table can calculates by function of IRR in EXCEL

新竹國際商業銀行九十四年度第一期無到期日累積次順位債券 本債券金額為新台幣五十萬元整，無到期日，受償順序次於一般債權，為無記名式，本債券得自由買賣、轉讓及提供擔保，承購人得隨時申請為記名式，記名式債券需先向該銀行辦理過戶手續方得為之。新竹國際商業銀行已於2007.7.2更名為渣打銀行。

Following the Financial News: Bond Prices and Interest Rates

零息債券通常為貨幣市場工具 短期票券 再買回協定(repurchase agreement, RP) 國庫券(Treasury Bill, TB) 可轉讓定期存單(Certificates of Deposit, CD) 商業本票(Commercial Paper, CP) 銀行承兌匯票(Banker’s Acceptance, BA) 再買回協定(repurchase agreement, RP) 同業拆款(interbank loan)

由利率換算成價格 公式：(台灣票券市場) 應用： 國庫券初級市場標售價格 國庫券、商業本票、銀行承兌匯票等工具的次級市場買斷或賣斷的價格(注意利息所得稅的計算)

票券利率另一常用公式 公式： (台灣票券市場)

由利率換算成價格 公式：

應用在商業本票的發行成本 貼現息=發行金額×市場利率×(天數/365) 保證費=發行金額×保證費率×(天數/365) 簽證費=發行金額×簽證費率×(天數/365) 承銷費=發行金額×承銷費率×(天數/365) 發行成本=貼現息+保證費+簽證費+承銷費

融資性商業本票(CP2)

交易性商業本票(CP1)

銀行承兌匯票

應用在附買回協定(RP) 附買回價格 =原約定價格 ×〔1+利率×(天數/365) ×(1-20%)〕

債券RP交易公式

債券RS交易公式

The Distinction Between Interest Rates and Returns

The Distinction(區別) Between Rate of Return and Interest Rates The return equals the yield to maturity only if the holding period(持有期間) equals the time to maturity(到期期間) A rise in interest rates(利率上升) is associated with a fall in bond prices(債券價格下降), resulting in a capital loss(資本損失) if time to maturity is longer than the holding period The more distant a bond’s maturity(距到期日越長), the greater the size of the percentage price change(價格變動百分比) associated with an interest-rate change(利率變量)

Rate of Return and Interest Rates (cont’d) The more distant a bond’s maturity(距到期日越遠), the lower the rate of return(報酬率下降越多) the occurs as a result of an increase in the interest rate(利率上升會導致) Even if a bond has a substantial initial interest rate, its return can be negative if interest rates rise (利率與報酬率成反比)

Table 2 One-Year Returns on Different-Maturity 10%-Coupon-Rate Bonds When Interest Rates Rise from 10% to 20% 作業：將此表用EXCEL做出來

Interest-Rate Risk(利率風險) Prices and returns for long-term bonds are more volatile(波動) than those for shorter-term bonds There is no interest-rate risk for any bond whose time to maturity matches the holding period

幾種常見的利率 名目利率與實質利率 市場利率與銀行利率 短期利率與長期利率 存款利率與放款利率 費雪效果解釋名目利率與預期通貨膨脹率關係，依據費雪方程式，當人們預期通貨膨脹率提高（下降），名目利率將會上升（下降）。 費雪方程式：名目利率=實質利率+預期通貨膨脹率 市場利率與銀行利率 短期利率與長期利率 存款利率與放款利率 貨幣銀行學 Ch4 利率的行為

Real(實質) and Nominal(名目) Interest Rates Nominal interest ratemakes no allowance for inflation(名目利率未考慮通貨膨脹) Real interest rate(實質利率) is adjusted for changes in price level so it more accurately reflects the cost of borrowing Ex ante(事前) real interest rate is adjusted for expected changes in the price level Ex post(事後) real interest rate is adjusted for actual changes in the price level

Fisher Equation(費雪方程式)

Figure 1 Real and Nominal Interest Rates (Three-Month Treasury Bill), 1953–2011 Sources: Nominal rates from www.federalreserve.gov/releases/H15 and inflation from ftp://ftp.bis.gov/special.requests/cpi/cpia.txt. The real rate is constructed using the procedure outlined in Frederic S. Mishkin, “The Real Interest Rate: An Empirical Investigation,” Carnegie-Rochester Conference Series on Public Policy 15 (1981): 151–200. This procedure involves estimating expected inflation as a function of past interest rates, inflation, and time trends and then subtracting the expected inflation measure from the nominal interest rate.