Tiền tệ ngân hàng FTU - Lý thuyết chương 2

Content • Introduction • Interest rates defined • Yield to maturity • Other measures of interest rates • The relationship between the coupon rate, interest rate and price relative to par value • Price-yield curves • Interest rate risk • Reinvestment risk • Real and nominal interest rates • Default risk Lecture 02 The Meaning of Interest Rates Readings 2 Introduction Mishkin (2021), The Economics of Money, Banking, and Financial Markets, 13th edition, Pearson, Chapter 4. Cecchetti and Schoenholtz (2012), Money, Banking, and Financial Markets, 4th edition, McGraw-Hill, Chapter 4. 3 4 Introduction Interest rate defined • Interest rates are among the most closely watched variables in the economy. • An interest rate is the price paid by a borrower to a lender for the use of resources that will be used during some time period then returned • Interest rates • Link the present to the future • Tell the future reward for lending today • Tell the cost of borrowing now and repaying later • In this lecture, we will explore what an interest rate is, and the relationship between interest rates, bond prices, and returns 5 Interest rate defined Dual” Definition: • Borrowing: the cost of borrowing or the price (%) paid for the “rental” of funds. • A financial liability for “deficit” (borrowing) entities. • Saving: the return from investing funds or the price (%) paid to delay consumption. • A financial asset for “surplus” (lending, investing) entities. Both concepts are expressed as a percentage per year (Percent per annum; “p.a.”). This is true regardless of maturity of instrument of the financial liability or financial asset. Thus, all observed interest rate data is annualized. 6 Interest rate defined 7 Basis Point: A unit that is equal to 1/100th of 1%, and is used to denote the changes in interest rates or differences in interest rates between various debt instruments. The relationship between interest rate changes (or differentials) and basis points can be summarized as follows: 1% change (or difference) = 100 basis points. Example 1: If Bond A’s yield increases from 5% to 6.5%, then Bond A’s yield increased150 basis points. Example 2: If Bond B’s yield falls from 7.00% to 6.93%, then Bond B’s yield decreased 7 basis points. Example 2: If Bond C has a yield of 6% and Bond D a yield of 2%, then Bond C is 400 basis points more than Bond D. 8 đo lường lãi suất Commonly used interest rate measures Commonly used interest rate measures • There are four important ways of measuring (and reporting) interest rates on financial instruments. • When people talk about bonds they use the terms yield and interest rate interchangeably, so we will too. These are: – Yield to Maturity: The interest rate that equates the future payments to be received from a financial instrument (coupons plus maturity value) with its market price today (i.e., to its present value). – Discount Yield and Investment Yield: These are yields on short term (one year or less) debt instruments that have no coupon payments and are selling at a discount of their par values. These interest rates are the “implied” returns from buying a debt instrument at a price below its par value. – Coupon Yield: The “promised” annual percent return on a coupon instrument. – Current Yield: Bond’s annual coupon payment divided by its current market price. 9 Coupon yield 10 Coupon yield • Coupon yield is the annual interest rate which was promised by the issuer when a bond was first sold. • Coupon information is found in the bond’s indenture (legal contract). Indenture will state the coupon payment (as a percent of the bond’s par value) and the schedule of payments (semi-annual or annual). • The coupon yield on a bond will not change during the lifespan of the bond. • Go to Bloomberg to view coupon yields: http://www.bloomberg.com/ • Note: U.S. Treasuries, 12 months and less have no coupons. Same is true for short term government bonds in other countries. 11 12 Current Yield Current Yield Premium bonds: The current yield on these bonds will always be below the coupon yield. • The current yield (or flat yield, or interest yield) is the coupon expressed as a percentage of the current price; this is the simplest of all return measures • This provides us with a measure of the “current” interest yield obtained at the bond’s current market price (i.e., cost associated with investing in a particular bond). • Current yield = annual coupon payment/market price • A 6 year, 1.50% bond selling at $1,003.75 (thus it is a premium bond). Thus the current yield = $15.00/1,003.75 = 1.4944% – Current Yield = Annual coupon payment/>$1,000 – Using the 1.5% coupon bond: – Current yield = $15.00/1,003.75 = 1.4944% Discount bonds: The current yield on these bonds will always be above the coupon yield (assume a market price of $985). – Current Yield – Annual coupon payment/<$1,000 – Current yield = $15.00/$985 = 1.5228% 13 Yield to Maturity 14 Yield to maturity The interest rate that equates the present value of cash flow payments received from a debt instrument with its value today Four Types of Credit Market Instruments • Simple Loan • Fixed Payment Loan • Coupon Bond • Discount Bond 15 16 Simple Loan Fixed Payment Loan PV = amount borrowed = $100 CF = cash flow in one year = $110 n = number of years = 1 The same cash flow payment every period throughout the life of the loan LV = loan value $110 (1 + i )1 (1 + i ) $100 = $110 $100 = FP = fixed yearly payment n = number of years until maturity $110 $100 i = 0.10 = 10% For simple loans, the simple interest rate equals the yield to maturity (1 + i ) = LV = Test question Test question What is the YTM of a simple loan whose today’s value is $1000 and next year’s value is $1100? 17 What is the YTM of a fixed payment loan whose today’s value is $1000 and the yearly payment is $126 for the next 25 years? 18 Table 1 Yields to Maturity on a 10%-Coupon-Rate Bond Maturing in Ten Years (Face Value = $1,000) Coupon Bond When the coupon bond is priced at its face value, the yield to maturity equals the coupon rate Using the same strategy used for the fixed-payment loan: P = price of coupon bond The price of a coupon bond and the yield to maturity are negatively related C = yearly coupon payment F = face value of the bond The yield to maturity is greater than the coupon rate when the bond price is below its face value n = years to maturity date P= FP FP FP FP ...+ 2 3 1 + i (1 + i ) (1 + i ) (1 + i ) n C C C C F . . . + 2 3 n 1+i (1+i ) (1+i ) (1+i ) (1+i ) n Test question What is the YTM of a $1000 face value 10% annual coupon bond with 10 years to maturity that now sells for $900? 19 20 Consol or Perpetuity Yield to Maturity A bond with no maturity date that does not repay prin cipal but pays fixed coupon payments forever P C / ic Pc price of the consol C yearly interest payment ic yield to maturity of the consol can rewrite above equation as this : ic C / Pc For coupon bonds, this equation gives the current yield, an easy to calculate approximation to the yield to maturity 21 22 Discount yields and investment yields Discount yields and investment yields • Discount yields and investment yields are calculated for U.S. T-bills and other short term money market instruments (e.g., commercial paper and bankers’ acceptances) where there are no stated coupons (and thus the assets are quoted at a discount of their maturity value). • The discount yield relates the return to the instrument’s par value (or face or maturity). The discount yield is sometimes called the bank discount rate or the discount rate. The investment yield relates the return to the instrument’s current market price. – The investment yield is sometimes called the coupon equivalent yield, the bond equivalent rate, the effective yield or the interest yield. – The investment yield is generally calculated so that we can compare the return on T-bills to “coupon” investment options r FP 360 rdb F days to maturity 23 FP 365(366) P days to maturity 24