Bond Prices and Yields Chapter 12

A. Introduction Review different types of bonds, how bonds are quoted E.g., Globeinvestor  Market Data  Bond Data Some bonds are listed on organized exchanges, but most bonds are traded over the counter by bond dealers (via a proprietary platform or via phone) U.S. OTC Corporate bond transaction database: FINRA TRACE: OTC represents 90%+ of total activity New trend: NYSE and London Stock Exchange Compared to the stock market, bond market has greater liquidity risk (treasury bonds much more liquid than corporate bonds) 11/7/2018

Real Return Bonds Inflation-indexed bonds Bonds with an inflation hedge Principal/par value is indexed to the Consumer Price Index (CPI) Fixed coupon rate (e.g., 4%) is applied to the inflation- indexed principal Hence, cash flow is fixed in real terms, because coupons are protected against inflation as well 11/7/2018

Cash Flow: Real Return Bond (4% coupon) 11/7/2018

Product developed in the 1980s Real Return Bonds Product developed in the 1980s Treasury Inflation-Protected Securities (TIPS) in U.S., Real-Return Bonds (RRB) in Canada Also available in many countries, e.g., Sweden, Australia, the U.K., France. Small investors can participate through a real- return bond mutual fund, or through an ETF 11/7/2018

Real Return Bonds For each inflation-indexed bond, there is a “real yield” plus an inflation protection (both are quoted by broker). The real yield is a proxy for the real rate of interest Hence, (nominal yield – real yield) is a proxy for the market’s inflation expectation E.g. U.S. 10-year Treasury yield minus 10-year TIPs yield 1.92% - 0.17% = 1.75% 11/7/2018

Bond Valuation Intrinsic value How do we estimate this value? PV of expected future cash flow Inputs Stream of expected future cash flows Timing and frequency of cash flows Most popular frequency for coupons: semi-annual Discount rate 11/7/2018

Bond Pricing PB = price of the bond Ct = interest or coupon payments T = number of periods to maturity r = “appropriate” discount rate 11/7/2018

Numerical Example PB = $810.71 Annual coupon = 8% (semiannual payments) Par value = 1000 Term = 30 years r = 5% (semi-annual discount rate) PB = $810.71 In Excel: =PRICE(DATE(2013,11,13),DATE(2043,11,13),0.08,0.10,100,2) = $81.07 11/7/2018

Bond Prices and Yields 11/7/2018

Relationship between Bond Prices and Yields Bond prices and yields have a nonlinear inverse (convex) relationship Sensitivity of bond prices to yield changes varies along the curve When yields approach zero, the value of the bond approaches the sum of the expected future cash flows from the bond 11/7/2018

Yield to Maturity (YTM) Rate of return most often quoted for investors Promised compound rate of return based on the current market price if: bond is held to maturity coupons are reinvested at the same rate 11/7/2018

Solve the bond pricing formula for YTM YTM equates the PV of expected cash flow to the market price ~ internal rate of return concept Solve the bond pricing formula for YTM 11/7/2018

YTM Example 10-year Maturity Coupon Rate = 7% Par value = 1000 Price = $950 Solve for YTM: Semiannual YTM = 3.8635% In Excel: =YIELD(DATE(2013,11,12),DATE(2023,11,12),0.07,95,100,2)/2 divide by 2 for the semiannual YTM 11/7/2018

YTM, Coupon Rate, and Bond Prices (8% Coupon Bond) Note: in the text, market interest rate is synonymous with YTM of the bond 11/7/2018

Price Paths of Coupon Bonds 11/7/2018

Converting to an Annual Yield Bond Equivalent Yield 3.86% x 2 = 7.72% Effective Annual Yield (1.0386)2 - 1 = 7.88% Current Yield (Annual coupon / Market Price) $70 / $950 = 7.37 % 11/7/2018

HPR where C = coupon(s) received over the period P1 = price at the end of the period P0 = purchase price at the beginning of the period 11/7/2018

HPR example Coupon = 8% ; YTM = 8%; Term =10 years Semiannual compounding; P0 = $1000 In 6 months, YTM falls to 7% New price =PRICE(DATE(2014,5,13),DATE(2023,11,13),0.08,0.07,100,2) =$1068.55 Semi-annual HPR = 10.85% over the six months 11/7/2018

Yield to Call (YTC) Bonds may have a call provision Purpose of a call? Especially popular in the U.S. Purpose of a call? When interest rates fall, PV of scheduled payments rises. If this PV > call price, firm will call the bond Refinance at a lower interest rate 11/7/2018

YTC (cont’d) In other words, price of callable bond is capped Yield to call may be more relevant to investors, especially if market price is close to the call price

YTC (cont’d) where CD is the call date Example: U.S. municipal bond (Massachusetts Port Authority): Mass Port 5 ¼% 7/1/18 call 7/1/08@101 Note: 1% call premium over par May be called on July 1, 2008 or after