Lecture4_6x1 - Why Is This Important Lecture 4 Bond...

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Lecture 4: Bond Valuation and the Term Structure of Interest Rates RSM 332 Capital Market Theory Rotman School of Management University of Toronto Mike Simutin October 5/6, 2011 Bond Valuation RSM 332, 1/32 Why Is This Important? I Bonds are an important component of an investment portfolio I Issuing bonds is the most common form of raising funds by governments and corporations I Bond markets are larger than stock markets I Understanding bonds may help to understand and even predict the health of an individual company and the overall economy Bond Valuation RSM 332, 2/32 DeFnition of a Bond I A bond is a legally binding contract between a borrower (bond issuer) and a lender (bondholder) I Borrower promises to make interest and principal payments I All payments are determined in the contract I Bonds can diFer in several diFerent respects: repayment type, issuer, maturity, collateral, priority in case of default I Abondspec i±es I ²ace (or par) value, F dollars, to be paid at maturity I Coupon rate, c , to be paid periodically I Fixed rate, e.g., 8% annually I Floating rate, e.g., 1-year Treasury bill rate + 100 basis points I Maturity, T years Bond Valuation RSM 332, 3/32 Example of a Bond Consider a four-year Government of Canada bond with a 6% annual coupon rate, issued on 1/1/2012 and maturing on 12/31/2015 I The par value of the bond is $1,000 I Coupons are paid semi-annually: June 30 and December 31 I The semiannual coupon payment is $1 , 000 · 0 . 06 2 = $30 $0 1/1/2012 $30 6/30/2012 $30 12/31/2012 $30 6/30/2013 $30 12/31/2013 $30 6/30/2014 $30 12/31/2014 $30 6/30/2015 $1,030 12/31/2015 Bond Valuation RSM 332, 4/32 How to Value Bonds Value of Bond = PV of Expected Future Cash Flows I Identify the size and timing of cash flows I Discount them at the correct discount rate, which depends on the default risk of the bond I Intrinsic risk of the issuer (often rated by an agency, e.g. Moody’s) I Collateralized or non-collateralized debt I Seniority I Is there default risk on government bonds? Bond Valuation RSM 332, 5/32 What If Bond Price ± = PV of ±uture Cash ±lows? I Consider a bond that pays $1,000 next year and now trades at $920. The relevant discount rate is r =5% . I Bond price ($920) is not equal to PV of future cash flows ($1 , 000 / 1 . 05 = 952 . 38)! I Let’s borrow $920 at 5% for one year and use it to buy the bond at $920. This leads to the following cash flows: Today Next Year Borrow 920 +920 920 · (1 + 0 . 05) = 966 Buy bond 920 +1 , 000 I You get a sure future payoF of $1 , 000 966 = $34 without paying anything today. This is a free lunch or arbitrage :a t least one cash flow of an arbitrage-based strategy is positive, and all other cash flows are zero (or also positive) I Can arbitrage persist? Bond Valuation RSM 332, 6/32
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Zero-Coupon Bonds Zero-coupon (or pure discount ) bonds do not pay coupons ( c =0) I Time to maturity, T = Maturity date today’s date I Face value F I Discount rate r P = F (1 + r ) T What is the value of a 30-year zero-coupon bond with a $1,000 par value and a discount rate of 6% (annual compounding)?
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Lecture4_6x1 - Why Is This Important Lecture 4 Bond...

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