The economics of money, banking, and financial institutions 2nd ch04

Chapter Understanding Interest Rates © 2005 Pearson Education Canada Inc Present Value Four Types of Credit Instruments Simple loan Fixed­payment loan Coupon bond Discount (zero coupon) bond Concept of Present Value Simple loan of $1 at 10% interest Year $1.10 $1.21 $1.33  $1 PV of future $1 =   (1 + i)n © 2005 Pearson Education Canada Inc n $1x(1 + i)n 4-2 Yield to Maturity: Loans Yield to maturity = interest rate that equates today’s value with  present value of all future payments Simple Loan (i = 10%) $100 = $110/(1 + i)  i = $110 – $100 $100   =  $10  $100 = 0.10 = 10% Fixed Payment Loan (i = 12%) $1000 = LV = $126 (1+i) FP (1+i) + + © 2005 Pearson Education Canada Inc $126 (1+i) FP (1+i) + + $126 (1+i) FP (1+i) + + + + $126 (1+i)25 FP (1+i)n 4-3 Yield to Maturity: Bonds Coupon Bond (Coupon rate = 10% = C/F) P= $100 $100 + + (1+i) (1+i)2 $100 $100 $1000 + + + (1+i)3 (1+i)10 (1+i)10 P= C (1+i) C C + + (1+i)3 (1+i)n + C + (1+i)2 + F (1+i)n Consol: Fixed coupon payments of $C forever C C P= i = i P Discount Bond (P = $900, F = $1000), one year $900 = $1000 (1+i) i= $1000 – $900 $900 i= F–P P  = 0.111 = 11.1% © 2005 Pearson Education Canada Inc 4-4 Relationship Between Price and Yield to Maturity Three Interesting Facts in Table 1 When bond is at par, yield equals coupon rate Price and yield are negatively related Yield greater than coupon rate when bond price is below par value © 2005 Pearson Education Canada Inc 4-5 Current Yield ic = C P Two Characteristics Is better approximation to yield to maturity, nearer price is to par and longer is maturity of bond Change in current yield always signals change in same direction as yield to maturity Yield on a Discount Basis idb = (F – P) P x 365 (number of days to maturity) A 91-day bill, P = $988, F = $1000 $1000 – $988 365 idb = x = 0.0487 = 4.8% $988 91 Two Characteristics Understates yield to maturity Change in discount yield always signals change in same direction as yield to maturity © 2005 Pearson Education Canada Inc 4-6 Bond Page of the Newspaper: Canada Bonds © 2005 Pearson Education Canada Inc 4-7 Bond Page of the Newspaper: Provincial and Municipal Bonds © 2005 Pearson Education Canada Inc 4-8 Bond Page of the Newspaper: Corporate Bonds © 2005 Pearson Education Canada Inc 4-9 Distinction Between Interest Rates and Returns Rate of Return RET = C + Pt+1 – Pt Pt C where: ic = g= Pt Pt+1 – Pt © 2005 Pearson Education Canada Inc Pt = ic + g = current yield = capital gain 4-10 Key Facts about Relationship Between Interest Rates and Returns © 2005 Pearson Education Canada Inc 4-11 Maturity and the Volatility of Bond Returns Key Findings from Table 2 Only bond whose return = yield is one with maturity = holding period For bonds with maturity > holding period, i  P implying capital loss Longer is maturity, greater is % price change associated with interest  rate change Longer is maturity, more return changes with change in interest rate Bond with high initial interest rate can still have negative return if i  Conclusion from Table 2 Analysis Prices and returns more volatile for long­term bonds because have  higher interest­rate risk No interest­rate risk for any bond whose maturity equals holding period © 2005 Pearson Education Canada Inc 4-12 Distinction Between Real and Nominal Interest Rates Real Interest Rate Interest rate that is adjusted for expected changes in the price level ir = i – e Real interest rate more accurately reflects true cost of borrowing When real rate is low, greater incentives to borrow and less to lend if i = 5% and  e = 3% then:  ir = 5% – 3% = 2% if i = 8% and  e = 10% then  ir = 8% – 10% =  –2% © 2005 Pearson Education Canada Inc 4-13 U.S Real and Nominal Interest Rates © 2005 Pearson Education Canada Inc 4-14 ... Page of the Newspaper: Canada Bonds © 2005 Pearson Education Canada Inc 4-7 Bond Page of the Newspaper: Provincial and Municipal Bonds © 2005 Pearson Education Canada Inc 4-8 Bond Page of the. .. When real rate is low, greater incentives to borrow and less to lend if i = 5% and  e = 3% then:  ir = 5% – 3% = 2% if i = 8% and  e = 10% then  ir = 8% – 10% =  –2% © 2005 Pearson Education Canada Inc 4-13 U.S Real and Nominal Interest... 4-10 Key Facts about Relationship Between Interest Rates and Returns © 2005 Pearson Education Canada Inc 4-11 Maturity and the Volatility of Bond Returns Key Findings from Table 2 Only bond whose return = yield is one with maturity = holding period