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Chapter Three

Part II Principles of Financial Markets. Chapter Three. UNDERSTANDING INTEREST RATES. Present Value. Four Types of Credit Instruments 1. Simple Loan 2. Fixed Payment Loan 3. Coupon Bond 4. Discount Bond Concept of Present Value Simple loan of $1 at 10% interest

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Chapter Three

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  1. Part II Principles of Financial Markets Chapter Three UNDERSTANDING INTEREST RATES

  2. Present Value • Four Types of Credit Instruments • 1. Simple Loan • 2. Fixed Payment Loan • 3. Coupon Bond • 4. Discount Bond • Concept of Present Value • Simple loan of $1 at 10% interest • Year 1 2 3 n • $1.10 $1.21 $1.33 $1x(1+i)n • PV of future $1 = $1 • (1+i)n

  3. Yield to Maturity: Loans • Yield to maturity = interest rate that equates today's value with present value of all future payments • 1. Simple Loan (i = 10%) • $100 = $110/(1+i)  • i = $110 - $100 = $10 = .10 = 10% • $100 $100 YTM=約定利率

  4. Yield to Maturity: Loans • 2. Fixed Payment Loan (i = 12%) • $1000 = $126 + $126 + $126 + ... + $126 • (1+i) (1+i)2 (1+i)3 (1+i)25 • LV = FP + FP + FP + ... + FP • (1+i) (1+i)2 (1+i)3 (1+i)N YTM=約定利率

  5. Mortgage Payments Table 每年支付：10.54×12=126

  6. Bond Table Coupon rate

  7. Yield to Maturity: Bonds YTMcoupon interest rate • 3. Coupon Bond (Coupon rate = 10% = C/F) • P = $100 + $100 + $100 + ... + $100 + $1000 • (1+i) (1+i)2 (1+i)3 (1+i)10 (1+i)10 • P = C + C + C + ... + C + F • (1+i) (1+i)2 (1+i)3 (1+i)N (1+i)N • Consol: Fixed coupon payments of $C forever • P = Ci = C • iP

  8. Yield to Maturity: Bonds • 4. One-year Discount Bond (P = $900, F = $1000) • $900 = $1000 • (1+i) • i = $1000 - $900 = .111 = 11.1% • $900 • i = F - P • P

  9. Relationship Between Price and Yield to Maturity • Three Interesting Facts in Table 1 1. When bond is at par, yield equals coupon rate 2. Price and yield are negatively related 3. Yield greater than coupon rate when bond price is below par value

  10. Current Yield To approximate coupon bond 的YTM • ic = C • P • Two Characteristics • 1. Is better approximation to yield to maturity, nearer price is to par and longer is maturity of bond • 2. Change in current yield always signals change in same direction as yield to maturity

  11. Yield on a Discount Basis To approximate discount bond 的YTM • One-year bill, P = $900, F = $1000 • Two Characteristics • 1.Understates yield to maturity; longer the maturity, greater is understatement • 2.Change in discount yield always signals change in same direction as yield to maturity

  12. Bond Page of the Newspaper

  13. Distinction Between Real and Nominal Interest Rates • Real interest rate • Interest rate that is adjusted for expected changes in the price level • ir = i - π e • 1. Real interest rate more accurately reflects true cost of borrowing • 2. When real rate is low, greater incentives to borrow and less to lend • if i = 5% and π e = 0% then: • ir = 5% - 0% = 5% • if i = 10% and π e = 20% then • ir = 10% - 20% = - 10% ∴有index bond其利率與本金皆隨物價水準調整

  14. U.S. Real and Nominal Interest Rates

  15. Distinction Between Interest Rates and Returns • Rate of Return

  16. Key Facts about Relationship Between Rates and Returns

  17. Maturity and the Volatility of Bond Returns Initial YTM • Key Findings from Table 2 • 1. Only bond whose return = yield is one with maturity = holding period • 2. For bonds with maturity > holding period, i P implying capital loss • 3. Longer is maturity, greater is price change associated with interest rate change • 4. Longer is maturity, more return changes with change in interest rate • 5. Bond with high initial interest rate can still have negative return if i

  18. Maturity and the Volatility of Bond Returns • Conclusion from Table 2 Analysis 1. Prices and returns more volatile for long-term bonds because have higher interest- rate risk 2. No interest-rate risk for any bond whose maturity equals holding period

  19. Reinvestment Risk • 1. Occurs if hold series of short bonds over long holding period • 2. i at which reinvest uncertain • 3. Gain from i, lose when i

  20. Calculating Duration, i =10% 10-yr 10% Coupon Bond

  21. Calculating Duration, i = 20% 10-yr 10% Coupon Bond

  22. Formula for Duration =effective maturity for n個zero coupon bond • Key facts about duration • Everything else equal, • 1. When the maturity of a bond lengthens, the duration rises as well. • 2. When interest rates rise, the duration of a coupon bond falls.

  23. Formula for Duration • 3. The higher is the coupon rate on the bond, the shorter is the duration of the bond. • 4. Duration is additive: the duration of a portfolio of securities is the weighted-average of the durations of the individual securities, with the weights equaling the proportion of the portfolio invested in each.

  24. Duration and Interest-Rate Risk • %ΔP - DUR x Δi/(1+i) • i 10% to 11%: • Table 4 -10% coupon bond • %ΔP = -6.76 x .01/(1+.10) • = -.0615 = -6.15%. • Actual decline = 6.23% • 20% coupon bond, DUR = 5.98 years • %ΔP = - 5.98 x .01/(1+.10) • = -.0540 = -5.40%

  25. Duration and Interest-Rate Risk • The greater is the duration of a security, the greater is the percentage change in the market value of the security for a given change in interest rates. Therefore, the greater is the duration of a security, the greater is its interest-rate risk.

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