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- 1. CSI Global Education Inc. Investment Products CHAPTER 7: Fixed-Income Securities: Pricing and Trading
- 2. Chapter Highlights <ul><li>Most bonds and fixed-income securities trade in the market on the basis of their yield or yield to maturity </li></ul><ul><li>Changes in interest rates play an important role in the pricing of bonds and fixed-income securities </li></ul><ul><li>The fair price to pay for a bond or fixed-income security is a function of current interest rates, the term to maturity, the coupon or income component on the security, and the required rate of return for that investment </li></ul>
- 3. Present Value <ul><li>Used to determine the value of a bond. </li></ul><ul><li>How much should be invested today to receive the face value of the security in the future. </li></ul><ul><li>Sum of the present value of the bond’s cash flows determines what you should be willing to pay for the bond today. </li></ul>
- 4. Present Value <ul><li>The present value is calculated using the following formula: </li></ul><ul><li>Where: </li></ul><ul><ul><li>PV = present value </li></ul></ul><ul><ul><li>FV = future value (the cash flows received) </li></ul></ul><ul><ul><li>r = the market discount rate </li></ul></ul><ul><ul><li>n = number of compounding period </li></ul></ul>
- 5. Present Value <ul><li>What is the present value of $1,040 to be received in 1 year’s time, discounted at 4%? </li></ul><ul><li>b) What is the present value of a 1-year bond with a $1,000 par value, a 4% coupon paid annually, discounted at 6%? </li></ul><ul><li>c) What is the present value of a 1-year bond with a $1,000 par value, a 4% coupon paid annually, discounted at 2%? </li></ul>
- 6. Present Value <ul><li>a) What is the present value of $1,040 to be received in 1 year’s time, discounted at 4%? </li></ul><ul><li>Solution: </li></ul><ul><li>This is a thinly disguised bond question. The investor receives $1,000 par and $40 in interest. </li></ul><ul><li>Since the discount rate equals the coupon rate the bond trades at par. </li></ul>
- 7. Present Value <ul><li>b) What is the present value of a 1-year bond with a $1,000 par value, a 4% coupon paid annually, discounted at 6%? </li></ul><ul><li>In the last year the bond repays par plus $40 (4% x 1000) in interest. </li></ul><ul><li>Solution: </li></ul><ul><li>Since the discount rate is greater than the coupon rate the bond trades at a discount. </li></ul>
- 8. Present Value <ul><li>c) What is the present value of a 1-year bond with a $1,000 par value, a 4% coupon paid annually, discounted at 2%? </li></ul><ul><li>Solution: </li></ul><ul><li>Since the discount rate is less than the coupon rate, the bond must trade at a premium. </li></ul>
- 9. Present Value <ul><li>What is the present value of an 8% 6 year semi-annual bond with a $10,000 par value and a 6% discount rate? </li></ul><ul><li>The cash flows are as follows (using a time line): </li></ul><ul><li> + + </li></ul><ul><li>PV $400 $400 $10,000 </li></ul>
- 10. Present Value <ul><li>This problem may be solved treating each value separately, or combining the last interest payment with the principal. </li></ul><ul><li>Solution: </li></ul><ul><li>Where: </li></ul><ul><li>FV 1 = $400 </li></ul><ul><li>FV 2 = $10,400 </li></ul><ul><li>r = 6% ÷ 2 = 3% </li></ul><ul><li>PV = $400/1.03 + $10,400/1.0609 = $388 + $9,803 = $10,191 </li></ul>
- 11. T-Bill Yields How to remember the formula: Yield = (positive number) × (number = or > 1)
- 12. T-Bill Yields a) What is the yield on a 181 day T-bill purchased for $98,000? b) What is the yield on a 90 day T-bill purchased for 99?
- 13. T-Bill Yields a) What is the yield on a 181 day T-bill purchased for $98,000? = (100,000 – 98,000) / 98,000 × 365/181 = 2,000 / 98,000 × 365/181 = 4.12% b) What is the yield on a 90 day T-bill purchased for 99? = 100 – 99 / 99 × 365/90 = 1/99 × 365/90 = 4.10%
- 14. Current Yield <ul><li>Current Yield is a short-term measure of return. </li></ul><ul><li>It allows investors to compare investments in bonds with other short-term investment opportunities (GICs, savings accounts, T-Bills etc.) </li></ul><ul><li>It is the actual interest income rate of return, compared with the coupon rate earned on the bond, based on the prevailing bond price and market interest rate. </li></ul>
- 15. Current Yield <ul><li>NFR issued a bond with a 10% coupon, a $1,000 par value and 10 years to maturity. </li></ul><ul><li>a) If an investor purchases the bond for $1,000, what is its current yield? </li></ul><ul><li>b) If an investor purchase the bond for 90 ($900), what is the investor’s current yield? </li></ul><ul><li>c) If an investor purchased the bond for 110, what is the investor’s current yield? </li></ul>
- 16. Current Yield <ul><li>a) If an investor purchases the bond for $1,000, what is its current yield? </li></ul><ul><li>$100/$1000 = .10 or 10% </li></ul><ul><li>Notice that since the bond sells at par, the coupon and the current yield are the same. </li></ul>
- 17. Current Yield <ul><li>b) If an investor purchases the bond for 90 what is the bond’s current yield? </li></ul><ul><li>$100/$900 = 11.11% </li></ul><ul><li>The price of 90 is simply 90% of par. Since par is $1,000, the price of the bond is: 0.90 × $1,000 = $900. </li></ul><ul><li>Why is the current yield higher than the coupon in this case? </li></ul>
- 18. Current Yield <ul><li>c) If an investor purchases the bond for 110, what is the bond’s current yield? </li></ul><ul><li>$100/$1,100 = 9.09% </li></ul><ul><li>Same rule applies here, the purchase price is 110% of par. </li></ul><ul><li>Why is the current yield less than the coupon in this case? </li></ul>
- 19. Approximate Yield to Maturity (AYTM) <ul><li>Where: </li></ul><ul><li>Annual Cash flow is the annual dollar amount of interest received on a bond. </li></ul><ul><li>Annual Capital gain (or loss) is the ending value (always par or $1,000) less the beginning value divided by the number of years from the calculation date to maturity . </li></ul><ul><li>Average Cost is amount at maturity plus present price divided by 2. </li></ul>
- 20. Approximate Yield to Maturity <ul><li>DKE Inc. issues a bond with an 10% coupon, a $1,000 par value and 10 years to maturity. </li></ul><ul><li>a) What is the bond’s AYTM? </li></ul><ul><li>b) If an investor purchase the bond for 90, what is the bond’s AYTM? </li></ul><ul><li>c) If an investor purchased the bond for 110, what is the bond’s AYTM? </li></ul>
- 21. Approximate Yield to Maturity <ul><li>a) What is the bond’s AYTM? </li></ul><ul><li> Interest + [($1,000 – Purchase Price)/Years] </li></ul><ul><li> ($1,000 + $900)/2 </li></ul><ul><li>$100 + [($1,000 – $1,000)/10] $1,000 </li></ul><ul><li>AYTM = 10% </li></ul>
- 22. Approximate Yield to Maturity <ul><li>AYTM when the bond is purchased for 90 </li></ul><ul><li>Interest + [($1,000 – Purchase Price)/Years] </li></ul><ul><li>($1,000 + $900)/2 </li></ul><ul><li>$100 + [($1,000 – $900)/10] $950 </li></ul><ul><li>AYTM = 11.57% </li></ul>
- 23. Approximate Yield to Maturity <ul><li>AYTM when the bond is purchased for 110 </li></ul><ul><li>Interest + [($1,000 – Purchase Price)/Years] ($1,000 + $1,100)/2 </li></ul><ul><li>$100 + [($1,000 – $1,100)/10] $1,050 </li></ul><ul><li>AYTM = 8.57% </li></ul>
- 24. Rules for AYTM, CY and Coupon Rates <ul><li>Using what you have learned from the calculations above, lets establish some rules: </li></ul><ul><li>a) If the bond sells at par… </li></ul><ul><li>Coupon Rate = AYTM = Current Yield </li></ul><ul><li>b) If the bonds sell at a discount… </li></ul><ul><li>AYTM and the Current Yield must be greater than the coupon rate. </li></ul><ul><li>c) If the bond trades at a premium… </li></ul><ul><li>AYTM and the Current Yield must be less than the coupon rate. </li></ul>
- 25. Bond Pricing Properties <ul><li>Bond prices move inversely to bond yields. </li></ul><ul><li>The longer to maturity the greater the price fluctuation. </li></ul><ul><li>Bonds with higher coupons move less (%) than bonds with lower coupons. </li></ul><ul><li>Special features lead to different pricing (e.g. convertible bonds). </li></ul><ul><li>Bond prices are more volatile when interest rates are low. </li></ul><ul><li>Bonds are subject to reinvestment risk. </li></ul>
- 26. Implications: Bond Pricing Properties <ul><li>Also: </li></ul><ul><li>Holding maturities constant , you make more money with a 1% price decline (capital gain), than you lose with the same percentage increase </li></ul><ul><li>Bonds with Higher Coupons Move Less (%) than Bonds with Lower Coupons </li></ul><ul><li>Example : Two 15-year bonds </li></ul><ul><li>Bond C (10% coupon) – 17.3% increase </li></ul><ul><li>Bond D (15% coupon) – 16% increase </li></ul>
- 27. Implications: Bond Pricing Properties <ul><li>Bond Prices Move Inversely to Bond Yields </li></ul><ul><li>Trading opportunities – “if” you can predict interest rate changes </li></ul><ul><li>The Longer to Maturity the Greater the Price Fluctuation </li></ul><ul><li>Example : Two bonds with 10% coupon and rates fall to 8% </li></ul><ul><li>Bond A (15 years) – $1,172.90 – 17.29% increase </li></ul><ul><li>Bond B (25 years) – $1,214.80 – 21.48% increase </li></ul>
- 28. Reinvestment Risk <ul><li>Since interest rates fluctuate, the interest rate prevailing at the time of purchase is unlikely to be the same as the interest rate prevailing at the time the investor reinvests cash flows from each coupon payment. </li></ul><ul><li>The longer the term to maturity, the less likely it is that interest rates will remain constant over the term. The risk that the coupons cannot be reinvested at the same interest rate that prevailed at the time the bond was purchased is called reinvestment risk . </li></ul>
- 29. Duration <ul><li>A measure of the sensitivity of a bond’s price to changes in interest rates. </li></ul><ul><li>It is the approximate percentage change in the price or value of a bond for a 1% point change in interest rates. </li></ul><ul><li>The higher the duration of a bond, the more it will react to a change in interest rates. </li></ul><ul><ul><li>i.e. the higher the duration the riskier the bond </li></ul></ul>
- 30. Duration <ul><li>Duration is used to determine the volatility or riskiness of a bond or a bond fund. </li></ul><ul><li>If the duration of a bond is 10, then its price will change by approximately 10% if interest rates change by 1%. </li></ul><ul><li>Assume you hold a bond with a 5% coupon that is currently priced at 104. </li></ul><ul><li>If interest rates rise by 1% then the price of the bond will fall by approximately 10% to 93.60. </li></ul>
- 31. Bond Investment Strategies <ul><li>What would you look for in a bond if your primary concern was “receiving a fixed amount” ? </li></ul><ul><li>If your goal was improving your portfolio? </li></ul><ul><li>If you were a speculator ? </li></ul>
- 32. Bond Investment Strategies <ul><li>What would you look for in a bond if your primary concern was “receiving a fixed amount” ? </li></ul><ul><li>High coupon rate or nominal yield </li></ul><ul><li>Look for high current yields </li></ul><ul><li>DANGER? </li></ul><ul><li>No hedge against inflation. </li></ul>
- 33. Bond Investment Strategies <ul><li>If your goal was improving your portfolio? </li></ul><ul><li>Bond Switches: </li></ul><ul><li>a) Net Yield Improvement: </li></ul><ul><li>– Match bond choices with tax bracket. </li></ul><ul><li>b) Term Extension or Reduction: </li></ul><ul><li>– Switch one comparable bond for another with a longer or shorter term. </li></ul>
- 34. Bond Investment Strategies <ul><li>Bond Switches (continued): </li></ul><ul><li>c) Improvement in Credit: </li></ul><ul><li>– Switch bonds in anticipation of a better credit rating. </li></ul><ul><li>d) Portfolio Diversification: </li></ul><ul><li>– Rebalance bonds to decrease risk. </li></ul><ul><li>e) Cash Take-Outs: </li></ul><ul><li>– Sell high-price bonds and replace with lower priced bonds and pocket the extra. </li></ul>
- 35. Bond Investment Strategies <ul><li>If you were a speculator? </li></ul><ul><li>Depends on your prediction as to the change in interest rates. </li></ul>
- 36. Bond Investment Strategies <ul><li>If rates are expected to decline? </li></ul><ul><li>Buy long-term low coupon bonds </li></ul><ul><li>If interest rates are expected to increase? </li></ul><ul><li>Buy short-term high coupon bonds </li></ul><ul><li>OR : Hold cash, short bonds </li></ul>
- 37. Settlement Exercise <ul><li>T-Bills _________________ </li></ul><ul><li>Govt. of Canada’s (less than 3 years) _________________ </li></ul><ul><li>Govt. of Canada Guaranteed bonds (less than 3 years) _________________ </li></ul><ul><li>All bonds with maturities of over 5 years _________________ </li></ul><ul><li>Confirmation notices _________________ </li></ul><ul><li>A trade on a mortgage-backed security _________________ </li></ul>
- 38. Settlement Exercise <ul><li>T-Bills Same day </li></ul><ul><li>Govt. of Canada’s (less than 3 years) T + 2 </li></ul><ul><li>Govt. of Canada Guaranteed bonds (less than 3 years) T + 2 </li></ul><ul><li>All bonds with maturities of over 5 years T + 3 </li></ul><ul><li>Confirmation notices Same or next working day </li></ul><ul><li>A trade on a mortgage-backed security 1 st clearing day on or after the 15 th </li></ul>

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