1. Finance 300 Financial Markets Lecture 9 Professor J. Petry, Fall, 2002© http://www.cba.uiuc.edu/jpetry/Fin_300_fa02/ http://webboard.cites.uiuc.edu/

2. 2 Housekeeping Equity projects due October 3 rd. You should be done with the numerical analysis, now focusing on writing the text. Form investment challenge teams this week for start on October 1 st. Next exam is October 15 th, will cover chapters IV and V. Class on October 10 th may have to be cancelled. I will keep you posted.

3. 3 Bond Pricing Things To Do: IV - 6 So what is our bond worth to us at issuance if mkt yld = 7%? Which equals?

4. 4 Bond Pricing So what is our bond worth to us at issuance if mkt yld = 5%? Which equals?

5. 5 Bond Pricing Which allows us to build the Price Yield Curve for this bond

6. 6 Bond Pricing How are prices determined when transactions take place at different times during the life of the bond? Things To Do: IV-7 You have 6% $1,000,000 bond issued June 1, 2002 and maturing June 1, 2014. A.John Q. Investor purchases this bond at issue when yields were 6%. Calculate the price of the bond at that time. Price = B.Yields increased to 8% by June 2004 when John sold his bond to Warren Buffet. At what price should the bond have changed hands? Price = C.Yields fell to 4% by June 2008 when Warren sold the bond to you. What price did you pay for the bond? Price =

7. 7 Debt Markets & Interest Rates Yield The rate of return on an investment under specific assumptions. Nominal Yield –The coupon rate. A bond with a 10% coupon, has a 10% nominal yield. Current or Income Yield –The current income divided by its price. A 5% coupon bond, which trades at 941/2 has a Current Yield of 5.29%. Promised Yield to Maturity –The fully compounded rate of return on a bond bought at the current market price and held to maturity. This is the IRR on the bond, and uses the net present value calculations we developed last class.

8. 8 Debt Markets & Interest Rates Yield (cont’d) Promised Yield to Maturity (cont’d) –Requires three assumptions for the promised yield to maturity to be realized. 1) Investor must hold to maturity; 2) Investor must reinvest coupons at the same yield as when the coupon was issued; 3) no defaults or payment delays. –Interest on interest is a large percentage of the earnings of a coupon bond. For instance a 20 year, $1,000 bond, w/ 8% coupon »Earns 0% of return from interest on interest at 0%, and returns 4.84% total realized compound yield. »Earns 47% of return from interest on interest ($1,416) at 6%, and returns 7.07% ($3016) total realized compound yield. »Earns 58% of return from interest on interest ($2,201) at 8%, and returns 8.0% ($3,801) total realized compound yield. »Earns 67% of return from interest on interest ($3,232) at 10%, and returns 9.01% ($4,832) total realized compound yield. –Yield illusion is the mistaken belief that the investor will receive the promised yield to maturity even if assumptions do not hold.

9. 9 Debt Markets & Interest Rates Yield (cont’d) Calculating Yield to Maturity –To approximately calculate this IRR, use the following formula: Example: –A $1,000 5% bond with 20 years to maturity selling at $1,200:

10. 10 Debt Markets & Interest Rates Yield (cont’d) Calculate the same example as above, but with Price = 900

11. 11 Debt Markets & Interest Rates Yield (cont’d) Realized Yield –The holding period yield for a bond which is sold prior to maturity. You calculate this the same way as a YTM, but with holding period rather than number of years to maturity, and with the estimated sale price of the bond instead of its par value.

12. 12 Debt Markets & Interest Rates Things to Do: IV-11 –A $100, 12% bond maturing March 1, 2014 is purchased September 1, 2001 at $147.99. It is sold March 1, 2010 for $118.85. What is the Yield to Maturity on the date of purchase? What is the Yield to Maturity on the date of sale? What is the Realized or Holding Period Yield?

13. 13 Debt Markets & Interest Rates Effective Annual Rate Calculations Most bonds pay out half the annual rate semi-annually. The effective annual rate is the rate of interest which provides an identical future value under annual compounding. r = the nominal interest rate m = the number of periods per year interest is compounded when m becomes continuous, we use the second formula Example: A $1,000 bond with 10% coupon or nominal rate, pays out $100 per year; $50 every six months. The effective annual rate = 10.25%. (1+.10/2) 2 =1.1025=1+10.25%.

14. 14 Debt Markets & Interest Rates Things To Do: IV-12 –You purchase a 12% bond (the nominal rate is 12%). A.What is the effective annual rate of interest if the bond pays coupons annually? B.What if the bond pays semi-annually? C.What if the bond pays quarterly? D.What if the bond pays monthly? E.What if the bond pays continuously? F.Since the bond remains a 12% bond under all these scenarios, why does the effective annual rate increase with the payment frequency?

15. 15 Bond Pricing If all bonds were identical in all aspects, we would just need to know the market interest rate, and we could use the relationship between r and p to find the price of the bond. In fact, bonds vary in many ways. Consequently, the yields (and therefore prices) vary considerably. The following items are the principal determinants of the yield structure (all facets and characteristics of existing yields): 1.Term to maturity. Life of the bond contract 2.Coupon Rate. Interest rate specified by the bond contract. 3.Call provisions. Contractual provisions whereby the bond can be paid off early. 4.Liquidity. Ability to buy or sell quickly without affecting price. 5.Risk of default. Risk that the issuer will not pay coupon and/or principal when it is due. 6.Tax Status. How income and capital gain are treated under the tax law.

16. 16 Bond Pricing The Term Structure of Interest Rates (cont’d) –Instead of looking at the Price/Yield curve for a single bond—how does the price vary as the yield moves--we frequently look at how the yield varies with the term to maturity. –We call this the “Term Structure of Interest Rates” and represent it graphically with the “yield curve”. The yield curve has the term to maturity on the horizontal axis and the yield on the vertical axis. –When we derive the “Term Structure” we are going to hold all things constant except the relationship between term to maturity and yield to maturity. Therefore we are assuming liquidity, call provisions, coupon rates, etc are equivalent. In other words, what would the yield be for this bond if it had differing maturity dates.

17. 17 Bond Pricing The Term Structure of Interest Rates (cont’d) –Interest rates over long durations can be thought of as nothing more than a series of short term interest rates spanning the same time period. –So what should the interest rate for 5 years be? It should be equivalent to what you could get if you invested your money in 1 year instruments for 5 consecutive years. –To develop this approach, we have to assume for a moment that there is perfect foresight, or certainty, regarding these future 1 year interest rates. –If I know that 1 year rates today are 6%, and that 1 year rates, 1 year from now are going to be 4.5%, I also know what the two year rate today should be. [(1.06)*(1.045)] 1/2 -1 =.052473 = 5.2473%

18. 18 Bond Pricing The Term Structure of Interest Rates (cont’d) –TERMINOLOGY: The interest rate from now to any time in the future is the “spot- rate”, so we talk about the 1 year spot rate, or the 5 year spot rate. The interest rates which take effect sometime in the future are “forward rates”. We have for instance, the “one year rate two years forward”, which is the one year rate, which takes effect two years from today. The ”two year rate, 5 years forward”, is the two year interest rate which takes effect 5 years from today. What we have concluded thus far is that the long term spot rate, is equivalent to the series of short-term forward rates. –Using this approach, we can easily derive the interest rates for whatever period we are interested in, provided we know one year rates for each year from now to the ultimate maturity we are interested in.

19. 19 Bond Pricing The Term Structure of Interest Rates (cont’d) Things to Do: IV-14 –My crystal ball tells me that the one year interest rates over the next five years will be: this year3.0% in one year (1 year rate, 1 year forward)5.0% in two years7.0% in three years8.0% in four years9.0% Calculate and plot the yield curve.