Adjust the bank discounted rate to make it comparable n P P r BEY 365

# Adjust the bank discounted rate to make it comparable

This preview shows page 37 - 44 out of 46 pages.

Adjust the bank discounted rate to make it comparable n P P r BEY 365 000 , 10 × = % 28 . 8 90 365 800 , 9 800 , 9 000 , 10 = × = BEY r BD BEY r P r = × × 365 360 000 , 10 Example: same as before BDR versus BEY
38 Spot Zero-Coupon (or Discount) Rate ! Spot Zero-Coupon (or Discount) Rate is the annualized rate on a pure discount bond ! where B(0,t) is the market price at date 0 of a bond paying off \$1 at date t ! General pricing formula ( ) t B R t t , 0 ) 1 ( 1 , 0 = + ( ) = = = + = T t t T t t t t t B F R F P 1 1 , 0 0 , 0 ) 1 ( Bond Par Yield ! Recall that a par bond is a bond with a coupon identical to its yield to maturity ! The bond's price is therefore equal to its principal ! Then we define the par yield c(n) so that a n-year maturity fixed bond paying annually a coupon rate of c(n) with a \$100 face value quotes at par ! Typically, the par yield curve is used to determine the coupon level of a bond issued at par = = + + = + + + = n i i i n n n n n i i i R R n c R R n c 1 , 0 , 0 , 0 1 , 0 ) 1 ( 1 ) 1 ( 1 1 ) ( ) 1 ( 100 ) 1 ( ) ( 100 100
39 Zero-Coupon Bonds ! Zero-Coupon Bond ! Does not make coupon payments ! Always sells at a discount (a price lower than face value), so they are also called pure discount bonds ! For example, ! In USA, Treasury Bills are U.S. government zero-coupon bonds with a maturity of up to one year. ! In France BTF : (bon du Trésor à taux fixe) are France government zero-coupon bonds (prepaid interest) with a maturity of up to one year. Zero-Coupon Bonds ! Suppose that a one-year, risk-free, zero-coupon bond with a \$100,000 face value has an initial price of \$96,618.36. The cash flows would be: ! Although the bond pays no “interest,” your compensation is the difference between the initial price and the face value.
40 Zero-Coupon Bonds ! Yield to Maturity ! The discount rate that sets the present value of the promised bond payments equal to the current market price of the bond. ! Price of a Zero-Coupon bond (1 ) = + n n FV P YTM Zero-Coupon Bonds ! Yield to Maturity ! For the one-year zero coupon bond: ! Thus, the YTM is 3.5%. 1 100,000 96,618.36 (1 ) = + YTM 1 100,000 1 1.035 96,618.36 + = = YTM
41 Zero-Coupon Bonds ! Yield to Maturity ! Yield to Maturity of an n -Year Zero-Coupon Bond 1 1 = n n FV YTM P Zero-Coupon Bonds Example ! Problem ! Suppose that the following zero-coupon bonds are selling at the prices shown below per \$100 face value. Determine the corresponding yield to maturity for each bond. Maturity 1 year 2 years 3 years 4 years Price \$98.04 \$95.18 \$91.51 \$87.14
42 Zero-Coupon Bonds Example ! Solution: 1/2 1/3 1/4 YTM (100 / 98.04) 1 0.02 2% YTM (100 / 95.18) 1 0.025 2.5% YTM (100 / 91.51) 1 0.03 3% YTM (100 / 87.14) 1 0.035 3.5% = = = = = = = = = = = Zero-Coupon Bonds ! Risk-Free Interest Rates ! A default-free zero-coupon bond that matures on date n provides a risk-free return over the same period. ! Thus, the Law of One Price guarantees that the risk-free interest rate equals the yield to maturity on such a bond. ! Risk-Free Interest Rate with Maturity n = n n r YTM
43 Zero-Coupon Bonds !

#### You've reached the end of your free preview.

Want to read all 46 pages?

• Spring '18
• carlitos

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern

Stuck? We have tutors online 24/7 who can help you get unstuck.
Ask Expert Tutors You can ask You can ask You can ask (will expire )
Answers in as fast as 15 minutes