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Measuring Yield

Measuring Yield. Zvi Wiener Based on Chapter 3 in Fabozzi Bond Markets, Analysis and Strategies. Yield. Yield = IRR = Internal Rate of Return. FRM-98, Question 12.

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Measuring Yield

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  1. Measuring Yield Zvi Wiener Based on Chapter 3 in Fabozzi Bond Markets, Analysis and Strategies http://pluto.mscc.huji.ac.il/~mswiener/zvi.html

  2. Yield Yield = IRR = Internal Rate of Return Fabozzi Ch 3

  3. FRM-98, Question 12 • A fixed rate bond, currently priced at 102.9, has one year remaining to maturity and is paying an 8% coupon. Assuming that the coupon is paid semiannually, what is the yield of the bond? • A. 8% • B. 7% • C. 6% • D. 5% Fabozzi Ch 3

  4. FRM-98, Question 12 • ys = 5% Fabozzi Ch 3

  5. Annualizing Yield • Effective annual yield = (1+periodic rate)m-1 examples • Effective annual yield = 1.042-1=8.16% • Effective annual yield = 1.024-1=8.24% Fabozzi Ch 3

  6. Bond selling at Relationship • Par Coupon rate=current yield=YTM • Discount Coupon rate<current yield<YTM • Premium Coupon rate>current yield>YTM • Yield to call uses the first call as cashflow. • Yield of a portfolio is calculated with the total cashflow. Fabozzi Ch 3

  7. YTM and Reinvestment Risk • YTM assumes that all coupon (and amortizing) payments will be invested at the same yield. Fabozzi Ch 3

  8. YTM and Reinvestment Risk • An investor has a 5 years horizon • Bond Coupon Maturity YTM • A 5% 3 9.0% • B 6% 20 8.6% • C 11% 15 9.2% • D 8% 5 8.0% • What is the best choice? Fabozzi Ch 3

  9. Yield to Call Yield to Put Yield to Worst Spread for a floater Total return for a bond Fabozzi Ch 3

  10. IRR of a portfolio • Aggregation of all cashflows and using the same formula. Fabozzi Ch 3

  11. Problems with yield • Many equivalent ways to measure? • Assumes reinvestment. • Does not reflect risk. • What if investment is very leveraged? • Options, Forwards, Swaps Fabozzi Ch 3

  12. Example Cost: 101 Promised cashflow: After 1 year 6 After 2 years 7 After 3 years 8 After 4 years 9 After 5 years 110 Fabozzi Ch 3

  13. Yield calculation y = 7.6% Fabozzi Ch 3

  14. Example 2 Cost: 101 Promised cashflow: After 1 year 6 After 2 years 7,callable at 100 After 3 years 8 After 4 years 9 After 5 years 110 Fabozzi Ch 3

  15. Yield to Call calculation y = 5.94% Fabozzi Ch 3

  16. How to treat Floaters • Floater is similar to a constantly renewed loan with fixed spread (!). • Thus the yield of a floater is equal to the yield on the basis plus the spread. • Note that some of the Israeli government bonds have funny linkage to other bonds. Fabozzi Ch 3

  17. Home AssignmentChapter 3 • Questions 1, 2, 5, 7, 10 Fabozzi Ch 3

  18. Reverse (Inverse) Floater • USD 5 year interest rates are 5%, however short term interest rates are Libor =2%. • Libor = London Interbank offered rate • on Bloomberg see FWCV + currency • One can construct so-called reverse floater: Fabozzi Ch 3

  19. Reverse Floater bond -100 5 5 5 5 105 loan +100 -L0 -L1 -L2 -L3 -100- L4 bond -100 5 5 5 5 105 Reverse Fl. -100 8 10-L1 10-L2 10-L3 110- L4 • Years • 0 • 1 • 2 • 3 • 4 • 5 Fabozzi Ch 3

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