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Yield, Total Return, and Reinvestment Risk

Yield, Total Return, and Reinvestment Risk. 1. Internal rate of return 2. Yields to maturity 3. Other Yields Current yield Cash flow yield Yield for a portfolio 4. Decompose total dollar returns 5. Reinvestment risk 6. Compute total return for a bond. Internal Rate of Return.

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Yield, Total Return, and Reinvestment Risk

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  1. Yield, Total Return, and Reinvestment Risk 1. Internal rate of return 2. Yields to maturity 3. Other Yields Current yield Cash flow yield Yield for a portfolio 4. Decompose total dollar returns 5. Reinvestment risk 6. Compute total return for a bond

  2. Internal Rate of Return The yield on an investment can be found as: The yield calculated from this relationship is the internal rate of return.  the return to make the above equation hold. What is the actual meaning of y: (1) (2) Example: see page 36.

  3. Yield to Maturity of A Bond • The yield on an investment can be found as: What is meant by y:

  4. The coupons of corporate bonds are typically semiannually paid, doubling the periodic interest rate or discount rate (y) gives the annual yield to maturity. • But this is simple annual interest rate. • What does YTM really mean?

  5. Annualizing Yields • Also known as effective annual yield (EAY) • EAY=(1+periodic interest rate)m-1 • Examples: • The periodic interest rate is 4%, interest semi-annually paid, what is EAY? • The periodic interest rate is 2%, interest quarterly paid, what is EAY? • If APR is 8%, interest semi-annually paid, what is EAY? • If APR is 8%, interest quarterly paid, what is EAY?

  6. Current Yield • Current yield = annual dollar coupon interest/price • Only consider coupon payment

  7. Yield to Call • Call price: the price at which the bond may be called • Yield to call: • Fixed call price • Call schedule

  8. Assumptions for Yield to Call • Cash flows can be reinvested at the yield to call until the assumed call date • The investor will hold the bond to the assumed call date • The issuer will call the bond on that date • Also note: callable bonds could be traded above the call price

  9. Bond price and call • This is a deviation from the yield to call, while it helps to understand the pricing of callable bonds • Example on page 375: • Consider a callable bond with a 10-year 13% coupon rate that is callable in 1 year at a call price of 104. Suppose the yields on 10-year and 1-year bonds are 6% and 5%. Investors expect the bond would be called in 1 year. What is the price of the bond? Assume the bond pays coupons semiannually.

  10. Cash Flow Yield • For amortizing securities • Cash flow in each period includes • - coupon interest • - scheduled principal repayment • - unscheduled prepayments • Calculated as internal rate of return for a cash flow

  11. Yield for a Portfolio • There are multi-bonds, their yields to maturity are known or are calculable. • What is the yield to maturity of the portfolio? • Example on page 43.

  12. Yield Spread for Floating Rate Securities • Floating rate = reference rate + quoted margin • Calculate the discount margin by assuming the reference is constant over the life of a bond. • Page 44-45

  13. What do we know here? • Maturity: 6 years • Coupon rate: reference rate + 80bp • Initial reference rate: 10% • Price of the bond: 99.3098 • Question: what is the yield spread of the bond? • yield spread = yield – reference rate

  14. Total Returns • If the bond is sold before maturity • If the bond is sold at maturity

  15. 1. If Bonds are Sold Before Maturity • 3-year investment horizon • purchasing a 20-year 8% coupon bond for $828.40. YTM is 10% • Reinvestment rate = 6% • YTM at the end of investment horizon is 7% • Total return for this bond?

  16. Step 1 • Compute the total coupon payment + interest on interest

  17. Steps 2 and 3 • Determine the resale value of the bond • Adding the amounts in steps (1) and (2)

  18. Steps 4 and 5 • Obtain semi-annual total return • Calculate annual return

  19. Reinvestment Risk • Future reinvestment rates will be less than the YTM at the time the bond is purchased. • Coupon payments • Length of maturity of the bond is shorter than the holding period • Is there any reinvestment risk associated with zero-coupon bonds?

  20. A Simple Example – Bond Held until Maturity • 15-year 7% bond, semi-annually paid, par $1000, price $769.40. YTM = 10%. The bond is held until maturity, reinvestment return = YTM=10%. Answer the following questions. • What is the total dollar return of the bond • Evaluate the return from each source • What is the reinvestment return? • What is the reinvestment risk?

  21. Decomposing Dollar Returns • Assumption: reinvestment return=YTM • Three sources • Periodic coupon interest payments made by the issuer -- nC • Capital gain -- M-P • Interest on interest – (reinvestment income, subject to reinvestment risk) • -- C[((1+r)n-1)/r]-nC

  22. Additions • Multiple reinvestment rate: see the example on page 53. • What is the implication of total return in practice? – horizon return/horizon analysis • How to reconcile the analysis we have done so far with the simple formula: • ret=(Ps-Pb+C)/Pb?

  23. Exercise

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