Yield, Total Return, and Reinvestment Risk

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# Yield, Total Return, and Reinvestment Risk - PowerPoint PPT Presentation

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

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

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.

Yield to Maturity of A Bond
• The yield on an investment can be found as:

What is meant by y:

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?
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?
Current Yield
• Current yield = annual dollar coupon interest/price
• Only consider coupon payment
Yield to Call
• Call price: the price at which the bond may be called
• Yield to call:
• Fixed call price
• Call schedule
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
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.
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
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.
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
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
Total Returns
• If the bond is sold before maturity
• If the bond is sold at maturity
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?
Step 1
• Compute the total coupon payment + interest on interest
Steps 2 and 3
• Determine the resale value of the bond
• Adding the amounts in steps (1) and (2)
Steps 4 and 5
• Obtain semi-annual total return
• Calculate annual return

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?

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?

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