Ch.9 Bond Valuation

1. Bond Valuation

• Bond: Security which obligates the issuer to pay the bondholder periodic interest payment and to repay the principal at maturity.

• Two types of Cash flows: Coupon and Face Value ($1000).

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• Ex) Wrent-a-Wreck, Inc has issued bonds with 20 years to maturity, an 8% coupon rate and $1,000 face value. If your yield to maturity is 9% and the bonds pay interest semiannually, what is the value of these bonds?

• Price (Settlement, Maturity, Rate, Yld, Redemption, Frequency, Basis)

• Settlement: date on which money and security change hands

• Maturity: date on which the last coupon payment is made and the principal is returned.

• Rate: Annual coupon rate• Yld: Yield to Maturity.• Redemption: the amount to be received

per $10 of face value when the bond is redeemed.

• Frequency: the number of coupon paid each year.

• Base: Assumptions regarding the number of days in a month and year.

2) Bond Return Measure

• (1) Current Yield: • Annual Coupon payment / Current bond

price

(2) Yield to Maturity:

• compounded annual rate of return

• Using trial and error approach

Or

• Yield (Settlement, Maturity, Rate, Pr, Redemption, Frequency, Basis)

• Here Pr means current bond price as a percentage of par value

(3) Yield to Call• Yield if we assume the bond is called at the first

opportunity. It usually provides call premiums to investors.

2. Return on discounted Debt Security

Money market securities are short term, high quality debt instruments that are sold on a discounted basis. They typically do not pay interests and are called discounted securities.

• Returns on discounted securities (bank discount rate)

• = (FV-P)/FV * 360/M• (Here, FV is a face value, p is the purchase

price, M is the number of days until maturity).• Disc (settlement, maturity, pp, redemption,

basis). Here 2 in basis means actual date/360 days)

• Ex) If you purchase a six-month (181 days) T-Bill for $985, the bank discount rate?

• 3. Duration and Convexity• Long term bonds and bonds with low

coupon rates are much more sensitive to changes in yields than are short-term bonds and those with high coupon rates.

• Thus if you believe that interest rates will rise, you should move into short term bonds with high coupon rates. On the other hand, if you believe that rates will fall, you should move into long term bonds with low coupon rates.

• Duration is a measurement combining the effects of maturity, coupon rate and yield into a single number that can be used to measure the interest rate risk of a bond.

• Macaulay’s duration: (Here, VB is the current price)

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• Macaulay Duration is a weighted average of the time to receive the cash flows of the bond in present value terms. It is measurement related to interest rate risk in bond valuation.

• The longer duration, the greater the interest rate sensitivity of a bond. Thus investors may have to determine which bonds are good for her or his portfolios over predicted interest rate movement.

2-2. Modified Duration• Using a duration, we can approximate the price

change of bond over changing interest rates. It is called Modified Duration. (here m is the payment frequency.)

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• The approximate measures are good only for small changes in yield due to nonlinear patterns of prices over yield changes.

• 2-3. Convexity• It is a measurement of the curvature (nonlinear

relationship of the price to yield). It is a rate of change in the bond’s duration. The higher the convexity, the more curved is the function.

• Application1: It is used to improve the price change approximate over the changing yield.

• Application2: The more convex bond will gain more or lose less if yield changes. More convexity is preferred.

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