Reading 65: Yield Measures, Spot Rates, and Forward Rates LO invest

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LOS c, (Part 1): Explain the importance of reinvestment income in generating the yield computed at the time of purchase, and calculate the amount of income required to generate that yield.

An investor purchases a 4-year, 6%, semiannual-pay Treasury note for $9,485. The security has a par value of $10,000. To realize a total dollar return equal to 7.515% (its yield to maturity), the investor must have which of the following reinvestment assumptions?

A) All payments must be reinvested at more than 7.515%.

B) All payments must be reinvested at less than 7.515%.

C) All payments must be reinvested at 7.515%.

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The reinvestment assumption that is embedded in any present value-based yield measure implies that all coupons and principal payments must be reinvested at the specific rate of return, in this case, the yield to maturity. Thus, to obtain a 7.515% total dollar return, the investor must reinvest all the coupons at a 7.515% rate of return. Total dollar return is made up of three sources, coupons, principal, and reinvestment income.

 

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If the promised yield is equal to the realized yield then:

A) the coupon payments are reinvested at the promised yield during the life of the issue.

B) nominal yield is smaller than the promised yield.

C) current yield is lesser than the yield to maturity.

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The promised yield is the YTM and the realized yield is the actual return earned during a specific horizon.  In order for the realized yield to equal the promised yield, reinvestments must occur at the promised yield.  When the realized yield is equal to the promised yield there are no conclusions that can be made about whether the bond is selling at par, a discount, or a premium.

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Which of the following is an incorrect statement when zero-coupon bonds are compared to coupon-paying bonds with the same maturity? Zero-coupon bonds:

A) are less sensitive to interest rate changes.

B) have a higher duration.

C) are sold at a lower price.

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Since zero-coupon bonds have a higher duration than coupon-paying bonds of the same maturity, they are more sensitive to interest rate changes.

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Jane Walker has set a 7% yield as the goal for the bond portion of her portfolio. To achieve this goal, she has purchased a 7%, 15-year corporate bond at a discount price of 93.50. What amount of reinvestment income will she need to earn over this 15-year period to achieve a compound return of 7% on a semiannual basis?

A) $459.

B) $574.

C) $624.

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935(1.035)³⁰ = $2,624

Bond coupons: 30 × 35 = $1,050

Principal repayment: $1,000

2,624 ? 1,000 – 1050 = $574 required reinvestment income

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All else being equal, which of the following bond characteristics will lead to lower levels of coupon reinvestment risk?

A) Shorter maturities and lower coupon levels.

B) Longer maturities and higher coupon levels.

C) Shorter maturities and higher coupon levels.

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Other things being equal, the amount of reinvestment risk embedded in a bond will decrease with lower coupons because the there will be a lesser dollar amount to reinvest and with shorter maturities because the reinvestment period is shorter.

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All else being equal, which of the following bond characteristics will lead to higher levels of coupon reinvestment risk?

A) Longer maturities and lower coupon levels.

B) Shorter maturities and higher coupon levels.

C) Longer maturities and higher coupon levels.

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Other things being equal, the amount of reinvestment risk embedded in a bond will increase with higher coupons because there is a greater dollar amount to reinvest, and with longer maturities because the reinvestment period is longer.

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If the coupon payments are reinvested at the coupon rate during the life of the issue, then the:

A) yield to maturity cannot be determined from the information given.

B) yield to maturity is less than the realized yield.

C) yield to maturity is greater than the realized yield.

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For the calculated YTM to hold true all reinvestments must occur at that YTM, otherwise a new YTM will occur and we will not be able to calculate it.