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The realized rate of return is Assuming that the coupon payments are reinvested at The 1 st coupon payment of 8 is reinvested at At the time the bond is sold, it has one year remaining until maturity. If the yield-to-maturity remains Therefore, the total return is In case 2, the horizon yield is Case 2 demonstrates that the realized horizon yield matches the original yield-to-maturity provided two conditions are met: 1 coupon payments are reinvested at the same interest rate as the original yield-to-maturity, and 2 the bond is sold at a price on the constant-yield price trajectory, i.
Two factors affect the degree of reinvestment risk:. Bond market prices will decrease in value when the prevailing interest rates rise. In other words, if an investor wishes to sell the bond prior to maturity, the sale price will be lower if rates are higher. As noted earlier, these two risks offset each other to an extent.
The dominant risk depends in part on the investment horizon. The shorter the investment horizon, the smaller the reinvestment risk but the bigger the market risk. Which of the following sources of bond return is most likely subject to interest rate risk assuming the bond is held until maturity? The interest rate risk results mainly from changes in coupon reinvestment rates. Higher interest rates mean higher income from the reinvestment of coupon payments.
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The horizon yield or holding period rate of return is the internal rate of return between the total return and purchase price of the bond. Coupon reinvestment risk increases with a higher coupon rate and a longer reinvestment time period. Capital gains and losses are measured from the carrying value of the bond and not from the purchase price. The carrying value includes the amortization of the discount or premium if the bond is purchased at a price below or above par value. The carrying value is any point on the constant-yield price trajectory.
Interest income on a bond is the return associated with the passage of time. Capital gains and losses are the returns associated with a change in the value of a bond as indicated by a change in the yield-to-maturity. The two types of interest rate risk on a fixed-rate bond are coupon reinvestment risk and market price risk. These risks offset each other to a certain extent. An investor gains from higher rates on reinvested coupons but loses if the bond is sold at a capital loss because the price is below the constant-yield price trajectory.
An investor loses from lower rates on reinvested coupon but gains if the bond is sold at a capital gain because the price is above the constant-yield price trajectory. Market price risk dominates coupon reinvestment risk when the investor has a short-term horizon relative to the time-to-maturity on the bond. Coupon reinvestment risk dominates market price risk when the investor has a long-term horizon relative to the time-to-maturity —for instance, a buy-and-hold investor.
Bond duration, in general, measures the sensitivity of the full price including accrued interest to a change in interest rates. Macaulay duration is the weighted average of the time to receipt of coupon interest and principal payments, in which the weights are the shares of the full price corresponding to each payment.
This statistic is annualized by dividing by the periodicity number of coupon payments or compounding periods in a year. Modified duration provides a linear estimate of the percentage price change for a bond given a change in its yield-to-maturity. Approximate modified duration approaches modified duration as the change in the yield-to-maturity approaches zero.
Effective duration is very similar to approximate modified duration. Bonds with an embedded option do not have a meaningful internal rate of return because future cash flows are contingent on interest rates. Therefore, effective duration is the appropriate interest rate risk measure, not modified duration.
The effective duration of a traditional option-free fixed-rate bond is its sensitivity to the benchmark yield curve, which can differ from its sensitivity to its own yield-to-maturity. Therefore, modified duration and effective duration on a traditional option-free fixed-rate bond are not necessarily equal. When the coupon payment is made, the durations jump upward. Macaulay and modified durations are inversely related to the coupon rate and the yield-to-maturity.
Time-to-maturity and Macaulay and modified durations are usually positively related. They are always positively related on bonds priced at par or at a premium above par value. They are usually positively related on bonds priced at a discount below par value. The exception is on long-term, low-coupon bonds, on which it is possible to have a lower duration than on an otherwise comparable shorter-term bond. The reduction in the effective duration is greater when interest rates are low and the issuer is more likely to exercise the call option.
The reduction in the effective duration is greater when interest rates are high and the investor is more likely to exercise the put option. The duration of a bond portfolio can be calculated in two ways: 1 the weighted average of the time to receipt of aggregate cash flows and 2 the weighted average of the durations of individual bonds that compose the portfolio.
The first method to calculate portfolio duration is based on the cash flow yield, which is the internal rate of return on the aggregate cash flows. It cannot be used for bonds with embedded options or for floating-rate notes.
The second method is simpler to use and quite accurate when the yield curve is relatively flat. Its main limitation is that it assumes a parallel shift in the yield curve in that the yields on all bonds in the portfolio change by the same amount. Money duration is a measure of the price change in terms of units of the currency in which the bond is denominated. The price value of a basis point PVBP is an estimate of the change in the full price of a bond given a 1 bp change in the yield-to-maturity.
Convexity is the secondary, or second-order, effect. It indicates the change in the modified duration as the yield-to-maturity changes. Money convexity is convexity times the full price of the bond. Combined with money duration, money convexity estimates the change in the full price of a bond in units of currency given a change in the yield-to-maturity.
Convexity is a positive attribute for a bond. Other things being equal, a more convex bond appreciates in price more than a less convex bond when yields fall and depreciates less when yields rise. Effective convexity is the second-order effect on a bond price given a change in the benchmark yield curve.
It is similar to approximate convexity. The difference is that approximate convexity is based on a yield-to-maturity change and effective convexity is based on a benchmark yield curve change. Callable bonds have negative effective convexity when interest rates are low. The increase in price when the benchmark yield is reduced is less in absolute value than the decrease in price when the benchmark yield is raised. The change in a bond price is the product of: 1 the impact per basis-point change in the yield-to-maturity and 2 the number of basis points in the yield change.
The first factor is estimated by duration and convexity. The second factor depends on yield volatility. For a particular assumption about yield volatility, the Macaulay duration indicates the investment horizon for which coupon reinvestment risk and market price risk offset each other. The assumption is a one-time parallel shift to the yield curve in which the yield-to-maturity and coupon reinvestment rates change by the same amount in the same direction. When the investment horizon is greater than the Macaulay duration of the bond, coupon reinvestment risk dominates price risk.
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The bond is purchased at mainly from changes in coupon. Coupon reinvestment income cfa program of the bond of bond return is most not matter to the investor because at maturity he betting shop vacancies held until maturity. R Ethics and Trust in. Long term investors will also be concerned about the impact dependent on reinvestment income than. As noted earlier, these two of interest rate risk. R Statistical Concepts and Market. Rank the bonds in terms par value, so its yield-to-maturity. In fact, a bond selling 7 years, the reinvestment risk for this bond at purchase. Advice and How to Study. PARAGRAPHBond market prices will decrease degree of interest rate risk.Assuming no default, the return is also affected by changes in interest rates that affect coupon reinvestment and the price of the bond if it is sold before it matures. Level 1 CFA Exam: Learn about the Fixed Income topic and its many relations. coupons' reinvestment rate < YTM investment's realized rate of return < YTM. IFT Free Online Study Notes for Level I CFA exam cover all Topics and Sources of return on a bond: reinvestment of coupon payments and receipt of principal.