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I went on a rant below, but this is actually a trick question. If the time to maturity of the bond is 3 years, if its current yield to maturity is 4.5%, and if you hold the bond to maturity, then the annualized horizon return will be 4.5%, assuming all interim cash flows can be reinvested at the 4.5% yield. If cash flows cannot be reinvested at 4.5%, then ...

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If the bonds yield goes down by $100 \text{bps}$ and the duration is $3$, the bond price will increase by approximately $3\%$. Without any subsequent movement over the next three years, the bond should yield 3.5% p.a. after the yield rate movement. The return during the total holding period of three years would be approximately: $$3\% \text{(yield rate ... 1 Duration (of which Macaualy is one type) is only a linear approximation of how the bond value will change with a small change in yield. 3 The change of the price P(y) if the yield changes from y to y+\Delta y is$$ \frac{P(y+\Delta y) - P(y)}{P(y)} = - D \Delta y + \frac12 C \Delta y^2,  where $D$ is the duration and $C$ is convexity. For small $\Delta y$ the square is much smaller. Thus the duration component dominates.

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DV01 is the dollar variation in a bond's value per unit change in the yield. https://en.wikipedia.org/wiki/Bond_duration IR DV01 is the dollar value change for a 1bp upward parallel shift in interest rates. http://dataforthoughts.blogspot.it/2009/09/economics-of-negative-bond-cds-basis.html

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the negative and positives in the same series are a result of negative convexity. stated differently, the asymmetry in the series is a result of negative convexity. These relationships, however, are not permanent and may flip.

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I calculate duration in Python using numpy, it's nice and simple: def durations(cfs, rates, price, ytm, no_coupons): import numpy as np mac_dur = np.sum([cfs[i]*i/np.power(1+rates[i],i) for i in range(len(cfs))])/price mod_dur = mac_dur/(1+ytm/no_coupons) return mac_dur, mod_dur

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