If the Duration is 20 and the present value of the bond $4000, then if the rates go up 10%, then you will approximately

Question

BlackTom AI · Accepted Answer

We start by identifying the given quantities: Duration = 20, present value (bond price) = $4000, and a yield increase Δy = 10% (0.10 in decimal form).

First, recall the approximate price change formula for a bond using duration: ΔP ≈ -Duration × Δy × P0, where P0 is the initial price.

Plugging in the numbers: ΔP ≈ -20 × 0.10 × $4000 = -2 × $4000 = -$8000.

This means the bond price would be expected to decrease by about $8000 under this linear approximation.

However, note an important caveat: applying the duration approximation with such a large yield change and a relatively small initial price can yield an implied price below zero (P ≈ $4000 + ΔP = $4000 - $8000 = -$4000), which is not possible in reality. The linear approximation is typically reliable only for small yield changes and does not account for convexity. With a 10% yield increase, the true price response would be less extreme than the raw linear estimate suggests, and the simple calculation signals the breakdown of the approximation rather than a precise future price.

Now, evaluate the provided options:
- 'gain $8000': This would require a positive price change, but the calculation shows a negative change due to the yield rise, so this is not consistent with the direction of price movement.
- 'lose $8000': This matches the magnitude and the negative direction given by the duration-based estimate, making it the best alignment with the computed result under the standard approximation.
- 'lose $80000': This is far larger in magnitude than the computed change; the formula does not support such a magnitude for the given inputs.
- 'gain $4000': This would imply the price rose from $4000 to $8000, which contradicts the expected negative impact of a yield increase on price.

In sum, the calculation using the duration approximation indicates a negative price change of about $8000, with the caveat that the linear model may overstate the true drop for such a large yield move and a small initial price.

If the Duration is 20 and the present value of the bond $4000, then if the rates go up 10%, then you will approximatelySingle choice

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