Jane Higgins, CFA, is analyzing a corporate bond that she believes is a suitable addition for a client's portfolio. The 10-year security has a 7.50% annual coupon and is non-callable by the issuer. The bond is currently priced at 104.5 to yield 7.177%. According to Higgins* analysis, for a 25 basis point decrease in yield, the bond's price will increase to 107.4166 and for a 25 basis point increase in yield, the bond's price will decrease to 101.3834. Higgins' estimation of the bond's effective duration is closest to:
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A. B. C.Explanation
To calculate the effective duration of a bond, we need to analyze the relationship between bond prices and yield changes. Effective duration measures the sensitivity of a bond's price to changes in its yield or interest rates.
In this case, Jane Higgins is analyzing a 10-year corporate bond. The bond has a 7.50% annual coupon rate and is non-callable, meaning it cannot be redeemed by the issuer before maturity. The bond is currently priced at 104.5, and its yield is 7.177%.
To estimate the bond's effective duration, we need to compare the bond's price changes for different yield changes. According to Higgins' analysis, a 25 basis point (0.25%) decrease in yield causes the bond's price to increase to 107.4166, while a 25 basis point increase in yield leads to the bond's price decreasing to 101.3834.
To calculate the bond's effective duration, we can use the formula:
Effective Duration = (P+ - P-) / (2 * ΔY * P0),
where P+ is the price increase, P- is the price decrease, ΔY is the change in yield, and P0 is the initial price.
Let's plug in the values:
P+ = 107.4166 P- = 101.3834 ΔY = 0.0025 (since it's a 25 basis point change, or 0.25%) P0 = 104.5
Effective Duration = (107.4166 - 101.3834) / (2 * 0.0025 * 104.5) Effective Duration = 6.0332 / 0.26125 Effective Duration ≈ 23.09
Therefore, Jane Higgins' estimation of the bond's effective duration is approximately 23.09. However, none of the given answer choices matches this value. It's possible that there was an error in the calculation or the answer choices provided are not accurate.