Rob Ealey, CFA, has just purchased an option-free bond with a 6.50% coupon that is currently selling at 94.73 to yield 7.25%. If yields increase by 50 bps, the new price of the bonds would be 91.41, and if yields decrease by 50 bps the new price of the bond would be 98.20. Determine the approximate new price of the bond if yields decrease by 75 basis points.
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A. B. C.B
To determine the approximate new price of the bond if yields decrease by 75 basis points, we can use the bond's price-yield relationship and perform a linear interpolation.
Let's break down the given information:
First, we need to calculate the price change due to a 100 basis point (1%) change in yield. We can do this by taking the difference between the prices when yields increase and decrease by 50 bps: Price change = Price if yields decrease by 50 bps - Price if yields increase by 50 bps Price change = $98.20 - $91.41 = $6.79
Next, we need to determine the approximate price change if yields decrease by 75 basis points. We can assume that the relationship between price change and yield change is linear, meaning that the price change will be proportional to the yield change. In this case, we can use the following proportion: Price change (75 bps) / Price change (100 bps) = Yield change (75 bps) / Yield change (100 bps)
Let x represent the price change if yields decrease by 75 bps. x / $6.79 = 75 bps / 100 bps
Solving for x: x = $6.79 * (75/100) x ≈ $5.09
Finally, we can calculate the approximate new price of the bond by subtracting the price change from the current bond price: New price ≈ Current bond price - Price change New price ≈ $94.73 - $5.09 New price ≈ $89.64
Therefore, the approximate new price of the bond if yields decrease by 75 basis points is $89.64.
The correct answer is A. $89.64.