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Interest Rate Sensitivity

Interest Rate Sensitivity - Interest Rate Sensitivity...

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Taking the derivative of the bond’s price with respect to the YTM (a complex manipulation of the bond valuation formula): [ΔP/P] [ΔR/(1+R)] = -D Interest Rate Sensitivity 1 % change in price % change in yield Measure of interest elasticity to a small change in yield; add a negative sign since bond prices and yields move in the opposite direction.

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Interest Rate Sensitivity 2 To apply MD to a specific asset: We can do this to calculate the percentage change in price: ΔP/P = (-D) [ΔR/(1+R)] or- ΔP/P = (-MD)(ΔR) And, we can do this to calculate the dollar change in price: MD = D/(1+R)
Interest Rate Sensitivity 3 Remember this example? What happens to the bond’s price if rates increase by 1 basis point (or 1/100th of 1%, or . 0001)? MD = D/(1+R) 4.6231=4.993/(1.08) Yield: 8.0% Coupon Rate: 8.0% CF x DF x t Time Cash Flows Discount Factor Discounted Cash Flows Weighted Average 1 \$80 0.9259259 \$74.07 74.07 2 \$80 0.8573388 \$68.59 137.17 3 \$80 0.7938322 \$63.51 190.52 4 \$80 0.7350299 \$58.80 235.21 5 \$80 0.6805832 \$54.45 272.23 6 \$1,080 0.6301696 \$680.58 4083.50 \$1,480 \$1,000.00 4992.71 Duration = 4992.71 / 1000 4.993 Years

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Interest Rate Sensitivity 4 What happens to the bond’s price if rates increase by 1 basis point (or 1/100th of 1%, or .0001? The new rate would be 8.01%. The % change in price for this % change in rate is: ΔP/P = (-D) [ΔR/(1+R)]

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Interest Rate Sensitivity - Interest Rate Sensitivity...

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