Bd2_lecture

# Bd2_lecture - Reinvestment Duration &amp; Convexity Money...

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Debt 2: Advanced concepts Reinvestment rates Duration Convexity 2/36 Roger Loh Explaining reinvestment risk ± A simple example: Assume that a 1 year fixed deposit of \$1000 pays you 5% interest. At the end of the year, the bank allows you to continue investing your principle + proceeds for another year at the same rate. What is your annual yield after 2 years? ± At the end of year 1, you have \$1000 + \$50 ± You invest \$1050 for another year at 5%. ± At the end of year 2 you have \$1050 x 1.05 = 1102.5 ± The yield is simply: ± You could also write this as: Money Markets Capital Markets Duration & Convexity Reinvestment 3/36 Roger Loh Bond Theorems ± Bond yields vary inversely with changes in bond prices . ± Bond price volatility increases as maturity increases. ± Bond price volatility decreases as coupon rates increase. Money Markets Capital Markets Duration & Convexity Reinvestment 4/36 Roger Loh Bond Price Volatility ± The percentage change in bond price for a given change in yield is bond price volatility. { % Δ PB = the percentage change in price. { P t = the new price in period t. { P t-1 = the price one period earlier. % Δ PB PP P tt t = × 1 1 100 Money Markets Capital Markets Duration & Convexity Reinvestment

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5/36 Roger Loh Relationship Betw Price, Maturity, Yield, and Price Volatility P RICE C HANGE IF Y IELD C HANGES TO 6 P ERCENT P RICE C HANGE IF Y IELD C HANGES TO 4 P ERCENT (1) Maturity (years) (2) Bond Price at 5 percent Yield (\$) (3) Bond Price (\$) (4) Loss from Increase in Yield (\$) (5) Price Volatility (percent) (6) Bond Price (\$) (7) Gain from Decrease in Yield (\$) (8) Price Volatility (percent) 1 \$1,000 \$990.57 \$ 9.43 -0.94% \$1,009.62 \$ 9.62 0.96% 5 1,000 957.88 42.12 -4.21 1,044.52 44.52 4.45 10 1,000 926.40 73.60 -7.36 1,081.11 81.11 8.11 20 1,000 885.30 114.70 -11.47 1,135.90 135.90 13.59 40 1,000 849.54 150.46 -15.05 1,197.93 197.93 19.79 100 1,000 833.82 166.18 -16.62 1,245.05 245.05 24.50 +1% in Yield has different magnitude effect on price as -1% Money Markets Capital Markets Duration & Convexity Reinvestment 6/36 Roger Loh Relationship Betw Price, Coupon Rate, Yield, and Price Volatility P RICE C HANGE IF Y IELD C HANGES TO 6 P ERCENT P RICE C HANGE IF Y IELD C HANGES TO 4 P ERCENT (1) Coupon Rate (percent) (2) Bond Price at 5 percent Yield (\$) (3) Bond Price (\$) (4) Loss from Increase in Yield (\$) (5) Price Volatility (percent) (6) Bond Price (\$) (7) Gain from Decrease in Yield (\$) (8) Price Volatility (percent) 0% \$613.91 \$ 558.39 \$ 55.52 -9.04% \$ 675.56 \$ 61.65 10.04% 5 1,000.00 926.40 73.60 -7.36 1,081.11 81.11 8.11 10 1,386.09 1,294.40 91.69 -6.62 1,486.65 100.56 7.25 10 year maturity Money Markets Capital Markets Duration & Convexity Reinvestment 7/36 Roger Loh Interest Rate Risk ± Reinvestment risk--variability in realized yield caused by changing market rates for coupon reinvestment. ± Price risk--variability in realized return caused by capital gains/losses or that the price realized may differ from par. ± Price risk and reinvestment risk offset one another, depending upon maturity and coupon rates. Money Markets Capital Markets Duration & Convexity Reinvestment 8/36 Roger Loh Duration ± Duration is a measure of interest rate risk that considers both coupon rate and term to maturity.
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## Bd2_lecture - Reinvestment Duration &amp; Convexity Money...

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