#16 FIN416 - We calculate the predicted price change by...

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16.) For a yield to maturity of 7% we get $1,620.45 For a yield to maturity of 8% we get $1,450.31 For a yield to maturity of 9% we get $1,308.21 Using the Duration Rule, assuming yield to maturity falls to 7%: We calculate the predicted price change by solving = –11.54 *(-0.01/1.08)*$1,450.31=$154.97 The predicted price will equal ($154.97 + $1,450.31) = $1,605.28 The actual price @ 7% YTM is $1,620.45. The percentage error equals ($1,620.45-$1,605.28)/ $1,620.45= 0.0094 or 0.94% Which is too low Using the Duration Rule, assuming yield to maturity increases to 9%: We calculate the predicted price change by solving = –11.54*(-0.01/1.08)*$1,450.31=$154.97 The predicted price will equal ( –$154.97 + $1,450.31)= $1,295.34 The actual price @ 9% YTM is $1,308.21. The percentage error equals ($1,308.21-$1,295.34) /$1,308.21=0.0098 or 0.98% This result is also too low Using Duration-with-Convexity Rule, assuming yield to maturity falls to 7%:
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Unformatted text preview: We calculate the predicted price change by solving = 11.54*(-0.01/1.08)+ (0.5*192.4*(-0.01) 2 )*$1,450.31=-$168.92 The predicted price will equal ($168.92 + $1,450.31) = $1,619.23 The actual price @ 7% YTM is $1,620.45. The percentage error equals ($1,620.45-$1,619.23)/$1,620.45= 0.00075 or 0.075% This result is low Using Duration-with-Convexity Rule, assuming yield to maturity rises to 9%: We calculate the predicted price change by solving = 11.54*(0.01/1.08)+ (0.5*192.4*(0.01) 2 )*$1,450.31=-$140.42 The predicted price will equal ($141.02 + $1,450.31)= $1,309.29 The actual price at a 9% yield to maturity is $1,308.21. The percentage error equals ($1,309.29 $1,308.21)/$1,308.21= 0.00083 or 0.083% This result is too high The duration-with-convexity rule gives us a more accurate approximation to the real change in price than we get from using only duration to estimate....
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#16 FIN416 - We calculate the predicted price change by...

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