#16 FIN416

# #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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