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1.1
Year
cash flow
present value of cash inflow = cash flow/(1+r)^n r= 5%
1
75
71.42857
2
75
68.02721
3
75
64.78782
4
1075
884.4052
value of bond
sum of present value of cash flow
1088.649
1.2
Year
cash flow
present value of cash inflow = cash flow/(1+r)^n r= 5.2%
1
75
71.29278
2
75
67.7688
3
75
64.41901
4
1075
877.6988
value of bond
sum of present value of cash flow
1081.179
1.3
% change in bond price if YTM increases by .2%
(1081.18-1088.65)/1088.65
-0.69%
1.4
Duration is a measure of a bond's sensitivity to interest rate changes. The higher the bond's
duration, the greater its sensitivity to the change (also know as volatility) and vice versa.
1.4
Year
cash flow
Year*cash flow
present value of Year*cash inflow = cash flow/(1+r)^n r= 5%
1
75
75
71.42857
2
75
150
136.0544
3
75
225
194.3635
4
1075
4300
3537.621
total
3939.467
Macculay duration in years
total/face value of bond
3939.467/1000
3.939467
1.4
modified duration
macculay duration/(1+YTM)
3.94/1.05
3.752381
1.5
change in price if YTM increases by .2%
modified duration*change in YTM
3.75*.2%
0.75%
1.1
Year
cash flow
present value of cash inflow = cash flow/(1+r)^n r= 5%
1
75
71.42857
2
75
68.02721
3
75
64.78782
4
1075
884.4052
value of bond
sum of present value of cash flow
1088.649
1.2
Year
cash flow
present value of cash inflow = cash flow/(1+r)^n r= 5.2%
1
75
71.29278
2
75
67.7688
3
75
64.41901
4
1075
877.6988
value of bond
sum of present value of cash flow
1081.179
1.3
% change in bond price if YTM increases by .2%
(1081.18-1088.65)/1088.65
-0.69%
1.4
Duration is a measure of a bond's sensitivity to interest rate changes. The higher the bond's
duration, the greater its sensitivity to the change (also know as volatility) and vice versa.
1.4
Year
cash flow
Year*cash flow
present value of Year*cash inflow = cash flow/(1+r)^n r= 5%
1
75
75
71.42857
2
75
150
136.0544
3
75
225
194.3635
4
1075
4300
3537.621
total
3939.467
Macculay duration in years
total/face value of bond
3939.467/1000
3.939467
1.4
modified duration
macculay duration/(1+YTM)
3.94/1.05
3.752381
1.5
change in price if YTM increases by .2%
modified duration*change in YTM
3.75*.2%
0.75%
Solution
1.1
Year
cash flow
present value of cash inflow = cash flow/(1+r)^n r= 5%
1
75
71.42857
2
75
68.02721
3
75
64.78782
4
1075
884.4052
value of bond
sum of present value of cash flow
1088.649
1.2
Year
cash flow
present value of cash inflow = cash flow/(1+r)^n r= 5.2%
1
75
71.29278
2
75
67.7688
3
75
64.41901
4
1075
877.6988
value of bond
sum of present value of cash flow
1081.179
1.3
% change in bond price if YTM increases by .2%
(1081.18-1088.65)/1088.65
-0.69%
1.4
Duration is a measure of a bond's sensitivity to interest rate changes. The higher the bond's
duration, the greater its sensitivity to the change (also know as volatility) and vice versa.
1.4
Year
cash flow
Year*cash flow
present value of Year*cash inflow = cash flow/(1+r)^n r= 5%
1
75
75
71.42857
2
75
150
136.0544
3
75
225
194.3635
4
1075
4300
3537.621
total
3939.467
Macculay duration in years
total/face value of bond
3939.467/1000
3.939467
1.4
modified duration
macculay duration/(1+YTM)
3.94/1.05
3.752381
1.5
change in price if YTM increases by .2%
modified duration*change in YTM
3.75*.2%
0.75%
1.1
Year
cash flow
present value of cash inflow = cash flow/(1+r)^n r= 5%
1
75
71.42857
2
75
68.02721
3
75
64.78782
4
1075
884.4052
value of bond
sum of present value of cash flow
1088.649
1.2
Year
cash flow
present value of cash inflow = cash flow/(1+r)^n r= 5.2%
1
75
71.29278
2
75
67.7688
3
75
64.41901
4
1075
877.6988
value of bond
sum of present value of cash flow
1081.179
1.3
% change in bond price if YTM increases by .2%
(1081.18-1088.65)/1088.65
-0.69%
1.4
Duration is a measure of a bond's sensitivity to interest rate changes. The higher the bond's
duration, the greater its sensitivity to the change (also know as volatility) and vice versa.
1.4
Year
cash flow
Year*cash flow
present value of Year*cash inflow = cash flow/(1+r)^n r= 5%
1
75
75
71.42857
2
75
150
136.0544
3
75
225
194.3635
4
1075
4300
3537.621
total
3939.467
Macculay duration in years
total/face value of bond
3939.467/1000
3.939467
1.4
modified duration
macculay duration/(1+YTM)
3.94/1.05
3.752381
1.5
change in price if YTM increases by .2%
modified duration*change in YTM
3.75*.2%
0.75%

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1.1Yearcash flowpresent value of cash inflow = cash flow(1+r).pdf

  • 1. 1.1 Year cash flow present value of cash inflow = cash flow/(1+r)^n r= 5% 1 75 71.42857 2 75 68.02721 3 75 64.78782 4 1075 884.4052 value of bond sum of present value of cash flow 1088.649 1.2 Year cash flow present value of cash inflow = cash flow/(1+r)^n r= 5.2% 1 75 71.29278 2 75 67.7688 3 75 64.41901 4 1075 877.6988
  • 2. value of bond sum of present value of cash flow 1081.179 1.3 % change in bond price if YTM increases by .2% (1081.18-1088.65)/1088.65 -0.69% 1.4 Duration is a measure of a bond's sensitivity to interest rate changes. The higher the bond's duration, the greater its sensitivity to the change (also know as volatility) and vice versa. 1.4 Year cash flow Year*cash flow present value of Year*cash inflow = cash flow/(1+r)^n r= 5% 1 75 75 71.42857 2 75 150 136.0544 3 75 225 194.3635 4 1075 4300 3537.621 total 3939.467 Macculay duration in years total/face value of bond 3939.467/1000
  • 3. 3.939467 1.4 modified duration macculay duration/(1+YTM) 3.94/1.05 3.752381 1.5 change in price if YTM increases by .2% modified duration*change in YTM 3.75*.2% 0.75% 1.1 Year cash flow present value of cash inflow = cash flow/(1+r)^n r= 5% 1 75 71.42857 2 75 68.02721 3 75 64.78782 4 1075 884.4052 value of bond sum of present value of cash flow 1088.649 1.2 Year cash flow present value of cash inflow = cash flow/(1+r)^n r= 5.2% 1 75
  • 4. 71.29278 2 75 67.7688 3 75 64.41901 4 1075 877.6988 value of bond sum of present value of cash flow 1081.179 1.3 % change in bond price if YTM increases by .2% (1081.18-1088.65)/1088.65 -0.69% 1.4 Duration is a measure of a bond's sensitivity to interest rate changes. The higher the bond's duration, the greater its sensitivity to the change (also know as volatility) and vice versa. 1.4 Year cash flow Year*cash flow present value of Year*cash inflow = cash flow/(1+r)^n r= 5% 1 75 75 71.42857 2 75 150 136.0544 3 75 225
  • 5. 194.3635 4 1075 4300 3537.621 total 3939.467 Macculay duration in years total/face value of bond 3939.467/1000 3.939467 1.4 modified duration macculay duration/(1+YTM) 3.94/1.05 3.752381 1.5 change in price if YTM increases by .2% modified duration*change in YTM 3.75*.2% 0.75% Solution 1.1 Year cash flow present value of cash inflow = cash flow/(1+r)^n r= 5% 1 75 71.42857 2 75 68.02721 3 75
  • 6. 64.78782 4 1075 884.4052 value of bond sum of present value of cash flow 1088.649 1.2 Year cash flow present value of cash inflow = cash flow/(1+r)^n r= 5.2% 1 75 71.29278 2 75 67.7688 3 75 64.41901 4 1075 877.6988 value of bond sum of present value of cash flow 1081.179 1.3 % change in bond price if YTM increases by .2% (1081.18-1088.65)/1088.65 -0.69% 1.4 Duration is a measure of a bond's sensitivity to interest rate changes. The higher the bond's duration, the greater its sensitivity to the change (also know as volatility) and vice versa. 1.4 Year cash flow
  • 7. Year*cash flow present value of Year*cash inflow = cash flow/(1+r)^n r= 5% 1 75 75 71.42857 2 75 150 136.0544 3 75 225 194.3635 4 1075 4300 3537.621 total 3939.467 Macculay duration in years total/face value of bond 3939.467/1000 3.939467 1.4 modified duration macculay duration/(1+YTM) 3.94/1.05 3.752381 1.5 change in price if YTM increases by .2% modified duration*change in YTM 3.75*.2% 0.75% 1.1 Year
  • 8. cash flow present value of cash inflow = cash flow/(1+r)^n r= 5% 1 75 71.42857 2 75 68.02721 3 75 64.78782 4 1075 884.4052 value of bond sum of present value of cash flow 1088.649 1.2 Year cash flow present value of cash inflow = cash flow/(1+r)^n r= 5.2% 1 75 71.29278 2 75 67.7688 3 75 64.41901 4 1075 877.6988 value of bond sum of present value of cash flow 1081.179
  • 9. 1.3 % change in bond price if YTM increases by .2% (1081.18-1088.65)/1088.65 -0.69% 1.4 Duration is a measure of a bond's sensitivity to interest rate changes. The higher the bond's duration, the greater its sensitivity to the change (also know as volatility) and vice versa. 1.4 Year cash flow Year*cash flow present value of Year*cash inflow = cash flow/(1+r)^n r= 5% 1 75 75 71.42857 2 75 150 136.0544 3 75 225 194.3635 4 1075 4300 3537.621 total 3939.467 Macculay duration in years total/face value of bond 3939.467/1000 3.939467 1.4 modified duration
  • 10. macculay duration/(1+YTM) 3.94/1.05 3.752381 1.5 change in price if YTM increases by .2% modified duration*change in YTM 3.75*.2% 0.75%