1. Bond Price Theorems
Dr. Irala Bonds

2. Current Market Price (Rs.)
Theorem-01
sss
Bond
Face Value (Rs.)
Coupon (%)
TTM
(Years)
Current Market Price (Rs.)
YTM A
1000 6 5
848.37 11 12 13 14
Dr. Irala Bonds

3. Current Market Price (Rs.)
Theorem-01
sss
Bond
Face Value (Rs.)
Coupon (%)
TTM
(Years)
Current Market Price (Rs.)
YTM A
1000 6 5
848.37 10 11 12 13 14
Dr. Irala Bonds

4. Current Market Price (Rs.)
Theorem-01
sss
Bond
Face Value (Rs.)
Coupon (%)
TTM
(Years)
Current Market Price (Rs.)
YTM A
1000 6 5
848.37 10
815.21 11 12 13 14
Dr. Irala Bonds

5. Current Market Price (Rs.)
Theorem-01
Bond
Face Value (Rs.)
Coupon (%)
TTM
(Years)
Current Market Price (Rs.)
YTM A
1000 6 5
848.37 10
815.21 11
783.71 12
753.79 13
725.35 14
Plot a Scatter Diagram (YTM on X- Axis, Bond Price on Y –Axis). What do you think the relationship to be?
Dr. Irala Bonds

6. Theorem-01
Dr. Irala Bonds

7. Theorem-01 The market price and YTM of a bond are inversely related
Dr. Irala Bonds

8. Current Market Price (Rs.) Size of the Discount / Premium
Theorem-02A
Bond
Face Value (Rs.)
Coupon (%)
TTM
(Years)
Current Market Price (Rs.)
YTM
Size of the Discount / Premium A
1000 6 5
848.37 10
151.63 4 3 2 1 A’
Premium/ Discount is the difference between FV and CMP
Dr. Irala Bonds

9. Current Market Price (Rs.) Size of the Discount / Premium
Theorem-02A
Bond
Face Value (Rs.)
Coupon (%)
TTM
(Years)
Current Market Price (Rs.)
YTM
Size of the Discount / Premium A
1000 6 5
848.37 10
151.63 4
873.21
126.79 3 2 1 A’
Premium/ Discount is the difference between FV and CMP
Dr. Irala Bonds

10. Current Market Price (Rs.) Size of the Discount / Premium
Theorem-02A
Bond
Face Value (Rs.)
Coupon (%)
TTM
(Years)
Current Market Price (Rs.)
YTM
Size of the Discount / Premium A
1000 6 5
848.37 10
151.63 4
873.21
126.79 3
900.53
99.47 2
930.58
69.42 1
963.64
36.36 A’
1,137.39
137.39
1,111.51
111.51
1,084.86
84.86
1,057.40
57.40
1,029.13
29.13
Dr. Irala Bonds

11. Current Market Price (Rs.) Size of the Discount / Premium
Theorem-02A
Bond
Face Value (Rs.)
Coupon (%)
TTM
(Years)
Current Market Price (Rs.)
YTM
Size of the Discount / Premium A
1000 6 5
848.37 10
151.63 4
873.21
126.79 3
900.53
99.47 2
930.58
69.42 1
963.64
36.36 A’
1,137.39
137.39
1,111.51
111.51
1,084.86
84.86
1,057.40
57.40
1,029.13
29.13
If a bond’s yield doesn’t change over its life, then the size of the discount or premium will decrease, as its TTM gets shorter.
Dr. Irala Bonds

12. Theorem-02A
If a bond’s yield doesn’t change over its life, then the size of the discount or premium will decrease, as its TTM gets shorter.
Dr. Irala Bonds

13. Current Market Price (Rs.) Size of the Discount / Premium
Theorem-02B
Bond
Face Value (Rs.)
Coupon (%)
TTM
(Years)
Current Market Price (Rs.)
YTM
Size of the Discount / Premium A
1000 6 5
883.31 B 2 9
If two bonds have the same coupon rate, Par value and yield then the one with the shorter life will sell at a smaller discount / premium
Dr. Irala Bonds

14. Current Market Price (Rs.) Size of the Discount / Premium
Theorem-02B
Bond
Face Value (Rs.)
Coupon (%)
TTM
(Years)
Current Market Price (Rs.)
YTM
Size of the Discount / Premium A
1000 6 5
883.31 9
116.69 B 2
947.23
52.77
Dr. Irala Bonds

15. Theorem-03 Bond Face Value (Rs.) Coupon (%) TTM (Years)
Current Market Price (Rs.)
YTM (%)
Size of the Discount / Premium (Rs.)
% Change in Discount / Premium A
1000 6 5
848.37
xxxx 4 10 3 2 1
% Change in Discount / Premium w.r.t the previous year
Dr. Irala Bonds

16. Theorem-03 Bond Face Value (Rs.) Coupon (%) TTM (Years)
Current Market Price (Rs.)
YTM (%)
Size of the Discount / Premium (Rs.)
% Change in Discount / Premium A
1000 6 5
848.37 10
151.63
xxxx 4
873.21
126.79
16.38% 3
900.53
99.47
21.55% 2
930.58
69.42
30.21% 1
963.64
36.36
47.62%
Dr. Irala Bonds

17. Theorem-03
Bond
Face Value (Rs.)
Coupon (%)
TTM
(Years)
Current Market Price (Rs.)
YTM (%)
Size of the Discount / Premium (Rs.)
% Change in Discount / Premium A
1000 6 5
848.37 10
151.63
xxxx 4
873.21
126.79
16.38% 3
900.53
99.47
21.55% 2
930.58
69.42
30.21% 1
963.64
36.36
47.62%
If a bond’s yield doesn’t change over its life, then the size of the discount or premium will decrease at an increasing rate, as its TTM gets shorter
Dr. Irala Bonds

18. Current Market Price (Rs.) Fall / Rise in Market Price
Theorem-04
Bond
Face Value (Rs.)
Coupon
(%)
TTM
(Years)
Current Market Price (Rs.)
YTM (%)
Fall / Rise in Market Price A
1000 6 5 12
xxxx
848.37 14
Dr. Irala Bonds

19. Current Market Price (Rs.) Fall / Rise in Market Price
Theorem-04
Bond
Face Value (Rs.)
Coupon
(%)
TTM
(Years)
Current Market Price (Rs.)
YTM (%)
Fall / Rise in Market Price A
1000 6 5
783.71 12
xxxx
848.37 10
64.66
725.35 14
58.36
How does the rise in bond’s price(….64.66…) owing to decrease in the bond’s yield compare with the fall in bond’s price (….58.36…) owing to increase in the bond’s yield (from 12 to 14%)?
Dr. Irala Bonds

20. Current Market Price (Rs.) Fall / Rise in Market Price
Theorem-04
Bond
Face Value (Rs.)
Coupon
(%)
TTM
(Years)
Current Market Price (Rs.)
YTM (%)
Fall / Rise in Market Price A
1000 6 5
783.71 12
xxxx
848.37 10
64.66
725.35 14
58.36
How does the rise in bond’s price(….64.66…) owing to decrease in the bond’s yield compare with the fall in bond’s price (….58.36…) owing to increase in the bond’s yield (from 12 to 14%)?
Do you have any thing to say about your assumption (in Table -01) of the relationship between YTM and Bond Price?
Dr. Irala Bonds

21. Current Market Price (Rs.) Fall / Rise in Market Price
Theorem-04
Bond
Face Value (Rs.)
Coupon
(%)
TTM
(Years)
Current Market Price (Rs.)
YTM (%)
Fall / Rise in Market Price A
1000 6 5
783.71 12
xxxx
848.37 10
64.66
725.35 14
58.36
A decrease in bond’s yield will raise the bond’s price by an amount that is greater in size than the corresponding fall in the bond’s price that would occur if there were an equal sized increase in the bond’s yield
Dr. Irala Bonds

22. Current Market Price (Rs.)
Theorem-04B
Bond
Face Value (Rs.)
Coupon
(%)
TTM
(Years)
Current Market Price (Rs.)
YTM A
1000 6 5
848.37 10
581.31 20
415.46 30
308.04 40
235.88 50
Plot the results on a graph sheet (YTM on X- Axis, Bond Price on Y –Axis).
How are the YTM and bond price related? Re visit your observations in Table -01 and Table -04 A
Dr. Irala Bonds

23. Theorem-04B The relation between YTM and Bond Price is Convex
Dr. Irala Bonds

24. Current Market Price (Rs.)
Theorem-05
Bond
Face Value (Rs.)
Coupon
(%)
TTM
(Years)
Current Market Price (Rs.)
YTM
% Change in Bond Price A
1000 6 5
848.37
XXXX 20 D 9 10
Dr. Irala Bonds

25. Current Market Price (Rs.)
Theorem-05
Bond
Face Value (Rs.)
Coupon
(%)
TTM
(Years)
Current Market Price (Rs.)
YTM
% Change in Bond Price A
1000 6 5
848.37 10
XXXX
581.31 20
31.48% D 9
962.09
671.03
30.25%
Dr. Irala Bonds

26. Current Market Price (Rs.)
Theorem-05
Bond
Face Value (Rs.)
Coupon
(%)
TTM
(Years)
Current Market Price (Rs.)
YTM
% Change in Bond Price A
1000 6 5
848.37 10
XXXX
581.31 20
31.48% D 9
962.09
671.03
30.25%
The percentage change in a bond’s price owing to a change in its yield will be smaller if the coupon rate is higher
Dr. Irala Bonds