Bond Price Theorems Dr. Irala 1 Bonds.

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Presentation transcript:

Bond Price Theorems Dr. Irala 1 Bonds

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 2 Bonds

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 3 Bonds

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 4 Bonds

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 5 Bonds

Theorem-01 Dr. Irala 6 Bonds

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

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 8 Bonds

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 9 Bonds

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 10 Bonds

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 11 Bonds

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 12 Bonds

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 13 Bonds

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 14 Bonds

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 15 Bonds

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 16 Bonds

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 17 Bonds

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 18 Bonds

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 19 Bonds

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 20 Bonds

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 21 Bonds

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 22 Bonds

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

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 24 Bonds

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 25 Bonds

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 26 Bonds