Duration - 01/07/2008 Christos Papahristodoulou, Mlardalen

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
01/07/2008 Christos Papahristodoulou, Mälardalen University/HST/Economics 01/07/2008 1 Duration, convexity and portfolio immunization Some principles of bonds’ prices As is known, a bond’s price is given by: n n n n t t r F r r C r C r F r C P ) 1 ( ) 1 ( ) 1 ( ) 1 ( 1 + + + = + + + = = If we derive that with respect to its parameters, C, F, r and t or n , partially, we can examine how its price is affected. An alternative method is to examine its price analytically, using numerical values. Among the principles, we can name the following: (i) The higher the r, the lower its P, because: 0 ) 1 ( ) 1 ( 1 1 1 p + = + + + = n n t t r nF r tC r P Example (i) : F = 1,000, C = 100, r= 0.01,. .,.0.20 , n = 20
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
01/07/2008 Christos Papahristodoulou, Mälardalen University/HST/Economics 01/07/2008 2 (ιι) The bond prices change over time, if r C F , because: n n n ) r 1 ( r ) r 1 ln( ) rF C ( ) r 1 ( ) r 1 ln( F ) r 1 ( r ) r 1 ln( C n P + + = + + + + = Example (ii) : F = 1,000, C = 100, r (a) = 0.10, r (b) = 0.08, r (c) = 0.12, n = 0, 5, 10, 15, 20 The following table shows the bond prices for various n r . n = 0 n = 5 n = 10 n = 15 n = 20 r = 0.10 1,000 1,000 1,000 1,000 1,000 r 0.08 1,000 1,079.8 1,134.2 1,171.2 1,196.4 r = 0.12 1,000 927.90 887 863.78 850.61 This means that premium bonds (i.e. bonds with coupons) fall over time, while discount bonds (i.e. with C = 0) increase. Both will reach P = F, at n = 0 . (iii) For similar interest rate changes, shorter bonds are less volatile compared to longer bonds If a corporation issues long bonds, it will pay the given coupons per period, irrespectively if the interest rate rises (and therefore the payments will be worth less) or if it falls (and consequently the corporation will pay more). In addition, if the interest rate falls, it would be better if it could issue new ones at lower coupons. That would happen if it had short bonds to replace. On the other hand, longer bonds are difficult, or more expensive to replace. This can explain why the short bonds are, relatively, risk free. Example (iii) : F = 1,000, C = 100, r = 0.01,. .., 0.20 n = 1,. .., 20
Background image of page 2
01/07/2008 Christos Papahristodoulou, Mälardalen University/HST/Economics 01/07/2008 3 The following three-dimensional graph shows clearly that the shorter bonds are less volatile than the longer ones, for all changes in the yield to maturity. 0.05 0.1 0.15 0.2 discount 5 10 15 20 time 500 1000 1500 2000 2500 Price (iv) The more frequent the coupon (C) payments, the lower the volatility, if the interest rate changes This is due to the fact that the investor who receives C often, she can save that to a higher interest rate, if it increases. Such an option does not exist if C is paid seldom. A similar argument applies if the interest rate declines. Example (iv)
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/06/2010 for the course MATH 3310 taught by Professor Frohmader during the Spring '10 term at Cornell University (Engineering School).

Page1 / 13

Duration - 01/07/2008 Christos Papahristodoulou, Mlardalen

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online