Bond price volatility and the price value of a basis point
Bond Valuation and Analysis in R
Clifford Ang
Senior Vice President, Compass Lexecon
Bond price volatility
- Bond price volatility depends on many factors
- Some examples:
- Size of yield change
- Coupon rate
- Time to maturity
Small change, symmetric effect
- Small changes in yield: % change for most bonds are similar whether yield goes up or down
- Example:
- 100 USD par value, 10% coupon rate, 20 years, 10% yield
bondprc(100, 0.10, 20, 0.101) / bondprc(100, 0.10, 20, 0.10) - 1
-0.008455776
bondprc(100, 0.10, 20, 0.099) / bondprc(100, 0.10, 20, 0.10) - 1
0.008571998
Large change, asymmetric effect
- For large changes in yield, the percentage change is higher when the yield decreases
- Example:
- 100 USD par value, 10% coupon rate, 20 years, 10% yield
bondprc(100, 0.10, 20, 0.14) / bondprc(100, 0.10, 20, 0.10) - 1
-0.2649252
bondprc(100, 0.10, 20, 0.06) / bondprc(100, 0.10, 20, 0.10) - 1
0.4587968
Lower coupon, more volatile
- Fixing the time to maturity and yield, bond price volatility is higher if the coupon rate is lower
- Example:
- 100 USD par value, 20 years, 10% initial yield, 8% new yield
bondprc(100, 0.10, 20, 0.08) / bondprc(100, 0.10, 20, 0.10) - 1
0.1963629
bondprc(100, 0.05, 20, 0.08) / bondprc(100, 0.05, 20, 0.10) - 1
0.228328
Lower coupon, more volatile
bondprc(100, 0.00, 20, 0.08) / bondprc(100, 0.00, 20, 0.10) - 1
0.4433731
Longer maturity, more volatile
- Fixing the coupon rate and yield, bond price volatility is higher if the time to maturity is longer
- Example:
- 100 USD par value, 10% coupon rate, 10% initial yield, 8% new yield
bondprc(100, 0.10, 20, 0.08) / bondprc(100, 0.10, 20, 0.10) - 1
0.1963629
bondprc(100, 0.10, 10, 0.08) / bondprc(100, 0.10, 10, 0.10) - 1
0.1342016
Shorter maturity, more volatile
bondprc(100, 0.10, 5, 0.08) / bondprc(100, 0.10, 5, 0.10) - 1
0.0798542
Price value of a basis point
- Or "dollar value of an 01" = measure of bond price volatility
- = price of the bond if the required yield changes by 0.01%
- Example:
bondprc(100, 0.05, 20, 0.05)
100
bondprc(100, 0.05, 20, 0.0501)
99.87548
Price value of a basis point
abs(bondprc(100, 0.05, 20, 0.0501) - bondprc(100, 0.05, 20, 0.05))
0.1245165
abs()to make sure the change is positive
Let's practice!
Bond Valuation and Analysis in R
