Price Volatility for bonds

Properties concerning the price volatility of an option free bond:
· Price is inversely related to yield.
· Price sensitivity depends on maturity and coupon.
· For small changes in yield, the price change is same whether yield moves up or down.
· For large changes in yield, the price increase for a fall in yield is greater than the price decrease for a similar rise in yield, i.e. the price yield curve is convex.
· The lower the coupon, the longer the term to maturity, the lower the initial yield -> the greater the bond price volatility
· Yield/price relationship for option free bonds is not linear but convex, referred to as positive Convexity.

Positive convexity:
· The decrease in an option-free bond’s price due to a rise in yield is lower than the increase for an equal fall in yield. This results a positive adjustment to the duration-based estimate of price change whether yield goes up or down.

Price-Volatility Characteristics of Callable and Prepayable Securities
· Embedded options can dramatically change the price-yield profile.
· At high yields the profiles of these bonds are similar, but at low yields price of callable/prepayable securities grows slower with a fall in yield than the price of option-free bonds {price compression}.

Negative convexity:
· For callable and prepayable securities, at low levels of yield, the price increase for a given fall in yield is less than the price decrease for an equal rise in yield. ie, Prices rise at a decreasing rate. The point where the curve starts to flatten is at ( or near a yield level of y’

Price Volatility Characteristics of Putable Bonds
· The advantage of these bonds to an investor is that if market yields rise and the value of the bond falls below the put price, the investor can exercise the put option and stem his losses to the put price.
· The price of a puttable bond will react same way as an option-free bond at low yield levels. As rates rise, the puttable bond’s price will decrease at the same rate as an option-free bond, but the decline will be lessened because of the value of the put option.

Value of puttable bond = value of option free bond + the option.