Final answer:
The price of an option-free bond with a higher coupon rate than the market interest rate will increase by more than 12% if market yields decrease by 100 basis points due to the inverse relationship between bond prices and market yields, and the effect of convexity.
Step-by-step explanation:
If an analyst accurately calculates that the price of an option-free bond with a 9 percent coupon would experience a 12 percent change if market yields increase 100 basis points, and you are asking about the reverse situation where yields decrease, we need to understand how bond prices react to changes in market interest rates to determine the likely outcome.
Bond prices and market yields have an inverse relationship. When market yields rise, the price of existing bonds falls to align the older bonds' yields with the new higher rates. Conversely, when market yields fall, the prices of existing bonds rise because they offer higher interest payments than new bonds issued at the current lower rates. Also, due to convexity, for an option-free bond, the price increase when yields fall is greater than the price decrease for an equivalent yield rise. This effect occurs because as yields fall, bond prices rise and the duration lengthens, resulting in a larger price sensitivity to changes in yield.
Given these principles and the fact that the bond has a 9 percent coupon, which is higher than the prevailing interest rates, if market yields decrease by 100 basis points, one would expect the bond's price to increase by more than 12%.