Excerpts: Lehman Brothers: Can Convexity Be Exploited?
Many investors believe that convexity is a desirable portfolio attribute. Whether the market moves up or down, high-convexity portfolios will always outperform low-convexity portfolios of equal duration and yield.
It can be demonstrated mathematically that if we simply model the possible changes to the yield curve as the set of all possible parallel shifts, a duration-neutral long-convexity position will outperform if the curve shifts in either direction, break even if yields remain unchanged, and never underperform.
The bottom line of the arbitrage-free assumption is that cashflow convexity, which is just a mathematical side effect of the price-yield relationship, should not have any material effect on expected returns.
This is in sharp contrast with the convexity that stems from optionality, in which changes in yield can result in a different payout of cashflows.
There is no denying that options have value; the arbitrage-free assumption merely requires that the premium paid for an option should equal the expected value of its eventual payoff.
Despite these theoretical arguments, many investors still hold the belief that positive convexity–of any sort–should enhance portfolio performance.