Lehman Brothers: Can Convexity Be Exploited?

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.