Convexity
Why do some positions gain more from big market moves than they give up on small ones, and what does that shape tell a risk-taker?
In plain words
Convexity describes a payoff whose value rises faster than the underlying price rises, and falls slower than the price falls. The position gains more from large moves than it loses from small ones, because the payoff curve bends rather than running in a straight line.
Why it matters
Convexity is what makes an option-like payoff different from holding the asset directly. The holder accepts a known, bounded cost, such as a premium or a limited loss, in exchange for exposure that accelerates when a move becomes large. This changes how a position behaves in a shock: losses stay capped while gains compound.
In a real week: ETH, week of 17 June 2019
ETH in the week starting 2019-06-17 shows the shape convexity rewards. It opened at 267.73 and closed at 308.52, a gain of 15.24%, inside a range of 23.04% between the low of 261.45 on Tuesday and the high of 321.70 on Sunday. The best day added 8.51% on Friday, while the worst day, Tuesday, took back only 3.10%. The weekly high came after the low, and the close sat in the upper third of the range at 78.1, so the larger part of the move landed on the upside.
A common mistake
Reading convexity as a guarantee of profit. It describes the shape of a payoff relative to the size of moves, not their direction, and the position can still lose its full cost if the market barely moves or moves the wrong way.