We study a segmented-markets setting in which self-fulfilling volatility can arise. The only requirements are (i) asset price movements redistribute wealth across markets (e.g., equities rise as bonds fall) and (ii) some stabilizing force keeps valuation ratios stationary (e.g., cash flow growth rises when valuations rise). We prove that when self-fulfilling volatility exists, arbitrage opportunities must also exist. Conversely, at times when arbitrage profits exist, asset markets are susceptible to self-fulfilling fluctuations. The tight theoretical connection between price volatility and arbitrage is detectable in currency markets by studying deviations from covered interest parity.