This paper examines how risk in trading activity can affect the volatility of asset prices. We look for this relationship in the behavior of interest rate swap spreads and in the volume and interest rates of repurchase contracts. Specifically, we focus on convergence trading, in which speculators take positions on a bet that asset prices will converge to normal levels. We investigate how the risks in convergence trading can affect price volatility in a form of positive feedback that can amplify shocks in asset prices. In our analysis, we see empirical evidence of both stabilizing and destabilizing forces in the behavior of interest rate swap spreads that can be attributed to speculative trading activity. We find that the swap spread tends to converge to a long-run level, although trading risk can sometimes cause the spread to diverge from that level.