The volatility of asset prices is believed by many to have important effects on the macroeconomy (see e.g. Phelps, 1999). This suggests that monetary and fiscal policy should be made taking into account the volatility of asset prices, and in particular, the volatility of stock prices. Farmer (2012) has advocated a policy of direct government intervention to reduce the volatility of the stock prices. If these views are correct, and the government should be offsetting or even preventing volatility of stock prices, it is important to find good predictors of stock price volatility. An obvious candidate is oil price volatility. There are many published estimates of the effect of oil shocks on macroeconomic variables.1 A growing literature has found evidence that oil price shocks have an effect on stock prices, with most authors finding that higher oil prices have a negative effect on stock returns. A natural question is whether oil price volatility is a useful predictor of stock market volatility. Several papers have considered this question and concluded that oil price volatility can be used to improve upon forecasts of stock return volatility. Elyasiani, Mansur, and Odusami (2011) estimated GARCH(1,1) models of industry stock returns that allowed the variance of the error term to depend on the previous day’s oil price volatility. For the period from December 1998 to December 2006, they were able to reject the null hypothesis of a zero coefficient in the variance equation for five of thirteen industries. Sadorsky (1999) reported impulse response functions and forecast error variance decompositions for real stock returns following shocks to the price of oil and oil price volatility. Papers with a more specialized focus include Sadorsky (2003), which investigated the effect of oil price volatility on the volatility of technology stocks, and Hammoudeh, Dibooglu, and Aleisa (2004), whichestimatedthe effect of oilprice volatility onthe volatility of oil industry stock prices. The conclusion of all of these papers is that there is a useful forecasting relationship between lagged oil price volatility and stock return volatility. This paper differs from the others by focusing on the out-ofsample forecast power of oil price volatility.3 As emphasized by Clark and McCracken (2013), “Forecasts need to be good to be useful for decision making. Determining if forecasts are good involves formal evaluation of the forecasts.” One reason in particular that a correlation identified in the full sample might not translate into good forecasts is parameter instability (Pettenuzzo & Timmerman, 2011). We build on the work done in the papers cited above by evaluating the out-of-sample forecast accuracy of stock return volatility models with and without oil price volatility. We investigate the stability of the parameters of the relationship through time. Full-sample Granger causality test results, along with the other in-sample evaluation techniques applied in the previous literature, can be misleading in the presence of parameter instability, and we find that to be the case.