On search keywords with trademarked terms, the brand owner ("focal brand") and other relevant firms compete for consumers. For the focal brand, paid clicks have a direct substitute in the organic links below the paid ad(s). The proximity of this substitute depends on whether competing firms are bidding aggressively to siphon off traffic. We study the returns to focal brands and competitors using large-scale experiments on Bing with data from thousands of brands. When no competitors are present, we find a positive, statistically significant impact of brand ads of 1-4%, with larger brands having a smaller causal effect. In this case, the effective "cost per incremental click" is significantly higher than what focal brands typically pay on other keywords. When the focal brand ad is present, competitors in paid positions 2-4 can "steal" 1-5% of the focal brand/s clicks and raise its costs by shifting traffic to the paid link. Finally, for a set of brands that face competition on their brand search but choose not to advertise, competitors "steal" 18-42% of clicks, suggesting a strong causal effect of position. Under such position effects, we find the ROI on defensive advertising to be strongly positive.