After analyzing portfolio differences between separate account‐mutual fund twins, we find that dissimilar “fraternal twins” show significantly lower joint performance than “identical twins.” This finding is consistent with fraternal twins competing for the limited attention of a manager while identical twins mutually profit. Furthermore, the effect is stronger for separate accounts, which is probably due to investors having the opportunity to influence managers’ investment decisions according to their preferences. These results are independent of differences in known investment constraints. However, the findings may be driven by separate account investors’ preferences for higher liquidity and lower idiosyncratic risk.