Stephen Weiss said he wouldn't buy Twitter shares right now. He wants to wait and see who is appointed as the next CEO.
Pete Najarian said if the stock moved into the low $30-range then he may consider putting money to work.
Trader disclosure: On June 15, 2015, the following stocks and commodities mentioned or intended to be mentioned on CNBC's "Fast Money" were owned by the "Halftime Report" traders: Stephen Weiss is long AAL, BAC, C, CDK, FINL, NCR, OA. Joe Terranova is long VRTS, S&P futures, Crude oil futures, he is long calls IWM (in the money). Jon Najarian is long MAT, AAPL, BABA, BAC, BMY, BP, CSX, DISCA, DKS, FOXA, GE, KKR, KO, LLY, MRK, PEP, PFE, TEVA, he is long calls AAL, ABX, BAC, BBY, BMY, C, COP, CSX, DAL, DE, EMC, ETFC, FCAU, GE, GS, IMAX, INTC, INVN, JPM, LEN, MT, MU, NUAN, OC, PFE, RAD, S, SXC, SYY, UAL, USB, VOYA, VZ, WFM, WSM, XLF, ZIOP. Today he bought INVN calls.