The "Halftime Report" traders highlighted the bond market as the second half of the day began.
Jim Lebenthal said the U.S. stock market and economy are healthy and can cope with higher interest rates.
Josh Brown agreed that stocks could still perform well in a rising rate environment.
Trader disclosure: On May 12, 2015, the following stocks and commodities mentioned or intended to be mentioned on CNBC's "Fast Money" were owned by the "Halftime Report" traders: Pete Najarian is long AMAT, AAPL, BABA, BAC, BMY, BP, CSX, DISCA, FOXA, GE, KKR, KO, LLY, MBLY, MRK, PEP, PFE, he is long calls AA, AAL, BBY, BK, CBS, COP, CSX, DB, EJ, F, FL, GE, GS, HSBC, HZNP, IMAX, KO, KSS, LEN, MAC, MYL, NEE, NTAP, NUAN, OC, PFE, SYY, TEVA, TSX, UAL, UUP, VALE, VMW, VZ, XLF, XOM, ZIOP. Josh Brown is long BAC, DE, DNKN, FSLR, JMBA, SAM, SHAK, SPWR, TNET, TWTR, XON, XLE. Steve Weiss is long AAL, C, CDK, ESPR, HEDJ, NBIX. Jim Lebenthal is long AAPL, BP, C, DCO, EEQ, GAIA, GM, IBM, INTC, JCP, MPC, OA, ORBC, PFE, QCOM, SJT, SPLS, TGT, TIF, TRMB, WGO.