The question of whether or not the big banks should be broken up is back in the news today.

Bartlett Naylor, a shareholder activist and a member of financial watchdog group Public Citizen, has once again called for J. P. Morgan and Citigroup to be broken up. Shareholders of the two financial institutions will vote on potential breakup plans later this year.

Naylor and CLSA bank analyst Mike Mayo joined the "Halftime Report" today to discuss whether or not a breakup would benefit shareholders.

The crux of Naylor's argument is that banks have grown to the point where their size is negatively impacting shareholder value. Since the banks are now trading below their book value, the parts are worth more than the whole, he argues.

"They [Citigroup and J.P. Morgan] are too big to manage. The banks' arithmetic of assets minus liabilities is a number that's bigger than the share value, which means even the shareholders think that these banks are worth more in parts," he said on the Halftime Report.

Banking analyst Mike Mayo disagrees with Naylor over J.P. Morgan's fate. Mayo argues that J.P. Morgan's 14% return on equity over the past decade is proof that they can successfully manage their size.

Steve Weiss also disagrees with Naylor, claiming that his underlying argument could be applied to any company--not just the banks.

"You make a compelling case to break up every company on the plant not trading on their asset value," Weiss said in response to Naylor. Weiss instead believes that a better solution would be to "break up the regulators because all they've done is throw barrier after barrier at these companies."

Trader disclosure: On March 16, 2016 the following stocks and commodities mentioned or intended to be mentioned on CNBC's "Halftime Report" were owned by the "Halftime Report" traders:

Jon Najarian: Long GDX, PDS, SCTY. Long calls AWI, BP, SLV, CA, ETE, FIT, IP, MCD, MSFT, MYL, NEM, SCHW, TSLA

Pete Najarian: Long AAPL, BAC, BMY, DIS, DISCA,GE, KMI, KMI-A, KO, MRK, PEP, PFE, SAVE, VIAB. Long calls AAL, AMJ, AWI, BAC, BAX, CLF, CMCSA, CNX, CX, DAL, EEM, EGO, EWZ, FIT, GDX, GE, GM, HAIN, HOG, KSS, LC, MDLZ, MET, MSFT, MXIM, NRF, SCHW, SLV, SLW, UAL, USG, WYNN, ZIOP. Long puts DB, EWH, RIG, RY, VLO, XME

Joe Terranova: Long VRTS

Steve Weiss: Long AAL, C, CVC, VIAB