Bitcoin (BTC), the first significant blockchain-based "cryptocurrency" has grown from near zero at its advent in 2013 to a market capitalization of about $38B USB as of June 2017 question launch. (see current market cap and time series here.) While Bitcoin is still the largest, hundreds of other blockchain-based currencies have been launched, and some are catching up.
Ethereum (ETH) started trading in 2015, and has reached almost half the market cap of Bitcoin as of June 2017; see current market cap and time series here. Ripple, a third major currency, stands at about half of Ethereum.
Will Ethereum surpass Bitcoin's total market capitalization by 2020?
Resolution will be based on the descendant blockchains of Bitcoin and Ethereum (including Ethereum classic) with the largest market cap at the time. Resolution is positive if at any point prior to Jan 1, 2020, Ethereum's total market capitalization surpasses that of Bitcoin, as reported on coinmarketcap.com, for two consecutive days. (If coinmarketcap.com is discontinued, then resolution will be based on substantially equivalent data or sources.)
For this question, a "descendant blockchain" is: (a) a continuation of a blockchain (e.g., both ethereum and ethereum classic are descendant blockchains of the pre-DAO blockchain), or (b) a snapshot-based fork where a new blockchain is initiated with balances equal to those from a snapshot of the parent blockchain (e.g., the upcoming zencash will be a descendent of zclassic because its genesis block will begin with balances equal to those from a snapshot of zclassic's blockchain, but zclassic is not a descendent of zcash because its genesis block had empty balances). In addition, the date of the snapshot must be after the creation of this question (2017-06-02).
(Edited 06/06/17 to require two consecutive days of resolution satisfaction, and to specify descendent blockchain provisions.)