Investment banks are torn on which way the market is heading. Citi warns stocks are 'way ahead of reality,' but JPMorgan says they can climb higher.

Stocks are either far too high or they have further to run, depending on which investment bank you listen to.

"We definitely feel that the markets are way ahead of reality," Manolo Falco, co-head of investment banking at Citigroup, told the Financial Times last week .

"As the second quarter comes along and we start seeing the pain, and the collateral effects of that, we think this is going to be much tougher than it looks," he continued.

Citi is telling all of its clients to "tap the market if they can" because it doubts the cost of raising fresh capital will go any lower, he added.

Read More: MORGAN STANLEY: The market's hottest stocks are in danger of being disrupted to a degree not seen since the Great Recession. Here's how to adjust your portfolio for the coming shift. In contrast, JPMorgan strategists led by Nikolaos Panigirtzoglou argue stocks could climb higher as rock-bottom interest rates and ample liquidity spur investors to shift their money from bonds to shares. "Investors are still underweight equities," they said in a recent note, according to Bloomberg . "There is still plenty of room for investors to raise their equity allocations." Indeed, the JPMorgan team expect non-bank investors such as households, pension funds, and sovereign-wealth funds to boost the percentage of equities in their portfolios from 40% to 49% in the coming years, Bloomberg said. Read More: GOLDMAN SACHS: Buy these 25 beaten-down stocks all poised to jump more than 18% from current levels Bears and bulls The strikingly different views of the stock market's future direction reflect a slew of factors. Bears argue investors are delusional to shrug off a global pandemic and a potential second wave of coronavirus cases. They point to historic unemployment , enduring damage to industries such as airlines , pressure on corporate profits, renewed US-China tensions, and now nationwide protests as reasons to worry about holding stocks. Read More: BANK OF AMERICA: Buy these 13 under-the-radar tech stocks poised to outperform amid flaring China tensions and lasting pandemic damage Meanwhile, bulls are betting on a swift, "v-shaped" recovery once economies reopen and people return to work, fueled by unprecedented support from central banks and global governments. They also see companies such as Amazon, Facebook, Peloton, and Zoom benefiting if another spike in infections and violent protests in some areas lead to more people staying at home. Nobody knows which group will be proven right, but the bulls are carrying the day so far, with the S&P 500 up more than 35% since hitting recent lows in mid-March. NOW WATCH: Pathologists debunk 13 coronavirus myths See Also: BANK OF AMERICA: Buy these 13 under-the-radar tech stocks poised to outperform amid flaring China tensions and lasting pandemic damage 'Embrace the coming crash': A notorious market bear who called the dot-com bust warns big tech stocks are on the verge of succumbing to the economy's downturn The European Union's $826 billion stimulus plan to battle the coronavirus is 'too small and too late,' analysts say