2020 has been the sort of year that makes people naturally look forward to 2021. Even though the stock market has done well this year, it's come with dramatic volatility.

Wall Street's finest are starting to come out with their stock market projections for 2021, and there's a lot of optimism among their forecasts. Below, we'll look more closely at their bull cases -- and also see what kind of downside risks there are lurking in the market.

How the market fared on Wednesday

The stock market had an up-and-down day on Wednesday, with stocks falling sharply late in the session. Early in the day, most market benchmarks were higher, but they gradually gave up gains in the afternoon. In the end, the Dow Jones Industrial Average (DJINDICES:^DJI), S&P 500 (SNPINDEX:^GSPC), and Nasdaq Composite (NASDAQINDEX:^IXIC) were all down in the neighborhood of 1%.

Today's stock market


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Data source: Yahoo! Finance.

A couple of optimistic views of the market

Those who want a better 2021 can look to a pair of bullish calls from prominent analysts. Morgan Stanley (NYSE:MS) projected that the S&P 500 will rise to 3,900 by December 2021. That's up from its initial estimate of 3,350, which didn't extend quite as far into next year.

Number cubes showing change from 2020 to 2021.

Image source: Getty Images.

Morgan Stanley's estimate is largely based on a return to focusing on fundamentals. During 2020, it's been impossible to gauge companies according to revenue and earnings, because nearly every business has suffered either huge disruptions or massive tailwinds from the COVID-19 pandemic. Assuming that a vaccine is effective in bringing the coronavirus crisis to an end, Morgan Stanley seems to believe that 2021 will give companies a chance to shine if they can outperform their competitors and generate solid growth in sales and profits.

Morgan Stanley believes that small-cap indexes like the Russell 2000 could do even better than large-cap benchmarks. Many small companies have taken a lot more damage from the pandemic than big multinationals, and they therefore stand to gain more when the economy returns to normal.

Even so, the short term could be ugly. A new wave of COVID-19 cases could force new lockdowns and restrain economic activity, causing dramatic swings and potentially a 10% correction in the coming months.

An even rosier outlook

JPMorgan Chase (NYSE:JPM) has an even more optimistic view on what's coming. Based on a quantitative model that incorporates macroeconomic factors and relative valuations across asset classes, JPMorgan set a target of nearly 4,200 for the S&P 500.

JPMorgan's forecast is interesting, though, in that it believes that the stock market is currently overvalued by roughly 10% to 12%. Yet analysts think that the market is already looking ahead to the end of the pandemic and a cyclical upturn in many of the hardest-hit parts of the economy.

Be ready for anything

Making positive predictions about the stock market is usually a safe bet, because stocks generally rise more often than they fall. That doesn't mean that the gains will come easily. When history looks back at 2020's stock market performance, positive returns might well mask the level of volatility that pervaded the market.

Hopefully, 2021 won't bring the huge surprises that 2020 did. Yet no matter what happens, the key to keeping your sanity is to remember your long-term strategic vision for stock market investing and not get swayed by short-term moves. If you can do that, you'll be well on your way to starting off 2021 on the right foot.

This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.