Hunting for bargains in a falling stock market can be hugely profitable, but it’s not without risk. Shares are sometimes in free-fall for a good reason and they may continue to fall.

With this in mind, I decided to take a look at three stocks which have all fallen significantly since December. Are ARM Holdings (LSE: ARM), Direct Line Insurance Group (LSE: DLG) and Old Mutual (LSE: OML) a buy at current prices, or is there worse to come?

ARM Holdings

Shares in highly-rated chip designer ARM Holdings have fallen by 21% since the start of December. The FTSE 100 has only fallen by 11% over the same period.

ARM’s 2015 results, which were published on Wednesday, do not suggest any serious problems. Revenue rose by 22% to £968.3m, while pre-tax profits were 24% higher at £138.7m. The group’s operating margin rose from 50.3% to 51.6%.

However, fourth quarter growth was slightly below expectations. There are also concerns that ARM’s gradual shift from smartphone chips to embedded chips for the Internet of Things could affect the firm’s profits. Profit margins are thought to be lower on embedded chips, which are cheaper and less powerful.

ARM shares currently trade on 25 times 2016 profits, falling to 21 times profits for 2017. That’s cheaper than they’ve been for a long time. The shares could fall further, but I think they are starting to look affordable.

Direct Line

Direct Line’s shares have skidded 14% lower this year, partly because claims from December’s bad weather are expected to cost the group between £110m and £140m. Analysts have cut 2015 earnings forecasts from 32p per share to 30p per share as a result.

A further fall to 28p per share is expected for 2016. One reason for this may be that intense competition in the home and motor sectors is limiting Direct Line’s ability to grow. Intense competition on price makes it harder for insurers to attract new customers, as doing so might require them to cut prices to unsustainably low levels.

For shareholders, the main risk is that Direct Line could be forced to cut its dividend.

Direct Line’s 2016 dividend payout is expected to be about 21.6p per share, or around 75% of forecast earnings per share. This gives an attractive forecast yield of 6.1%, but it does mean that the firm is expected to payout 75% of its forecast earnings this year. That’s quite a high ratio, and is more than in previous years. Shareholders should be aware that the dividend could be cut if earnings continue to fall.

Old Mutual

An alternative choice in the insurance sector is pension and investment firm Old Mutual. After falling by 20% over the last three months, the South Africa-based firm currently trades on 8.8 times 2015 forecasts. The expected dividend yield for 2015 is an appealing 6.1%.

Old Mutual’s nine-month update in November suggested that the firm has put in a strong performance this year. Sales for the first nine months were 31% higher than the previous year.

However, analysts have trimmed their earnings forecasts for the firm since these results were published. Earnings per share growth is now expected to be just 2-3% in 2016. I’m tempted to wait for the firm’s 2015 results before making a decision about Old Mutual.

Indeed, if you're uncertain about the outlook for Direct Line, Old Mutual or ARM, you may want to consider the company selected for "A Top Income Share From The Motley Fool".

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Roland Head has no position in any shares mentioned. The Motley Fool UK has recommended ARM Holdings. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors.