Monday featured yet another meaningful decline in broader-market indices, extending a period of decline that began in October. The S&P 500 was down 1.7% as of 2:20 p.m. EST on Monday, Dec. 17, and down about 13% since Oct. 1.

While market declines can be painful for investors as they occur, they have historically turned out to look like good investment opportunities in retrospect. Therefore, if you're willing to get a little greedy as fear is surfacing in the market, there's a good chance it will pay off nicely over the long haul.

But what stocks are buys amid this market sell-off? Two stocks to consider are Apple (NASDAQ:AAPL) and Amazon.com (NASDAQ:AMZN).

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Apple

Shares of tech giant Apple have been rocked recently. The stock is down about 28% since Oct. 1 as concerns mount about sales trends of the company's latest iPhones. Investors worry that iPhone sales could decline in fiscal 2019, making it difficult for Apple to grow its overall business.

But the big pullback in Apple's stock price has arguably already priced in risk for the company's important iPhone business. Apple currently has a conservative price-to-earnings ratio of 13.8. Further highlighting the stock's cheap valuation, Apple's price-to-free cash flow ratio is just 12.2. With a valuation like this, Apple's aggressive share-repurchase program, combined with its healthy services segment, is likely enough to make up for weakness in the company's iPhone segment.

Sure, since iPhone accounts for about 60% of Apple's revenue, investors may want to keep an eye on the segment. If iPhone revenue begins to decline and if management's outlook for the segment becomes less optimistic (or even pessimistic), today's concerns may be justifiable. For now, however, the severity of Apple stock's recent decline looks like an overreaction.

Amazon.com

Amazon has also fallen sharply recently. Shares are down 24% since Oct. 1. Beyond the broader-market sell-off that has contributed to Amazon stock's pullback recently, another key factor that has weakened investor confidence was the company's weaker-than-expected outlook for the important holiday quarter. Shares fell sharply in October, the day after the company reported its third-quarter results and guided for fourth-quarter revenue to rise about 15% year over year -- a significant deceleration from the company's recent growth.

But a look under the hood of Amazon's business reveals some exciting momentum. First and foremost, Amazon's cloud-computing business, Amazon Web Services, is surging. AWS revenue was up 46% year over year in the third quarter of 2018. This is an acceleration from 42% year-over-year growth in the third quarter of 2017. More importantly, AWS operating income has been skyrocketing. The segment's operating income for the trailing-nine-month period ending Sept. 30 was $5.1 billion, up from $3 billion in the year-ago period. 

In addition, Amazon is supplementing its e-commerce business with significant momentum in subscriptions and third-party seller services. Subscription revenue jumped 52% year over year in Q3, while revenue from services for third-party sellers increased 31% over the same time frame. Together, these segments account for about a third of Amazon's total e-commerce revenue, making them promising catalysts.

With a price-to-earnings ratio of 86, Amazon stock doesn't look cheap on the surface. But once investors realize how fast the company's earnings are growing, the stock begins to look more attractive. Amazon's trailing-nine-month earnings per share of $14.49, for instance, are up from $2.46 in the same period last year. Amazon's growing economies of scale will likely lead to further margin improvements and, thus, more outsize earnings growth in the quarters ahead.

John Mackey, CEO of Whole Foods Market, an Amazon subsidiary, is a member of The Motley Fool's board of directors. Daniel Sparks owns shares of Apple. The Motley Fool owns shares of and recommends Amazon and Apple. The Motley Fool has the following options: long January 2020 $150 calls on Apple and short January 2020 $155 calls on Apple. The Motley Fool has a disclosure policy.