High-end auction sales rely particularly on the confidence of the high net worth consumer and their willingness to spend lavishly. Any plunge in the stock market can make the rich more conscious of their spending, especially when it comes to luxury pieces auctioned at Sotheby's. In fact, Sotheby's stock performance has historically correlated highly with the , according to Cowen analyst Oliver Chen, who downgraded the iconic auction house to market perform from outperform, citing the December stock market tumble.

A tumbling market can hurt many stocks, but Sotheby's is one name that usually feels a lot of pain.

"As financial volatility looms, we believe consumers will be more conscious of their spending, which can be a factor contributing to weaker auction sales," Chen said in a note Thursday. "As consumers become less optimistic about valuation, they will likely hold back on putting their pieces up for auctions, leading to contracted supply gathering for Sotheby's."

Cowen also slashed its 12-month price target for Sotheby's to $44 from $50. Shares of the premium auction house tumbled more than 6 percent to $38.56 on Thursday after the negative call.

"We believe supply gathering is key to Sotheby's success and a combination of lower consumer confidence at the high-end, S&P 500 market volatility, and tough comparisons given prior years of solid momentum are all negatives for 2019," Chen said.

Sotheby's has suffered from weaker sales globally. Sales in Asia were down about 20 percent in October, while sales growth in continental Europe declined by 2.4 percent in 2018, Chen pointed out.

The slowing global economy is also putting more pressure on Sotheby's and luxury sector stocks, he added.