Shares of restaurant company Yum China Holdings (YUMC -1.39%) soared 33.2% in September, according to data provided by S&P Global Market Intelligence. It was a welcome development for shareholders who have been enduring a multiyear downtrend. But what's interesting here is that Yum China didn't report any news during the month.

Zooming out a little, investors can see that Yum China stock wasn't alone last month. To the contrary, many companies that do business in China saw their stock prices surge. The iShares MSCI China ETF (NASDAQ: MCHI) is a fund holding a basket of Chinese stocks. And looking at its returns side-by-side with Yum China stock shows the broader trend.

YUMC Total Return Level Chart

YUMC Total Return Level data by YCharts

Why were China stocks up during September? Interest rates in China were cut late in the month, sparking a the stock rally. Generally speaking, central banks lower interest rates when they're trying to stimulate growth in an economy. Therefore, stocks tend to respond favorably when rates go down.

With over 15,000 restaurant locations in China -- mostly Pizza Hut and KFC -- Yum China would certainly be a beneficiary if China's economy grew at a faster rate.

Interest rates aside...

Lauded investor Peter Lynch said, "Nobody can predict interest rates," which is true. And this is why investors should generally avoid speculating on this subject. It's far better to focus on Yum China's business regardless of interest rates. If it gets help eventually from rates, then that's a nice little bonus. But it shouldn't be the central focus of investors.

For its part, business is mostly good for Yum China. It's same-store sales are a little weak at the moment -- they fell 3% year over year in the first half of 2024. But sales are up overall thanks to the brisk pace of new restaurant openings. And the company's second-quarter operating profit of $266 million was its best since it spun off from Yum! Brands in 2016.

There's room for improvement. But for the most part, these are strong numbers from Yum China.

A couple of things to keep in mind

Yum China is a high-growth company. Management plans to open between 1,500 and 1,700 new locations in 2024, which is a strong growth rate. Its operating margin of about 10% is pretty good for a restaurant company. And management is giving $1.5 billion back to shareholders this year through dividends and share buybacks, which is a good amount for a company this size.

Trading at about 24 times earnings, I believe Yum China stock is pretty fairly valued today. If it can keep opening new restaurant locations, earning a profit, and returning capital to shareholders, then this could be a quiet compounder over the long term, just like its former parent company, Yum! Brands, has been.