Despite surging 9% in a week, are BHP shares still cheap?

BHP Group Ltd (ASX: BHP) shares are up 1.34% in afternoon trade, currently priced at $44.53 per share.

BHP shareholders have enjoyed a positive five days of trading, with the S&P/ASX 200 Index (ASX: XJO) mining stock up 9.64% since this time last week.

Materials stocks have broadly outperformed over the week, which sees the S&P/ASX 200 Materials Index (ASX: XMJ) up 7.3% compared to the 2.2% gain posted by the ASX 200.

And the big iron ore miners have done particularly well, with Fortescue Metals Group Ltd (ASX: FMG) soaring 18.4% over the week.

Which brings us back to the question at hand. With the past week's gains in the bag, are BHP shares still cheap?

Despite surging 9% in a week, are BHP shares still cheap?

Looking at trailing data rather than forecast estimates, BHP trades on a price-to-earnings (P/E) ratio of 7.0 times with a trailing dividend yield of 11%, fully franked.

Those figures certainly sound promising. But as I said, they are backwards looking.

As my Fool colleague Bruce Jackson pointed out last week:

When it comes to investing, there's always a catch.

Commodity prices are hard to predict, and typically the time to buy mining stocks is at the bottom of the cycle, not near the top, as is the case now due to booming oil, iron ore and coal prices.

Indeed, few analysts predict that we'll see iron ore back at the US$160 per tonne it was fetching back in early March this year. Prices which sent BHP shares flying higher.

In fact, the federal budget forecasts that iron ore prices will fall to US$55 per tonne (FOB Australia) by the end of the first quarter in 2023. Though many analysts, including those over at Commonwealth Bank of Australia (ASX: CBA), believe the budget estimate is too conservative and that prices will take longer to retreat.

Indeed, November has seen the iron ore price rebound from some US$81 per tonne on 1 November to just under US$96 per tonne today.

Copper prices are also up 9% in November. And with its copper segment coming in as its second highest revenue earner, that's also helped boost BHP shares over the week.

Why are copper and iron ore prices rebounding?

The rebound in iron ore and copper has been fuelled on two fronts.

First, the lower-than-expected inflation data out of the United States has raised optimism that global interest rates may not have to ramp up as quickly or as high as previously expected. That would bode well for the construction industries, and copper and iron ore demand.

Second, signs are emerging that China's government will stimulate its economy and its battered real estate markets. The Middle Kingdom has also indicated it is prepared to scale back some of its economy-hampering COVID-zero policies. China's voracious appetite for iron ore, used in steel manufacturing, has slipped as its economic growth has sputtered this year.

So, are BHP shares still cheap after the past week's rally?

The answer there really sits with how the industrial metals fare over the coming months.

Investors would do well to keep their eyes on the economic developments occurring in China and the US, the world's top two economies.

Should China push forward with stimulus and easing pandemic restrictions amid a softening rate-hiking stance from the US Federal Reserve, BHP shares certainly have the potential to run higher from here.