Shares in FTSE 100 mega miners BHP Billiton (LSE: BLT), Rio Tinto (LSE: RIO) and Anglo American (LSE: AAL) have all posted double-digit gains over the last month, despite BHP and Rio cutting their dividends.

What’s behind this optimism? One possible reason is that investors were mostly reassured by each firm’s 2015 results. There were no nasty surprises. Even the dividend cuts gained some respect as prudent and sensible decisions.

However, visibility of future profits remains very poor. In this article I’ll explain just why this is and why these miners’ profits could be much higher — or lower — than expected in 2016.

Small numbers with a big impact?

Stashed away at the very end of each miner’s annual results presentation is an explanation of how changes in commodity prices and exchange rates would affect the firm’s profits.

For example, BHP says that if the price of iron ore rises by $1/tonne, then all else being equal, the group’s 2016 net profit will rise by $147m. Given that BHP is only expected to report a net profit of $873m in 2016, it’s clear that a small improvement in the price of iron ore could give a big boost to profits.

Exchange rates are also very important as Anglo American’s results from last year show.

Falling commodity prices caused Anglo’s underlying operating profit to drop by $4.2bn in 2015. However, weaker currencies in the countries where Anglo’s mines are located provided a $1.8bn boost to underlying operating profit.

Overall, Anglo’s underlying operating profit fell by 55% to $2.2bn. But if exchange rates had remained unchanged while commodity prices fell, then this profit figure would have fallen by 97% to just $190m!

Predicting the future

Rio Tinto’s sensitivities table includes nine different parameters. BHP specifies eight, while Anglo specifies 14. In reality, there are many more on top of these core figures.

The problem is that in real life, these figures don’t move in isolation. As Rio Tinto explains in its notes: “The relationship between currencies and commodity prices is a complex one and movements in exchange rates can affect movements in commodity prices and vice versa.”

For example, big swings in the price of iron ore may affect the strength of the Australian dollar. The oil price affects the cost of operations, but the local price of fuel in each country may also be influenced by exchange rates.

On top of this, the prices of different commodities will often move in opposite directions at the same time. Coal may get cheaper, while iron ore and gold might rise in price.

It’s clear that miners’ profits are a very complex mixture of moving parts. They’re also fairly unpredictable.

I suspect that the profits reported by these three firms in 2016 will be very different to current market forecasts. It’s simply not possible to predict that far in the future.

If you’re not convinced, then remember that over the last 12 months, the consensus forecast for BHP’s 2016 earnings per share has fallen from $1.59 per share to just $0.18 per share. Similar declines have affected forecasts for Rio Tinto and Anglo American.

I suspect 2016 will be full of surprises for mining investors. Big gains are possible if market conditions improve.

However, the outlook for many commodities remains unclear, as supply seems to have grown faster than demand.

If you're already invested in mining companies, then you may want to consider diversifying into other sectors.

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Roland Head owns shares of Rio Tinto, BHP Billiton and Anglo American. The Motley Fool UK has recommended Rio Tinto. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors.