The idea of becoming a stock market millionaire may seem a fantastical one without having lots of money in the first place. But in fact it is possible for someone to aim for a million even from a starting place of zero, if they take the right approach.

Being realistic about how much to invest

To do that, they could get into the habit of drip-feeding money into a portfolio of carefully selected blue-chip shares.

How much an investor puts in depends on their individual circumstances. Everyone is different. In this example, I use a sum of £800 per month.

To use the money to buy shares, our investor will need a way to do so! There are lots of share-dealing accounts and Stocks and Shares ISAs available.

I think it makes sense to take some time and choose the most suitable one. Even small-seeming fees and charges can add up over the long term, making it harder to aim for a million!

Aiming for outstanding stock market performers

How long might such an approach take before the champagne corks start popping?

Putting aside £800 per month and achieving compound annual growth of 5%, the answer is 38 years.

But wait. What if that compound annual growth rate was 10%?

Then, still investing the same £800 per month, the answer would be 26%.

At a 15% compound annual growth rate? Just two decades.

It is not easy to beat the market, let alone achieve a compound annual growth rate of 15%. But, as some investors demonstrate, it is possible.

Buying just a few great shares

Some FTSE 100 shares have achieved compound annual growth rates of 15% (or more).

Rather than buying the whole FTSE 100 index, instead an investor could aim simply to buy the five to 10 best-performing shares as they target a 15% compound annual growth rate.

Easy in theory – but what about in practice? After all, nobody ever know in advance how a share will perform.

That is true, but I also think success leaves clues. Consider, for example, equipment hire group Ashtead (LSE: AHT). Its share price has more than doubled in the past decade (and it has a 2% dividend yield to boot).

The company operates in an area of high demand. Not only that, but it has pricing power. When a building site needs a specific, critical piece of heavy plant, it needs it and will pay even a high price.

Thanks to its network of depots and proprietary stock of equipment, Ashtead is able to offer a solution in such situations sometimes with limited or no competition. Such rentals can go on for months or even years.

So, this is a simple business to understand. But it is one that benefits from high demand and has high barriers to entry in terms of the cost and complexity of building a network of depots and kitting them out with the right equipment to rent out.

There are risks, of course. A clear one is the danger of a big downturn in construction activity due to economic weakness. That could eat badly into revenues.

Still, even now Ashtead’s price-to-earnings ratio of 17 means it is a share I think an investor could consider as they aim for a million.