High Frequency Traders (HFTs) are not investors, they are market makers. They find a willing buyer and a willing seller, arrange the transaction, and execute the trade. They make a profit on the spread between the buy price and the sell price.
Except that a neutral third party (the exchange) could connect the willing buyer and willing seller who both are willing to perform the transaction at higher prices, and split the difference. i.e. the Seller is selling for $1.05 and the buyer is willing to pay $1.06. HFT makes money by buying from the seller, selling to the buyer, and pocketing the $0.01 (minus expenses and trading costs.)
But wouldn't the buyer and seller be better off if the exchange, who is taking a transaction fee to perform the service, closed the transaction at $1.055? And if the buyer and seller are serious about wanting to make the trade, requiring the offer to be valid for a full second (for example) would give the market plenty of time to guarantee that the trade occurs.
Since the introduction of high frequency trading, transaction costs have fallen considerably, saving plenty of people a lot of money
It is not clear if this is a case of cause or effect. Without cheap transactions, HFT doesn't make sense. (And if the number of transactions were an order of magnitude smaller without the HFT noise, the cost of the infrastructure to execute the trades would be dramatically cheaper as well, which would reduce the cost of trades.)
But the fact remains that HFT acts as a hidden transaction fee on every trade. All of the money they make comes at the expense of someone executing an order.