Nice find! I was thinking of something like that, though 10% might be a lot.

Companies could either issue new shares or they could buy back shares from the market (which is, in a manner of speaking, a silent dividend). They could issue similar things as shares, there are several variations on the topic out there. :-)

The shares (or similar papers) could be handed out in a competition: "Our 1.000 top mileage accruers this year will receive..." Or a more long-term loyalty approach might be another idea: "If you fly with us every quarter for 5 consecutive years, you'll get...." Or a simple draw: "For every mile in your account you will have one ticket in the raffle..."

The shares/papers could be available for purchase for miles (someone mentioned that already). Reminds me of http://www.gwei.org :-)

Or there could be "virtual" shares that don't give you real ownership and don't give you cash dividends but dividends in miles. The more profit the airline makes, the more miles you will receive. (Then again not many airlines pay dividends, so this might limit itself.)

Of course, giving miles to shareholders (if they are natural persons) would be another interesting idea.

Yes, there might be tax issues in the US and some other jurisdictions, but the same is true for miles in the first place (ask the Germans). And airlines exist in most countries, so there might be countries where such a program might not be too difficult to pull off.

The airline could cooperate with one online broker only ("If you open an account with Hobo Booby Trading (Senchen) Inc, you will receive...) thus entering a marketing cooperation with them, earning commissions AND strengthening the emotional tie with frequent passengers. Legally, the shares could be awarded by the online broker and not the airline, if that makes it easier for the airline.

Many banks have "reward points" programmes where you can use points to buy investment products or pay back loans. So I don't see why an airline-broker-tandem couldn't come up with some clever scheme. :-)