Millions of new shareowners have now had their first real feel of what a rollercoaster ride the stock market can be.

The endlessly rising share prices of the converted building societies have been sliding back, bringing home in a pretty dramatic fashion the fact that share investments are all too capable of going down as well as up.

This is worrying if you are used to the steadiness of an ordinary savings account, but not an occasion to panic. After all, the shares issued when major building societies converted into banks did not cost anything to acquire, are still a very valuable investment - and promise a stream of income payments in the future as well as the potential for capital growth.

This income arrives in the shape of a dividend cheque - next week Halifax will be sending out its first dividends to shareholders.

With the largest share register in the UK, that's going to be quite an undertaking. The payout means Halifax will be using more than 6000 kilos of paper, stretching half a million feet. Some 700,000 cheques will be sent out, 350,000 payments made through the banking system and 2.7 million dividend payments credited directly to Halifax savings accounts.

''I'm not sure if this is the largest dividend cheque mailing - but it must be one of the biggest,'' says Halifax's Mark Hemingway. The process will have to be repeated all over again in October when the new bank pays its second dividend for the year.

Halifax shareholders will receive 17.5p for each share they hold, that's a minimum payout of #35 for on the basic 200 shares that customers received during

the conversion.

This was confirmed at Halifax's recent annual meeting, although fewer than 500 of the almost three million remaining shareholders bothered to turn up.

Anyone who also qualified for shares as a borrower - or for the variable bonus share issue if their savings totalled #1000 or more - will get an even higher payout.

By comparison with the rates of interest savers are used to receiving on their accounts, the dividend payment is likely to look pretty slim. It's worth less than 2.5% after tax - but doesn't mean the bank is being particularly mean.

The value of Halifax's dividend is bang in line with the average paid by our biggest companies. Dividends are a portion of a company's profits and, all being well, as those profits increase over time, so will the value of the payments.

Many first-time shareholders are likely to be confused by the dividend and Halifax is bracing itself for a flood of enquiries. When Abbey National paid its first dividend many people thought it was a bill and tried to pay it at branches.

Savers may be more used to the idea of owning shares now, but it still makes sense to keep a careful watch on what you receive. Accompanying your dividend cheque - or sent separately to you if the payment goes directly to your savings account - should be a voucher showing the amount that is payable and a figure detailing the ''tax credit''.

Make sure that you keep this voucher in a safe place. At the end of this tax year - that's in April 1999 - you will be able to reclaim the tax credit if your total income is below your annual personal

tax allowances.

Remember too, parents who received shares from the building society conversions because they were the first named on their children's savings accounts should also be able to reclaim this tax credit on behalf of their children. This will boost the #35 dividend payment for the basic issue of 200 shares to #43.75.

A word of warning though - if the money for the child's account was provided by a parent, and the account produces more than #100 of pre-tax interest a year, the income and the share dividends are treated as the parent's not the child's. So the tax won't be reclaimable, unless the parent who gave the money is a non-taxpayer. The #100 rule applies separately to each parent.

The job of reclaiming tax on behalf of a child must be done by a parent or guardian. So if you are a grandparent or other relative or friend who opened a savings account for a child and received shares because of money held in that account, keep the voucher and liaise with the parents at the end of the tax year so they can make the refund claim.

This is the last year for which non-taxpayers will be able to reclaim the tax credit. Government changes to the way tax is paid on dividends means it will no longer be possible in future.

While Halifax investors have to wait until the end of this tax year for a refund, anyone who received Woolwich or Alliance & Leicester shares can put in a claim now.

Woolwich has already paid out 3p a share - and tax on this can now be claimed back if you're eligible. Woolwich is due to pay a further 13p on May 18, with another dividend due in October. So it might be worth waiting until the end of this tax year and lumping all the dividends together before requesting a refund.

Alliance & Leicester has already paid 6.4p on each share - a total of #16 if you qualified for 250 free shares - and the tax on this can be claimed back now by, or on behalf of, non-taxpayers. Again, though, it might be worth waiting and doing the job all in one go next year. A further 14.4p is due on May 18 and another dividend payable in October.

Another big building society opting to convert into a bank was Northern Rock, which is due to pay out a #35 dividend to each shareholder on May 29.