Helping a child learn to like the nest egg in her Christmas stocking

What will you give your child this Christmas? Imagine her, um, surprise when she finds a mutual-fund certificate tucked into her Christmas stocking among the barrettes, Barbie clothes, and fruit.

As you explain that she could buy a hundred Cabbage Patch dolls with the money her fund could yield someday - if she still wants them - your child may begin to show some enthusiasm for the colorless bits of paper.

And the day you turn to the stock quotes in the newspaper and suggest to her, ''Let's see how your mutual fund is doing today,'' she may begin to understand simple investment principles through her own experience.

Gifts of mutual funds to your child, niece, nephew, or grandchild have several advantages over gifts of individual stocks, fund executives point out. Even a small amount invested in mutual funds will provide a child with a diversified portfolio, says Ronald T. Schroeder, president of New York-based J. & W. Seligman & Co. Your investment is spread over a wide variety of securities - and so is the risk.

And although mutual funds spread the risk, they also allow an investor to choose the desired level of risk, to zero in on the investment objective. Generally, the longer the period of investment, the more risk is acceptable, as higher-risk investments tend to yield higher returns than safer investments over the long term. ''One thing a child has,'' says Reg Green, of the Washington-based Mutal Fund News Service, ''is time on his side.''

Yields of a high-risk ''capital appreciation'' fund can swing markedly up and down each year with the market. There is the possibility of losing or gaining a lot in any given year. For instance, the yield on Seligman's long-term fund was minus 19 percent in the year ending Sept. 30.

A baby or small child has the time for the gains to overbalance the losses for a greater net gain: Over the last 10 years, Seligman's capital appreciation fund has yielded 621 percent, compared with a Standard & Poor's 500 yield of 326 percent for the same period. The Seligman figure assumes reinvestment of capital gains and dividends, less all sales charges.

For the 16-year-old who needs his money in a few years for college, Mr. Schroeder suggests the common stock (middle risk) fund, which yields both growth and income, or the safer money market fund, which yields only income.

Many funds, such as those listed above, are of part of a ''family of funds,'' which permit one to switch the child's assets fairly easily from a capital appreciation growth fund (higher risk) to a cash management income fund (lower risk) within the group.

For their capital appreciation growth fund, Seligman seeks out stocks of small, rapidly growing companies or of established companies making significant progress. The lower-risk cash management income fund invests in CDs, commercial paper, or government securities.

Catherine Taylor, an attorney in the tax department at Minneapolis-based IDS/American Express, suggests giving a child income-yielding mutual funds instead of an allowance. ''Then when the (monthly) check comes, that's their money.'' She notes that the monthly allowance can help kids learn how to budget.

And that ''allowance'' will be coming out of funds that are taxed at the child's lower tax rate. As with any other income-yielding gift, mutual funds can be used to transfer income from your higher rate, saving up to 50 percent in taxes on income that would ordinarily be given to a child or used for his expenses.

For example, if you gave $2,000 annually to a child who had no other income, and he received a 10 percent yield on the investment, at the end of 10 years he would have $35,062. If you yourself had kept and invested these funds (assuming a 30 percent tax bracket), your after-tax total would have been $29,567, more than a $5,000 difference.

So maybe she didn't get a Cabbage Patch Kid this year, but your gift of mutual fund shares will be providing for her future long after the doll is forgotten.