Growth of the stock and bond markets is expected to slow to about 10 percent annually over the next three years, according to a survey released today by the Securities Industry Association.

The industry, which showed a loss during the second quarter, is now back in the black, although 1984 is still expected to be the worst year for profits since 1977.

Arthur Andersen & Co., the Big Eight accounting firm that conducted the study, interviewed 600 people, including chief executives of securities firms, banks and other financial institutions, as well as regulators, academics and clients.

The study sought to identify key forces within and outside of the industry to help companies shape strategy for the rest of the decade. The results also provide a good profile of the industry almost a decade after the end of fixed commissions began to revolutionize it.

Among the findings were:

* The largest growth is predicted for the new derivative products. Broad-based stock indexes, which permit investors to bet on large market shifts rather than individual stock movements, will grow by 23 percent annually. Narrow-based indexes, which allow betting on changes in industry stocks such as technology or energy, will grow at a 54 percent annual rate. Their growth will thus be similar to the 25 percent increase shown by the New York Stock Exchange and the 42 percent increase in over-the-counter trading in the last five years.

* U.S. investment overseas will double to $62 billion in the five-year period ending in 1988, while foreign investment in U.S. securities will reach $167 billion, up from $134 billion in 1983. The projections are based on high interest rates, a strong dollar and a favorable economic outlook.

* Corporations are expected to increase both debt and equity issues dramatically, with underwriting reaching the $67 billion level by 1988. Trading and investment profits will exceed commissions for the first time as a percentage of the industry's total revenue by 1988.

Figures released by the SIA indicate that after suffering losses of $98 million during the second quarter, the securities industry made a pre-tax third-quarter profit of $689 million. The fourth quarter is expected to be the same or better, according to SIA Assistant Research Director Ira Epstein. After-tax return on assets will be about 7 to 8 percent, the worst since 1977's 6.9 percent.

One of the more surprising conclusions of the Andersen study is that the securities industry as a whole has done a poor job in understanding its customers. Offering a wide variety of products rated last in a poll of customers with incomes of $40,000 to $60,000 as a reason for selecting a particular firm. Prices rated next to last. Soundness and stability ranked first, followed by prior relationship and image or reputation.

The firms, however, rated variety of products second in importance in attracting customers. This suggests the industry may be paying researchers to invent products customers may not want. Andersen said that marketing campaigns to lure retail customers -- who pay higher commissions proportionately than institutions -- would be emphasized more in the future.

As for competition in the deregulated financial services field, the securities industry sees it mainly coming from diversified financial companies such as Sears, Roebuck & Co. and American Express Co., followed by banks.

The vast majority of the survey respondents said securities firms would continue to dominate corporate underwriting but that competitors would take over discount brokerages. However, opinion was divided on whether banks and diversified financial companies would prevail in providing venture capital or financial planning.

The poll indicated a discrepancy between the regulator and the regulated. Industry officials said the trend was still toward more deregulation, except perhaps for banking. But the regulators foresaw little additional change with the exception of mutual funds.

Finally, while regulators would like to have a system organized by function, in which any company engaged in the same type of venture would be supervised by the same agency regardless of whether the company is a bank or an insurance firm, the regulated expressed a preference for a single regulator for all types of activities. They were not asked who this "super cop" should be, however.