Sallie Mae. Quite a lady. She's a little hard to understand, perhaps. But green is her favorite color and the circle of her admirers is growing fast.

The fellows who are really smitten are those megabuck investors from pension funds and other institutions. They've managed to buy up 78 percent of her nonvoting stock.

Sallie's game is high finance. She specializes in helping students get loans so they can go to college. Like her housing industry pals, Fannie Mae and Freddie Mac, Sallie toils in what they call "the secondary market."

That's a sort of a swap-shop for bankers and lenders. A banker lends money to a student for college, waits until the student graduates and then sells that loan to Sallie Mae. The banker thus gets his money back and can lend it to another student.

Sallie Mae then collects the payments from the student, sparing the banker the cost of doing all that bookkeeping.

About half of Sallie Mae's lending activity is in the recycling of student loan money in the secondary market; the other half is in lending activity that creates additional student loans.

Sallie Mae, whose full name is the Student Loan Marketing Association, is a government-chartered, profit-making, stockholder-owned corporation that began in 1973. It seems to be in the right business at the right time.

College costs are up sharply and more students need loans than ever before. New student loans were up 84 percent in the last five years. In 1985, about 12.2 million students were enrolled in 3,200 colleges at a total educational cost of $55 billion.

The market for new college loans, about $10.2 billion this year, is expected to rise to about $15.1 billion by 1991.

The demand for loans has helped make Sallie Mae a growth company. The lines on the company's financial charts -- both assets and profits -- go up at a 45-degree angle.

Assets -- the total of loans Sallie Mae makes and buys -- rose from about $5.2 billion in 1981 to $14.4 billion in 1985.

Profits moved even more quickly, rising from about $18 million to $123 million during the same period, while earnings per share increased from 52 cents to $2.45.

Analyst John Kalmbach at Merrill Lynch calls Sallie Mae "one of the most sophisticated financial organizations in the world today."

"The growth prospects are excellent," he said. "The stock is cheap." Sallie Mae closed Friday at $49.50, only a $1 shy of its all-time high.

Kalmbach estimates the company will earn $3.60 a share in 1987 and his target price-earnings ratio is 18. That would give Sallie Mae a market price of almost $65 a share.

Analyst John E. Keefe of Drexel Burnham Lambert, who is a longtime booster of Sallie Mae shares, looks for a price-earnings ratio of about 17.5 on estimated 1987 earnings of $3.75, or also about $65 a share.

The rapid growth of Sallie Mae earnings in recent years has given the company a five-year growth rate of about 47 percent. That pace will slow, most analysts and company officials agree. Kalmbach said he expects Sallie Mae to grow at a 20 percent rate during the next five years. Keefe is a bit more optimistic. He sees a 22 percent growth rate.

Sallie Mae began selling common stock to the public in September 1983 at $20 a share. It traded at first in the $24 range. In mid-1984, it moved to the $30 area, then fell back for a time. It returned to the low $30s in mid-1985 and rose to the $40 area earlier this year.

Whenever the stock lagged, it generally was because of uncertainty over whether Congress would cut back on the Guaranteed Student Loan program -- the mainstay of Sallie Mae business.

One major plus for Sallie Mae is that its credit operations are virtually risk-free. When Sallie Mae lends money to a bank to create new student loans, the bank will put up as collateral either an equal amount of existing student loans or an equal amount of government securities.

Moreover, the loans that Sallie Mae buys and services are guaranteed by the federal government against default. If a student doesn't pay his loan, the government reimburses Sallie Mae.

For the institutions that hold student loans, the government also helps make up the difference between the rate the student pays and the cost of short-term money.

One of the chief continuing goals of Sallie Mae's management is to reduce their sensitivity to interest rate fluctuations. They work hard to match the interest rates on money that they lend against the interest rates on money that they borrow -- while building in a profit for themselves.

To do this, Sallie Mae has raised money abroad in a rather dramatic way. Last year it sold $100 million of Euroyen notes and another $700 million of securities targeted to foreign investors. It also engaged in interest rate "swaps," a technique that converts fixed interest rate debt to debt that has floating rates.

Having managed to lay off most of the credit and interest rate risk involved in their business, the growth of Sallie Mae's earnings seems likely to depend on the growth of its loans -- both loans they make and loans they buy. And given the demand for student loans, it appears that Sallie Mae's earnings are on a solid upward track.

Is there any downside?

"In the whole scheme of things, the fact that the business is closely tied to government spending is the big risk. But the Guaranteed Student Loan program is very valuable and there is a minimum risk that it will be cut back," analyst Keefe said.

Sallie Mae President Edward A. Fox, talking recently to the New York Society of Security Analysts, said that while there might be changes in the GSL program, "It is not only likely but highly probable that the program will remain the predominant form of education finance in this country and the main source of our future income."

"It is hard to think of a program which has a broader or more influential base than the guaranteed student loan: its constituency is the American middle class," Fox said.

Fox noted that the administration's budget package suggested that borrowers bear more of the interest cost of their loans, that lenders' yields be reduced and that lenders and state agencies share some of the risks of defaults. But, he added, "both House and Senate have declared the proposal dead."

The better news, Fox told the analysts, was that Congress might adopt a measure to increase loan amounts. Indeed, the Senate Education Committee reported out a bill doubling annual loan limits to $5,000 for undergrads and boosting graduate student loan limits to $8,000 from $5,000 a year.

One of the most interesting prospects for the future is contained in legislation that would permit Sallie Mae to get into the business of financing college construction projects. It is estimated that colleges need$5 billion a year for maintainence, $1 billion a year for equipment financing and perhaps$50 billion for needs that have been postponed.

If that program is adopted, it could open up a large new market and Sallie Mae is likely to be a prime beneficiary.

Sallie Mae is popular not only with the analysts from major brokerage houses but also with the Franklin Research and Development Corp. of Boston, a firm that screens investments for their contributions to society.

Thus, analyst Darrell Reeck, a professor of religion at the University of Puget Sound in Tacoma, Wash., rates the stock favorably, not only on its fundamentals but because "Sallie Mae serves real human needs."

And he raises a question that few other analysts would ever ask:

Should an investor make profits off the financial needs of a student?

Reeck's answer:

"No one likes to see students graduate with debt obligations of up to $10,000. In an ideal society, government would pay those costs. Living in our real less-than-perfect society, however, there are arguments on the other side.

"The loans are interest free to the student until six months after graduation, when principal and interest payments begin. Many student borrowers would be under greater hardship, if in college at all, if it were not for the loans which support them until they are in a better position to repay."