Banking is the business of managing money, and where money is involved everything must be carefully assessed, valued and measured. To that end, bankers make use of various mathematical concepts. While the specific function of an executive in a bank will dictate the mathematical tools needed, all bankers must have an excellent understanding of fundamental quantitative concepts.

## Interest Rates

The concept of interest rates is perhaps the most frequently used mathematical concept in banking and finance. Interest rate is simply the cost of money over a specific period of time. If a bank is willing to lend money to a borrower for a year at a rate of 8 percent, the cost of borrowing over a year's time is 8 percent of the original sum borrowed. So the cost of taking out a $1,000 loan for a year equals 8 percent of $1,000, or $80. While the basic idea is simple, the math can get complicated if the interest rate changes or the sum borrowed is paid back in installments.

## Present Value

Present value is closely related to interest rates and allows the banker to assess the value of a future payment stream. If, for example, an investment in a laundromat will be worth $110,000 in a year, and annual interest rates are at 10 percent, what's a reasonable price to pay for such an investment? To answer this question, the banker would calculate the present value of $110,000 expected in a year. Present value equals future value in one year divided by 1 plus the annual interest rate. So the present value of $110,00 is $110,00 /(1+0.1) = $100,000. In other words, getting $110,000 in a year is the same as getting $100,000 today.

## Risk Assessment

Most future payments involve risk, since some or all of the payment may fail to materialize. To quantify the probability of loss, bankers use mathematical tools such as standard deviation. Standard deviation is a measure of how much the value of a variable tends to vary. For example, a stock whose price moves up or down by 2 percent per day on average has a higher standard deviation than one whose price fluctuates 1.5 percent per day on average. The higher the standard deviation of an investment, the greater the probability of both a surprise gain as well as a big loss. These tools help bankers make key investment decisions.

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## Portfolio Management

Bankers also manage portfolios on behalf of both the bank and clients. A portfolio is a collection of such investments as stocks, bonds and currencies. How likely the assets are to move up or down in lockstep versus in opposing directions determines the potential performance of the portfolio. To quantify these moves, bankers use a measure called correlation coefficient, which varies between -1 and 1. If two assets have a correlation coefficient of -1 they always exhibit opposing moves, while a figure of 1 means they mirror each other's moves. Using the correlation coefficient, the banker can calculate the maximum gain and loss in the portfolio.

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