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# Calculating rate of return

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Arate of return is a measure of the increase (or decrease) in an investment over a period of time. You invest to earn a return in the form of income (interest and dividends) and/or capital appreciation (when the price of the investment sold is higher than the purchase price). Some investments, such as savings accounts and CDs, offer only income with no capital appreciation; others, such as common stock, offer the potential for capital appreciation and may or may not pay dividends. If the price of a stock declines below the purchase price and you sell the stock, you have a capital loss. The simple definition of total return includes income and capital gains and losses.

Calculating a return is important because it measures the growth or decline of your investment, and it provides a yardstick for evaluating the performance of your portfolio against your objectives. You can calculate the total rate of return as follows:

Rate of return for the holding period = [(ending value - beginning value) + income]/gross purchase price

You should include spreads and commissions in the calculation. For example, if you bought a stock at the beginning of the year for \$1,000 (including the commission), sold it at the end of the year for \$1,500 (net proceeds received after deducting the commission), and earned a dividend of \$50, the rate of return is 55 percent:

Rate of return = [(1,500 - 1,000) + 50]/1,000 = 55%

This rate of return is simple and easy to use, but it is somewhat inaccurate if the investment is held for a long period of time because the time value of money is not taken into account. The time value of money is a concept that recognizes that a dollar today is worth more in the future because of its earnings potential. For example, if you invested a dollar at 5 percent for one year, it would be worth \$1.05 at the end of one year. Similarly, if you expect to receive a dollar at the end of one year, it would have a present value of less than a dollar (now).

This simple average rate of return of 55 percent does not take into account the earnings capacity of the interest. In other words, you would reinvest the \$50 of dividends you received, which would increase the rate of return above 55 percent owing to compounding of the interest.

Using the time value of money to calculate the rate of return gives you a more accurate rate-of-return figure. However, it is more difficult to calculate because the rate of return on a stock equates the discounted cash flows of future dividends and the stock’s expected sale price to the stock’s current purchase price. This formula works better for bonds than for common stocks because the coupon rate for bonds is generally fixed, whereas dividend rates on common stocks fluctuate (and you therefore need to make assumptions). When companies experience losses, they might reduce their dividend payments, as Ford Motor Company did to preserve its cash in 2006. If a company’s earnings increase, the company might increase the amount of its dividend payments. The future sale price of a stock has even less certainty. Bonds are retired at their par price (\$1,000 per bond) at maturity; but when a stock eventually is sold, the future sale price is anyone’s guess.

How do you calculate a return for a portfolio? It is useful to be able to compute a return for a portfolio of investments. The following example illustrates the steps to determine such a return. The portfolio has five stocks with the following returns:

 Stock Return A 7.5% B 6.2% C & D 2.0% E -3.1%

The returns for the stocks are weighted and then summed to give the portfolio weighted average return:
To be able to compare your portfolio return with the return of the market, you need to be able to determine your return accurately.
 Stock Weighting Rate Weighted Average Return A 1/5 * 0.075 = 1.5% B 1/5 * 0.062 = 1.24% C & D 2/5 * 0.02 = 0.8% E 1/5 * -0.031 = -0.62% 2.92%

This process may not be easy if you add funds to purchase securities and withdraw funds during the holding period. You may recall that a few years ago the Beardstown Ladies Investment Club had a problem calculating its returns accurately. The members claimed to have earned average annual returns in the low 20 percent range for an extended period, beating annual market averages, only to find that they had computed their returns incorrectly. In fact, an audit by a prominent accounting firm showed that their average annual returns were in single digits during that same period. For a portfolio where you have not added or withdrawn any funds, the simple holding-period return discussed earlier is sufficient:

Holding-period return = (ending balance - beginning balance)/ beginning balance

Table 5–1 illustrates how to calculate a return for a portfolio where funds have been added and withdrawn.

Table 5-1
Measuring a Portfolio Return with Additions and Withdrawals to the Portfolio

If you had \$100,000 in your portfolio at the beginning of the year, and at the end of the year your portfolio had increased to \$109,000, you had a 9 percent return [(\$109,000 -100,000)/100,000].
For additions and withdrawals during the year, the holding-period return for a portfolio is calculated as follows:

For example, a portfolio that began with \$110,500 at the beginning of the year, received dividends of \$8,600 and capital gains of \$12,000, suffered unrealized losses of \$6,000 during the year, had new funds of \$10,000 added at the beginning of April, and had \$4,000 withdrawn at the end of October had an annual return of 12.44 percent:
This portfolio earned a 12.44 percent return before taxes and can be compared with a comparable benchmark index for the same period of time.

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