in value is 1,030 − 1,000 = 30, so the return is . Negative initial value Return measures the increase in size of an asset or liability or short position. A negative initial value usually occurs for a liability or short position. If the initial value is negative, and the final value is more negative, then the return will be positive. In such a case, the positive return represents a loss rather than a profit. If the initial value is zero, then no return can be calculated. Currency of measurement The return, or rate of return, depends on the currency of measurement. For example, suppose a 10,000 USD (US dollar) cash deposit earns 2% interest over a year, so its value at the end of the year is 10,200 USD including interest. The return over the year is 2%, measured in USD. Let us suppose also that the exchange rate to Japanese yen at the start of the year is 120 yen per USD, and 132 yen per USD at the end of the year. The value in yen of one USD has increased by 10% over the period. The deposit is worth 1.2 million yen at the start of the year, and 10,200 x 132 = 1,346,400 yen at the end of the year. The return on the deposit over the year in yen terms is therefore: This is the rate of return experienced either by an investor who starts with yen, converts to dollars, invests in the USD deposit, and converts the eventual proceeds back to yen; or for any investor, who wishes to measure the return in Japanese yen terms, for comparison purposes. Annualization Without any reinvestment, a return over a period of time corresponds to a rate of return : For example, let us suppose that 20,000 USD is returned on an initial investment of 100,000 USD. This is a return of 20,000 USD divided by 100,000 USD, which equals 20 percent. The 20,000 USD is paid in 5 irregularly-timed installments of 4,000 USD, with no reinvestment, over a 5-year period, and with no information provided about the timing of the installments. The rate of return is 4,000 / 100,000 = 4% per year. Assuming returns are reinvested however, due to the effect of compounding, the relationship between a rate of return , and a return over a length of time is: which can be used