the SEC in compiling return on investment in its Pension Bulletins. The basis of this measure is to find a rate of return by dividing income by one-half the beginning investment plus one-half the ending investment, minus one-half the investment income. Thus where A equals beginning investment, B equals ending investment, and I equals income, return R is equivalent to For the purpose of measuring pension fund investment performance, income should be defined to include ordinary income plus realized and unrealized gains and losses." "The investment base to be used is market value as opposed to book value. There are several reasons for this choice: First, market value represents the true economic value which is available to the investment manager at any point in time, whereas book value is arbitrary. Book value depends on the timing of investments, that is, book value will be high or low depending on when investments were made. Second, an investment manager who realizes capital gains will increase his investment base as opposed to a manager who lets his gains ride, even though the funds have the same economic value. Such action would result in an artificially lower return for the fund realizing gains and reinvesting if book value were used." Using and for beginning and ending market value respectively, he then uses the following relation: to transform into hence He goes on to rearrange this into: This formula "reveals that the market value at the end of any period must be equal to the beginning market value plus net contributions plus the rate of return earned of the assets in the fund at the beginning of the period and the return earned on one-half of the contributions. This assumes contributions are received midway through each investment period, and alternately, that half the contributions are received at the beginning of the period, and half at the end of the period." See also Internal rate of return Modified Dietz method Rate of return Further reading MEASURING INVESTMENT PERFORMANCE References Finance theories Investment Mathematical finance