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... The following question is based on the paper "Managerial Discretion and Optimal Financing Policies," by Stulz (JFE, 1990). A firm is established in date 0 and operates in periods 1 and 2. In period 1, the firm’s earnings are given by a random variable X% distributed on [0, X] according to a cumulati ...
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Modified Dietz method

The modified Dietz method is a measure of the historical performance of an investment portfolio in the presence of external flows. (External flows are movements of value such as transfers of cash, securities or other instruments in or out of the portfolio, with no equal simultaneous movement of value in the opposite direction, and which are not income from the investments in the portfolio, such as interest, coupons or dividends.) To calculate the modified Dietz return, divide the gain or loss in value, net of external flows, by the average capital over the period of measurement. The result of the calculation is expressed as a percentage rate of return for the time period. The average capital weights individual cash flows by the amount of time from when those cash flows occur until the end of the period.This method has the practical advantage over Internal Rate of Return (IRR) that it does not require repeated trial and error to get a result.The cash flows used in the formula are weighted based on the time they occurred in the period. For example if they occurred in the beginning of the month they would have a higher weight than if they occurred at the end of the month. This is different from the simple Dietz method, in which the cash flows are weighted equally regardless of when they occurred during the measurement period, which works on an assumption that the flows are distributed evenly throughout the period.With the advance of technology in the past 15 years, most systems can calculate a true time-weighted return by calculating a daily return and geometrically linking in order to get a monthly, quarterly, annual or any other period return. However, the modified Dietz method remains useful for performance attribution, because it still has the advantage of allowing modified Deitz returns on assets to be combined with weights in a portfolio, calculated according to average invested capital, and the weighted average gives the modified Dietz return on the portfolio. Time weighted returns do not allow this.This method for return calculation is used in modern portfolio management. It is one of the methodologies of calculating returns recommended by the Investment Performance Council (IPC) as part of their Global Investment Performance Standards (GIPS). The GIPS standard is intended to standardize the way portfolio returns are calculated internationally.The method is named after Peter O. Dietz.
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