Modified Dietz method

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behaviour of a liability or short position, even if the investment is not actually a liability or a short position. In cases where the average capital is zero, no Modified Dietz return can be calculated. If the average capital is close to zero, the Modified Dietz return will be large (large and positive, or large and negative).

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flows, there is no difference between the modified Dietz return, the unannualized IRR, or any other method of calculating the holding period return. If the flows are small, or if the returns themselves are small, then the difference between the modified Dietz return and the unannualized internal rate of return is small.

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In the case of a purchase, followed by a sale of more shares than had been bought, resulting in a short position (a negative number of shares), the average capital can also be negative. What was an asset at the time of the purchase became a liability after the sale. The interpretation of the Modified

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In normal circumstances, average capital is positive. When an intra-period outflow is large and early enough, average capital can be negative or zero. Negative average capital causes the Modified Dietz return to be negative when there is a profit, and positive when there is a loss. This resembles the

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There are sometimes difficulties when calculating or decomposing portfolio returns, if all transactions are treated as occurring at a single time of day, such as the end of the day or beginning of the day. Whatever method is applied to calculate returns, an assumption that all transactions take place

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The first step is to calculate the average capital in each of the cash account and the shares over the full year period. These should sum to the $ 10,000 average capital of the portfolio as a whole. From the average capital of each of the two components of the portfolio, we can calculate weights. The

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The only sensible answer to the example above is that the holding period return is unambiguously 1 percent. This means the start date should be adjusted to the date of the initial external flow. Likewise, if the portfolio is empty at the end of the period, the end date should be adjusted to the final

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is a special case of the Modified Dietz method, in which external flows are assumed to occur at the midpoint of the period, or equivalently, spread evenly throughout the period, whereas no such assumption is made when using the Modified Dietz method, and the timing of any external flows is taken into

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One partial workaround solution involves as a first step, to capture the exception, detecting for example when the start value (or first inflow) is positive, and the average capital is negative. Then in this case, use the simple return method, adjusting the end value for outflows. This is equivalent

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With the advance of technology, most systems can calculate a 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

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The method is named after Peter O. Dietz. The original idea behind the work of Peter Dietz was to find a quicker, less computer-intensive way of calculating an IRR as the iterative approach using the then-quite-slow computers that were available was taking a significant amount of time; the research

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The answer is that firstly, the reference to the holding period year to-date until the end-of-day on 17 November includes both the purchase and the sale. This means the effective adjusted holding period is actually from the purchase at the start of the day on 14 November until it is sold three days

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Suppose that a bond is bought for HKD 1,128,728 including accrued interest and commission on trade date 14 November, and sold again three days later on trade date 17 November for HKD 1,125,990 (again, net of accrued interest and commission). Assuming transactions take place at the start of the day,

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Suppose we are calculating the 2016 calendar year return, and that the portfolio is empty until a transfer in of EUR 1m cash in a non-interest bearing account on Friday 30 December. By the end of the day on Saturday 31 December 2016, the exchange rate between euros and Hong Kong dollars has changed

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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 are intended to provide consistency to

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Another situation in which average capital can be negative is short selling. Instead of investing by buying shares, shares are borrowed and then sold. A decline in the share price results in a profit instead of a loss. The position is a liability instead of an asset. If the profit is positive, and

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so in this case, the modified Dietz return is noticeably less than the unannualized IRR. This divergence between the modified Dietz return and the unannualized internal rate of return is due to a significant flow within the period, together with the fact that the returns are large. If there are no

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Suppose the value of a portfolio is $ 100 at the beginning of the first year, and $ 300 at the end of the second year, and there is an inflow of $ 50 at the end of the first year/beginning of the second year. (Suppose further that neither year is a leap year, so the two years are of equal length.)

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For example, consider a fund opening with just $ 100 of a single stock that is sold for $ 110 during the day. During the same day, another stock is purchased for $ 110, closing with a value of $ 120. The returns on each stock are 10% and 120/110 - 1 = 9.0909% (4 d.p.) and the portfolio return is

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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,

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The average capital of the shares over the last quarter requires no calculation, because there are no flows after the beginning of the last quarter. It is the $ 8,000 invested in the shares. However, the average capital in the shares over the whole year is something else. The start value of the

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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 average capital weights individual cash flows by the length of time between those cash flows until the end of the period. Flows which occur

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Suppose that at the beginning of the year, a portfolio contains cash, of value $ 10,000, in an account which bears interest without any charges. At the beginning of the fourth quarter, $ 8,000 of that cash is invested in some US dollar shares (in company X). The investor applies a buy-and-hold

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This method of restricting the calculation to the actual holding period by applying an adjusted start or end date applies when the return is calculated on an investment in isolation. When the investment belongs inside a portfolio, and the weight of the investment in the portfolio, and the

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Peter O. Dietz published his seminal work, Pension Funds: Measuring Investment Performance, in 1966. The Bank Administration Institute (BAI), a U.S.-based organization serving the financial services industry, subsequently formulated rate-of-return calculation guidelines based on Dietz's

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It is not ideal, for two further reasons, which are that it does not cover all cases, and it is inconsistent with the Modified Dietz method. Combined with Modified Dietz contributions for other assets, the sum of constituent contributions will fail to add up to the overall return.

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still has the advantage of allowing modified Dietz 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.

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method shares this practical advantage with the modified Dietz method. Conversely, if there exists a portfolio valuation at any point in time, the implied modified Dietz valuation of cashflows at that point in time is quite unlikely to agree with the actual valuation.

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weight of the cash account is the average capital of the cash account, divided by the average capital ($ 10,000) of the portfolio, and the weight of the shares is the average capital of the shares over the whole year, divided by the average capital of the portfolio.

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For example, consider a scenario where a portfolio is empty at the start of a day, so that the start value A is zero. There is then an external inflow during that day of F = $ 100. By the close of the day, market prices have moved, and the end value is $ 99.

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account. Note that in the example above, the flow occurs midway through the overall period, which matches the assumption underlying the simple Dietz method. This means the simple Dietz return and modified Dietz return are the same in this particular example.

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The end value of the portfolio is $ 2,100 in cash, plus shares worth $ 8,800, which is in total $ 10,900. There has been a 9 percent increase in value since the beginning of the year. There are no external flows in or out of the portfolio over the year.

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However, blindly applying the modified Dietz formula, using an end-of-day transaction timing assumption, the day-weighting on the inflow of 8.1m HKD on 30 December, one day before the end of the year, is 1/366, and the average capital is calculated as:

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Note that the Modified Dietz return is a holding-period return, not an annual rate of return, unless the period happens to be one year. Annualisation, which is conversion of the holding-period return to an annual rate of return, is a separate process.

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This does not mean that the correct holding period return on the shares is 40 percent, but for calculation of the contribution, use the unadjusted period return, which is the 40 percent figure, not the actual 10 percent holding period return.

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To measure returns net of fees, allow the value of the portfolio to be reduced by the amount of the fees. To calculate returns gross of fees, compensate for them by treating them as an external flow, and exclude accrued fees from valuations.

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This 9% portfolio return breaks down between 8 percent contribution from the $ 800 earned on the shares and 1 percent contribution from the $ 100 interest earned on the cash account, but how more generally can we calculate contributions?

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An alternative to the modified Dietz method is to link geometrically the modified Dietz returns for shorter periods. The linked modified Dietz method is classed as a time-weighted method, but it does not produce the same results as the

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If all transactions are treated as occurring at the end of the day, then there is zero start value A, and zero value for average capital, because the day-weight on the inflow is zero, so no modified Dietz return can be calculated.

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A slightly improved version of this method is the day-weighted, or modified Dietz, method. This method adjusts the cash flow by a factor that corresponds to the amount of time between the cash flow and the beginning of the

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is the number of calendar days during the return period being calculated, which equals end date minus start date (plus 1, unless you adopt the convention that the start date is the same as the end date of the previous

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This assumes that the flow happens at the end of the day. If the flow happens at the beginning of the day, the flow is in the portfolio for an additional day, so use the following formula for calculating the weight:

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The adjusted holding period return on the shares is 10 percent. If we multiply this by the 20 percent weight of the shares in the portfolio, the result is only 2 percent, but the correct contribution is 8 percent.

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strategy, and there are no further transactions for the remainder of the year. At the end of the year, the shares have increased in value by 10% to $ 8,800, and $ 100 interest is capitalized into the cash account.

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from 8.1 HKD per EUR to 8.181, which is a 1 percent increase in value, measured in Hong Kong dollar terms, so the right answer to the question of what is the return in Hong Kong dollars is intuitively 1 percent.

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Some such problems are resolved if the modified Dietz method is further adjusted so as to put purchases at the open and sales at the close, but more sophisticated exception-handling produces better results.

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method, which applies a compounding principle, but if the flows and rates of return are large enough, the results of the Modified Dietz method will significantly diverge from the internal rate of return.

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For convenience, we will assume the time weight of the outflow of $ 8,000 cash to pay for the shares is exactly 1/4. This means that the four quarters of the year are treated as having equal length.

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The return annualized using a simple method of multiplying-up 1 percent per day by the number of days in the year will give the answer 366 percent, but the holding period return is still 1 percent.

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Instead, we notice that the start value is positive, but the average capital is negative. Furthermore, there is no short sale. In other words, at all times, the number of shares held is positive.

2666: 384: 73: 3151: 1775: 2677: 3911: 2599:, measured over a common matching time interval, then the modified Dietz return on the two portfolios put together over the same time interval is the weighted average of the two returns: 3810: 1301: 732: 3734: 3393: 580: 3343: 3471: 3435: 311: 3960:

the average capital is negative, the Modified Dietz return is negative, indicating that although the number of shares is unchanged, the absolute value of the liability has shrunk.

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The example above is corrected if the start date is adjusted to the end of the day on 30 December, and the start value is now 8.1m HKD. There are no external flows thereafter.

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The modified Dietz return in this case goes awry, because the average capital is negative, even though this is a long position. The Modified Dietz return in this case is:

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What is the return on the portfolio over the year? What are the contributions from the cash account and the shares? Furthermore, what is the return on the cash account?

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later on 17 November. The adjusted start value is the net amount of the purchase, the end value is the net amount of the sale, and there are no other external flows.

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but the unannualized holding period return, using the IRR method, is 125%. Compounding an annual rate of 50% over two periods gives a holding period return of 125%:

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If either the start or the end value is zero, or both, the start and/or end dates need to be adjusted to cover the period over which the portfolio has content.

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contribution of that return to that of the portfolio as a whole is required, it is necessary to compare like with like, in terms of a common holding period.

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method, in that the calculation of a modified Dietz return does not require portfolio valuations at each point in time whenever an external flow occurs. The

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For example, in a scenario where only part of the holdings are sold, for significantly more than the total starting value, relatively early in the period:

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There are sometimes other difficulties when decomposing portfolio returns, if all transactions are treated as occurring at a single point during the day.

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towards the beginning of the period have a higher weight than flows occurring towards the end. The result of the calculation is expressed as a percentage

2809:) required to get the returns for these two assets to roll up to the portfolio return are 1200% for the first stock and a negative 1100% for the second: 3659: 6459:

Dietz, Peter (May 1968). "Measurement of Performance of Security Portfolios COMPONENTS OF A MEASUREMENT MODEL: RATE OF RETURN, RISK, AND TIMING".

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is the net external inflow for the period (so contributions to a portfolio are treated as positive flows while withdrawals are negative flows)

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One of these return calculation methods, the Modified Dietz method, is still the most common way of calculating periodic investment returns.

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what is the modified Dietz holding-period return in HKD for this bond holding over the year to-date until the end-of-day on 17 November?

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to the sum of constituent contributions, where the contributions are based on simple returns and weights depending on start values.

3619: 6573: 6497: 2867: 198:{\displaystyle {\cfrac {\text{gain or loss}}{\text{average capital}}}={\cfrac {B-A-F}{A+\sum _{i=1}^{n}W_{i}\times F_{i}}}} 2224:

shares at the beginning of the year was zero, and there was an inflow of $ 8,000 at the beginning of the last quarter, so:

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and combine these returns with the weights of these two portions of the shares within the starting position, which are:

3102: 2742:{\displaystyle W_{i}={\frac {{\text{average capital}}_{i}}{{\text{average capital}}_{1}+{\text{average capital}}_{2}}}} 1705: 6632: 6618: 6604: 3847:{\displaystyle {\text{Simple return}}={\frac {{\text{adjusted end value}}-{\text{start value}}}{\text{start value}}}} 1370:{\displaystyle {\text{average capital}}=A+\sum {\text{weight}}\times {\text{flow}}=100+0.5\times 50=\$ 125{\text{,}}} 743: 1059:(IRR). The IRR (or more strictly speaking, an un-annualized holding period return version of the IRR) is a solution 6517: 3858: 1789:, in which the cash flows are weighted equally regardless of when they occurred during the measurement period. The 2437:

The answer is to use the return on the shares over the unadjusted full-year period to calculate the contribution:

676: 3698: 3354: 530: 3304: 6657: 3440: 3404: 262: 3199: 3483: 3524: 2918: 917:{\displaystyle B=A\times (1+R)+\sum _{i=1}^{n}F_{i}\times \left(1+R\times {\frac {T-t_{i}}{T}}\right)} 6647: 6397: 1558:{\displaystyle 100\times (1+125\%)+50\times (1+125\%)^{\frac {2-1}{2}}=225+50\times 150\%=225+75=300} 3572: 2541:

The modified Dietz method is an example of a money (or dollar) weighted methodology (as opposed to

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The modified Dietz method is based upon a simple rate of interest principle. It approximates the

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This workaround has limitations. It is possible only if the holdings can be split up like this.

3740: 6518:"Global Investment Performance Standards (GIPS®) Guidance Statement on Calculation Methodology" 3285:{\displaystyle {\frac {\text{gain or loss}}{\text{average capital}}}={\frac {450}{-50}}=-900\%} 2267:

We can see immediately that the weight of the cash account in the portfolio over the year was:

6487: 1425:{\displaystyle {\frac {\text{gain or loss}}{\text{average capital}}}={\frac {150}{125}}=120\%} 6563: 4040:' Note that all the dates of the flows need to exist in the date vector that is provided. 2991:

There is a gain, and the position is long, so we would intuitively expect a positive return.

3776: 6422: 3917: 2759: 2575: 2548: 2542: 1008: 641: 614: 500: 473: 446: 416: 389: 55:

was produced for BAI, Bank Administration institute. The modified Dietz method is a linear

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where the weights of the portfolios depend on the average capital over the time interval:

1689:{\displaystyle 100\times (1+50\%)^{2}+50\times (1+50\%)^{1}=225+50\times 150\%=225+75=300} 638:

is the number of days from the start of the return period until the day on which the flow

8: 6652: 6417: 3028:{\displaystyle {\text{start value}}-{\text{time weight}}\times {\text{outflow on Day 5}}} 1790: 1786: 2820:

The problem only arises because the day is treated as a single, discrete time interval.

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occurs and the end of the period. Assuming that the flow happens at the end of the day,

6472: 1062: 1035: 981: 957: 933: 776: 591: 238: 214: 6628: 6614: 6600: 6569: 6493: 6402: 1198:{\displaystyle B=A\times (1+R)+\sum _{i=1}^{n}F_{i}\times (1+R)^{\frac {T-t_{i}}{T}}} 6468: 737: 6542: 6443: 2035:

and the average capital equals the start value, so the modified Dietz return is:

1821: 6547:. Vol. 32–33. Institute of Chartered Financial Analysts. 2002. p. 72. 762:(IRR) method that it does not require repeated trial and error to get a result. 6412: 5105:* numD: number of days between beginning of the period and date of cashFlow 3687:{\displaystyle {\text{Adjusted end value}}={\text{end value}}+{\text{outflow}}} 3613:

This is equivalent to the simple return, adjusting the end value for outflows:

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At the end of Day 40, the remaining 20 shares are worth 12.50 dollars per share

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external flow. The end value is effectively the final external flow, not zero.

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is the proportion of the time period between the point in time when the flow

4022:' FlowMap. Nx2 matrix of Dates (left column) and flows (right column) 1845:

end value - start value - net inflow = 8,181,000 - 0 - 8,100,000 = 81,000

4043:' when a flow is entered, it only starts accumulating after 1 period. 4007:' This function calculates the modified Dietz return of a time series 2076: 1285:{\displaystyle {\text{gain or loss}}=B-A-F=300-100-50=\$ 150{\text{.}}} 6485: 2776:

simultaneously at a single point in time each day can lead to errors.

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Investment Performance Measurement: Evaluating and Presenting Results

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Such weights are absurd, because the second stock is not held short.

2545:). In particular, if the modified Dietz return on two portfolios are 2430:

How about the contribution to the portfolio return from the shares?

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The (unannualized) internal rate of return in this example is 125%:

3091:{\displaystyle =100\times 10-{\frac {40-5}{40}}\times 80\times 15} 2494:

Then the contribution from the shares to the portfolio return is:

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method, which requires valuations at the time of each cash flow.

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The modified Dietz method also has the practical advantage over

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Comparison with time-weighted return and internal rate of return

5680: 4025:' scaler. Scales the returns to the appropriate frequency 3477:

This gives the contributions to the overall return, which are:

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At the end of Day 5, 80 shares are sold at 15 dollars per share

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The modified Dietz method has the practical advantage over the

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Practical Portfolio Performance Measurement and Attribution.

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We can calculate the return on the cash account, which was:

3648:{\displaystyle {\text{Start value}}=1,000{\text{ dollars}}} 1295:

To calculate the average capital over the two-year period,

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So which is the correct return, 1 percent or 366 percent?

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the way portfolio returns are calculated internationally.

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end value - start value = 1,125,990 - 1,128,728 = -2,738

2015: 2005: 1936: 1923: 1922:

end value - start value = 8,181,000 - 8,100,000 = 81,000

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The formula for the modified Dietz method is as follows:

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Philip Lawton, CIPM; Todd Jankowski, CFA (18 May 2009).

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We then measure the simple return from the shares sold:

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To calculate the gain or loss over the two-year period,

2907:{\displaystyle 20\times 12.50-100\times 10+80\times 15} 2861:

The gain or loss is end value - start value + outflow:

135: 111: 92: 80: 138: 114: 95: 83: 3920: 3861: 3813: 3779: 3743: 3701: 3662: 3622: 3575: 3527: 3486: 3443: 3407: 3357: 3307: 3241: 3202: 3160: 3105: 3042: 3003: 2969: 2921: 2870: 2680: 2608: 2578: 2551: 2077:

Contributions - when not to adjust the holding period

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is the time between the start of the period and flow

1011: 984: 960: 936: 802: 779: 679: 644: 617: 594: 533: 503: 476: 449: 419: 392: 326: 265: 241: 217: 76: 5129:// initialize modified dietz with a debugging number 2848:

At the start of Day 1, the share price is 10 dollars

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Portfolio Performance Measurement and Benchmarking.

3964:Dietz return varies from one situation to another. 2823: 2770: 2661:{\displaystyle W_{1}\times R_{1}+W_{2}\times R_{2}} 379:{\displaystyle \sum _{i=1}^{n}W_{i}\times {F_{i}}=} 4019:' myReturns. Tx1 vector of financial returns 3932: 3905: 3846: 3794: 3764: 3728: 3686: 3647: 3602: 3554: 3513: 3465: 3429: 3387: 3337: 3284: 3219: 3187: 3145: 3090: 3027: 2978: 2954: 2906: 2845:At the start of Day 1, the number of shares is 100 2741: 2660: 2591: 2564: 1917:The corrected gain or loss is the same as before: 1769: 1688: 1557: 1424: 1369: 1284: 1197: 1071: 1044: 1024: 990: 966: 942: 916: 785: 726: 657: 630: 600: 574: 516: 489: 462: 432: 405: 378: 305: 247: 223: 197: 5102:* numCD: actual number of days in the period 3146:{\displaystyle =1,000-{\frac {7}{8}}\times 1,200} 2234:= start value - time weight × outflow amount 2185:= start value - time weight × outflow amount 6639: 1785:The modified Dietz method is different from the 1770:{\displaystyle (1+50\%)^{2}-1=2.25-1=1.25=125\%} 6561: 6445:Pension Funds: Measuring Investment Performance 2813:w*10/100 + (1-w)*10/110 = 20/100 → w = 12. 1943:so the corrected modified Dietz return is now: 1853:so the modified Dietz return is calculated as: 6441: 3566:The sum of these contributions is the return: 2753:Linked return versus true time-weighted return 3906:{\displaystyle ={\frac {1,450-1,000}{1,000}}} 2413:The contribution to the portfolio return is: 5681:Excel VBA function for modified Dietz return 2175:The average capital of the cash account is: 2022:There are no flows, so the gain or loss is: 727:{\displaystyle W_{i}={\frac {C-D_{i}+1}{C}}} 3729:{\displaystyle =20\times 12.50+80\times 15} 3388:{\displaystyle {\frac {12.50-10}{10}}=25\%} 3348:and from the shares still held at the end: 6479: 1935:start value + weighted net inflows = 8.1m 1930:but the corrected average capital is now: 1780: 773:The modified Dietz return is the solution 575:{\displaystyle W_{i}={\frac {C-D_{i}}{C}}} 6555: 2425:= 80 % × 1.25 % = 1 % 2118:average capital = start value = $ 10,000 1897: 29:such as interest, coupons or dividends.) 6492:. John Wiley & Sons. pp. 828–. 6435: 3338:{\displaystyle {\frac {15-10}{10}}=50\%} 2536: 2527: 6568:. John Wiley & Sons. pp. 41–. 6640: 3466:{\displaystyle {\frac {20}{100}}=20\%} 3430:{\displaystyle {\frac {80}{100}}=80\%} 306:{\displaystyle F=\sum _{i=1}^{n}F_{i}} 6458: 5765:'Jelle-Jeroen Lamkamp 10 Jan 2008 5024:Java method for modified Dietz return 3220:{\displaystyle =-50{\text{ dollars}}} 2994:The average capital in this case is: 1055:Compare this with the (unannualized) 5096:* bmv: Beginning Market Value 4016:' myDates. Tx1 vector of dates 3514:{\displaystyle 50\%\times 80\%=40\%} 1909: 24:(i.e. historical) performance of an 6611:Investment Performance Measurement. 3555:{\displaystyle 25\%\times 20\%=5\%} 2276:average capital in the cash account 13: 6589: 6565:Investment Performance Measurement 6473:10.1111/j.1540-6261.1968.tb00802.x 5093:/* emv: Ending Market Value 3927: 3597: 3588: 3579: 3549: 3540: 3531: 3508: 3499: 3490: 3460: 3424: 3382: 3332: 3279: 2318:and the weight of the shares was: 1764: 1721: 1665: 1634: 1600: 1534: 1490: 1463: 1419: 1356: 1271: 998:is the total length of time period 14: 6669: 6562:Bruce J. Feibel (21 April 2003). 5360:// total time weighted cash flows 2507:= 20% × 40 % = 8 % 2458:unadjusted period average capital 1984: 1380:so the modified Dietz return is: 744:true time-weighted rate of return 2955:{\displaystyle =250-1,000+1,200} 2824:Negative or zero average capital 2802:(as opposed to the time weights 2771:Problems with timing assumptions 2333:average capital in the portfolio 2282:average capital in the portfolio 4034:' Modified Dietz Returns. 3967: 2502:× unadjusted period return 6623:Christopherson, Jon A. et al. 6535: 6510: 6452: 5573:ArrayIndexOutOfBoundsException 4421:' Create a vector of Flows 3947: 1797: 1725: 1709: 1638: 1622: 1604: 1588: 1494: 1478: 1466: 1451: 1166: 1153: 1113: 1101: 827: 815: 1: 6428: 3603:{\displaystyle 40\%+5\%=45\%} 3188:{\displaystyle =1,000-1,050} 2836: 2085: 1805: 231:is the starting market value 7: 6391: 2851:Start value = 1,000 dollars 2097: 10: 6674: 6599:West Sussex: Wiley, 2003. 3765:{\displaystyle =250+1,200} 2369:which sum to 100 percent. 1208: 255:is the ending market value 62: 6398:Accounting rate of return 5189:"numCD <= 0" 2765: 2327:average capital in shares 1993: 1832:× 1/366 = 22,131.15 413:multiplied by its weight 49: 37:over the holding period. 5858:'Some error trapping 5684: 5282:"numD<0 , " 5027: 3971: 2442:Unadjusted period return 2004:start value = 1,128,728 6613:New York: Wiley, 2003. 6442:Peter O. Dietz (1966). 6408:Internal rate of return 5450:// total net cash flows 2795:20%. The asset weights 2518: 1781:The simple Dietz method 1057:internal rate of return 767:internal rate of return 760:internal rate of return 748:internal rate of return 40: 6461:The Journal of Finance 3934: 3907: 3848: 3796: 3795:{\displaystyle =1,450} 3766: 3730: 3688: 3649: 3604: 3556: 3515: 3467: 3431: 3389: 3339: 3286: 3221: 3189: 3147: 3092: 3029: 2980: 2956: 2908: 2743: 2662: 2593: 2566: 2014:end value = 1,125,990 1898:Adjusted time interval 1771: 1690: 1572:The IRR is 50% since: 1559: 1426: 1371: 1286: 1199: 1139: 1073: 1046: 1026: 992: 968: 944: 918: 853: 787: 728: 659: 632: 602: 576: 518: 491: 464: 434: 407: 386:the sum of each flow 380: 347: 307: 292: 249: 225: 199: 166: 5099:* cashFlow: Cash Flow 4685:' Cumulated Flows 3935: 3933:{\displaystyle =45\%} 3908: 3849: 3797: 3767: 3731: 3689: 3650: 3605: 3557: 3516: 3468: 3432: 3390: 3340: 3287: 3222: 3190: 3148: 3093: 3030: 2981: 2957: 2909: 2744: 2663: 2594: 2592:{\displaystyle R_{2}} 2567: 2565:{\displaystyle R_{1}} 2537:Money-weighted return 2528:Annual rate of return 2071:= -0.24 % 2 d.p. 1772: 1691: 1560: 1427: 1372: 1287: 1200: 1119: 1074: 1047: 1027: 1025:{\displaystyle t_{i}} 993: 969: 945: 919: 833: 788: 729: 660: 658:{\displaystyle F_{i}} 633: 631:{\displaystyle D_{i}} 603: 577: 524:can be calculated as 519: 517:{\displaystyle W_{i}} 492: 490:{\displaystyle F_{i}} 465: 463:{\displaystyle W_{i}} 435: 433:{\displaystyle W_{i}} 408: 406:{\displaystyle F_{i}} 381: 327: 308: 272: 250: 226: 200: 146: 18:modified Dietz method 6658:Mathematical finance 6423:Time-weighted return 4136:' Get dimensions 3918: 3859: 3811: 3777: 3741: 3699: 3660: 3620: 3573: 3525: 3484: 3441: 3405: 3355: 3305: 3239: 3200: 3158: 3103: 3040: 3001: 2979:{\displaystyle =450} 2967: 2919: 2868: 2678: 2606: 2576: 2549: 1706: 1579: 1442: 1387: 1302: 1224: 1086: 1063: 1036: 1009: 982: 958: 934: 800: 777: 677: 642: 615: 592: 531: 501: 474: 447: 417: 390: 324: 263: 239: 215: 74: 26:investment portfolio 20:is a measure of the 6627:McGraw-Hill, 2009. 6418:Simple Dietz method 5606:ArithmeticException 5276:ArithmeticException 5183:ArithmeticException 1791:simple Dietz method 1787:simple Dietz method 137: 113: 94: 82: 4319:' Redim arrays 3930: 3903: 3844: 3827:adjusted end value 3792: 3762: 3726: 3684: 3665:Adjusted end value 3645: 3600: 3552: 3511: 3463: 3427: 3385: 3335: 3282: 3217: 3185: 3143: 3088: 3025: 2976: 2952: 2904: 2760:true time weighted 2739: 2658: 2589: 2562: 2211:= 10,000 - $ 2,000 2123:so the return is: 2108:weighted flows = 0 1767: 1686: 1555: 1422: 1367: 1282: 1195: 1069: 1042: 1022: 988: 964: 950:is the start value 940: 914: 783: 724: 655: 628: 598: 572: 514: 487: 460: 430: 403: 376: 303: 245: 221: 195: 191: 132: 101: 89: 6609:Bruce J. Feibel. 6575:978-0-471-44563-0 6544:The C.F.A. Digest 6499:978-0-470-47371-9 6403:Capital budgeting 6206:WorksheetFunction 5933:WorksheetFunction 4919:WorksheetFunction 4883:WorksheetFunction 4454:WorksheetFunction 4250:"Range" 4160:"Range" 3901: 3842: 3841: 3836: 3828: 3817: 3682: 3674: 3666: 3643: 3626: 3452: 3416: 3374: 3324: 3268: 3250: 3249: 3246: 3215: 3129: 3074: 3023: 3015: 3007: 2737: 2728: 2713: 2700: 1910:Example corrected 1840:and the gain is: 1513: 1411: 1398: 1397: 1394: 1365: 1333: 1325: 1308: 1280: 1230: 1192: 1079:to the equation: 1072:{\displaystyle R} 1045:{\displaystyle i} 991:{\displaystyle T} 967:{\displaystyle B} 943:{\displaystyle A} 907: 793:to the equation: 786:{\displaystyle R} 722: 601:{\displaystyle C} 570: 248:{\displaystyle B} 224:{\displaystyle A} 193: 136: 112: 103: 99: 93: 87: 81: 6665: 6648:Finance theories 6583: 6582: 6559: 6553: 6552: 6539: 6533: 6532: 6530: 6528: 6522: 6514: 6508: 6507: 6483: 6477: 6476: 6456: 6450: 6449: 6439: 6387: 6384: 6381: 6378: 6375: 6372: 6369: 6366: 6363: 6360: 6357: 6354: 6351: 6348: 6345: 6342: 6339: 6336: 6333: 6330: 6327: 6324: 6321: 6318: 6315: 6312: 6309: 6306: 6303: 6300: 6297: 6294: 6291: 6288: 6285: 6282: 6279: 6276: 6273: 6270: 6267: 6264: 6261: 6258: 6255: 6252: 6249: 6246: 6243: 6240: 6237: 6234: 6231: 6228: 6225: 6222: 6219: 6216: 6213: 6210: 6207: 6204: 6201: 6198: 6195: 6192: 6189: 6186: 6183: 6180: 6177: 6174: 6171: 6168: 6165: 6162: 6159: 6156: 6153: 6150: 6147: 6144: 6141: 6138: 6135: 6132: 6129: 6126: 6123: 6120: 6117: 6114: 6111: 6108: 6105: 6102: 6099: 6096: 6093: 6090: 6087: 6084: 6081: 6078: 6075: 6072: 6069: 6066: 6063: 6060: 6057: 6054: 6051: 6048: 6045: 6042: 6039: 6036: 6033: 6030: 6027: 6024: 6021: 6018: 6015: 6012: 6009: 6006: 6003: 6000: 5997: 5994: 5991: 5988: 5985: 5982: 5979: 5976: 5973: 5970: 5967: 5964: 5961: 5958: 5955: 5952: 5949: 5946: 5943: 5940: 5937: 5934: 5931: 5928: 5925: 5922: 5919: 5916: 5913: 5910: 5907: 5904: 5901: 5898: 5895: 5892: 5889: 5886: 5883: 5880: 5877: 5874: 5871: 5868: 5865: 5862: 5859: 5856: 5853: 5850: 5847: 5844: 5841: 5838: 5835: 5832: 5829: 5826: 5823: 5820: 5817: 5814: 5811: 5808: 5805: 5802: 5799: 5796: 5793: 5790: 5787: 5784: 5781: 5778: 5775: 5772: 5769: 5766: 5763: 5760: 5757: 5754: 5751: 5748: 5745: 5742: 5739: 5736: 5733: 5730: 5727: 5724: 5721: 5718: 5715: 5712: 5709: 5706: 5703: 5700: 5697: 5694: 5691: 5688: 5676: 5673: 5670: 5667: 5664: 5661: 5658: 5655: 5652: 5649: 5646: 5643: 5640: 5637: 5634: 5631: 5628: 5625: 5622: 5619: 5616: 5613: 5610: 5607: 5604: 5601: 5598: 5595: 5592: 5589: 5586: 5583: 5580: 5577: 5574: 5571: 5568: 5565: 5562: 5559: 5556: 5553: 5550: 5547: 5544: 5541: 5538: 5535: 5532: 5529: 5526: 5523: 5520: 5517: 5514: 5511: 5508: 5505: 5502: 5499: 5496: 5493: 5490: 5487: 5484: 5481: 5478: 5475: 5472: 5469: 5466: 5463: 5460: 5457: 5454: 5451: 5448: 5445: 5442: 5439: 5436: 5433: 5430: 5427: 5424: 5421: 5418: 5415: 5412: 5409: 5406: 5403: 5400: 5397: 5394: 5391: 5388: 5385: 5382: 5379: 5376: 5373: 5370: 5367: 5364: 5361: 5358: 5355: 5352: 5349: 5346: 5343: 5340: 5337: 5334: 5331: 5328: 5325: 5322: 5319: 5316: 5313: 5310: 5307: 5304: 5301: 5298: 5295: 5292: 5289: 5286: 5283: 5280: 5277: 5274: 5271: 5268: 5265: 5262: 5259: 5256: 5253: 5250: 5247: 5244: 5241: 5238: 5235: 5232: 5229: 5226: 5223: 5220: 5217: 5214: 5211: 5208: 5205: 5202: 5199: 5196: 5193: 5190: 5187: 5184: 5181: 5178: 5175: 5172: 5169: 5166: 5163: 5160: 5157: 5154: 5151: 5148: 5145: 5142: 5139: 5136: 5133: 5130: 5127: 5124: 5121: 5118: 5115: 5112: 5109: 5106: 5103: 5100: 5097: 5094: 5091: 5088: 5085: 5082: 5079: 5076: 5073: 5070: 5067: 5064: 5061: 5058: 5055: 5052: 5049: 5046: 5043: 5040: 5037: 5034: 5031: 5019: 5016: 5013: 5010: 5007: 5004: 5001: 4998: 4995: 4992: 4989: 4986: 4983: 4980: 4977: 4974: 4971: 4968: 4965: 4962: 4959: 4956: 4953: 4950: 4947: 4944: 4941: 4938: 4935: 4932: 4929: 4926: 4923: 4920: 4917: 4914: 4911: 4908: 4905: 4902: 4899: 4896: 4893: 4890: 4887: 4884: 4881: 4878: 4875: 4872: 4869: 4866: 4863: 4860: 4857: 4854: 4851: 4848: 4845: 4842: 4839: 4836: 4833: 4830: 4827: 4824: 4821: 4818: 4815: 4812: 4809: 4806: 4803: 4800: 4797: 4794: 4791: 4788: 4785: 4782: 4779: 4776: 4773: 4770: 4767: 4764: 4761: 4758: 4755: 4752: 4749: 4746: 4743: 4740: 4737: 4734: 4731: 4728: 4725: 4722: 4719: 4716: 4713: 4710: 4707: 4704: 4701: 4698: 4695: 4692: 4689: 4686: 4683: 4680: 4677: 4674: 4671: 4668: 4665: 4662: 4659: 4656: 4653: 4650: 4647: 4644: 4641: 4638: 4635: 4632: 4629: 4626: 4623: 4620: 4617: 4614: 4611: 4608: 4605: 4602: 4599: 4596: 4593: 4590: 4587: 4584: 4581: 4578: 4575: 4572: 4569: 4566: 4563: 4560: 4557: 4554: 4551: 4548: 4545: 4542: 4539: 4536: 4533: 4530: 4527: 4524: 4521: 4518: 4515: 4512: 4509: 4506: 4503: 4500: 4497: 4494: 4491: 4488: 4485: 4482: 4479: 4476: 4473: 4470: 4467: 4464: 4461: 4458: 4455: 4452: 4449: 4446: 4443: 4440: 4437: 4434: 4431: 4428: 4425: 4422: 4419: 4416: 4413: 4410: 4407: 4404: 4401: 4398: 4395: 4392: 4389: 4386: 4383: 4380: 4377: 4374: 4371: 4368: 4365: 4362: 4359: 4356: 4353: 4350: 4347: 4344: 4341: 4338: 4335: 4332: 4329: 4326: 4323: 4320: 4317: 4314: 4311: 4308: 4305: 4302: 4299: 4296: 4293: 4290: 4287: 4284: 4281: 4278: 4275: 4272: 4269: 4266: 4263: 4260: 4257: 4254: 4251: 4248: 4245: 4242: 4239: 4236: 4233: 4230: 4227: 4224: 4221: 4218: 4215: 4212: 4209: 4206: 4203: 4200: 4197: 4194: 4191: 4188: 4185: 4182: 4179: 4176: 4173: 4170: 4167: 4164: 4161: 4158: 4155: 4152: 4149: 4146: 4143: 4140: 4137: 4134: 4131: 4128: 4125: 4122: 4119: 4116: 4113: 4110: 4107: 4104: 4101: 4098: 4095: 4092: 4089: 4086: 4083: 4080: 4077: 4074: 4071: 4068: 4065: 4062: 4059: 4056: 4053: 4050: 4047: 4044: 4041: 4038: 4035: 4032: 4029: 4026: 4023: 4020: 4017: 4014: 4011: 4008: 4005: 4002: 3999: 3996: 3993: 3990: 3987: 3984: 3981: 3978: 3975: 3939: 3937: 3936: 3931: 3912: 3910: 3909: 3904: 3902: 3900: 3889: 3866: 3853: 3851: 3850: 3845: 3843: 3839: 3838: 3837: 3834: 3829: 3826: 3823: 3818: 3815: 3801: 3799: 3798: 3793: 3771: 3769: 3768: 3763: 3735: 3733: 3732: 3727: 3693: 3691: 3690: 3685: 3683: 3680: 3675: 3672: 3667: 3664: 3654: 3652: 3651: 3646: 3644: 3641: 3627: 3624: 3609: 3607: 3606: 3601: 3561: 3559: 3558: 3553: 3520: 3518: 3517: 3512: 3472: 3470: 3469: 3464: 3453: 3445: 3436: 3434: 3433: 3428: 3417: 3409: 3394: 3392: 3391: 3386: 3375: 3370: 3359: 3344: 3342: 3341: 3336: 3325: 3320: 3309: 3291: 3289: 3288: 3283: 3269: 3267: 3256: 3251: 3247: 3244: 3243: 3226: 3224: 3223: 3218: 3216: 3213: 3194: 3192: 3191: 3186: 3152: 3150: 3149: 3144: 3130: 3122: 3097: 3095: 3094: 3089: 3075: 3070: 3059: 3034: 3032: 3031: 3026: 3024: 3022:outflow on Day 5 3021: 3016: 3013: 3008: 3005: 2985: 2983: 2982: 2977: 2961: 2959: 2958: 2953: 2913: 2911: 2910: 2905: 2748: 2746: 2745: 2740: 2738: 2736: 2735: 2734: 2729: 2726: 2720: 2719: 2714: 2711: 2707: 2706: 2701: 2698: 2695: 2690: 2689: 2667: 2665: 2664: 2659: 2657: 2656: 2644: 2643: 2631: 2630: 2618: 2617: 2598: 2596: 2595: 2590: 2588: 2587: 2571: 2569: 2568: 2563: 2561: 2560: 2508: 2503: 2488: 2483: 2482: 2480: 2479: 2476: 2473: 2463: 2462: 2460: 2459: 2456: 2453: 2443: 2426: 2409: 2407: 2405: 2404: 2401: 2398: 2391: 2389: 2388: 2385: 2382: 2363: 2358: 2357: 2355: 2354: 2351: 2348: 2338: 2337: 2335: 2334: 2331: 2328: 2312: 2307: 2306: 2304: 2303: 2300: 2297: 2287: 2286: 2284: 2283: 2280: 2277: 2261: 2256: 2254: 2252: 2251: 2248: 2245: 2235: 2230: 2217: 2212: 2207: 2205: 2203: 2202: 2199: 2196: 2186: 2181: 2160: 2158: 2156: 2155: 2152: 2149: 2142: 2140: 2139: 2136: 2133: 2119: 2109: 2072: 2070: 2068: 2067: 2064: 2061: 2054: 2052: 2051: 2048: 2045: 2031: 2018: 2008: 1980: 1978: 1976: 1975: 1972: 1969: 1962: 1960: 1959: 1956: 1953: 1939: 1926: 1890: 1888: 1886: 1885: 1882: 1879: 1872: 1870: 1869: 1866: 1863: 1849: 1836: 1776: 1774: 1773: 1768: 1733: 1732: 1695: 1693: 1692: 1687: 1646: 1645: 1612: 1611: 1564: 1562: 1561: 1556: 1515: 1514: 1509: 1498: 1431: 1429: 1428: 1423: 1412: 1404: 1399: 1395: 1392: 1391: 1376: 1374: 1373: 1368: 1366: 1363: 1334: 1331: 1326: 1323: 1309: 1306: 1291: 1289: 1288: 1283: 1281: 1278: 1231: 1228: 1204: 1202: 1201: 1196: 1194: 1193: 1188: 1187: 1186: 1170: 1149: 1148: 1138: 1133: 1078: 1076: 1075: 1070: 1051: 1049: 1048: 1043: 1031: 1029: 1028: 1023: 1021: 1020: 997: 995: 994: 989: 974:is the end value 973: 971: 970: 965: 949: 947: 946: 941: 923: 921: 920: 915: 913: 909: 908: 903: 902: 901: 885: 863: 862: 852: 847: 792: 790: 789: 784: 733: 731: 730: 725: 723: 718: 711: 710: 694: 689: 688: 664: 662: 661: 656: 654: 653: 637: 635: 634: 629: 627: 626: 607: 605: 604: 599: 581: 579: 578: 573: 571: 566: 565: 564: 548: 543: 542: 523: 521: 520: 515: 513: 512: 496: 494: 493: 488: 486: 485: 469: 467: 466: 461: 459: 458: 439: 437: 436: 431: 429: 428: 412: 410: 409: 404: 402: 401: 385: 383: 382: 377: 372: 371: 370: 357: 356: 346: 341: 312: 310: 309: 304: 302: 301: 291: 286: 254: 252: 251: 246: 230: 228: 227: 222: 204: 202: 201: 196: 194: 192: 190: 189: 188: 176: 175: 165: 160: 133: 131: 109: 104: 102: 100: 98:average capital 97: 90: 88: 85: 78: 6673: 6672: 6668: 6667: 6666: 6664: 6663: 6662: 6638: 6637: 6592: 6590:Further reading 6587: 6586: 6576: 6560: 6556: 6541: 6540: 6536: 6526: 6524: 6520: 6516: 6515: 6511: 6500: 6484: 6480: 6457: 6453: 6440: 6436: 6431: 6394: 6389: 6388: 6385: 6382: 6379: 6376: 6373: 6370: 6367: 6364: 6361: 6358: 6355: 6352: 6349: 6346: 6343: 6340: 6337: 6334: 6331: 6328: 6325: 6322: 6319: 6316: 6313: 6310: 6307: 6304: 6301: 6298: 6295: 6292: 6289: 6286: 6283: 6280: 6277: 6274: 6271: 6268: 6265: 6262: 6259: 6256: 6253: 6250: 6247: 6244: 6241: 6238: 6235: 6232: 6229: 6226: 6223: 6220: 6217: 6214: 6211: 6208: 6205: 6202: 6199: 6196: 6193: 6190: 6187: 6184: 6181: 6178: 6175: 6172: 6169: 6166: 6163: 6160: 6157: 6154: 6151: 6148: 6145: 6142: 6139: 6136: 6133: 6130: 6127: 6124: 6121: 6118: 6115: 6112: 6109: 6106: 6103: 6100: 6097: 6094: 6091: 6088: 6085: 6082: 6079: 6076: 6073: 6070: 6067: 6064: 6061: 6058: 6055: 6052: 6049: 6046: 6043: 6040: 6037: 6034: 6031: 6028: 6025: 6022: 6019: 6016: 6013: 6010: 6007: 6004: 6001: 5998: 5995: 5992: 5989: 5986: 5983: 5980: 5977: 5974: 5971: 5968: 5965: 5962: 5959: 5956: 5953: 5950: 5947: 5944: 5941: 5938: 5935: 5932: 5929: 5926: 5923: 5920: 5917: 5914: 5911: 5908: 5905: 5902: 5899: 5896: 5893: 5890: 5887: 5884: 5881: 5878: 5875: 5872: 5869: 5866: 5863: 5860: 5857: 5854: 5851: 5848: 5845: 5842: 5839: 5836: 5833: 5830: 5827: 5824: 5821: 5818: 5815: 5812: 5809: 5806: 5803: 5800: 5797: 5794: 5791: 5788: 5785: 5782: 5779: 5776: 5773: 5770: 5767: 5764: 5761: 5758: 5755: 5752: 5749: 5746: 5743: 5740: 5737: 5734: 5731: 5728: 5725: 5722: 5719: 5716: 5713: 5710: 5707: 5704: 5701: 5698: 5695: 5692: 5689: 5686: 5683: 5678: 5677: 5674: 5671: 5668: 5665: 5662: 5659: 5657:printStackTrace 5656: 5653: 5650: 5647: 5644: 5641: 5638: 5635: 5632: 5629: 5626: 5624:printStackTrace 5623: 5620: 5617: 5614: 5611: 5608: 5605: 5602: 5599: 5596: 5593: 5591:printStackTrace 5590: 5587: 5584: 5581: 5578: 5575: 5572: 5569: 5566: 5563: 5560: 5557: 5554: 5551: 5548: 5545: 5542: 5539: 5536: 5533: 5530: 5527: 5524: 5521: 5518: 5515: 5512: 5509: 5506: 5503: 5500: 5497: 5494: 5491: 5488: 5485: 5482: 5479: 5476: 5473: 5470: 5467: 5464: 5461: 5458: 5455: 5452: 5449: 5446: 5443: 5440: 5437: 5434: 5431: 5428: 5425: 5422: 5419: 5416: 5413: 5410: 5407: 5404: 5401: 5398: 5395: 5392: 5389: 5386: 5383: 5380: 5377: 5374: 5371: 5368: 5365: 5362: 5359: 5356: 5353: 5350: 5347: 5344: 5341: 5338: 5335: 5332: 5329: 5326: 5323: 5320: 5317: 5314: 5311: 5308: 5305: 5302: 5299: 5296: 5293: 5290: 5287: 5284: 5281: 5278: 5275: 5272: 5269: 5266: 5263: 5260: 5257: 5254: 5251: 5248: 5245: 5242: 5239: 5236: 5233: 5230: 5227: 5224: 5221: 5218: 5215: 5212: 5209: 5206: 5203: 5200: 5197: 5194: 5191: 5188: 5185: 5182: 5179: 5176: 5173: 5170: 5167: 5164: 5161: 5158: 5155: 5152: 5149: 5146: 5143: 5140: 5137: 5134: 5131: 5128: 5125: 5122: 5119: 5116: 5113: 5110: 5107: 5104: 5101: 5098: 5095: 5092: 5089: 5086: 5083: 5080: 5077: 5074: 5071: 5068: 5065: 5062: 5059: 5056: 5053: 5050: 5047: 5044: 5041: 5038: 5035: 5032: 5029: 5026: 5021: 5020: 5017: 5014: 5011: 5008: 5005: 5002: 4999: 4996: 4993: 4990: 4987: 4984: 4981: 4978: 4975: 4972: 4969: 4966: 4963: 4960: 4957: 4954: 4951: 4948: 4945: 4942: 4939: 4936: 4933: 4930: 4927: 4924: 4921: 4918: 4915: 4912: 4909: 4906: 4903: 4900: 4897: 4894: 4891: 4888: 4885: 4882: 4879: 4876: 4873: 4870: 4867: 4864: 4861: 4858: 4855: 4852: 4849: 4846: 4843: 4840: 4837: 4834: 4831: 4828: 4825: 4822: 4819: 4816: 4813: 4810: 4807: 4804: 4801: 4798: 4795: 4792: 4789: 4786: 4783: 4780: 4777: 4774: 4771: 4768: 4765: 4762: 4759: 4756: 4753: 4750: 4747: 4744: 4741: 4738: 4735: 4732: 4729: 4726: 4723: 4720: 4717: 4714: 4711: 4708: 4705: 4702: 4699: 4696: 4693: 4690: 4687: 4684: 4681: 4678: 4675: 4672: 4669: 4666: 4663: 4660: 4657: 4654: 4651: 4648: 4645: 4642: 4639: 4636: 4633: 4630: 4627: 4624: 4621: 4618: 4615: 4612: 4609: 4606: 4603: 4600: 4597: 4594: 4591: 4588: 4585: 4582: 4579: 4576: 4573: 4570: 4567: 4564: 4561: 4558: 4555: 4552: 4549: 4546: 4543: 4540: 4537: 4534: 4531: 4528: 4525: 4522: 4519: 4516: 4513: 4510: 4507: 4504: 4501: 4498: 4495: 4492: 4489: 4486: 4483: 4480: 4477: 4474: 4471: 4468: 4465: 4462: 4459: 4456: 4453: 4450: 4447: 4444: 4441: 4438: 4435: 4432: 4429: 4426: 4423: 4420: 4417: 4414: 4411: 4408: 4405: 4402: 4399: 4396: 4393: 4390: 4387: 4384: 4381: 4378: 4375: 4372: 4369: 4366: 4363: 4360: 4357: 4354: 4351: 4348: 4345: 4342: 4339: 4336: 4333: 4330: 4327: 4324: 4321: 4318: 4315: 4312: 4309: 4306: 4303: 4300: 4297: 4294: 4291: 4288: 4285: 4282: 4279: 4276: 4273: 4270: 4267: 4264: 4261: 4258: 4255: 4252: 4249: 4246: 4243: 4240: 4237: 4234: 4231: 4228: 4225: 4222: 4219: 4216: 4213: 4210: 4207: 4204: 4201: 4198: 4195: 4192: 4189: 4186: 4183: 4180: 4177: 4174: 4171: 4168: 4165: 4162: 4159: 4156: 4153: 4150: 4147: 4144: 4141: 4138: 4135: 4132: 4129: 4126: 4123: 4120: 4117: 4114: 4111: 4108: 4105: 4102: 4099: 4096: 4093: 4090: 4087: 4084: 4081: 4078: 4075: 4072: 4069: 4066: 4063: 4060: 4057: 4054: 4051: 4048: 4045: 4042: 4039: 4036: 4033: 4030: 4027: 4024: 4021: 4018: 4015: 4012: 4009: 4006: 4003: 4000: 3997: 3994: 3991: 3988: 3985: 3982: 3979: 3976: 3973: 3970: 3950: 3919: 3916: 3915: 3890: 3867: 3865: 3860: 3857: 3856: 3833: 3825: 3824: 3822: 3814: 3812: 3809: 3808: 3778: 3775: 3774: 3742: 3739: 3738: 3700: 3697: 3696: 3679: 3671: 3663: 3661: 3658: 3657: 3640: 3623: 3621: 3618: 3617: 3574: 3571: 3570: 3526: 3523: 3522: 3485: 3482: 3481: 3444: 3442: 3439: 3438: 3408: 3406: 3403: 3402: 3360: 3358: 3356: 3353: 3352: 3310: 3308: 3306: 3303: 3302: 3260: 3255: 3248:average capital 3242: 3240: 3237: 3236: 3212: 3201: 3198: 3197: 3159: 3156: 3155: 3121: 3104: 3101: 3100: 3060: 3058: 3041: 3038: 3037: 3020: 3012: 3004: 3002: 2999: 2998: 2968: 2965: 2964: 2920: 2917: 2916: 2869: 2866: 2865: 2839: 2826: 2807: 2800: 2773: 2768: 2755: 2730: 2727:average capital 2725: 2724: 2715: 2712:average capital 2710: 2709: 2708: 2702: 2699:average capital 2697: 2696: 2694: 2685: 2681: 2679: 2676: 2675: 2652: 2648: 2639: 2635: 2626: 2622: 2613: 2609: 2607: 2604: 2603: 2583: 2579: 2577: 2574: 2573: 2556: 2552: 2550: 2547: 2546: 2539: 2530: 2521: 2506: 2498: 2486: 2477: 2474: 2471: 2470: 2468: 2466: 2457: 2454: 2451: 2450: 2448: 2446: 2441: 2417: 2402: 2399: 2396: 2395: 2393: 2387:average capital 2386: 2383: 2380: 2379: 2377: 2376: 2361: 2352: 2349: 2346: 2345: 2343: 2341: 2332: 2329: 2326: 2325: 2323: 2322: 2310: 2301: 2298: 2295: 2294: 2292: 2290: 2281: 2278: 2275: 2274: 2272: 2271: 2259: 2249: 2246: 2243: 2242: 2240: 2238: 2233: 2229:average capital 2228: 2215: 2210: 2200: 2197: 2194: 2193: 2191: 2189: 2184: 2180:average capital 2179: 2153: 2150: 2147: 2146: 2144: 2138:average capital 2137: 2134: 2131: 2130: 2128: 2127: 2117: 2107: 2100: 2088: 2079: 2065: 2062: 2059: 2058: 2056: 2050:average capital 2049: 2046: 2043: 2042: 2040: 2039: 2026: 2013: 2003: 1996: 1987: 1973: 1970: 1967: 1966: 1964: 1958:average capital 1957: 1954: 1951: 1950: 1948: 1947: 1934: 1921: 1912: 1900: 1883: 1880: 1877: 1876: 1874: 1868:average capital 1867: 1864: 1861: 1860: 1858: 1857: 1844: 1819: 1808: 1800: 1783: 1728: 1724: 1707: 1704: 1703: 1641: 1637: 1607: 1603: 1580: 1577: 1576: 1499: 1497: 1493: 1443: 1440: 1439: 1403: 1396:average capital 1390: 1388: 1385: 1384: 1362: 1330: 1322: 1307:average capital 1305: 1303: 1300: 1299: 1277: 1227: 1225: 1222: 1221: 1211: 1182: 1178: 1171: 1169: 1165: 1144: 1140: 1134: 1123: 1087: 1084: 1083: 1064: 1061: 1060: 1037: 1034: 1033: 1016: 1012: 1010: 1007: 1006: 983: 980: 979: 959: 956: 955: 935: 932: 931: 897: 893: 886: 884: 871: 867: 858: 854: 848: 837: 801: 798: 797: 778: 775: 774: 740: 706: 702: 695: 693: 684: 680: 678: 675: 674: 649: 645: 643: 640: 639: 622: 618: 616: 613: 612: 593: 590: 589: 560: 556: 549: 547: 538: 534: 532: 529: 528: 508: 504: 502: 499: 498: 481: 477: 475: 472: 471: 454: 450: 448: 445: 444: 424: 420: 418: 415: 414: 397: 393: 391: 388: 387: 366: 362: 361: 352: 348: 342: 331: 325: 322: 321: 297: 293: 287: 276: 264: 261: 260: 240: 237: 236: 216: 213: 212: 184: 180: 171: 167: 161: 150: 139: 134: 115: 110: 108: 96: 91: 84: 79: 77: 75: 72: 71: 65: 52: 43: 12: 11: 5: 6671: 6661: 6660: 6655: 6650: 6636: 6635: 6621: 6607: 6591: 6588: 6585: 6584: 6574: 6554: 6534: 6509: 6498: 6478: 6467:(2): 267–275. 6451: 6433: 6432: 6430: 6427: 6426: 6425: 6420: 6415: 6413:Rate of return 6410: 6405: 6400: 6393: 6390: 5685: 5682: 5679: 5288:"i=" 5028: 5025: 5022: 4031:' Outputs. 3972: 3969: 3966: 3949: 3946: 3945: 3944: 3943: 3942: 3941: 3940: 3929: 3926: 3923: 3899: 3896: 3893: 3888: 3885: 3882: 3879: 3876: 3873: 3870: 3864: 3832: 3821: 3805: 3804: 3803: 3802: 3791: 3788: 3785: 3782: 3772: 3761: 3758: 3755: 3752: 3749: 3746: 3736: 3725: 3722: 3719: 3716: 3713: 3710: 3707: 3704: 3678: 3670: 3655: 3639: 3636: 3633: 3630: 3611: 3610: 3599: 3596: 3593: 3590: 3587: 3584: 3581: 3578: 3564: 3563: 3551: 3548: 3545: 3542: 3539: 3536: 3533: 3530: 3510: 3507: 3504: 3501: 3498: 3495: 3492: 3489: 3475: 3474: 3462: 3459: 3456: 3451: 3448: 3426: 3423: 3420: 3415: 3412: 3396: 3395: 3384: 3381: 3378: 3373: 3369: 3366: 3363: 3346: 3345: 3334: 3331: 3328: 3323: 3319: 3316: 3313: 3293: 3292: 3281: 3278: 3275: 3272: 3266: 3263: 3259: 3254: 3230: 3229: 3228: 3227: 3211: 3208: 3205: 3195: 3184: 3181: 3178: 3175: 3172: 3169: 3166: 3163: 3153: 3142: 3139: 3136: 3133: 3128: 3125: 3120: 3117: 3114: 3111: 3108: 3098: 3087: 3084: 3081: 3078: 3073: 3069: 3066: 3063: 3057: 3054: 3051: 3048: 3045: 3019: 3011: 2989: 2988: 2987: 2986: 2975: 2972: 2962: 2951: 2948: 2945: 2942: 2939: 2936: 2933: 2930: 2927: 2924: 2903: 2900: 2897: 2894: 2891: 2888: 2885: 2882: 2879: 2876: 2873: 2859: 2858: 2855: 2852: 2849: 2846: 2838: 2835: 2825: 2822: 2815: 2814: 2805: 2798: 2772: 2769: 2767: 2764: 2754: 2751: 2750: 2749: 2733: 2723: 2718: 2705: 2693: 2688: 2684: 2669: 2668: 2655: 2651: 2647: 2642: 2638: 2634: 2629: 2625: 2621: 2616: 2612: 2586: 2582: 2559: 2555: 2538: 2535: 2529: 2526: 2520: 2517: 2512: 2511: 2510: 2509: 2492: 2491: 2490: 2489: 2484: 2464: 2428: 2427: 2411: 2410: 2367: 2366: 2365: 2364: 2359: 2316: 2315: 2314: 2313: 2308: 2265: 2264: 2263: 2262: 2257: 2255:× $ 8,000 2236: 2221: 2220: 2219: 2218: 2213: 2208: 2206:× $ 8,000 2187: 2162: 2161: 2121: 2120: 2111: 2110: 2099: 2096: 2087: 2084: 2078: 2075: 2074: 2073: 2033: 2032: 2020: 2019: 2010: 2009: 1995: 1992: 1986: 1985:Second example 1983: 1982: 1981: 1941: 1940: 1928: 1927: 1911: 1908: 1899: 1896: 1892: 1891: 1851: 1850: 1838: 1837: 1820:start value + 1807: 1804: 1799: 1796: 1782: 1779: 1778: 1777: 1766: 1763: 1760: 1757: 1754: 1751: 1748: 1745: 1742: 1739: 1736: 1731: 1727: 1723: 1720: 1717: 1714: 1711: 1697: 1696: 1685: 1682: 1679: 1676: 1673: 1670: 1667: 1664: 1661: 1658: 1655: 1652: 1649: 1644: 1640: 1636: 1633: 1630: 1627: 1624: 1621: 1618: 1615: 1610: 1606: 1602: 1599: 1596: 1593: 1590: 1587: 1584: 1566: 1565: 1554: 1551: 1548: 1545: 1542: 1539: 1536: 1533: 1530: 1527: 1524: 1521: 1518: 1512: 1508: 1505: 1502: 1496: 1492: 1489: 1486: 1483: 1480: 1477: 1474: 1471: 1468: 1465: 1462: 1459: 1456: 1453: 1450: 1447: 1433: 1432: 1421: 1418: 1415: 1410: 1407: 1402: 1378: 1377: 1361: 1358: 1355: 1352: 1349: 1346: 1343: 1340: 1337: 1329: 1321: 1318: 1315: 1312: 1293: 1292: 1276: 1273: 1270: 1267: 1264: 1261: 1258: 1255: 1252: 1249: 1246: 1243: 1240: 1237: 1234: 1210: 1207: 1206: 1205: 1191: 1185: 1181: 1177: 1174: 1168: 1164: 1161: 1158: 1155: 1152: 1147: 1143: 1137: 1132: 1129: 1126: 1122: 1118: 1115: 1112: 1109: 1106: 1103: 1100: 1097: 1094: 1091: 1068: 1053: 1052: 1041: 1019: 1015: 1000: 999: 987: 976: 975: 963: 952: 951: 939: 925: 924: 912: 906: 900: 896: 892: 889: 883: 880: 877: 874: 870: 866: 861: 857: 851: 846: 843: 840: 836: 832: 829: 826: 823: 820: 817: 814: 811: 808: 805: 782: 739: 736: 735: 734: 721: 717: 714: 709: 705: 701: 698: 692: 687: 683: 667: 666: 652: 648: 625: 621: 610: 597: 583: 582: 569: 563: 559: 555: 552: 546: 541: 537: 511: 507: 484: 480: 457: 453: 441: 440: 427: 423: 400: 396: 375: 369: 365: 360: 355: 351: 345: 340: 337: 334: 330: 315: 314: 300: 296: 290: 285: 282: 279: 275: 271: 268: 257: 256: 244: 233: 232: 220: 206: 205: 187: 183: 179: 174: 170: 164: 159: 156: 153: 149: 145: 142: 130: 127: 124: 121: 118: 107: 64: 61: 51: 48: 42: 39: 9: 6: 4: 3: 2: 6670: 6659: 6656: 6654: 6651: 6649: 6646: 6645: 6643: 6634: 6633:9780071496650 6630: 6626: 6622: 6620: 6619:0-471-26849-6 6616: 6612: 6608: 6606: 6605:0-470-85679-3 6602: 6598: 6594: 6593: 6581: 6577: 6571: 6567: 6566: 6558: 6551: 6546: 6545: 6538: 6519: 6513: 6506: 6501: 6495: 6491: 6490: 6482: 6474: 6470: 6466: 6462: 6455: 6448:. Free Press. 6447: 6446: 6438: 6434: 6424: 6421: 6419: 6416: 6414: 6411: 6409: 6406: 6404: 6401: 6399: 6396: 6395: 5039:modifiedDietz 4013:' Inputs. 3965: 3961: 3957: 3953: 3924: 3921: 3914: 3913: 3897: 3894: 3891: 3886: 3883: 3880: 3877: 3874: 3871: 3868: 3862: 3855: 3854: 3830: 3819: 3816:Simple return 3807: 3806: 3789: 3786: 3783: 3780: 3773: 3759: 3756: 3753: 3750: 3747: 3744: 3737: 3723: 3720: 3717: 3714: 3711: 3708: 3705: 3702: 3695: 3694: 3676: 3668: 3656: 3642: dollars 3637: 3634: 3631: 3628: 3616: 3615: 3614: 3594: 3591: 3585: 3582: 3576: 3569: 3568: 3567: 3562:respectively. 3546: 3543: 3537: 3534: 3528: 3505: 3502: 3496: 3493: 3487: 3480: 3479: 3478: 3473:respectively. 3457: 3454: 3449: 3446: 3421: 3418: 3413: 3410: 3401: 3400: 3399: 3379: 3376: 3371: 3367: 3364: 3361: 3351: 3350: 3349: 3329: 3326: 3321: 3317: 3314: 3311: 3301: 3300: 3299: 3296: 3276: 3273: 3270: 3264: 3261: 3257: 3252: 3235: 3234: 3233: 3214: dollars 3209: 3206: 3203: 3196: 3182: 3179: 3176: 3173: 3170: 3167: 3164: 3161: 3154: 3140: 3137: 3134: 3131: 3126: 3123: 3118: 3115: 3112: 3109: 3106: 3099: 3085: 3082: 3079: 3076: 3071: 3067: 3064: 3061: 3055: 3052: 3049: 3046: 3043: 3036: 3035: 3017: 3009: 2997: 2996: 2995: 2992: 2973: 2970: 2963: 2949: 2946: 2943: 2940: 2937: 2934: 2931: 2928: 2925: 2922: 2915: 2914: 2901: 2898: 2895: 2892: 2889: 2886: 2883: 2880: 2877: 2874: 2871: 2864: 2863: 2862: 2856: 2853: 2850: 2847: 2844: 2843: 2842: 2834: 2830: 2821: 2818: 2812: 2811: 2810: 2808: 2801: 2792: 2789: 2785: 2781: 2777: 2763: 2761: 2731: 2721: 2716: 2703: 2691: 2686: 2682: 2674: 2673: 2672: 2653: 2649: 2645: 2640: 2636: 2632: 2627: 2623: 2619: 2614: 2610: 2602: 2601: 2600: 2584: 2580: 2557: 2553: 2544: 2543:time-weighted 2534: 2525: 2516: 2505: 2504: 2501: 2497: 2496: 2495: 2485: 2465: 2445: 2444: 2440: 2439: 2438: 2435: 2431: 2424: 2420: 2416: 2415: 2414: 2408:= 1.25 % 2375: 2374: 2373: 2370: 2360: 2340: 2339: 2321: 2320: 2319: 2309: 2289: 2288: 2270: 2269: 2268: 2258: 2237: 2232: 2231: 2227: 2226: 2225: 2214: 2209: 2188: 2183: 2182: 2178: 2177: 2176: 2173: 2170: 2166: 2126: 2125: 2124: 2116: 2115: 2114: 2106: 2105: 2104: 2095: 2092: 2083: 2038: 2037: 2036: 2030: 2025: 2024: 2023: 2017: 2012: 2011: 2007: 2002: 2001: 2000: 1991: 1946: 1945: 1944: 1938: 1933: 1932: 1931: 1925: 1920: 1919: 1918: 1915: 1907: 1904: 1895: 1856: 1855: 1854: 1848: 1843: 1842: 1841: 1835: 1831: 1827: 1823: 1818: 1817: 1816: 1812: 1803: 1795: 1792: 1788: 1761: 1758: 1755: 1752: 1749: 1746: 1743: 1740: 1737: 1734: 1729: 1718: 1715: 1712: 1702: 1701: 1700: 1683: 1680: 1677: 1674: 1671: 1668: 1662: 1659: 1656: 1653: 1650: 1647: 1642: 1631: 1628: 1625: 1619: 1616: 1613: 1608: 1597: 1594: 1591: 1585: 1582: 1575: 1574: 1573: 1570: 1552: 1549: 1546: 1543: 1540: 1537: 1531: 1528: 1525: 1522: 1519: 1516: 1510: 1506: 1503: 1500: 1487: 1484: 1481: 1475: 1472: 1469: 1460: 1457: 1454: 1448: 1445: 1438: 1437: 1436: 1416: 1413: 1408: 1405: 1400: 1383: 1382: 1381: 1359: 1353: 1350: 1347: 1344: 1341: 1338: 1335: 1327: 1319: 1316: 1313: 1310: 1298: 1297: 1296: 1274: 1268: 1265: 1262: 1259: 1256: 1253: 1250: 1247: 1244: 1241: 1238: 1235: 1232: 1220: 1219: 1218: 1215: 1189: 1183: 1179: 1175: 1172: 1162: 1159: 1156: 1150: 1145: 1141: 1135: 1130: 1127: 1124: 1120: 1116: 1110: 1107: 1104: 1098: 1095: 1092: 1089: 1082: 1081: 1080: 1066: 1058: 1039: 1017: 1013: 1005: 1004: 1003: 985: 978: 977: 961: 954: 953: 937: 930: 929: 928: 910: 904: 898: 894: 890: 887: 881: 878: 875: 872: 868: 864: 859: 855: 849: 844: 841: 838: 834: 830: 824: 821: 818: 812: 809: 806: 803: 796: 795: 794: 780: 771: 768: 763: 761: 756: 752: 749: 745: 719: 715: 712: 707: 703: 699: 696: 690: 685: 681: 673: 672: 671: 650: 646: 623: 619: 611: 595: 588: 587: 586: 567: 561: 557: 553: 550: 544: 539: 535: 527: 526: 525: 509: 505: 482: 478: 455: 451: 425: 421: 398: 394: 373: 367: 363: 358: 353: 349: 343: 338: 335: 332: 328: 320: 319: 318: 298: 294: 288: 283: 280: 277: 273: 269: 266: 259: 258: 242: 235: 234: 218: 211: 210: 209: 185: 181: 177: 172: 168: 162: 157: 154: 151: 147: 143: 140: 128: 125: 122: 119: 116: 105: 70: 69: 68: 60: 58: 47: 38: 36: 30: 27: 23: 19: 6624: 6610: 6596: 6595:Carl Bacon. 6579: 6564: 6557: 6548: 6543: 6537: 6525:. Retrieved 6512: 6503: 6488: 6481: 6464: 6460: 6454: 6444: 6437: 3968:Visual Basic 3962: 3958: 3954: 3951: 3612: 3565: 3476: 3397: 3347: 3297: 3294: 3245:gain or loss 3231: 2993: 2990: 2860: 2840: 2831: 2827: 2819: 2816: 2803: 2796: 2793: 2790: 2786: 2782: 2778: 2774: 2756: 2670: 2540: 2531: 2522: 2513: 2493: 2452:gain or loss 2436: 2432: 2429: 2412: 2381:gain or loss 2371: 2368: 2317: 2266: 2222: 2174: 2171: 2167: 2163: 2132:gain or loss 2122: 2112: 2101: 2093: 2089: 2080: 2044:gain or loss 2034: 2021: 1997: 1988: 1952:gain or loss 1942: 1929: 1916: 1913: 1905: 1901: 1893: 1889:= 366 % 1862:gain or loss 1852: 1839: 1813: 1809: 1801: 1784: 1698: 1571: 1567: 1434: 1393:gain or loss 1379: 1294: 1229:gain or loss 1216: 1212: 1054: 1001: 926: 772: 764: 757: 753: 741: 668: 584: 442: 316: 207: 86:gain or loss 66: 53: 44: 31: 21: 17: 15: 6371:dStartValue 6353:dStartValue 6200:Application 5927:Application 5699:dStartValue 4913:Application 4877:Application 4448:Application 3948:Limitations 3840:start value 3835:start value 3625:Start value 3014:time weight 3006:start value 2487:= 40 % 2362:= 20 % 2311:= 80 % 2190:= 10,000 - 1828:= 0 + 8.1m 1798:Adjustments 443:The weight 6653:Investment 6642:Categories 6527:13 January 6429:References 5972:xlErrValue 5912:xlErrValue 4931:matchFlows 4895:matchFlows 4889:SumProduct 4841:matchFlows 4742:matchFlows 4496:matchFlows 4358:matchFlows 4082:matchFlows 2159:= 9 % 1979:= 1 % 6347:dEndValue 5711:dEndValue 5639:Exception 4937:georet_MD 4820:myReturns 3989:myReturns 3977:georet_MD 3928:% 3878:− 3831:− 3721:× 3709:× 3673:end value 3598:% 3589:% 3580:% 3550:% 3541:% 3535:× 3532:% 3509:% 3500:% 3494:× 3491:% 3461:% 3425:% 3383:% 3365:− 3333:% 3315:− 3280:% 3274:− 3262:− 3207:− 3174:− 3132:× 3119:− 3083:× 3077:× 3065:− 3056:− 3050:× 3018:× 3010:− 2929:− 2899:× 2887:× 2881:− 2875:× 2646:× 2620:× 2260:= $ 2,000 2216:= $ 8,000 2066:1,128,728 1884:22,131.15 1765:% 1747:− 1735:− 1722:% 1666:% 1660:× 1635:% 1620:× 1601:% 1586:× 1535:% 1529:× 1504:− 1491:% 1476:× 1464:% 1449:× 1420:% 1357:$ 1348:× 1328:× 1320:∑ 1272:$ 1263:− 1257:− 1245:− 1239:− 1176:− 1151:× 1121:∑ 1099:× 891:− 882:× 865:× 835:∑ 813:× 700:− 665:occurred. 554:− 359:× 329:∑ 274:∑ 178:× 148:∑ 126:− 120:− 6392:See also 6386:Function 5981:Function 5921:Function 5879:<> 5690:Function 5510:cashFlow 5480:cashFlow 5426:cashFlow 5390:cashFlow 5225:cashFlow 5066:cashFlow 5018:Function 4976:TotFlows 4955:cumFlows 4907:TotFlows 4784:cumFlows 4763:cumFlows 4721:cumFlows 4325:cumFlows 4238:TypeName 4148:TypeName 4127:TotFlows 4094:cumFlows 3974:Function 6550:period. 6377:TempSum 6359:SumCash 6311:iPeriod 6290:iPeriod 6281:TempSum 6275:TempSum 6224:TempSum 6194:SumCash 5954:iPeriod 5849:TempSum 5834:SumCash 5813:Integer 5777:Integer 5729:Integer 5723:iPeriod 5030:private 4985:AvFlows 4871:AvFlows 4631:FlowMap 4610:myDates 4586:FlowMap 4565:FlowMap 4517:FlowMap 4484:myDates 4466:FlowMap 4301:FlowMap 4271:FlowMap 4244:FlowMap 4232:StrComp 4211:myDates 4181:myDates 4154:myDates 4142:StrComp 4121:AvFlows 3995:FlowMap 3983:myDates 3681:outflow 2837:Example 2481:⁠ 2469:⁠ 2461:⁠ 2449:⁠ 2421:× 2406:⁠ 2394:⁠ 2390:⁠ 2378:⁠ 2356:⁠ 2344:⁠ 2336:⁠ 2324:⁠ 2305:⁠ 2293:⁠ 2285:⁠ 2273:⁠ 2253:⁠ 2241:⁠ 2204:⁠ 2192:⁠ 2157:⁠ 2145:⁠ 2141:⁠ 2129:⁠ 2086:Example 2069:⁠ 2057:⁠ 2053:⁠ 2041:⁠ 1977:⁠ 1965:⁠ 1961:⁠ 1949:⁠ 1887:⁠ 1875:⁠ 1871:⁠ 1859:⁠ 1824:× 1806:Example 1209:Example 609:period) 63:Formula 22:ex post 6631: 6617: 6603: 6572: 6496: 6338:MDIETZ 5960:MDIETZ 5900:MDIETZ 5855:Double 5840:Double 5795:Double 5762:Double 5717:Double 5705:Double 5693:MDIETZ 5687:Public 5666:return 5486:length 5435:double 5420:weight 5396:length 5345:double 5312:double 5303:weight 5231:length 5150:double 5141:weight 5138:double 5111:double 5063:double 5054:double 5045:double 5036:double 5033:static 4997:scaler 4901:Tflows 4535:Tflows 4391:Tflows 4295:UBound 4205:UBound 4133:Double 4103:Double 4088:Tflows 4001:scaler 2766:Issues 2500:weight 2423:return 2419:weight 2353:10,000 2302:10,000 2239:= 0 + 2154:10,000 2098:Answer 2060:-2,738 1994:Answer 1968:81,000 1878:81,000 1826:weight 1822:inflow 1324:weight 927:where 585:where 208:where 50:Origin 35:return 6523:. IPC 6521:(PDF) 6505:work. 6263:Count 6257:Cells 6251:rCash 6218:rCash 6167:Value 6143:rDays 6095:Value 6071:rCash 6038:Count 6032:Cells 6026:rDays 6017:ReDim 6005:Count 5999:Cells 5993:rCash 5984:ReDim 5966:CVErr 5945:rDays 5906:CVErr 5894:Count 5888:Cells 5882:rDays 5876:Count 5870:Cells 5864:rCash 5825:Range 5753:Range 5747:rDays 5741:Range 5735:rCash 5633:catch 5600:catch 5567:catch 5558:ttwcf 5414:ttwcf 5348:ttwcf 5336:numCD 5321:numCD 5270:throw 5177:throw 5165:<= 5162:numCD 5123:99999 5075:numCD 4460:Match 4388:ReDim 4355:ReDim 4322:ReDim 4283:Count 4193:Count 4046:' 4037:' 4028:' 4010:' 3712:12.50 3362:12.50 2878:12.50 2478:2,000 2403:8,000 2347:2,000 2296:8,000 6629:ISBN 6615:ISBN 6601:ISBN 6570:ISBN 6529:2015 6494:ISBN 6332:Next 6320:Cash 6296:Days 6191:Cell 6188:Next 6161:Cell 6146:Days 6137:Cell 6134:Each 6119:Cell 6116:Next 6089:Cell 6074:Cash 6065:Cell 6062:Each 6020:Days 5987:Cash 5978:Exit 5957:Then 5951:> 5918:Exit 5897:Then 5819:Cell 5804:Days 5786:Cash 5540:tncf 5504:tncf 5477:< 5438:tncf 5387:< 5327:numD 5258:< 5255:numD 5222:< 5084:numD 4865:Next 4760:Else 4718:Then 4679:Next 4661:Then 4490:True 4286:Else 4277:Rows 4262:Then 4196:Else 4187:Rows 4172:Then 4115:Long 4076:Long 3521:and 3437:and 2572:and 2519:Fees 1974:8.1m 1756:1.25 1744:2.25 1332:flow 1002:and 317:and 41:GIPS 16:The 6469:doi 6383:End 6287:((( 6233:For 6212:Sum 6131:For 6059:For 5939:Max 5846:Dim 5831:Dim 5816:Dim 5801:Dim 5783:Dim 5768:Dim 5660:(); 5627:(); 5594:(); 5552:bmv 5534:bmv 5528:emv 5459:int 5453:for 5369:int 5363:for 5273:new 5204:int 5198:for 5180:new 5147:new 5132:try 5081:int 5072:int 5057:bmv 5048:emv 5015:End 4925:Sum 4859:End 4688:For 4424:For 4313:End 4223:End 4118:Dim 4106:Dim 4091:(), 4085:(), 4079:Dim 4049:Dim 3898:000 3887:000 3875:450 3790:450 3760:200 3748:250 3638:000 3450:100 3414:100 3277:900 3258:450 3183:050 3171:000 3141:200 3116:000 3047:100 2974:450 2950:200 2938:000 2926:250 2884:100 2472:800 2397:100 2148:900 2113:so 2029:HKD 2016:HKD 2006:HKD 1937:HKD 1924:HKD 1847:HKD 1834:HKD 1830:HKD 1762:125 1684:300 1672:225 1663:150 1651:225 1583:100 1553:300 1541:225 1532:150 1520:225 1488:125 1461:125 1446:100 1417:120 1409:125 1406:150 1360:125 1345:0.5 1339:100 1275:150 1260:100 1254:300 57:IRR 6644:: 6578:. 6502:. 6465:23 6463:. 6329:)) 6305:)) 6245:To 6140:In 6068:In 5975:): 5924:If 5915:): 5861:If 5852:As 5837:As 5822:As 5810:As 5807:() 5792:As 5789:() 5774:As 5759:As 5750:As 5738:As 5726:As 5714:As 5702:As 5669:md 5561:); 5519:md 5507:+= 5495:++ 5417:+= 5405:++ 5297:); 5249:if 5240:++ 5192:); 5156:if 5114:md 5108:*/ 5003:np 4862:If 4835:)) 4706:If 4700:To 4664:np 4649:If 4646:)) 4601:)) 4481:), 4436:To 4412:To 4400:To 4379:To 4367:To 4346:To 4334:To 4316:If 4247:), 4229:If 4226:If 4157:), 4139:If 4130:As 4112:As 4109:np 4100:As 4097:() 4073:As 3925:45 3724:15 3718:80 3706:20 3595:45 3577:40 3538:20 3529:25 3506:40 3497:80 3488:50 3458:20 3447:20 3422:80 3411:80 3380:25 3372:10 3368:10 3330:50 3322:10 3318:10 3312:15 3265:50 3210:50 3086:15 3080:80 3072:40 3062:40 3053:10 2902:15 2896:80 2890:10 2872:20 2467:= 2447:= 2392:= 2342:= 2291:= 2143:= 2055:= 1963:= 1873:= 1719:50 1678:75 1657:50 1632:50 1617:50 1598:50 1547:75 1526:50 1473:50 1351:50 1266:50 59:. 6531:. 6475:. 6471:: 6380:) 6374:+ 6368:( 6365:/ 6362:) 6356:- 6350:- 6344:( 6341:= 6335:i 6326:i 6323:( 6317:* 6314:) 6308:/ 6302:i 6299:( 6293:- 6284:+ 6278:= 6272:) 6269:1 6266:- 6260:. 6254:. 6248:( 6242:0 6239:= 6236:i 6230:0 6227:= 6221:) 6215:( 6209:. 6203:. 6197:= 6185:1 6182:+ 6179:i 6176:= 6173:i 6170:: 6164:. 6158:= 6155:) 6152:i 6149:( 6128:0 6125:= 6122:i 6113:1 6110:+ 6107:i 6104:= 6101:i 6098:: 6092:. 6086:= 6083:) 6080:i 6077:( 6056:0 6053:= 6050:i 6047:) 6044:1 6041:- 6035:. 6029:. 6023:( 6014:) 6011:1 6008:- 6002:. 5996:. 5990:( 5969:( 5963:= 5948:) 5942:( 5936:. 5930:. 5909:( 5903:= 5891:. 5885:. 5873:. 5867:. 5843:: 5828:: 5798:: 5780:: 5771:i 5756:) 5744:, 5732:, 5720:, 5708:, 5696:( 5675:} 5672:; 5663:} 5654:. 5651:e 5648:{ 5645:) 5642:e 5636:( 5630:} 5621:. 5618:e 5615:{ 5612:) 5609:e 5603:( 5597:} 5588:. 5585:e 5582:{ 5579:) 5576:e 5570:( 5564:} 5555:+ 5549:( 5546:/ 5543:) 5537:- 5531:- 5525:( 5522:= 5516:} 5513:; 5501:{ 5498:) 5492:i 5489:; 5483:. 5474:i 5471:; 5468:0 5465:= 5462:i 5456:( 5447:; 5444:0 5441:= 5432:} 5429:; 5423:* 5411:{ 5408:) 5402:i 5399:; 5393:. 5384:i 5381:; 5378:0 5375:= 5372:i 5366:( 5357:; 5354:0 5351:= 5342:} 5339:; 5333:/ 5330:) 5324:- 5318:( 5315:) 5309:( 5306:= 5300:} 5294:i 5291:+ 5285:+ 5279:( 5267:{ 5264:) 5261:0 5252:( 5246:{ 5243:) 5237:i 5234:; 5228:. 5219:i 5216:; 5213:0 5210:= 5207:i 5201:( 5195:} 5186:( 5174:{ 5171:) 5168:0 5159:( 5153:; 5144:= 5135:{ 5126:; 5120:- 5117:= 5090:{ 5087:) 5078:, 5069:, 5060:, 5051:, 5042:( 5012:1 5009:- 5006:) 5000:/ 4994:( 4991:^ 4988:) 4982:/ 4979:) 4973:- 4970:) 4967:1 4964:, 4961:T 4958:( 4952:( 4949:+ 4946:1 4943:( 4940:= 4934:) 4928:( 4922:. 4916:. 4910:= 4904:) 4898:, 4892:( 4886:. 4880:. 4874:= 4868:i 4856:) 4853:1 4850:, 4847:i 4844:( 4838:+ 4832:1 4829:, 4826:i 4823:( 4817:+ 4814:1 4811:( 4808:* 4805:) 4802:1 4799:, 4796:1 4793:- 4790:i 4787:( 4781:= 4778:) 4775:1 4772:, 4769:i 4766:( 4757:) 4754:1 4751:, 4748:i 4745:( 4739:= 4736:) 4733:1 4730:, 4727:i 4724:( 4715:1 4712:= 4709:i 4703:T 4697:1 4694:= 4691:i 4682:i 4676:j 4673:- 4670:T 4667:= 4658:1 4655:= 4652:i 4643:1 4640:, 4637:1 4634:( 4628:- 4625:) 4622:1 4619:, 4616:T 4613:( 4607:( 4604:/ 4598:1 4595:, 4592:1 4589:( 4583:- 4580:) 4577:1 4574:, 4571:i 4568:( 4562:( 4559:- 4556:1 4553:= 4550:) 4547:1 4544:, 4541:j 4538:( 4532:) 4529:2 4526:, 4523:i 4520:( 4514:= 4511:) 4508:1 4505:, 4502:j 4499:( 4493:) 4487:, 4478:1 4475:, 4472:i 4469:( 4463:( 4457:. 4451:. 4445:= 4442:j 4439:N 4433:1 4430:= 4427:i 4418:) 4415:1 4409:1 4406:, 4403:T 4397:1 4394:( 4385:) 4382:1 4376:1 4373:, 4370:T 4364:1 4361:( 4352:) 4349:1 4343:1 4340:, 4337:T 4331:1 4328:( 4310:) 4307:1 4304:, 4298:( 4292:= 4289:N 4280:. 4274:. 4268:= 4265:N 4259:0 4256:= 4253:) 4241:( 4235:( 4220:) 4217:1 4214:, 4208:( 4202:= 4199:T 4190:. 4184:. 4178:= 4175:T 4169:0 4166:= 4163:) 4151:( 4145:( 4124:, 4070:N 4067:, 4064:T 4061:, 4058:j 4055:, 4052:i 4004:) 3998:, 3992:, 3986:, 3980:( 3922:= 3895:, 3892:1 3884:, 3881:1 3872:, 3869:1 3863:= 3820:= 3787:, 3784:1 3781:= 3757:, 3754:1 3751:+ 3745:= 3715:+ 3703:= 3677:+ 3669:= 3635:, 3632:1 3629:= 3592:= 3586:5 3583:+ 3547:5 3544:= 3503:= 3455:= 3419:= 3377:= 3327:= 3271:= 3253:= 3204:= 3180:, 3177:1 3168:, 3165:1 3162:= 3138:, 3135:1 3127:8 3124:7 3113:, 3110:1 3107:= 3068:5 3044:= 2971:= 2947:, 2944:1 2941:+ 2935:, 2932:1 2923:= 2893:+ 2806:i 2804:W 2799:i 2797:w 2732:2 2722:+ 2717:1 2704:i 2692:= 2687:i 2683:W 2654:2 2650:R 2641:2 2637:W 2633:+ 2628:1 2624:R 2615:1 2611:W 2585:2 2581:R 2558:1 2554:R 2475:/ 2455:/ 2400:/ 2384:/ 2350:/ 2330:/ 2299:/ 2279:/ 2250:4 2247:/ 2244:1 2201:4 2198:/ 2195:1 2151:/ 2135:/ 2063:/ 2047:/ 1971:/ 1955:/ 1881:/ 1865:/ 1759:= 1753:= 1750:1 1741:= 1738:1 1730:2 1726:) 1716:+ 1713:1 1710:( 1681:= 1675:+ 1669:= 1654:+ 1648:= 1643:1 1639:) 1629:+ 1626:1 1623:( 1614:+ 1609:2 1605:) 1595:+ 1592:1 1589:( 1550:= 1544:+ 1538:= 1523:+ 1517:= 1511:2 1507:1 1501:2 1495:) 1485:+ 1482:1 1479:( 1470:+ 1467:) 1458:+ 1455:1 1452:( 1414:= 1401:= 1364:, 1354:= 1342:+ 1336:= 1317:+ 1314:A 1311:= 1279:. 1269:= 1251:= 1248:F 1242:A 1236:B 1233:= 1190:T 1184:i 1180:t 1173:T 1167:) 1163:R 1160:+ 1157:1 1154:( 1146:i 1142:F 1136:n 1131:1 1128:= 1125:i 1117:+ 1114:) 1111:R 1108:+ 1105:1 1102:( 1096:A 1093:= 1090:B 1067:R 1040:i 1018:i 1014:t 986:T 962:B 938:A 911:) 905:T 899:i 895:t 888:T 879:R 876:+ 873:1 869:( 860:i 856:F 850:n 845:1 842:= 839:i 831:+ 828:) 825:R 822:+ 819:1 816:( 810:A 807:= 804:B 781:R 720:C 716:1 713:+ 708:i 704:D 697:C 691:= 686:i 682:W 651:i 647:F 624:i 620:D 596:C 568:C 562:i 558:D 551:C 545:= 540:i 536:W 510:i 506:W 483:i 479:F 456:i 452:W 426:i 422:W 399:i 395:F 374:= 368:i 364:F 354:i 350:W 344:n 339:1 336:= 333:i 299:i 295:F 289:n 284:1 281:= 278:i 270:= 267:F 243:B 219:A 186:i 182:F 173:i 169:W 163:n 158:1 155:= 152:i 144:+ 141:A 129:F 123:A 117:B 106:=

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