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R=EMV+1BMV+1+CF-1*100
R1=5%=10501000+0-1*100
R2=4.3%=12001050+100-1*100
To calculate the 1 month return, you link the sub-period returns, shown below:
R=1+R1*1+R2-1*100
9.56%=1+.05*1+.043-1*100
Where:
R is return
EMV is ending market value
BMV is beginning market value
I is income
CF is cash flow
A "True" Time Weighted Return requires re-valuing the portfolio each time a net contribution occurs. If the portfolio does not include the cash position, then every buy and sell decision creates a cash flow in the portfolio. Thus, the portfolio has to be re-valued every time a transaction takes place.
Many firms estimate True Time Weighted Returns by compounding monthly sub-period Money Weighted Returns, where the sub-period returns are generated by Modified Dietz or Internal Rate of Return calculations. When estimating Time Weighted Returns using this method, intra-period cash flows into and out of a portfolio can distort the sub-period returns.
Daily valuations and single-period return calculations are solutions to this problem. However, many firms do not have daily valuations available for all types of entities. Another way to address this problem is to create a special valuation when there are large external cash flows. In Eagle Performance, this is called Significant Cash Flow Processing (SCF). See "Chapter 4: Processing Significant Cash Flows (SCF)" for details.
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The Money Weighted Return reconciles the beginning value and cash contributions with the ending value of the fund. It is an average return of all dollars invested in the portfolio for the period. This type of return calculates the actual return earned on a portfolio, including the impact of the timing of external contributions and withdrawals. The Money Weighted Return is not a good proxy if there are large cash flows or the market is volatile during the measurement period.
Money Weighted Returns are frequently used in place of, or as an approximation of Time Weighted Returns when portfolio valuations are not available at each cash flow date. GIPS recommends a valuation when there is a cash flow greater than 10% of the portfolio beginning value. One way of interpreting the Money Weighted Return is to define it as a rate of return that can be multiplied by the beginning value, plus each cash flow, to give the ending market value.
To calculate returns over longer periods, Eagle Performance links the holding period returns the same way two sub-period returns are linked to calculate a Time Weighted Return. If the sub-period returns are Money Weighted Returns, they can be compounded to approximate a long term, Time Weighted Return.
For investment performance, the Money Weighted Return is often used as an approximation of the Time Weighted Return. A common method for calculating an approximate Money Weighted Return is the Modified Dietz.
The Modified Dietz method overcomes the need to know the valuation of the portfolio on the date of each cash flow by assuming a constant rate of return during the period. Each cash flow is weighted by the amount of time it is held in the portfolio. The Modified Dietz method assumes that net contributions are invested at the end of the respective day they occur.