Composite Time-Weighted Return Calculations

Composites are collections of different portfolios grouped together for tracking and measurement purposes. When dealing with composites, it’s essential to follow GIPS^® standards diligently because they can potentially distort clients’ perceptions of performance and returns.

According to the GIPS standards, all fee-paying, discretionary segregated accounts must be part of at least one composite. Additionally, fee-paying, discretionary pooled funds meeting composite criteria must also be included. This rule ensures that firms cannot showcase only their best-performing portfolios to potential clients.

Three Compliant Time-weighted Return Calculation Methods

Here are three compliant methods for calculating time-weighted returns within a composite, even when external cash flows are involved. We have data representing a composite comprised of four portfolios. In column one, you’ll see the relative weight of each portfolio. Column two takes this a step further by incorporating not only the relative weight of each portfolio within the composite but also the impact of additional cash flows. These cash flows can be either positive or negative and can influence the portfolio’s overall weighting.

$$ \begin{array}{c|c|c|c}
\textbf{Portfolio} & \textbf{Beginning} & \textbf{Beginning} & \textbf{Return for} \\
& \bf{\text{Assets }(\%)} & \bf{ \text{Assets} + \text{Weighted CF’s } (\%)} & \textbf{Month of} \\
& & & \textbf{Nov.} \\ \hline
\bf A & 50.00\% & 51.36\% & 0.41\% \\ \hline
\bf B & 25.00\% & 25.41\% & 0.23\% \\ \hline
\bf C & 12.5\% & 15.61\% & 0.45\% \\ \hline
\bf D & \underline{12.5\%} & \underline{10.42\%} & 1.78\% \\ \hline
& \bf{100.00\%} & \bf{100.00\%} &
\end{array} $$

$$ \begin{array}{lr}
\text{Composite Return:} & {} \\
{\#1. \text{ Based on beginning assets} } & 0.541\% \\
{\#2. \text{ Based on beginning assets and weighted cash flows}} & 0.525\% \\
\end{array} $$

1. “Beginning assets” weighting method:

   $$ \begin{align*}
   \textit{Composite return} & = (0.0041 \times 0.5) + (0.0023 \times 0.25) \\ & + (0.0045 \times 0.125) + (0.0178 \times 0.125) \\ & = 0.00541 = 0.541\% \end{align*} $$

   This method takes the monthly return for each portfolio, and multiplies that value by the beginning portfolio weight in the composite for that period. This is repeated and the sum of all weighted returns gives composite return #1.

2. “Beginning assets plus weighted cash flows” method:

   $$ \begin{align*}
   \textit{Composite return} & = (0.0041 \times 0.5136) + (0.0023 \times 0.2541) \\ & + (0.0045 \times 0.1561) + (0.0178 \times 0.1042) \\ & = 0.00525 = 0.525\%
   \end{align*} $$

   This method takes the monthly return for each portfolio, and multiplies that value by the beginning portfolio weight in the composite with the addition of the cash flows into or out of that portfolio for the period. This is repeated and the sum of all weighted returns gives composite return #2.

3. Aggregate return method:

   Now, let’s look at the Aggregate Return Method, which employs the Modified Dietz Approach. This method comes into play when the portfolio encounters cash flows that aren’t considered large. If the firm doesn’t calculate daily performance, returns for the portfolio should be determined using a method that accounts for daily weighted cash flows. There are two acceptable approaches for this: the Modified Dietz method and the Modified Internal Rate of Return (Modified IRR) method. Both methods assign weight to each cash flow based on the portion of the measurement period it occupies within the portfolio.

   $$ r_\text{ModDietz} = \frac {V_1 – V_o – CF}{V_o + \sum_{i=1}^{n}(CF_i \times w_i)} $$

   Where:

   \(V_o + \sum_{i=1}^{n}(Cf_i \times w_i)\) = sum of each cash flow multiplied by its weight, and weight \((w_i)\) is simply the proportion of the measurement period, in days, that each cash flow has been in the portfolio.

   $$ w_i = \frac {CD – D_i}{CD} $$

   Where:

   \(CD\) = Calendar days in the measurement period

   \(D_i\) = the number of calendar days from the beginning of the period to the time the cash flow \(Cf_i\) occurs.

Question

The Modified Dietz Approach considers which of the following:

1. All portfolio cash flows.
2. No portfolio cash flows.
3. Only cash flows deemed “large” by the firm.

Solution:

The correct answer is A.

The formula for this approach shows that each cash flow is considered using this method.

$$ r_\text{ModDietz} = \frac {V_1 – V_o – CF}{V_o + \sum_{i=1}^{n}(CF_i \times w_i)} $$

Where:

\({V_o + \sum_{i=1}^{n}(CF_i \times w_i)}\) = sum of each cash flow multiplied by its weight, and weight \((w_i)\) is simply the proportion of the measurement period, in days, that each cash flow has been in the portfolio.

B is incorrect. The Modified Dietz Approach does take portfolio cash flows into account. Ignoring cash flows would not provide an accurate representation of the investment’s return.

C is incorrect. The Modified Dietz Approach does not discriminate between “large” or “small” cash flows. It considers all cash flows, regardless of their size, during the measurement period to calculate the rate of return accurately.

Performance Measurement: Learning Module 3: Overview of Global Investment Performance Standards; Los 3(d) Explain requirements of the GIPS standards with respect to composite return calculations, including methods for asset-weighting portfolio returns