Time Weighted Return

Time weighted return (“TWR”) is a method of calculating portfolio returns via linking sub-period returns and adjusting for the effect of large external cash flows.

• Portfolios using TWR must be valued monthly.
• Portfolios must also be valued at the time of large external cash flows (large is defined by the firm ahead of time).

No External Cash Flows

In the simplest case, when no external cash flows (i.e., client-initiated additions to or withdrawals from invested assets) occur during the period, calculating the TWR is straightforward:

$$ R_t = \frac {(V_1 – V_0)}{V_0} $$

Where:

\(r_t\) = the TWR for period t.

\(V_1\) = the ending value of the portfolio, including cash and accrued income, at the end of the period.

\(V_0\) = the portfolio’s beginning value, including cash and accrued income, at the beginning of the specified period.

Minimal Cash Flows

When there are minimal cash flows in a portfolio (not large), the GIPS Standards for Firms don’t mandate valuing the portfolio on the cash flow date. Instead, firms can use a method that adjusts for daily weighted cash flows, approximating a true Time Weighted Return (TWR).

The most accurate way to calculate total return while eliminating the impact of external cash flows is to value the portfolio whenever such cash flows happen, compute a sub-period return, and geometrically link these sub-period returns expressed in relative form using a specific equation.

$$ r_{twr} = (1 + r_{t,1}) \times (1 + r_{t,2}) \times \cdots \times (1 + r_{t,n}) − 1 $$

where:

\(r_{twr}\) = The time-weighted total return for the entire period.

\(r_{t,1}\) through \(r_{t,n}\) = The subperiod returns.

The GIPS standards require that the periodic returns be geometrically linked.

Modified Dietz Approach

When a portfolio encounters cash flows that aren’t considered large, and the firm doesn’t compute daily performance, it should calculate portfolio returns using a method that adjusts for daily weighted cash flows. Acceptable approaches for this calculation include the Modified Dietz method and the Modified Internal Rate of Return (Modified IRR) method. Both of these methods assign weight to each cash flow based on the proportion of the measurement period it remains in 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.

$$ w_i = \frac{CD – Di}{CD} $$

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.

Modified Internal Rate of Return

Another acceptable approach for calculating portfolio returns when there are non-large cash flows, and daily performance isn’t computed is the Modified Internal Rate of Return (MIRR). While the computational details of MIRR can be complex, candidates can use computer programs or approved exam business calculators to perform the calculation if necessary. This topic is introduced in Level 1, and candidates are encouraged to review it for better understanding.

Reading 33: Global Investment Performance Standards

Los 33 b: Discuss requirements of the GIPS standards with respect to return calculation methodologies, including the treatment of external cash flows, cash and cash equivalents, and expenses and fees