# Performance Calculations

Two main approaches are typically used for presenting performance over time for a portfolio of fund holdings - Time-Weighted Return (TWR) and Money-Weighted Return (MWR).

### Time-Weighted Return (TWR)

Performance of the investments themselves, independent of the timing/size of client deposits and withdrawals (matches how fund factsheets report).

**How it's computed (conceptually):**

1. Split the timeline at every external cash flow.
2. Compute a sub-period return for each flow-free segment.
3. Chain (geometrically multiply) the sub-period returns.


**Sub-period i:**

```
rᵢ = (UBᵢ − CFᵢ) / IBᵢ − 1
```

**Chain across n sub-periods:**

```
TWR = ∏(1 + rᵢ) − 1
for i = 1 to n
```

**Pros/Cons & usage:**

- ✅ Neutralizes client cash flows → fair view of manager/strategy skill.
- ✅ Standard for public performance comparisons.
- ⚠️ Not the investor's personal experience if they time cash flows poorly/well.


### Money-Weighted Return (MWR)

The investor's actual, cash-flow-timing-aware return on capital. Formally the internal rate of return (IRR) of all dated cash flows:

```
Σ CFₜ / (1 + r)^(t/T) = 0
```

- `CFₜ` are dated cash flows (deposits positive, withdrawals negative; final value treated as an outflow).
- `T` normalizes time units (e.g., days per year).


**Practical approximation — Modified Dietz:**

```
r_MD = (EV − BV − Σ CFₖ) / (BV + Σ wₖ × CFₖ)
```

- `BV` = beginning value, `EV` = ending value
- `CFₖ` = each external cash flow during the period
- `wₖ` = time weight for each flow (fraction of the period remaining after the flow)


**Pros/Cons & usage:**

- ✅ Reflects the client's real, dollar-weighted outcome.
- ✅ Useful for personal statements, planning, and advisor reviews.
- ⚠️ Not ideal for comparing manager skill (timing dominates).
- ⚠️ IRR can be non-unique or fail with certain cash-flow patterns; Modified Dietz is a robust proxy.


### In the Fondo context

- **Displayed portfolio performance (%) — TWR:** We present time-weighted return, consistent with fund factsheets and isolated from external cash flows.
- **Client-specific performance — MWR/IRR is not supported.** For questions like *"How did my money grow given when I invested?"* you'd use a **money-weighted** method rather than TWR.


**Note:** Beyond deposits and withdrawals, other events (e.g., **corporate actions, distributions, and fees**) can affect performance and must be taken into account to ensure adequate TWR calculations.