Money-Weighted Rate of Return (MWRR) is calculated as the sum of the daily returns of each asset, weighted by its proportion within the portfolio, relative to the total portfolio value at that time.
Mathematically, the MWRR is given by:
\( \displaystyle
\text{MWRR} = \sum_{t=1}^{T} \sum_{i=1}^{N} w_{i,t} \times r_{i,t}
\)
where:
- \( w_{i,t} = \) weight of asset \( i \) in the portfolio at day \( t \), calculated as the value of asset \( i \) divided by the total portfolio value at day \( t \)
- \( r_{i,t} = \) return of asset \( i \) on day \( t \)
- \( N = \) total number of assets in the portfolio
- \( T = \) total number of days (or periods) considered
This weighted sum reflects the contribution of each asset’s daily return according to its portfolio weight, providing an accurate measure of portfolio performance over time.