Total, Factor, and Alpha Returns
The portfolio's daily return is taken from the weighted returns of each security in the portfolio. The weight of each security is the dollar position size divided by the equity, and is also displayed as “% Equity” in the application. The daily security returns are taken directly from the risk model and include split and/or dividend adjustments.
The daily portfolio return can be decomposed into a daily portfolio factor return and a daily portfolio alpha return:
- The daily portfolio factor return is calculated from the dot product of portfolio factor exposures and daily factor returns.
- The daily portfolio alpha return (or idiosyncratic return) is taken as the difference between the daily total portfolio return and the daily portfolio factor return.
The portfolio factor exposures are calculated from the weighted factor exposures for each security in the portfolio. The factor exposures for each security are taken directly from the model and are displayed under Analyze/Exposure in the application.
The daily factor returns are taken directly from the risk model.
Portfolio position sizes on a particular date refer to the end of day position sizes. The return calculation assumes that the closing portfolio positions are held until the end of the next day. To calculate the return on the next date, the position weights and security factor exposures are taken from the same date as the holdings date when calculating the portfolio factor exposures. The daily factor returns are taken from the next day.
The cumulative percent return over a period is the compound sum of the daily portfolio returns.
For daily portfolio returns of r1, r2, ... rT,
the compound sum over T days is (1+r1)*(1+r2)*...*(1+rT) - 1
The cumulative dollar return over a period is the algebraic sum over the dollar portfolio returns. The dollar portfolio return is calculated by taking the dollar position size as the weight without dividing by equity.