Portfolio Statistics

Portfolio Return

This is a one year portfolio return.

where:

E[R] = Portfolio Return
w_i = weight of asset i
E[R_i] = Forcast Return of asset i
n = number of assets

Portfolio Risk

This is the one year standard deviation of the portfolio.

where:

Portfolio Risk
w_i = weight of asset i
w_j = weight of asset j
correlation of asset i with asset j
standard deviation of asset i
standard deviation of asset j
n = number of assets

R-Squared

The R-Squared is the correlation squared of the benchmark to a weighted portfolio return series. Correlation Squared is the classical statistical method for measuring how closely related the variances of two series are. R-Squared is calculated using the common date range of the benchmark and the weighted portfolio return series.

where:

R-Squared
covariance of weighted portfolio return series and benchmark
standard deviation of weighted portfolio return series
standard deviation of benchmark

Residual

Residual is the volatility of weighted portfolio return series that is not explained by the variation in the return series of the benchmark.

R-Squared + Residual = 100%

 

Tracking Error

Tracking Error (also known as 'active risk') is the annualized standard deviation of excess return to the benchmark. Like R-Squared, Tracking Error is calculated using the common date range of the benchmark and the weighted portfolio return series.

where:

Tracking Error
std = standard deviation
arithmetic return of weighted portfolio return series at time t
arithmetic return of benchmark at time t
N = periods per year

Turnover

Turnover shows the total one-way turnover to move from the current portfolio to the efficient portfolio. That is, the proportion of the current portfolio that must be sold.