20. Relative and Absolute Returns

Relative Returns

Relative return is a fund’s return minus its benchmark’s return.
For an actively managed fund, this is called the active return.
For a passively managed fund, this is the tracking error.

Tracking Error

Tracking Error measures how the returns of a portfolio differ from the returns of its benchmark. To operationalize the definition of tracking error, we first take the portfolio’s daily returns minus the benchmark’s daily returns. This daily difference is referred to as the excess return and also the active return. Next, we take the sample standard deviation of the active return. Finally, we annualize the daily sample standard deviation by multiplying by the square root of 252, since there are 252 trading days in a year.

The formula is:
ExcessReturn_{portfolio} = return_{portfolio} - return_{benchmark}
DailyTrackingError = SampleStandardDeviation(ExcessReturn_{portfolio})
AnnualizedTrackingError = \sqrt[2]{252} * DailyTrackingError

In Summary:
TE = \sqrt[2]{252} * SampleStdev(return_{portfolio }- return_{benchmark})

Absolute Returns

Absolute returns refer to a fund’s goal to target a certain return regardless of how the market performs. Hedge funds are usually evaluated by absolute returns.
Note that LIBOR stands for London Interbank Offer Rate, and is the rate that banks charge to lend to other banks.