criteria. Firstly, we use the mean return of the strategy in excess of the mean return of the buy-and-hold (BH) strategy
Secondly, we use the Sharpe ratio of the strategy in excess of the Sharpe ratio of the buy-and-hold strategy in which case
where
rf is the mean risk-free interest rate and
s.
e.(.) is the standard error of the corresponding return series. The Sharpe ratio measures the excess return of a strategy over the risk-free interest rate per unit of risk, as measured by the standard deviation, of the strategy. The higher the Sharpe ratio, the better the reward attained per unit of risk taken.
The null hypothesis can be evaluated by applying the stationary bootstrap algorithm of Politis and Romano (1994). This algorithm resamples blocks with varying length from the original data series, where the block length follows the geometric distribution4, to form a bootstrapped data series. The purpose of the stationary bootstrap is to capture and preserve any dependence in the original data series in the bootstrapped data series. The stationary bootstrap algorithm is used to generate B bootstrapped data series. Applying strategy k to the bootstrapped data series yields B bootstrapped values of fk, denoted as fk,b*, where b indexes the bth bootstrapped sample. Finally the RC p-value is determined by comparing the test statistic
to the quantiles of
In formula this is
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