The Probabilistic Sharpe Ratio

Difficulty

Asked at D.E. Shaw, Two Sigma

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xxxxxxxxx xxxx_xxxxxx(xx_xxx, xx_xxxx, x, xxxx, xxxx), xxxxx xxxxxxx xxx xxxxxxxxxxxxx xxxxxx xxxxx: xxx xxxxxxxxxxx xxxx xxx xxxx xxxxxx xxxxx xxxxxxx x xxxxxxxxx, xxxxx xxx xxxxxx xxx xxxxx xx xxx xxxxx xxxxxx. x xxxxxx xxxxx xxxxxxxx xxxx x xxxxxx xxxxxx xx xx xxxxxxxx xxxx xxxxx xxxx, xxx xxx xxxxx xxxx xxxxx xxxx xxxxxxx xxx xxxxxx xxx xxx-xxxxxx. xx_xxx: xxx xxxxxxxx xxx-xxxxxx xxxxxx xxxxx. xx_xxxx: xxx xxxxxxxxx xx xxxx. x: xxx xxxxxx xx xxxxxx xxxxxxxxxxxx (( xxx x )). xxxx: xxx xxxxxxxx xx xxx xxxxxxx. xxxx: xxx xxxxxxxx xx xxx xxxxxxx (xxxxxx xxxxxxx xxxx xxxx = x). xxxxxxx xxx xxxxxxxx xxxxx xx xxx xxxxxx xxxxxxxxx (xxxxxxx): [ xxxxx_{xxxxxxx{xx}} = xxxx{xxxx{x - xxxxx_x,xxxxxxx{xx} xxxx{xxxxx_x - x}{x},xxxxxxx{xx}^x}{x - x}} ] xxx xxxxxx [ xxx = xxx!xxxx(xxxx{xxxxxxx{xx} - xx^*}{xxxxx_{xxxxxxx{xx}}}xxxxx) ] xxxxxxx xx x xxxxxxxx. xx xxxxx: xxxxx xxx xxxxxxxx xxxxxx xxx xxxx xxxx.xxx, xxxxx ( xxx(x) = xxxxx{x}{x}xxxx(x + xxxxxxxxxxxx{xxx}(x/xxxx{x})xxxxx) ). xxxxxxxx xxxx_xxxxxx(x.x, x.x, xxx, x.x, x.x) # x.xxx xxxx_xxxxxx(x.xx, x.xx, xxx, -x.x, x.x) # x.x x xxxx xx xxxxx xxxx xx x xxxxx xxxxxx xx x.x xx xx% xxxxxx xx xxxx xxxx xxxxx xxxxxx xxxxxxx. x xxxxxxxxx xxxxx xx xxx xxxxxxxx xxxxx xx x xxxx xxxx xx xxxxxxxxxxxx, xxxxxxxx xxx xxxxx xxxxxxxxxx xx.

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Language: Python 3.12prob_sharpe

import math


def prob_sharpe(sr_hat: float, sr_star: float, T: int, skew: float, kurt: float) -> float:
    """..."""
    # ...
    pass

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