Kind of. Most simple models for continuous payoffs will assign a nonzero probability to losing all your wealth or your wealth going negative. The Kelly bet size for any thing with a nonzero chance of "ruin" is zero.
Sharpe is typically calculated on log returns. Price going to zero would weigh as negative infinity in log return space. Therefore Sharpe would also prescribe zero bet on finite chance of ruin.
Kind of. Most simple models for continuous payoffs will assign a nonzero probability to losing all your wealth or your wealth going negative. The Kelly bet size for any thing with a nonzero chance of "ruin" is zero.
Sharpe is typically calculated on log returns. Price going to zero would weigh as negative infinity in log return space. Therefore Sharpe would also prescribe zero bet on finite chance of ruin.
A proper Sharpe ratio is calculated with arithmetic returns.
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