Maximizing the compounding rate of equity is only equivalent to minimizing the risk of ruin under the following two conditions:
(1) certain MATHturbational assumptions about the distributions of returns hold true, and
(2) “ruin” is defined strictly as losing 100% or more of the equity.
I haven’t done a proof since taking topology and real analysis in the mid-1990s, so I’ll let the intelligentsia debate the “assumptions” in (1), above.
It is good to note, however, that “ruin” is most definitely NOT strictly defined as losing 100% or more of equity. Yes, that would be ruinous, but that definition is only a subset of the events which make up the broader class of “ruin.”
For a retail trader, “ruin” means any drawdown large enough to stop them from trading or discourage them from continuing to trade a proven system. If they’re trading for a living, they may well hit a drawdown sufficient to make them either change their lifestyle, or go back to work for “the man.” That is truly an onerous amount of ruinage.
For a hedge fund manager, “ruin” could be any drawdown, volatility from month to month, or even insufficient returns over time, which is marked enough to encourage investors to seek redemption from the fund.
In real life, maximizing the compounding rate of equity often results in an INCREASED risk of ruin.





