The point of a tail hedge is not expected value but shape. It converts an unbounded portfolio loss into a bounded one, and does so exactly when correlations go to one and diversification stops working. Most of the time it is a steady cost.
Two things decide whether the programme works. Budget: an annual spend measured in tenths of a percent, not percent. And monetisation: an unsold hedge that spikes and decays back is a hedge that paid nothing, so the rules for taking profit matter more than the strike selection.
Example: a portfolio benchmarked to a broad index buys 10% out-of-the-money one-year puts, rolling quarterly, for around 1% a year. In four quiet years it costs 4%. In a 35% drawdown the puts return several multiples of that — but only if they are sold near the low rather than held to expiry.
Related: protective-put, vega-convexity, long-volatility-trade, skew-index