Per a previous question on this topic -- markets generally fall fast and rise slowly: what options strategies or other strategies can one use to take advantage of this common occurrence?
To avoid confusion, this only applies to most equity/index option. In a return distribution, there's a measurement called skewness which measures the asymmetry of upside and downside. Let's define that as 30d Put Premium/ 30d Call Premium. It's already priced in because most of the time, skew > 1.
However, if you trade commodities or companies that might get bought, you'll often see skew < 1. You'd expect skew < 1 for a commodity because it's the safe heaven when the market tanks. For companies that might get bought (especially for a big premium), people are willing to pay for calls in case of a big upside gap move.
Typically mega cap companies have larger skew than a mid/small cap because it probably won't get taken out, doesn't have much upside because it's so established and so people are paying for the puts to protect against a black swam event like the BP spill.
So you can't really "take advantage" of that statement given there's implied skew already. It comes down to what you think about skew versus implied skew.
After all, realized skew is generally lower than implied skew so you'd expect to make money by shorting skew. However, in crisis times like 2008 and now, you need a lot of capital to stay short skew.
Nassim Taleb has a strategy that he described in Active Trader magazine (partial interview here. As I recall, he would buy deep out-of-the-money puts, anticipating the faster fall.
He is called the actions of some traders, to sell deep OTM puts, to be "picking up pennies in front of steam rollers." In this case (buying those puts), he is the steam roller.
Of course, he is losing money every day due to time decay, so this strategy is for those with a long-term view.