In trading jargon, certain situations are "mean-mode". Translated, if returns are mapped versus trades, the mode and mean are on opposite sides of zero. Where the average or mean return is positive, the largest cluster of returns (the mode) is negative. And vice-versa, when the mean return is negative, the mode is positive.
This occurs less often than situations where mean and mode are on the same side of zero, either positive or negative. But consider option-writers who usually garner premium income and make occasional massive losses. Or, to take another example, an insurance company may get wiped out by one disaster per decade. Both are positive mode and potentially negative mean.
Then, we find venture capitalists (VC), oil prospectors and single mothers writing fantasies about boy-wizards. One VC business in eight or nine will come through, one well in 10 or 12 will strike oil and maybe, one in a million manuscripts will be another Harry Potter. The positive returns are rare but they are very big.
These are long-tailed distributions where the extreme values are important. The conservative value investor will try to pick only positive mean- positive mode trades such as undervalued stocks, which appear to have only an upside.
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But there is nothing illogical about looking at mean-modes. The risk: reward equation may be a great deal better for mean-modes than for "double positives". There must be a balancing off of several factors. Actuaries are well-paid and deserve to be because they assess these situations and value them.
A single massive return (positive or negative) may never be replicated. But a steady income stream can accrue or there may be sporadic large payoffs interspersed by many small losses. Nassim Nicholas Taleb for example, has always sought positive mean, negative mode situations where one killing compensates amply for years of losses.
His big payoff was in the October 2007 bear market where he held cheap long puts. Taleb claims to have made over 90 per cent of his fortune on one crazy day when the Dow dropped 17 per cent.
Most traders prefer to stick with trades that have positive mode and hope that they will be able to duck and run for cover in the big loss situations. If you know what you're doing, you can cut losses most of the time.
But Warren Buffett is the world's biggest insurer and that essentially means he's selling very long-term options. And once in a while, even Warren Buffett gets caught by something like Hurricane Katrina. Of course, the insurer has some cushion of safety because the actuary sets the premium.
In practice, there is evidence to suggest that positive mode, negative mean situations are very rare. Options writers do stay in business