The Fourfold Pattern

The expected value of a gamble (and every investment decision we make) is the average of each potential outcome, weighted by its probability.  However, this concept does not correctly describe how most people think about the probabilities related to risky prospects.  Possibility and certainty exert a powerful influence when it comes to losses.

For instance, the move from a zero percent probability to a five percent probability illustrates the “possibility effect,” which causes highly unlikely outcomes to be weighted more heavily than they deserve.  This is precisely why people who buy lottery tickets are willing to throw away so much money for a very small chance to win.  Because of the possibility effect, we are naturally inclined to overweight small risks and are quite happy to overpay to eliminate them altogether.

Alternatively, the move from 95% to 100% certainty represents another qualitative change with a similarly large impact in terms of psychological value. In this case, less weight is given to near certain outcomes than their probability justifies.  In Thinking, Fast and Slow, Daniel Kahneman, refers to this as the “certainty effect.”  Simply put, the perceived difference between a 95% risk of disaster and a certain tragedy seems much greater than it is – an inkling of hope that everything may be fine is priceless.

The conclusion is simple: overweighting of small probabilities increases our attraction to both gambles and insurance policies.  Kahneman proposes, “People attach values to gains and losses rather than to wealth, and the decision weights that they assign to outcomes are different from probabilities.”  This heuristic is illustrated below. The top row in each cell shows a hypothetical prospect. The second describes the emotion evoked by each possibility.  The third indicates our typical behavior when offered the choice between a gamble and a sure thing.  Finally, the bottom row describes the predictable attitude of a defendant and a plaintiff as they discuss a settlement.

This fourfold pattern of preferences is considered one of the core achievements of prospect theory, and earned Kahneman the 2002 Nobel Memorial Prize in Economics for his work in the psychology of judgment and decision-making, behavioral economics and hedonic psychology.

  • In the top left cell, people are willing to accept less than the expected value of a gamble to lock in a sure thing.  We all know “something” is better than “nothing.”
  • The possibility effect in the bottom left cell explains why lotteries are popular.  Dangle a big enough Powerball number in front of people and ticket buyers will line up, almost indifferent to their odds of winning. A ticket comes with the right to dream.
  • The bottom right cell is where insurance is bought. People are willing to pay much more than expected value for an insurance policy, to eliminate anxiety and purchase peace of mind.
  • Many difficult situations develop in the top right cell, where people faced with bad options make reckless wagers.  Risk taking in this instance can turn a manageable failure into a complete disaster, simply because the thought of taking a large loss is too painful to make the rationale decision that it is time to move on.  Instead, this is where many companies in structurally challenging industries burn precious assets in wasted attempts to catch up.

Businesses that find themselves in the top right corner of this matrix are faced with difficult decisions. Shares of the Hewlett Packard have tumbled 29 percent this year and now trade at a forward price-to- earnings ratio of 4 down from 10 in 2009. Jim Chanos calls the company a value trap, explaining “Hewlett-Packard finds itself in that difficult position today, having to make pricey and risky acquisitions, just to stop itself from shrinking.”  HP and many of its peers, have their work cut out for it.  Investors better hope they understand the typical behavior of management when offered the choice between a gamble (overpaying for acquisitions) and a sure thing (returning capital to shareholders).

In Kahneman’s words:

When you take the long view of many similar decisions, you can see that paying a premium to avoid a small risk of a large loss is costly. A similar analysis applies to each of the cells of the fourfold pattern: systematic deviations from expected value are costly in the long run – and this rule applies to both risk aversion and risk seeing.  Consistent overweighting of improbable outcomes – a feature of intuitive decision making – eventually leads to inferior outcomes.

Next week, we’ll explore what prospect theory means for high quality stocks.