How do investors prefer to save for their pensions: the 1/N heuristic.

How do investors prefer to save for their pensions: the 1/N heuristic.

Mark and Harvey were sat having coffee in their regular café that they visited every Thursday for breakfast before work. They discussed the latest football results and eventually ended up on the subjects of retirement. Harvey had never got around to starting an investment for his retirement so wanted to ask Mark for advice. Mark simply suggested that Harvey allocate his retirement investments equally across several funds, explaining that this reduce risk.

Saving or investing for retirement is one of the most important decisions that a person can make in their lifetime. Picking the right pension plan and / or allocating resources to the right fund(s) is crucial for enjoying their retirement years. Pension plans and retirement schemes differ from country-to-country. In some pension schemes investors have the choice of how to allocate their funds. When planning for their retirement individuals with a pension plan that allows them to allocate resources to different funds must choose how to invest their money. One popular strategy for making decisions about how to allocated resources is to use the 1/N heuristic (Benartzi & Thaler, 2001). The 1/N heuristic removes the confusion and stress of weighing up the pros and cons of how to invest resources and simply states that a given amount of resources should be divided equally between ‘x’ funds, for example, when a sum of £100,000 is to be invested this would be distributed into £20,000 into 5 different funds.

Image 1.png

In the Swedish pension system investors have the option of deciding how to invest 2.5% of their income. They can allocate 2.5% of their income to either a stock or interest fund (Hedesstrom et al., 2007). Once an individual makes the decision to invest part of their income they receive a brochure with 655 potential funds, they are then required to decide which of the funds they’d like to invest in. In 2004 researchers at Goteborg University analysed 392 investment decisions. The researchers found that investors used at least 5 different heuristics and biases to make their decisions. Investors had a tendency to avoid funds with extreme high and low risks (extremeness aversion – Simonson & Tversky, 1992), a tendency to select the default option (default bias – Johnson et al., 1992), to choose many funds in an attempt to seek maximal variety (diversification heuristic – Read & Loewenstein, 1995), to select domestic funds (home bias – Kilka & Weber, 2000), and to use the 1/N heuristic (Benartzi & Thaler, 2001).

A larger study of more than half a million pension plan participants in Defined Contribution pension plans from the records of the Vanguard Group investigated the use of the 1/N heuristic (Huberman & Jiang, 2004). They found that when deciding how to allocate pension funds participants tended to use the 1/N to divide their funds over 3 or 4 funds.

Image 3.png

A third study of 1000 people examined how Dutch citizens planned for their retirement (Van Rooij et al., 2007). After analysing retirement decisions the results of this study revealed that Dutch citizens are risk-averse and considered themselves to be financially unsophisticated. When given the option these investors used one three strategies (i) the default bias, (ii) the 1/N heuristic, or were susceptible to (iii) framing.

So, depending on what country you work in and decide to retire to there are many different ways to prepare for your retirement. Since most of us, like Harvey, are not financial experts when given complex important decisions to make for our retirement we choose to avoid risk by allocating our money equally across several funds by using the 1/N strategy. When planning for retirement the 1/N heuristic can be an effective and useful way to decrease risk and ensure a substantial retirement fund.

So, depending on what country you work in and decide to retire to there are many different ways to prepare for your retirement. Since most of us, like Harvey, are not financial experts when given complex important decisions to make for our retirement we choose to avoid risk by allocating our money equally across several funds by using the 1/N strategy. When planning for retirement the 1/N heuristic can be an effective and useful way to decrease risk and ensure a substantial retirement fund.

Advertisements

How do we make decisions quickly when placing bets in a casino?

How do we make decisions quickly when placing bets in a casino?

Like many tourists, Rebecca and Catherine always wanted to visit Las Vegas. They took in the dazzling sights of the bright lights, enjoyed the stage magic and drifted into one of large casinos. When they walked into the casino they were amazed by the sounds and lights. Catherine had always enjoyed the game of roulette so headed straight to the roulette table. Catherine placed three consecutive bets, losing all three. Watching this Rebecca quietly said to Catherine “Maybe you should try another game, the odds are against you winning.” To this Catherine replied “No, I have lost three times I am overdue a win, I will win soon.”

When we make decisions, we like to think that we make all of our decisions rationally. Casino environments are designed to be one of the most complex environments that we ever encounter, there are colourful, flashing lights, loud machines playing music and people cheering. It is hard to deal with the environment, tune-out and make clear decisions. To deal with complex environments the brain has developed a number of judgement heuristics. Judgement heuristics are mental short cuts that enable us to make quick decisions whilst ignoring part of the decision-making environment. One classic example of a judgement heuristic was given by Catherine above when speaking to Rebecca at the roulette table. The aptly named gambler’s fallacy, as demonstrated above can also be seen in the following classic scenario. Imagine that someone is flipping a coin multiple times, the coin lands head side up three times in a row. Someone watching the coin flipping is asked to guess whether the next coin will land head side up or tail side up. If the person guesses tail side up they are using the gambler’s fallacy, a belief that randomness follows a pattern. Many people believe that for the coin flipping to be truly random the outcome of a sequence of five coin flips must be something like HEADS-TAILS-HEADS-TAILS-HEADS. If an outcome of five flips is HEADS-HEADS-HEADS-HEADS-HEADS then the coin is overdue to land with the tail side up otherwise this is not random. The belief in a pattern of randomness persists in most areas of life.

post 5 image 1.png

In a field study by researchers at the University of Navada 18 hours worth of overhead security camera footage of a roulette table was obtained from a large Reno casino, consisting for 904 bets (Sundali & Croson, 2006). The researchers watched all of the bets and coded the patterns of betting for every gambler that sat down at the table. On an American-style roulette table there are 36 different sections of the roulette wheel, coloured as red or black (European-style roulette has 37 sections). Players can bet on more than one number and colour by placing their chips on the corners or side of each of the numbered squares. If a gambler bets randomly then after the researchers coded each bet there should be a 2.6% chance that a bet would fall on each number. The researchers found that after an outcome of RED-RED-RED gamblers responded with a gambler’s fallacy type logic by betting on BLACK. Like Catherine above and the coin flipping above, the gamblers believed in a representation, or pattern of randomness.

A study by Gal and Baron in 1996 investigated the gambler’s fallacy in a laboratory-based experiment. Gal and Baron examined whether a change in betting strategy was due to boredom by asking participants why they choose to bet in the way that they did. Most of the participants in the Gal and Baron study responded by saying that they were attempting to maximize their earnings by using the gambler’s fallacy-type logic. It would appear that the gambler’s fallacy is not simply caused by boredom.

post 5 image 2.png

Besides gambling at the roulette table other casino games in which heuristics play a major role include the craps table and fruit machines. One prominent heuristic at the craps table is the belief in illusory correlations. When rolling the dice at the craps table gamblers often blow on the dice for luck or roll the dice softly in the belief that a low number will come up, and roll the dice harder when they want a higher number (Griffths. 1994). These gamblers believe that if a number comes up that they did not want then they did not through the dice hard or soft enough.

Cognitive short cuts as heuristics are used in every area of life where decisions need to be made. With respect to gambling, heuristics have been documented in fruit machine users, and at the poker, blackjack, roulette and craps tables. Even when betting on horse or dog races gamblers reliably use these mental short cuts (Terrell, 1998). I have highlighted two of uses of heuristics above, namely the gambler’s fallacy and illusory control. Like Catherine above many people fall for these heuristics and make sub-optimal decisions based on incorrect beliefs. When it comes to gambling, there are two ways to avoid these cognitive traps. If gambling alone take your time to think about the decisions that you want to make. When gambling in a group of with a friend you could listen to the advice of your friend as Catherine should have above.