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How people feel about the prospects of risk and reward is important to 'journey planning' in DC schemes. But does an individual's natural aversion to losing money impact their retirement saving?

The behavioural trait of loss aversion means there can be tension between what appears attractive in the short term and what appears attractive in the long term. Let's explore the behavioural trait of loss aversion and how it can impact glidepath design

**A series of bets**

The Nobel Prize winner Paul Samuelson once asked a colleague if he’s be willing to accept a bet: a 50% chance to win $200 and a 50% chance to lose $100. The colleague turned the bet down but said that he would accept 100 such bets. The colleague’s rationale for the turning down the bet was that he would feel the $100 loss more than the $200 gain. The table below illustrates this idea. The happiness (or 'utility' as economists like to call it) of a loss has been weighted by 2.5 times the utility of an equivalent gain.

#bets won |
Chance |
Gain |
Utility |

0 | 0.5 | -100 | -250 |

1 | 0.5 | 200 | 200 |

The expected utility is negative, and is found by probability-weighting the utility of the possible outcomes*. This explains why he would turn down the bet. However if you do the same calculation for just two such bets in a row, the table would look like:

#bets won |
Chance |
Gain |
Utility |

0 | 0.25 | -200 | -500 |

1 | 0.5 | 100 | 100 |

2 | 0.25 | 400 | 400 |

The expected utility is now a positive number**, so it is now seen as an acceptable bet. The more bets that are taken, the more attractive the proposition appears. Indeed, with 100 such bets, the chance of Samuelson’s colleague losing money is less than 1 in 2,000 and the expected gain is $5,000.

This presents a puzzle – if the colleague was allowed to watch and control the 100 bets being played out one after another, he would stop just before the last bet. However if he refuses that bet then the previous bet now becomes the last bet, which he will refuse by the same logic and so on until he has refused all bets. He would only accept two or more bets if he did not have to watch the bets being played out. If only he could 'close his eyes' and avoid reviewing his strategy, he could achieve a more attractive distribution of outcomes over the long term!

The above betting example is taken from Benartzi and Thaler’s paper on “Myopic loss aversion and the equity premium puzzle” (1995). The equity premium puzzle refers to the phenomenon that the observed returns on stocks in excess of government bonds over the past century is much greater than can be plausibly explained by traditional economics where everyone is assumed to behave in a purely rational way.

Loss aversion refers to a tendency to strongly prefer avoiding losses to acquiring gains, even small ones. This is reflected in the 2.5 factor used for losses in the betting example above (although a factor of 2 is actually more common). Bernartzi and Thaler suggested that loss aversion, not captured in traditional economics, can help explain the equity premium puzzle. Even long-term investors review their portfolio regularly and feel the pain of losses more acutely than the pleasure of gains.

**The pain of monitoring**

Nassim Taleb also explains the pain of frequent monitoring in his book *Fooled by Randomness*. He considers a brilliant investor who has an (arithmetic) expected return of 15% return, with 10% volatility. He makes the point that over short time frames (such as one hour) the probability of an investor making money is roughly 50% whereas over one year it is about 93% and over longer time horizons even higher. Given that losses register broadly twice as strongly as gains psychologically, monitoring will likely be a more unpleasant experience the more frequently that it occurs.

**Glidepath design**

It is interesting to explore the potential consequences of loss aversion, and Samuelson’s bet, on glidepath design. A glidepath is a plan for how the investment strategy of a pension scheme will evolve over time. For both defined contribution (DC) pension investors and defined benefit (DB) pension investors (i.e. trustees), glidepath design is *like choosing a series of bets.*

In an ideal world, the choice of bets wouldn’t depend on the frequency with which an investor reviewed their strategy. However, the reality of loss aversion (a now well-established description of risk preferences), means that this is not the case. Furthermore, even for a defined contribution investor, one cannot realistically expect an investment strategy to remain unreviewed for a long period of time, particularly as retirement nears.

In the case of a DC retiree choosing to purchase an annuity at retirement (from an insurance company), loss aversion implies that they will not want to take much risk relative to annuity prices shortly before they retire. Similar to the example above, they are effectively refusing any risky bet. As the investor moves further from retirement, however, the strategy is reviewed less frequently and they will be aware that they cannot access their retirement money for decades. This should encourage a longer-term outlook (i.e. considering the series of bets as grouped) and a higher allocation to growth assets.

Of course there are many other factors to consider when considering the degree and speed of de-risking for a DC glidepath. The payoffs from the sequence of investment choices also compound, as opposed to the example above where they simply add. Notwithstanding these differences, Samuelson’s bet is a potentially useful analogy that can shed light on the potential influence of loss aversion on glidepath construction.

*For maths enthusiasts, the expected utility here is -25, calculated as 0.5 x 200 + 0.5 x -250 = 100 - 125 = -25

** And the expected utility here is 25, calculated as 0.25 x -500 + 0.5 x 100 + 0.25 x 400 = -125 + 50 + 100 = 25