I visited my sister in the UK last summer and spent time with my young nieces and nephews. One evening, we found a compendium of board games and I introduced my five-year-old nephew to Snakes and Ladders. The rules were explained, although not completely absorbed, and off we started. My nephew was excited to storm into the lead but crestfallen to encounter his first snake. His first response was to want to throw again, because he had “made a mistake”. A brief discourse on the harsh realities of life ensued. Eventually, he slid his counter glumly down the snake, vowing to get back to “where he should be” as quickly as possible. The game continued, and after more setbacks that meant he trailed for 80% of the game, he had a series of fortunate moves that secured victory.
Investors exposed to market risk play their own game of Snakes and Ladders, experiencing both unexpected gains and losses. Behavioural finance researchers are interested in not only how investors behave when experiencing losses but how they remember the experience once it is over. My nephew demonstrated two common behavioural biases early in the game: anchoring and framing. The goal of Snakes and Ladders is to be first to the end, but after his experience with his first snake he re-framed his objective to regaining the ground he had lost. Similarly, investors are often focused on getting back to where they were before a market (or stock price) tumble, even though this position had held no special meaning prior to the decline. They do so to avoid regret. People who do not have meaningful personal financial targets can be most susceptible to anchoring effects, whatever their level of wealth, because of the absence of consistent framing.
We are also prone to assume that people feel the same about the same level of wealth, but this can be a mistake. Compare Joe’s experience with Mar’s. At the time that Joe’s portfolio was worth $500,000 Mary’s was also worth $500,000. We might assume that Joe and Mary are equally happy. But if we are told that Mary’s portfolio had been worth $5 million when Joe’s was worth $550,000, we can understand Mary might be in distress. The observation of behavioural economists is that people attach values to gains and losses rather than to absolute wealth. Like my nephew, Mary had slid down a long snake and wasn’t happy.
Losses can persist for a day, a month, a year or a decade. Do investors simply sum the daily pain for as long as it takes to recover, or how is the experience remembered?
Consider the situation in illustrated below. Both Alice and Bob start with a portfolio of $100,000. Alice sees her portfolio reduce in value to $40,000 and then recovers quickly. Bob’s portfolio declines to only $80,000, a smaller decline than Alice’s, but takes longer to recover. In both case the “area under the curve” is the same: so have they both experienced the same overall pain?
Source: PWL Capital
To gain some insights, we shift focus from board games to colonoscopies. In the 1990s, colonoscopies were not routinely administered with an anaesthetic. A Canadian doctor, Don Redelmeier, and psychologist, Daniel Kahneman1 set up a study that had patients record their pain during the procedure. The patients were then interviewed after the procedure about their memory of their experience.
The conclusions were that the memory of pain associated with the colonoscopy was closely predicted by the average of the worst moment of pain and the pain at the end. The duration of the pain had no impact on the rating of the total pain. Related studies showed that simply adding an additional period that was less painful was sufficient for most participants to prefer this extended option even though the duration and total pain had increased. Based on these, and similar, studies, we are not pain integrators, so we expect Alice to remember her portfolio decline as a more painful experience than Bob.
Focusing only on the intensity of a pain or pleasure can lead to poor decision making. To consider an extreme example, studies of rats2 show that they use the same heuristic as humans for pain and pleasure. By using electrical stimulation to produce a sensation of pleasure in rat’s brains researchers observed rats, who can self-stimulate by pressing a lever, will starve themselves to death rather than interrupt the stimulation. In the study, only the intensity of the stimulation impacted the rat’s behaviour, not the duration.
When designing investment strategies for clients we need to assess a client’s risk tolerance. Typically, investors are asked to think back to past periods of decline (often 2008) but we now understand that such memories ignore the duration of the painful experience and focus only on the intensity. The client’s experience during a future market downturn may be rather different.
To compensate for the way our memories work we can provide historic data showing the duration as well as the magnitude of the decline. In the figure below we consider a range of model portfolios from 0% equities (100% fixed income) to 100% equities3. We compute the performance of each portfolio over the past 30 years and select the most severe one year decline and also the longest period for the portfolio to recover a previous high. We summarise the results in the table below.
| EQUITY ALLOCATION | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 0% | 10% | 20% | 30% | 40% | 50% | 60% | 70% | 80% | 90% | 100% | |
| Time to Recover (years) | 1.25 | 1.25 | 1.25 | 1.33 | 3.08 | 3.42 | 3.50 | 4.75 | 5.25 | 5.58 | 5.67 |
| Maximum Drawdown | -6.07% | -5.46% | -4.86% | -8.36% | -12.28% | -15.96% | -19.62% | -23.15% | -26.47% | -29.77% | -32.95% |
Source: PWL Capital
We see that the higher the equity allocation (above 20% equity), the higher the maximum drawdown and the longer the recovery period. The time to recover a previous high can vary from just over a year to over 5 years. The period that experience the maximum drawdown does not always correspond to the period with the longest time to recover.
To reduce the likelihood of anchoring on portfolio highs, we can help our clients by reminding them of their wealth goals, such as retirement. That can help reduce anxiety during a market decline.
When setting future investment goals and understanding client’s risk tolerance we know that there will be a tendency to remember only the intensity of past market downturns and neglect of the duration. We can compensate for this bias by introducing relevant data on the duration of downturns into the client conversation.
We end with a quote from Meir Statman:
“We are susceptible to cognitive and emotional errors, yet can correct them by human-behavior and financial facts knowledge. This knowledge transforms us from normal-ignorant to normal-knowledgeable, and transforms our choices from normal-foolish to normal-smart.”4
While researching this article I discovered that the person who starts Snakes and Ladders has a slightly better chance of winning. As a fiduciary, I will, of course, be sharing this knowledge with my nieces and nephews at the earliest opportunity.
1 Thinking, Fast and Slow, Daniel Kahneman, 2011, Chapter 35
2 Olds J, Milner P (1954). “Positive reinforcement produced by electrical stimulation of septal area and other regions of rat brain”. Journal of Comparative and Physiological Psychology. 47 (6): 419–27. PMID 13233369.
3 Details of the portfolio construction are here. Thanks to Jason Primmer for the calculations.
4 Finance for Normal People: how investors and markets behave, Meir Statman, 2017, Oxford University Press
