Thinking, Fast and Slow - Looking at the Big Picture

By The Boy Who Procrastinates - July 31, 2019

In the previous few posts, I have touched on the topics of Anchoring Effect, Prospect Theory and Endowment Effect in the book review of Thinking, Fast and Slow by Daniel Kahneman. 

Building on the concept of loss aversion, we will explore another fundamental shortcoming that may lead to irrational decisions and common financial mistakes. 

A Brilliant Mistake

Imagine that you are presented with the following pair of concurrent decisions and asked to examine both decisions before making your choice. 

Decision (i): Choose between
A. Sure gain of $240
B. 25% chance to gain $1,000 and 75% chance to gain nothing

Decision (ii): Choose between
C. Sure loss of $750
D. 75% chance to lose $1,000 and 25% chance to lose nothing.


As elucidated in Prospect Theory and Loss Aversion, most people tend to overweigh options that are certain and adopt a risk averse attitude towards gains. Conversely, when the prospect of certain loss is dangled before them, it drives them to be risk-seeking in the domain of losses.

Going by the reasoning, majority of the respondents would prefer A to B and D to C. 

Intuitively, the motivation behind the preferences for the two decisions appears to be compelling. However, what they may have overlooked in their decision-making processes is to consider the possible results of the four combinations of choices. 

Now consider the following options:
A+D. 25% chance to win $240 and 75% chance to lose $760
B+C. 25% chance to win $250 and 75% chance to lose $750

This time round, it is unambiguous to recognise that the option, B+C is unequivocally better than A+D. The dominant choice, B+C is actually a combination of the two rejected options in the first pair of decision problems. 

Broad and Narrow Framing

This is mainly attributed to an inherent cognitive bias that impairs the quality of decision-making. Known as "narrow framing", it refers to the tendency to evaluate a risky prospect in isolation instead of merging it with the other risk faced. 

Compared to solving multiple problems simultaneously, it is less laborious to solve one problem at a time. Humans, by nature, are averse to mental effort and we tend to make decisions as problems arise. This exemplifies the limits of human rationality. 

In contrast, broad framing takes all the other options into consideration before reaching a single comprehensive decision. Broad framing is adopted when a rational agent is able to consider all 4 options before deciding on the choice of B+C. 

Samuelson's Problem

Paul Samuelson, a Nobel laureate in Economics, has devised a well-known problem. He asked his colleague if he would accept a gamble on the toss of a coin in which he could lose $100 or win $200. 

Even though it may be apparent that a participant is expected to win more than he may lose in this bet, the pain of loss looms larger than the joy of gain. Needless to say, the colleague rejected the gamble. 

Now, a follow-up question: Would you be willing to play the same bet twice or even thrice? 

In response, most people would find it to be less appealing. If a participant did not fancy a single gamble, it is unsurprising that he would not want to participate in the same bet multiple times. A utility maximiser who rejects a single bet, should also reject the offer of many. 

To be sure, let's compute the odds of gain and loss for the tosses.

Now, the bet appears to be more enticing with each coin toss. By flipping the coin twice, a participant has a 25% chance of winning $400, 50% chance of winning $100 and 25% chance of losing $200.

Furthermore, it is discernible from the table that the probability of losses diminishes with the repetition of tosses. 

Responding to Samuelson's offer, his colleague has suggested that he will take on the bet if he is able to make 100 such bets. 

The aggregated gamble of a hundred repetition of such bets has an expected return of $5,000, with 1/2,300 chance of losing any money and merely a 1/62,000 chance of losing more than $1,000. 

Looking at the Big Picture

The Samuelson's Problem leads us back to the issue of narrow framing. When engaged in narrow framing, an individual is likely to consider each coin flip independently and wrapped up in the 50% chance of losing money. 

But once the overall odds are aggregated, realising the attractiveness of the bet is an effortless task. 

An interesting illustration of broad framing is observed when Nobel Prize-winning economist, Richard Thaler approached 25 managers from a large company, each of whom manages a separate division. He asked them to consider a risky venture in which there is an equal probability that they could lose a large amount of the capital they controlled or earn double that amount. 

None of the executives was willing to take on the risk. But when Thaler turned to the CEO of the company and asked for his opinion, the CEO would like all of them to accept the venture. 

Trap of Narrow Framing 

One of the common traits that most investors may share is the tendency to check on the portfolios on a daily basis. While it may seem innocuous to get an status update on our investments, this additional information could possibly have an adverse impact on our investment returns.

Constantly barraged by daily stock market newsletters and instant updates on the latest swings of the market, it is easy to be caught in the trap of narrow framing especially in this era of aggressive digital evolution. 

Having access to information on daily fluctuations in stock markets creates the potential for investors to fall prey to our emotions and make sub-optimal decisions for our investing activities. 

Kahneman said it best in this book when he advised the following:

Closely following daily fluctuations is a losing proposition, because the pain of the frequent small losses exceeds the pleasure of the equally frequent small gains. 
In addition to improving the emotional quality of life, the deliberate avoidance of exposure to short-term outcomes improves the quality of both decisions and outcomes. 
Similar to the acceptance of risky ventures by the CEO, each investment idea should be a bet offering huge upside and small downside with the odds in our favor. On the whole, a collection of such investment ideas will lead to better outcome. 

Instead of focusing on the gains and losses of individual stocks, we should consider the overall performance of our portfolios. Ultimately, it is wiser to act on changes in the economy or other circumstances affecting the company than reacting purely on price changes. 

In addition, we may consider developing a structured and disciplined investment policy which we can adhere to. This will allow us to react less impulsively to the gyrations of the stock markets. 

Notably, Benjamin Graham, the father of value investing, has also advocated this notion in The Intelligent Investor:

The investor with a portfolio of sound stocks should expect their prices to fluctuate and should neither be concerned by sizable declines nor become excited by sizable advances. He should always remember that market quotations are there for his convenience, either to be taken advantage of or to be ignore. 
In life, you win a few, you lose a few.

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Disclaimer: Kindly note that this is not a sponsored post. The author is in no way affiliated with the publisher/author and does not receive any form of remuneration for this post. The Boy who Procrastinates has compiled the information for his own reference, with the hope that it will benefit others as well.

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