Life

Properties of Risk

Howard Marks continues with his memos for his clients by explaining a few properties of risk. According to him:

Risk is counterintuitive

  1. The riskiest thing in the world is the belief that there is no risk. As per Nassim Taleb, the way many investors view the market is often worse than Russian Roulette. In Roulette, there is one bullet in one of the six chambers of the revolver. But in investing, the frequency of bad events is so scarce (many chambers) that people start believing that there is no bullet inside.
  2. Good awareness that the market is risky improves the investors’ due diligence, making it less risky.
  3. When the asset price declines, people think it becomes riskier to invest, but it actually becomes safer. The opposite is also true; when the price increases, people are attracted to it as a safe instrument, forgetting the asset has actually become riskier.
  4. Having only safe assets of one type (lack of diversification) can make the portfolio vulnerable. On the contrary, having a few riskier but different types can make the portfolio more diversified and less vulnerable.

Risk aversion makes markets safer

As seen above, a risk-conscious investor does proper due diligence on the market, makes conservative assumptions, and demands a higher premium for the risk.

Risk is invisible

Most of the knowledge of risk comes from hindsight, i.e., after the event has happened.

Risk control is not risk avoidance
While proper control is necessary, avoiding the risk altogether prevents the investor from reaching her goals.

Reference

Howard Mark’s Memo: Risk Revisited

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The Capital Market Line: Illusion of Return

The relationship between risk and rewards, that reward increases with risk, is much engrossed in common knowledge. In investing, we have seen portfolio theory and capital market lines that confirm this notion.

But the risk-return line is far from straight. We have seen earlier that the X-axis (risk) in the case of an investment is the volatility of the portfolio. In the language of statistics, volatility is the standard deviation of the distribution. In other words, each point of the line represents a distribution (of returns), with higher and higher standard deviations from left to right.

While the expected returns, the mean of the distribution, are higher to the right, the chances of higher and lower returns (including losses) are also higher. The critical issue here is that no one knows the breadth of the distribution or its shape. Imagine if it is what Nassim Taleb calls a fat tail, an asymmetric distribution, or the occurrence of a heavy impact-low probability event.

Reference

Howard Mark’s Memo on Risk

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Risk and Return – The Capital Market Line

We have seen how simple portfolio theory explains the relationship between risk and returns. For example, the representation below.

This leads to the development of what is known as the Capital Market Line (CML). CML is a concept that combines the risk-free asset and the market portfolio. It is the line connecting the risk-free return and tangent to the ‘efficient frontier’ of the portfolio.

The slope of the Capital Market Line (CML) is the Sharpe Ratio of the portfolio.
Sharpe Ratio = (Return of the portfolio – risk-free rate) / Standard deviation

But there is something wrong with this line – or at least how people perceive the line of risk vs return. That is, next.

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Only Trade-Offs

American economist and political commentator Thomas Sowell summarises the core of decision-making, like nobody has, in his famous quote: There Are No Solutions, Only Trade-offs.

A crucial thing in trade-off is the assessment of the consequence of each option. A common practice in investment decisions is the cost-benefit analysis.

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Survival in a Truel

Anna, Bob and Claire are doing a three-way duel (a truel). Anna has an accuracy of 1/3, Bob has 2/3, and Claire is an excellent marksman with 1 (100%) accuracy. They must take turns shooting. Since each player knows others’ skills and all are rational, what would Anna do in the competition?

If Anna starts the duel and aims at Bob, there is a 1/3 chance she will shoot Bob. In that case, Claire has the next turn and will end Anna. On the other hand, if Anna aims at Claire, there is a 1/3 chance that Bob gets a chance to aim at Anna and end her with a 2/3 chance. So, it is clear that missing shots is a better option for Anna. So, she must shoot in the air first.

In the next chance, Bob will aim at the more prominent threat, i.e., Claire. Then there is a 2/3 chance of a showdown with Anna and a 1/3 chance that the showdown will be between Anna and Claire. Let P(A) be the probability that Anna survives, P(A, B) be the chance Alice wins the duel with Bob and P(A, C) Alice wins against Claire.

P(A) = 2/3 x P(A, B) + 1/3 x P(A, C)
P(A) = 2/3 x 3/7 + 1/3 x 1/3 = 25/63

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Charlie Munger’s Wisdom – Continued

We saw the first 10 of the 24 Cognitive Biases from Charlie Munger’s 1995 speech – Human Misjudgement. In this post, we will go through the rest.

11. Bias from deprival super-reaction syndrome: This is akin to the loss aversion bias, illustrating how we react when possessions, even trivial ones, are taken away. Consider, for instance, the intensity of employee-management negotiations where every inch is fiercely contested.

12. Bias from envy/jealousy:

13. Bias from chemical dependency, 14. Bias from gambling dependency: These biases don’t need a lot of explanation. They trigger attentional bias, leading individuals to allocate disproportionally more attention to addiction-relevant cues than to neutral stimuli. Businesses, whether pubs or casinos, are well-versed in exploiting these vulnerabilities. Being aware of these tactics can help you navigate such situations more effectively.

15. Bias from liking distortion: It’s about liking oneself, one’s ideas, and community. And making stupid ideas only because they came from someone you liked.

16. Bias from disliking distortion: Opposite of liking distortion. In this case, you dismiss ideas from people who you don’t like.

17. Bias from the non-mathematical nature of the human brain: Human brains in their natural state (i.e., untrained state) are notoriously inefficient when dealing with probabilities. Within this entity, Munger conveniently folds various fallacies of the human mind – crude heuristics, availability, base-rate neglect, hindsight – into one.

18. Bias from fear of scarcity: The fear of scarcity can bring out pure dumbness in otherwise perfectly normal people. A familiar example is the toilet paper rush during the early days of the Covid pandemic.

19. Bias from sympathy: It’s about leaders keeping employees with dubious personal qualities. Often, this happens out of pity for the person or her family. Munger says that while paying them the proper severance is essential, keeping such people in jobs can make the whole organisation poor.

20. Bias from over-influence and extra evidence:

21. Bias caused by confusion due to information not being properly processed by the mind: Munger stresses the need to understand the reasons (answer to the question – why?) for the information to be properly registered in the brain. Like for individuals themselves, it is also important for people to explain the reasoning clearly while communicating the key decisions and proposals to their stakeholders.

22. Stress-induced mental changes: What later happened to the Pavlovian dogs (conditioned for certain behaviours) after their cages were flooded was a good example of what stress can do. The canines forgot all the training and responses that they had acquired.

23. Common mental declines:

24. Say-something syndrome: It’s a habit of many individuals to do the talk irrespective of their expertise and capacities to impact the decision-making process. They remain just soundbites, and Munger cautions to watch out for those quiet selves that eventually add quality.

Charlie Munger’s Wisdom – Continued Read More »

Charlie Munger’s Wisdom

One of the greatest investors in history, Charles Munger, passed away on the 28th of November 2023, 33 days short of his 100th birthday. His celebrated talk at Harvard University in 1995 on the subject of ‘Human Misjudgment’ is undoubtedly a masterclass about the patterns of human irrationality. This and the next posts are about those 24 tendencies of the human brain that Mr Munger has immortalised in his celebrated lecture.

1. Underrecognition of the power of incentives: Munger illustrates his point using the cases of FedEx and Xerox, demonstrating that it was not logic but incentives that drove their employees. The incentives were intended to speed up work and improve sales. However, the workers maximised the commissions and overtime by selling inferior products and working longer.

2. Psychological denial: It is a type of mechanism by the brain to avoid reality, as it can cause deep pain and anxiety. Examples are parents refusing to believe the loss of their children or youths getting into crimes.

3. Incentive-caused bias: It’s also known as the Principal-Agent problem in companies. The people entrusted to lead companies (on behalf of the owners/shareholders) erode the long-term value of companies (principals’ interest) by going after short-term fixes or management’s vested interests (agent’s gain).

4. Self-confirmation bias: People tend to persist on already-made conclusions even when (newly) available evidence disproves them.

5. Bias from cognitive dissonance: It is similar to the earlier one. Cognitive dissonance bias is the mental discomfort that a person goes through if they have to hold two conflicting views about something. Most often, the receiver of the new information revolts with it, leading to selective perception and decision-making.

6. Bias from Pavlovian association: This refers to the famous experiments on dogs carried out by Pavlov. The experiments prove a great deal about the mental shortcuts of humans in making decisions. In other words, people choose a ‘go’ for an incentive stimulus, whereas they select a ‘no go’ on punishment stimuli. A wonderful example is how advertisements work in our minds.

7. Bias from reciprocation tendency: Humans return favour when they receive something from others. While this may seem a virtue, the behaviour can be manipulated, compelling individuals to substantially lower the cost of services.

8. Bias from over-influence of social proof: This is the absolute compliance to the ‘wisdom of the crowd’ or inability to act against social norms. Social proof works in unclear social situations where people follow what the surrounding people do. Munger gives an example of how all major oil companies started buying fertiliser companies when one of them initiated the trend. Another term closely related to this topic is the ‘power of reinforcement‘. Typical causes of bull or bear runs of stock markets.

9. Bias from distortions caused by distortion, sensation, and perceptions: In Cialdini’s famous experiment, students who first dipped their hands in hot water felt cold and cold water felt hot on a subsequent dip in the water at room temperature. He cites the familiar trick of a real estate broker who manages to sell her client a moderately over-priced house by first showing an outrageously overpriced house.

10. Bias from over-influence by authority: It is a tendency of the brain to be influenced by the opinion of an authority figure, even when the content is inaccurate. Like all cognitive biases, the authority bias is a shortcut our brains use to save energy in decision-making.

Reference

The Psychology of Human Misjudgement – Charlie Munger Full Speech: Warren Buffett

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Braess’s Paradox

Another counterintuitive experience similar to Downs–Thomson’s is Braess’s Paradox. As per this phenomenon, adding more roads to an existing network can slow down the overall traffic. Similar to the previous, we will see the mathematical explanation first.

Suppose there are two routes to city B from city A, as shown in the picture – the top and bottom roads. The first part is narrow on the top road, followed by a broad highway. The situation is the opposite for the bottom road.

The highways are not impacted by the number of cars, whereas, for the narrower roads, the traffic time is related to the number of vehicles on the road – N/100, where N is the number of cars.

If there are 1000 cars in the city, the system will reach the Nash equilibrium by cars getting equally divided (in the longer term), i.e., 500 on each road. Therefore, each car to take
500/100 + 15 = 20 mins

Imagine a new interconnection built by the city to reduce traffic congestion. The travel time on the connection section is 1 minute. Let’s look at all scenarios.

Scenario 1: A car starts from the bottom highway, takes the connection, and moves to the top highway. Total time = 15 + 1 + 15 = 31 mins.
Scenario 2: One car starts from the top road, takes the connection, and moves to the bottom road, while the others follow the old path (not using the connection). Total time = 50/100 + 1 + 51/100 ~ 11 mins.

Scenario 2 seems a no-brainer to the car driver. But this news invariably reaches everyone, and soon, everyone starts taking the narrow paths! In other words, the narrow route is the dominant strategy. The total travel time now becomes:
1000/100 + 1 + 1000/100 = 21 min. This is more than the old state, a situation with no connection possible.

So, the condition without the connection road (or closing down the connection road) seems a better choice. And this is Braess’s paradox suggesting that a more complex system may not necessarily be a better choice.

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Downs–Thomson paradox

Here is a game theory puzzle for you. The government proposes to build a highway between the two cities, A and B, that reduces the burden of the existing freeway. Here is the rationale behind the proposal.

There are two modes of arriving from A to B: 1) take the train, which takes 20 minutes, or 2) take the freeway using a car, which takes (10 + n/5) minutes, where n is the total number of cars on the road. Since the train is a public transit, it doesn’t matter how many people take it – it always takes 20 minutes to reach the destination. But if the new highway operates, the travel time becomes (5 + n/5) minutes. Note that the old freeway stops functioning once the new road is available.

What is your view on building the highway as a solution to reduce travel time, or are there alternate ideas to meet the objective?

The existing case

Suppose there are 100 commuters. Each can take the train and reach B in 20 minutes. That gives a few people the advantage of taking cars and reaching their destination earlier – until the travel time matches the following way.
20 = 10 + n/5
n = 50
Beyond 50 commuters, car travel will take longer than the train; therefore, 50 is an equilibrium number in the longer term.

The new case

The new equilibrium is estimated as follows:
20 = 5 + n/5
n = 75
In other words, more people will take the new route, but the travel time remains the same.

The paradox

This is a simplified game-theory explanation of what is known as the Downs–Thomson paradox. It says that comparable public transport journeys or the next best alternative defines the equilibrium speed of car traffic on the road.

Alternatives

On the other hand, if modifications are possible to reduce the commute time of the train, then overall travel time (for both railways and roads) can be reduced.

References

Downs–Thomson paradox: Wiki

The Problem with Faster Highways: William Spaniel

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The Auction Game

Amy and Becky are in an auction for a painting. The rules of the auction are:

  1. Bidders must submit one secret bid.
  2. The minimum amount to bid is $10 and can be done in increments of $10
  3. Whoever bids the highest wins and will be charged an amount equal to the bid amount.
  4. In the event of a tie, the auction house will choose a winner based on a lot with equal probabilities.

Amy thinks the fair value of the painting is $56, and Becky thinks it’s $52. These valuations are also known to both. What should be the optimal bid?

The payoff matrix is:

Becky
Bid $40Bid $50
AmyBid $408, 60, 2
Bid $506, 03, 1

If Amy bids $40 and Becky $50, Becky wins the painting and her payoff is the value she attributes (52) – the payment (50)= $2. The loser wins or loses nothing.
If Amy bids $50 and Becky $40, Amy gets it, and her payoff will be the value (56) – what she pays (50) = $6.
If both bid at $40, Amy can get a net gain of 16 (56 – 40) at a probability of 0.5. That implies the payoff for Amy = $8. For Becky, it’s $12 x 0.5 = $6.
If both bid for $50, Amy’s payoff = $6 x 0.5 = $3 and Becky’s = $2 x 0.5 = $1

At first glance, it seems obvious that the equilibrium is where both are bidding for $40. If Amy thinks Becky will bid $40, Amy’s best response is to bid the same as her payoff is $8. The same is the case for Becky.
But if Amy expects Becky to go for $50, then Amy must also bid $50. Becky will also go along the same logic.

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