The University of Oxford
The concept of equilibrium is one of the most central ideas in economics. It is one of the core assumptions in the vast majority of economic models, including models used by policymakers on issues ranging from monetary policy to climate change, trade policy and the minimum wage. But is it a good assumption? In a forthcoming Science Advances paper, Marco Pangallo, Torsten Heinrich and Doyne Farmer from the University of Oxford, investigate this question in the simple framework of games, and show that when the game gets complicated this assumption is problematic. If these results carry over from games to economics, this raises deep questions about when economics models are useful to understand the real world.
Kids love to play tic-tac-toe, aka noughts and crosses, but when they are about 8 years old they learn that there is a strategy for the second player that always results in a draw. This strategy is what is called an equilibrium in economics. If all the players in the game are rational they will play an equilibrium strategy. In economics, the word rational means that the player can evaluate every possible move and explore its consequences to their endpoint and choose the best move. Once kids are old enough to discover the equilibrium of tic-tac-toe they quit playing because the same thing always happens and the game is really boring. One way to view this is that, for the purposes of understanding how children play tic-tac-toe, rationality is a good behavioural model for eight year olds but not for six year olds.
In a more complicated game like chess, rationality is never a good behavioural model. The problem is that chess is a much harder game, hard enough that no one can analyse all the possibilities, and the usefulness of the concept of equilibrium breaks down. In chess no one is smart enough to discover the equilibrium, and so the game never gets boring. This illustrates that whether or not rationality is a sensible model of the behaviour of real people depends on the problem they have to solve. If the problem is simple, it is a good behavioural model, but if the problem is hard, it may break down.
Doyne Farmer, Professor of Mathematics at the University of Oxford, said: ‘Many of the problems encountered by economic actors are too complicated to model easily using a normal form game. Nonetheless, this work suggests a potentially serious problem. Many situations in economics are complicated and competitive. Our research raises the possibility that many important theories in economics may be wrong. If the key behavioural assumption of equilibrium is wrong, then the predictions of the model are likely to be wrong too. In this case new approaches are required that explicitly simulate the behaviour of the players and take into account the fact that real people are not good at solving complicated problems.’
Theories in economics nearly universally assume equilibrium from the outset. But is this always a reasonable thing to do? To get insight into this question, the researchers studied when equilibrium is a good assumption in games. They didn’t just study games like tic-tac-toe or chess, but rather they studied all possible games of a certain type (called normal form games). They made up games at random and had two simulated players play them to see what happens. The simulated players used strategies that do a good job of describing what real people do in psychology experiments. These strategies are simple rules of thumb, like doing what has worked well in the past or picking the move that is most likely to beat the opponent’s recent moves.
The researchers demonstrated that the intuition about tic-tac-toe vs. chess holds up in general, but with a new twist. When the game is simple enough, rationality is a good behavioural model: players easily find the equilibrium strategy and play it. When the game is more complicated, whether or not the strategies will converge to equilibrium depends on whether or not the game is competitive. If the incentives of the players are lined up they are likely to find the equilibrium strategy, even if the game is complicated. But when the incentives of the players are not lined up and the game gets complicated, they are unlikely to find the equilibrium. When this happens their strategies always keep changing in time, usually chaotically, and they never settle down to the equilibrium. In these cases equilibrium is a poor behavioural model.
A key insight from the research is that cycles in the logical structure of the game influence the convergence to equilibrium. The researchers analyse what happens when both players are myopic, and play their best response to the last move of the other player. In some cases this results in convergence to equilibrium, where the two players settle on their best move and play it again and again forever. However, in other cases the sequence of moves never settles down and instead follows a best reply cycle, in which the players’ moves keep changing but periodically repeat – like “ground hog day” over and over again. When a game has best reply cycles convergence to equilibrium becomes less likely.
Using this result the authors have been able to derive quantitative formulas for when the players of the game will converge to equilibrium and when they won’t, and show explicitly that in complicated and competitive games cycles are prevalent and convergence to equilibrium is unlikely.
TWO TO TANGO? MARKET DATA AND OPINIONS IN INVESTMENT MANAGEMENT
Sebastien Lleo is Associate Professor of Finance and Head of the MSc in Risk and Financial Technologies at NEOMA Business School (France)
Analyst views and expert opinions matter. They are an invaluable complement to market data when it comes to formulating relevant capital market expectations and to strengthening risk management models and practices. But watch out for behavioral biases!
“Garbage in – garbage out!” Every investment management professional has heard the warning that poorly formulated capital market expectations will get portfolio optimisers to produce inefficient, unrealistic, and even outright dangerous portfolios.
Thus, considerable efforts have taken place to turn available economic and market data into accurate capital market expectations. These lead to the development of slick statistical methods, effective econometric techniques, and powerful machine learning algorithms.
Opinions can also be an invaluable source of insights to construct accurate capital market expectations.
What are the types of opinions on financial markets?
Opinions take multiple forms in financial markets. They include analyst views, opinions from political and economic experts, super forecaster predictions, and investor polls.
Moreover, opinions abound on financial markets. Consultancy Quinlan & Associates reported that the bigger banks and brokerages emailed over 40,000 pieces of research every week in 2016, despite continuing job cuts in the financial sector. Social media also contribute to the spread of opinions: according to the financial website Modestmoney.com, there are at least 839 active financial blogs published in English.
Why should I use expert opinions?
Opinions have three key benefits.
First, opinions can be a crucial complement to traditional economic, corporate and financial market data to construct realistic capital market expectation, and keep those up-to-date. This statement is especially true in times of heightened uncertainty, such as market bubbles and financial crises, when traditional data fail to provide an accurate assessment of market conditions.
Second, opinions can strengthen risk management models and practices. Opinions can widen the range of scenarios considered in portfolio optimisation and risk management. Dissenting opinions provide a cornerstone for the construction of meaningful stress test scenarios.
Third, we can use opinions, even when traditional data are not. For example, assessors evaluate insurance claims, and appraisers estimate the value of illiquid assets, such as real estate and collectables, periodically.
How easy is it to collect opinions?
The inclusion of opinions requires extreme care.
Let’s look at analyst views and expert opinions. We all know that not all experts or forecasters are equally accurate. A widely reported study by CXO Advisory Group LLC tracked 6,582 forecasts for the U.S. stock market published by 68 experts between 2005 and 2012. The study found that average accuracy across experts was 47.4%, with individual accuracies ranging from a low of 21% to a high of 68%.
Therefore, investment management teams need to implement a process to guarantee the relevance of the opinions used in their models. This process, known as “elicitation,” is described in abundant literature. The books by O’Haghan (2006) and by Meyer and Booker (2001) are an excellent place to start. Essentially, the elicitation process helps to construct views that are specific, explicit, and structured. Opinions need to focus on a specific variable or parameter, such as the price of a given asset or the mean of a distribution. Opinions need to explicitly provide a mid-point or most-likely scenario, a confidence interval, and to relate the confidence interval to a probability distribution. Finally, opinions need to be structured to provide a transparent and auditable trail.
What are the implementation challenges?
Three main implementation challenges need addressing.
The first and most dangerous challenge is that opinions are often subject to the behavioral biases. Behavioral biases, in particular overconfidence, excessive optimism, conservatism, confirmation bias, and groupthink play an essential role in how finance professionals perceive and process information, and on how they form their forecasts. Recently, in a simulation study, Davis and Lleo (2020) recently found that the presence of biases explained nearly 70% of excess risk-taking. Therefore, it is crucial to debias forecasts before using them in any model.
Second, expert opinion models are Bayesian and therefore require the specification of a prior distribution. We can overcome this difficulty with some original thinking, as with Black and Litterman’ reverse optimisation exemplifies.
Third, aggregating of multiple expert opinions is considered an essential conceptual and computational problem because it requires engineering a joint distribution out of a collection of univariate distributions.
How can I integrate opinions in my portfolio selection model?
Currently, several families of portfolio selection models use opinions as input. The best-known and oldest is the Black and Litterman (1992) model, which uses analyst views to generate capital market expectations in a Markowitz-style single-period optimisation framework. This approach has been extensively discussed and developed in a large number of subsequent papers and chapters.
However, the Black-Litterman approach has two fundamental limitations. First, it is static, meaning that it locks portfolio managers into a “buy-and-hold” strategy, ignoring the possibility that portfolio managers may shift their asset allocation as financial market conditions change. Second, it ignores the presence of behavioral biases in expert opinions.
To address the first limitation, Frey et al. (2012) and Davis and Lleo (2013,2020) proposed two closely-related dynamic portfolio management models. Although both models are developed in continuous time, we can transpose them to a multiperiod discrete-time setting.
The second limitation has proved more elusive. At the moment, Davis and Lleo (2020) is the only dynamic portfolio selection model that addresses for behavioral biases.
Black, F., Litterman, R., 1992. Global portfolio optimisation. Financial Analyst Journal 48 (5), 28–43. Davis, M., Lleo, S., 2013. Black-Litterman in continuous time: the case for filtering. Quantitative Finance Letters. 1 (1), 30–35.
Davis, M., Lleo, S., 2020, Debiased expert forecasts in continuous-time asset allocation. Journal of Banking and Finance. 113.
Frey, R., Gabih, A., Wunderlich, R., 2012. Portfolio optimisation under partial information with expert opinions. International Journal of Theoretical and Applied Finance 15 (1). O’Hagan, A., 2006. Uncertain Judgments: Eliciting Expert’s Probabilities. Wiley.
Meyer, M., Booker, J., 2001. Eliciting and analysing expert judgment: a practical guide. ASA-SIAM Series on Statistics and Applied Probability. Society for Industrial and Applied Mathematics.
AN ULTIMATE GUIDE TO TURNING YOUR EARLY RETIREMENT DREAM INTO A REALITY
Rick Pendykoski is the owner of Self Directed Retirement Plans LLC, a retirement planning firm based in Goodyear, AZ.
This article is for all those who are counting their IRAs, 401 (k), self-directed 401k and other retirement planning options to enjoy that late-life freedom as early as 45 or 40. Financial freedom at 55 has become a thing of the past because today it all depends on your ability to take the right decisions. If your 9 to 5 life has left you drained and you are serious about an early retirement, here are 8 ways to coach you from scratch:
- Free yourself from the vicious circle of debt
The first step to securing an early retirement is getting yourself free from debt. If you do not wish to enter your early retirement with any financial lags or large payments that can eat away a massive chunk of your modest savings, you need to increase your cash flow by clearing all your debts. Paying off your mortgage or lease early will help you divert the funds into a Roth IRA or other retirement savings.
- Start living a frugal life
Saving is the only way to increase the cash flow as your career progresses and this can be done by controlling your expenses. It does not mean giving up on all your desires but only requires you to live a frugal lifestyle. A few compromises and you can save a significant amount which will eventually bring you closer to your early retirement dream. From giving up on your expensive memberships and cutting down your HVAC usage to making a few compromises in your lifestyle and sacrificing a few golf games, your day-to-day frugal acts will free you from your cubicle and give you the freedom to retire early.
- Be open to the idea of changing
Prioritize between your wants and your needs. This will help you break free from the shackles of your tiring nine to five schedule. Enjoying life to the fullest sounds like a great idea to most of us, but it also means that you are losing on the real joy of retiring at 40 for momentary happiness. If fancy dinners and long drives in luxury cars mean more to you, an early retirement is obviously out of your reach. Mindful spending needs major lifestyle changes for which you may need to give up on stylish clothing, lavish parties, exotic vacations and more. This is only possible if you change your perception of conventional societal programming which demands that you give up on your desires of bigger houses and new cars. It calls for a complete mind shift from spending to saving.
- Take a head start with a high-paying industry
It is possible to retire well before you turn 60 if you are working for an industry that pays really well right from the start. A good-paying job plays a critical role in paving your path to a financially independent future. You too can enjoy a retirement of rest and relaxation if you are willing to take up personal responsibility in professional life. Getting closer to your goal of early retirement requires you to be self-sufficient early on in life.
- Automate 50% of Your Annual Income to Retirement Savings
Allocate as high a percentage of your annual income as possible to pay up your previous debts, pending bills, leases, and loans. Once you are done with of all these, automate your income towards retirement savings. You can start with 30% and raise the bar every year as your income increases. Every time you get a raise, increase the amount you add to your retirement reserve.
- Be sure to invest in a 401 (k) plan
Many employers are offering 401 (k) plans where you can invest a certain amount of your income and your employer makes a matching contribution to bolster your retirement savings.
- Stick to a frugal lifestyle
You need to revamp your investment plan as your career keeps progressing. What you want to achieve – an early retirement is an extraordinary goal and so your efforts should be focused on living frugally. Always keep a rewarding retirement at the top of your mind and you will remain motivated to keep the passion alive and pursuit kicking.
- Invest in an IRA
An IRA is a preferred and popular choice for retirement savings. You can consult an experienced and reputed financial advisor to guide you in selecting right IRA. An IRA will allow you to enjoy tax benefits if you choose to retire early. It will get to where you want faster than you think.
Start investing right away and make your retirement the best phase of your life.
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