This document is for Professional Clients and is not for consumer use. Thaler,

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1 Behavioural finance and portfolio construction Whitepaper This document is for Professional Clients and is not for consumer use. I predict that in the not too distant future, the term behavioural finance will be correctly viewed as a redundant phrase. What other kind of finance is there? In their enlightenment, economists will routinely incorporate as much behaviour into their models as they observe in the real world. After all, to do otherwise would be irrational. Thaler, Georgina Taylor, David Millar and Dave Jubb Invesco Perpetual, Multi Asset team As fund managers, we constantly have to review what impacts financial asset prices and what influences our own decision-making processes for investing in those assets. The efficient market hypothesis suggests that financial markets consistently reflect a fair value based on all available information. That claim is underpinned by the assumption that we are all rational human beings in the way that we respond to information and, therefore, market prices react instantly and uniformly to new information. Many studies and indeed our own day-to-day observations of financial markets would challenge that premise. One particular branch of finance and economics theory, behavioural finance, has therefore become increasingly popular and important for explaining the patterns of financial market price performance and goes a long way in helping us understand particular market dynamics, such as asset price bubbles. It now plays a significant role in how we understand decision making and we, as a team, have factored an awareness of behavioural finance into both our team structure and our underlying investment process. 1 The End of Behavioral Finance, Richard H. Thaler, Source: Financial Analysts Journal, Vol. 55, No. 6, Behavioral Finance (. - Dec., 1999)

2 The role of uncertainty In part, behavioural finance has evolved because of the dynamics of human behaviour that can be observed when individuals make decisions under uncertainty. Here, we address some of the key concepts underpinning behavioural finance and then apply them to our own view of decision making within the asset management industry. Behavioural finance has been through various iterations over the years but was traditionally anchored around the concept of expected utility theory. In a financial wealth context, this theory was based on the premise that our decision-making processes are driven by an assessment of the probability of an event occurring and its subsequent impact on our total level of wealth. As individuals, we weigh up the probability of an event happening, work out the expected payoff on that basis and always choose the option with the most favourable outcome. This approach to decision making was considered a way to capture and illustrate diagrammatically the way in which we all make decisions under uncertainty. The key assumption made in illustrating this concept is the individual s approach to risk. If an individual is risk neutral then the diagram is simple to construct. There is a one-for-one relationship between the expected utility, or pleasure, from achieving an increase in wealth and the same amount of displeasure, or reduced utility, if the outcome reduces the overall wealth of the individual, as illustrated in figure 1. However, we are a little more complicated than that as human beings and, therefore, two more diagrams were required to make this theory incorporate a more holistic approach to human behaviour. The first captured the behaviour of a risk-seeking individual and the second was to capture the behaviour of a risk-averse individual. This is where expected utility theory starts to become more intuitive. A risk-seeking individual will gain more pleasure from a significant increase in wealth and would favour the opportunity to increase wealth at the expense of losing wealth. However, a risk-averse individual will place much more weight on maintaining a certain level of income or assets rather than taking risk to increase those assets significantly. This is captured by either a concave or convex curve reflecting the relative biases of those individuals as illustrated in figures 2 and 3. These differences in decision making are reflected in the risk rating that financial advisers attribute to their clients to understand their attitude to risk and therefore their expected utility curve in relation to a range of investment choices. Figure 1 Utility curve of a risk-neutral individual Risk Neutral Figure 2 Utility curve of a risk-seeking individual Risk Seeker Figure 3 Utility curve of a risk-averse individual Risk Averse Utility function Utility function Utility function Total wealth Total wealth Total wealth Source: Invesco Perpetual. For illustrative purposes only. 02 Behavioural finance and portfolio construction

3 Behavioural finance and the fund management industry The aim of this article is to link behavioural finance to the behaviour of fund managers and try to capture how careful the fund management industry needs to be in trying to remove, or at least reduce, behavioural biases in its investment processes. The issue with expected utility theory discussed above is that it is based upon how we are expected to behave as individuals, not necessarily how we do behave in practice. Here, we go on to discuss how expected utility theory falls a long way short of explaining our decisionmaking processes on a day-to-day basis. One observation that has been made of the fund management industry is that fund managers have a tendency to hold on to loss-making positions for too long. If fund managers were rational human beings then cutting a losing position makes sense, particularly for a risk-averse individual. The utility from making further losses should outweigh the possibility of breaking even or making a small gain from that existing position. In contrast to holding on to loss-making positions too long, it has also been observed that fund managers tend to cut profit-making positions too early. These two observations are together known as the disposition effect 2 and suggest that there is some inconsistency in how fund managers approach decisions under uncertainty. This also explains why expected utility theory is deemed to be inadequate for capturing behaviour consistently over time. In 1979, Tversky and Kahneman 3 introduced a new theory, which challenged expected utility theory. This new theory was called prospect theory and goes much further in capturing how we all, as individuals, make decisions. Prospect theory differs from utility theory in two distinct ways. Firstly, the decision-making process is not anchored around the total wealth of an individual but around a reference point, which is entirely subjective. This is an incredibly important consideration for a fund manager and is something we will come back to. The second difference is the use of decision weights rather than simple probabilities in assessing how likely the potential outcome of an uncertain situation may be. As individuals, we do not view risk in the same way because our own individual reference points for making decisions are different. When making a decision under uncertainty there are two considerations: the certain outcome and the probability of the uncertain outcome occurring. In expected utility theory, the certain outcome is merely the level of wealth. So, if a stock price fell from $100 to $90 then the starting point is $90 and a decision should be made as to whether to continue to hold the stock or whether to sell the stock. Figure 4 shows the different decisions made based on whether the utility curve of the individual is concave or convex and is based on a scenario where there is a chance of the stock rising or falling by $10. A risk-neutral individual would be indifferent, demonstrating how incomplete a theory this is, a risk averse individual would sell the stock, a risk-seeking individual would continue to hold the stock. Figure 4 The outcome for individuals on different utility curves Starting utility Risk neutral Risk seeking Hold the stock Risk averse Expected utility Starting level of utility Indifferent Sell the stock Source: Invesco Perpetual. For illustrative purposes only. 2 The Disposition to Sell Winners Too Early and Ride Losers Too Long: Theory & Evidence; Hersh Shefrin and Meir Statman, Source: The Journal of Finance. 3 Prospect Theory: An Analysis of Decision under Risk; Daniel Kahneman and Amos Tversky, Source: Econometrica. 03 Behavioural finance and portfolio construction

4 The certain outcome in prospect theory is a loss of $10. An individual reaches this starting point by going through an editing phase, during which the individual organises and reformulates the available options, so as to simplify the choice. It is only post the editing phase that the individual will enter an evaluation phase, when the individual considers all the edited prospects and chooses the one with what they consider to be the highest likely payoff. This is a very different starting point for how a decision is made as it puts the individual on an entirely different utility function. Figure 5 Prospect theory combines two utility curves Losses Value Gains Outcome Because the reference point for decision making is defined by the individual, a fund manager could anchor their decisions around the entry price to a stock or index rather than reviewing that reference point and anchoring their decision around a new fair value of a stock. This shows how, perhaps counterintuitively, individuals can be more risk seeking when they have incurred losses this has been referred to as a case of get evenitis because their certain outcome is a loss. Therefore, they are willing to take the risk of holding on to the stock rather than realising the loss, in the hope that the stock price will rise and the loss will reduce or the position will break even. This also leads to individuals being more risk averse when they have profit making positions within their portfolios to crystallise the gains. Another set of terminology that captures this is pride versus regret and, unfortunately, regret can be the strongest emotion in driving our decision processes. Reference point Source: Invesco Perpetual. For illustrative purposes only. This is illustrated in figure 5, which captures prospect theory. Instead of an individual being defined by one type of utility curve, there are two utility curves joined together. These reflect a different decision being made dependent upon the starting point, the outcome of the editing and then subsequent evaluation phase for that particular decision. When a loss has been incurred, the theory hypothesises that individuals tend to reflect the behaviour of a risk-seeking individual as described previously (illustrated by a convex utility curve) in the hope that they will close their losses. When a position is in profit they tend to cut that position sometimes too early because they become risk averse. The certain outcome is a profit and they would rather take that than risk losing some of the profit in the hope of further gains. One final part of prospect theory is our tendency to give too much weight to small probabilities. This is where the decision weights play a role in how individuals make their decisions and is not merely a calculation of the probability of an event versus the payout should that event take place. If the reference point for a trade is a loss then because of the tendency to seek pride and avoid regret, having a distorted reference point means that the investor may place too much weight on the probability of an event happening as they seek to close a loss on a particular position. Decision weights again are subjective and therefore are a behavioural bias, which can clearly influence how fund managers make decisions for portfolios. Decision weights can influence an outcome markedly. Look at the calculation below (figure 6). By merely attaching a higher decision weight to an outcome in a loss-making position, individuals can be encouraged to take far more risk than perhaps they should. Figure 6 Calculation showing influence of decision weight to an outcome in a loss-making position Utility theory Utility of Probability Calculated utility Outcome based on outcome of outcome based on total level of wealth ($) (risk seeking) occurring (%) probabilities 1 Decision Sell the stock Prospect theory Utility of Probability Calculated utility Bias the decision Outcome based on outcome of outcome based on with a decision Revised utility change in wealth ($) (risk seeking) occurring (%) probabilities 2 Decision weight calculation 3 Decision Sell the stock Hold the stock (0.9*80%) + (1.2*20%) 2 (-1*80%) + (2*20%) 3 1(-1*80%) + 3(2*20%) Source: Invesco Perpetual. For illustrative purposes only. 04 Behavioural finance and portfolio construction

5 Practical applications to try and avoid our own behavioural downfalls All of the observations above have a number of consequences for the fund management industry. It is important to distinguish between difference types of products and different approaches to investing when assessing what is most appropriate. However, we all have a responsibility to our clients to try and eliminate some of these behavioural biases from our processes. 1. Subjective reference point Within the Invesco Perpetual Global Targeted Returns strategy, we attempt to reduce some of these behavioural biases through the way in which we have constructed our Multi Asset investment team at Invesco Perpetual. Firstly, we have three joint fund managers. This is incredibly important for the way in which decisions are made. With reference back to the factors that underpin prospect theory, we all have different utility functions based on different reference points. As individuals within the team, we can all bring an idea to the table for consideration for the portfolio, but all three fund managers must agree that an idea should be put into the portfolio. With that in mind, the sponsoring fund manager may have a reference point which is anchored around the current price relative to the value of that idea on the day it went into the portfolio. If that idea loses money, then that individual may have a risk-seeking bias and a clear case of get evenitis for holding on to that idea until it breaks even or moves into profit. However, one of the other fund managers may have a reference point that is more neutral or anchored around the aggregate performance of the portfolio. Therefore, they may have a higher tolerance for realising a loss and removing the idea from the portfolio, if the drivers that underpin that idea have meaningfully changed. One investment idea that could serve as an example of how the team structure does not allow for get evenitis was our UK versus Swiss equities idea. Here we believed that in a rising equity market, the more cyclical UK market would outperform its more defensive Swiss counterpart. We also thought the Swiss currency looked expensive and would prove a drag for Swiss corporates. However, as shown in figure 7, the idea moved against us and was losing money for the strategy s portfolio. The idea was reviewed regularly by the team and while we continued to believe in the fundamentals that backed the idea, our conviction in the idea gradually reduced and we reduced exposure to the theme accordingly locking in losses and reducing risk in line with conviction rather than trying to recoup losses. Then, at the beginning of this year, a number of market dynamics changed significantly. The impact of the falling oil price was increasing deflationary pressures around the world and the European Central Bank was all but committed to launching quantitative easing. Most significantly, Swiss National Bank (SNB) shocked markets by moving to unpeg the Swiss Franc from the euro. This move by the SNB changed everything about the idea and a sharp move lower in Swiss equities meant that the idea regained about half of recent losses in the idea in one morning. We then removed the idea from the strategy s portfolio as the two- to threeyear outlook had completely changed. Figure 7 FTSE 100 Index vs Swiss Market Index Idea reviewed Relative performance Idea enters portfolio Idea removed Mar May Mar 0.65 Source: Invesco Perpetual and Bloomberg as at 31 March Behavioural finance and portfolio construction

6 Figure 8 Euro vs US dollar idea Review and implementation Idea approved and added to fund Idea reviewed Euro strengthens despite weakening fundamentals Mar May Implementation changed Mar 1.00 Source: Invesco Perpetual and Bloomberg as at 31 March 20. One of the team s currency ideas also demonstrates how the team s approach influences the adoption and implementation of ideas. We introduced a long position in the US dollar versus the euro at the beginning of May 20 (see figure 8). We had looked at the idea previously, but didn t fully understand the drivers behind why the euro continued to rise despite the obvious divergence of the US and European economies. Having identified that the currency was probably being supported by foreign central banks diversifying holdings away from the dollar, when we saw this trend petering out, we introduced the idea into the strategy s portfolio. The idea worked well and the team reviewed the idea a number of times to ensure that potential returns were still sufficient to justify its place in the portfolio. When the euro went through the team s fair value, rather than closing the idea, we moved the implementation into the forward space. The currency s continued fall meant this too was reviewed and the idea is now implemented using an options structure that is intended to earn a premium, even if the euro does not depreciate much further from here. The freedom to structure an idea in a different way means the team s reference points can change and an idea can remain relevant, even after significant outperformance of the market that the team is exposed to. The temptation to close an idea too soon can be overcome through having repeated team reviews and adopting a flexible approach to implementation. 2. Probability of events occurring The decision weights and tendency to place too much weight on small probabilities is also an important consideration. If a position is loss making but the fund manager believes in the risk of a particular scenario playing out over time, they may bias their decision making by placing a high weighting as to the probability of the scenario, thus influencing how tolerant they are of a loss-making position, or how far they want to run the profit-making positions within the portfolio. Given these decision weights are subjective, having different people in the room with different subjective starting points is important for discussions around the construction of an absolute return portfolio. In addition, the scenario testing part of our process does not involve applying a probability to a scenario playing out over time. If a scenario is worth testing because it is possible, even if it is not probable, then it is worth testing the portfolio against that potential risk. We do this independently across all of the scenarios which we construct, as opposed to assigning a particular probability weight to each scenario. This removes any bias towards a particular scenario impacting the portfolio going forward (see our white paper Risk management in Multi Asset investing for further discussion of our risk management and scenario testing analysis). Figure 9 Invesco Perpetual Multi Asset Investment team - hypothetical scenarios Scenario Characteristics Commodity Glut Oil price falls, S&P 500 index rallies (+20%), Brazilian real weakens (-20%) China Bust Hang Seng China Enterprises index underperforms S&P 500 (by 20%), volatility spikes (VIX index to 50), South African bond yields up (+300bps) International QE Yen falls ( /US$ to 125), French yields 1 fall to Japanese levels Foreign Policy Failure Oil prices rise (+20%), Polish zloty falls (-%) Cash is King S&P 500 index falls to 1000, yield on US 10-yr Treasuries rises to 5% Melt Up US equities up 10%, Brazilian equities rise (+50%) 2 Recession 20 S&P 500 index falls to 1000, German bund prices rise (yields to 0.4%) 1 As measured by 10 year OAT futures. 2 As measured by Ibovespa. 06 Behavioural finance and portfolio construction

7 3. Managing risk within an idea as well as at the portfolio level The probability and decision weights issue also feeds into the way we manage risk both at an idea level and at a portfolio level. Some multi asset portfolios are constructed using a core holding of strategic views and then a buffer is allocated around it to manage downside risk sometimes termed a tactical overlay. We do not think about the Invesco Perpetual Global Targeted Returns strategy in this way. Rather, we focus on managing the risk of an individual idea with regards to implementing it in the most efficient way and a consideration of the idea still working should our core scenario not play out. As an example (see figure 10), we have added a buffer to some of our equity ideas using a put options structure. The options should provide a positive return if equities sell off, but this approach also makes us think very carefully about cost and about not tilting the portfolio to one particular risk scenario, which can prove very costly (again with regards to placing undue weighting towards low probability events dependent upon the original reference point). Every one of our ideas has to deliver a positive return in our central scenario to get approved for the portfolio and the return projection also needs to be positive once any cost of managing the downside risks has also been taken into account. Figure 10 Global equity idea to include a put option structure to manage downside risk Jun Aug Oct MSCI World (LHS) Eurostoxx put option structure (RHS) Dec Source: Bloomberg as at 31 March Quantitative versus qualitative The use of quantitative techniques can also reflect an initial behavioural bias, which perhaps feels counterintuitive. However, if analysis is solely anchored around a single reference period, which one individual believes is most representative of conditions for markets going forward, then that is potentially dangerous for a portfolio. This is why, within the structure of our processes, we combine quantitative techniques with qualitative analysis in order to challenge and analyse why a model is suggesting a particular outcome. It may be more intuitive to think of quantitative modelling as a way of removing behavioural biases from a process but all models are built upon a number of set assumptions. The individual who sets these assumptions and builds the quantitative model could potentially introduce a systematic bias into the analysis of asset prices. By challenging this quantitative output at various points in the process, with challenges coming from different individuals with different biases built into their own analysis, we hope to go some way to mitigating these behavioural risks in our underlying process. As one example of this, we not only carry out principal components analysis, as illustrated in figure 11, to analyse the dominance of any one particular factor on the return profile of the strategy portfolio, we also qualitatively assess which themes we believe are running through the portfolio at any one time. An example of these is shown in figure 12. Figure 11 Factor analysis of the Invesco Perpetual Global Targeted Returns strategy 10 factors explain 70.4% of strategy returns Source: Invesco Perpetual. Chart data covers 180 weeks to 31 uary 20. For illustrative purposes only. 07 Behavioural finance and portfolio construction

8 Figure 12 Themes we believe are playing out in the Invesco Perpetual Global Targeted Returns strategy s ideas Idea Theme 1 Theme 2 Theme 3 Theme 4 European Curve Flattener Euro corp strength Credit term premium Loose EUR monetary policy High Yield Credit alpha Global growth Search for yield Indian Rupee vs Chinese Renminbi India growth EM reform Search for yield China econ weakness Norwegian Krone vs UK Pound Strong oil UK econ weakness Fiscal sustainability US Dollar vs Canadian Dollar Strong USD Weak commodities Canada econ weakness US Dollar vs Euro Strong USD Weak EUR Loose EUR monetary policy European Divergence European growth German corp strength French corp weakness Italian corp weakness Global Global corp strength Global growth Cyclical equities Selective Asia Exposure Asian growth Cheap Asian equity vol Australian econ weakness Commodity weakness Sell Puts as Long DAX German corp strength Global growth Weak EUR Cheap bank volatility Sell Puts as Long US Equity Global growth US corp strength UK Global growth UK corp strength Cyclical recovery Strong commodities/oil US Large Cap vs Small Cap Valuation gap large/small US econ weakness Short UK inflation UK econ weakness Global disinflation Australian vs Europe Australian econ weakness Global disinflation Europe reflation Japanese Curve Flattener Japanese recovery Japanese deflation Selective EM Local Currency Debt Search for yield EM growth Weak USD JPYKRW Korean econ weakness Japan strength UK vs France UK econ weakness UK disinflation French disinflation French credit weakness Asian Equities vs US Equities Cheap Asian equity vol Asian econ weakness US strength/stability AUDJPY vs USDJPY Australian econ weakness Weak commodities US strength/stability UK Equity vs Rates Reduced rates vol UK corp weakness UK disinflation Source: Invesco Perpetual, as at 28 February 20. Colour scheme highlights themes which we believe are related. Conclusion Thaler s 1999 prediction that behavioural finance would go mainstream has come true, possibly faster than he expected. In this paper, we have described how utility theory and, more recently, prospect theory have implications for fund manager behaviour in the investment industry. The team behind the Global Targeted Returns strategy at Invesco Perpetual was intentionally designed to incorporate multiple viewpoints (and therefore reference points in behavioural finance theory). Also, while making use of extensive quantitative analysis, it blends this with qualitative judgement. We hope that this should help prevent the strategy being guided by any one dominant behavioural bias and enable it to deliver its targeted, risk-adjusted returns over time. Important information This document is for Professional Clients and is not for consumer use. All date is sourced from Invesco Perpetual as at 31 March 20, unless otherwise stated. The value of investments and any income will fluctuate (this may partly be the result of exchange rate fluctuations) and investors may not get back the full amount invested. Past performance is not a guide to future returns. Where Invesco Perpetual has expressed views and opinions, these may change. Where securities are mentioned in this document they do not necessarily represent a specific portfolio holding and do not constitute a recommendation to purchase, hold or sell. Invesco Perpetual is a business name of Invesco Asset Management Limited Perpetual Park, Perpetual Park Drive, Henley-on-Thames, Oxfordshire RG9 1HH, UK Authorised and regulated by the Financial Conduct Authority 585/PDF/04 UK