A stylized model of home buyers’ and bankers’ behaviours during the 2007-2009 US subprime mortgage crisis: a predatory perspective

ABSTRACT

We examine the behaviour of market agents during the years leading to the 2008 US subprime mortgage crisis using a stylized capital asset pricing model model. In our study, an average investor eager to make money by flipping houses meets a banker who offers him subprime mortgage deals. We refer to recent research that shows the mechanics of the psychological and behavioural components of these two market agents. In particular, much in line with the famous Stanford experiment, it is assumed that investors adopt a predator or a prey position. Our analysis shows that, given a historical tendency towards financial predatory acts on the part of market agents (including buyers), government regulations should be adapted and strengthened to face this dooming reality.

KEYWORDS:

• Behavioural finance
• predatory mortgages
• stylized CAPM
• market bubbles
• crashes

JEL CLASSIFICATION:

• D84
• D81

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ See studies showing the neurobiological correlates of the predator–prey positions (Mesly 2013, 2014; Mesly 2015).

² Buyers can also at times act as financial predators by misleading the lenders (see Cowen 2008).

³ Note: For all intents and purposes, the graph is bounded by an upper time limit of 2.3. The mathematical reasoning for this assumption can be provided upon request.

⁴ The Utility Predatory curve expresses the fact that investor J finds a certain utility by developing predatory behaviours given market risks and his own risk. A Utility Predatory curve meets the five characteristics of utility curves: (1) no quantities of risk – market or individual – are negative; (2) more is always preferred to less; (3) they use an ordinal measure; (4) they can be associated with a budget constraint; (5) they cannot cross each other.

⁵ Note: J is only active on a small portion of the Utility Predatory curve. The mathematical reasoning can be provided upon request.

⁶ Where k = 1.3. The mathematical reasoning can be provided upon request.

⁷ If this did not hold true, we could not infer on the rest of the behaviours that we shall examine.

⁸ The derivative will be used further along in this article.

⁹ For all intents and purposes, this is the only point of interest as, at that point, as we will proceed to show, J maximizes his position in all respects.

¹⁰ In either case, there is potential predator/prey interplay: taking advantage of a position (out of fear) to gain an advantage (predator) or withdrawing from a position (out of fear) (prey).

¹¹ J can adopt any of these profiles over time; the market at large is considered to consist of an aggregate of these three investors’ profiles.

¹² Note that the addition or subtraction of a factor such as ε is in line with the well-known build-up method used to estimate the required return of an asset (Pinto et al. 2010).

¹³ At Ψ = 1, J suffers from total blind trustfulness.

¹⁴ Recall that Sharpe (1991) had a similar provision in his version of the CAPM model, variable τ_m standing for ‘societal risk tolerance’. See also Dawson (2015).

¹⁵ The formula is similar to the one found in past research (Mesly, 2015, 2014): Cooperation (or decision to invest) = 0.3 (initial trust endowment or, put differently, r_f, within the upper limit of the model set at 2.3) + 0.9 Trust + ε, where 0.9 = 3 × (k–1). Trust = self-confidence in ability to make money. The mathematical reasoning can be provided upon request.

¹⁶ The chaos function follows a logistic map function in the form of Panic_t+1 = k Panic_t (1–Panic_t) where t is time. Within the boundaries set by our model, ε = the Feigenbaum value, or twice the upper limit of 2.3 (2.3 for σ_m and 2.3 for σ_J). The mathematical reasoning can be provided upon request.

¹⁷ Note: we can calculate the exact slope of both F_ne and F_nx curves because we know the shape of the Utility Predatory curve (see further in the article) and we know that its lowest point corresponds to y = 0 for the Panic curve. The mathematical reasoning can be provided upon request.

¹⁸ The system is closed (in the sense used in dynamic systems theory) because J operates on a finite time horizon. The mathematical reasoning can be provided upon request.

¹⁹ In our model, this curve has the function: S(x_J) = −2k^1/2 + 2k/x + x = −2.28 + 2.6/x + x, within the boundaries set at 2.3 with k = 1.3. The S(x_J) is related to the Utility Predatory curve, which is the geometric resulting curve between the Budget curve and this Satisfaction curve. The mathematical reasoning can be provided upon request.

²⁰ Research has shown that the positivity bias increases with age (Mesly 2015). Furthermore, J is likely financially illiterate (Gorton 2008; Tremoulinas 2009; Wang 2009; Gayraud 2011).

²¹ The predator–prey model can be used in other types of interactions: equal-to-equal, buyer–seller, supervisor–supervisee, etc. Here, we show the interaction between the naïve investor J and a sneaky banker J₂.

²² In fact, there are a number of possibilities where J and J₂ can meet, depending on the capacities of each. In Figure 7, it is assumed that J and J₂ have equal capabilities and weaknesses. This point is called a dynamic POE. At all points where J and J₂ meet along the contract curve (see Varian 2006), there is Pareto efficiency. There is no reallocation between DI and Trust that could make J better off without making J₂ worse off, and vice-versa.

²³ A political example of such equilibrium is the episode of the Bay of Pigs opposing two super-powers: both the US and the Soviet Union had the capacity to destroy the arch-rival enemy, however destroying oneself by the same token.

²⁴ Recall that once J faces J₂, the timeline goes both ways: left to right (initially from J’s perspective) and right to left (initially from J₂’s perspective). Hence, the Edgeworth box displays the fact that J can have an effect on J₂’s agenda, and J₂ could possibly have an effect on J’s agenda. In a predatory situation, J₂ imposes his agenda upon J.

²⁵ This is equivalent to taking the r_f rate, established at 0.3 in the original model by Mesly (2015), out of k, the reasoning being that this value corresponds to the initial trust endowment a person has towards another. This is like saying that the first person considers the second as being at a minimal risk, expressed by the level of 0. The mathematical reasoning can be provided upon request.

²⁶ Interestingly, the ln of 5% is ln 0.05 = −3, which is −10 × k.

²⁷ Recall that this curve stems from the original Utility Predatory curve which displays the fact that at all points in time J is equal to himself. So, even though J seems greedy at times, and he appears to become increasingly irrational, the bottom line from his perspective is that he endeavours to remain equal to himself, given the information I he has.

²⁸ This would be in line with De Bondt and Thaler (1985)’s findings on the ‘winner–loser’ effect. This phenomenon cannot be explained by risk σ, but by Ψ as it gets powered by predatory acts.

²⁹ That he does not become a prey to market forces. Hence, J has truly entered into a predator/prey dynamic by way of J₂’s predatory actions.

³⁰ Reference is made, of course, to Ulysses.

³¹ They are often illiterate, poor, from a disadvantaged ethnic background, and older.

³² De Bondt (1993) study indicates that over confidence leads to a narrower focus, so that J is increasingly limited, by the reduction in width and depth of his portfolio. He may for example focus solely on residential homes, and residential homes of a certain type, as opposed to investing in various venues to spread the risk. Odean (1999) posits that overconfidence reduces the perception of real risk. J is becoming increasing blind, because he has trusted and keeps trusting J₂.

³³ This entails that the market is filled with investors fearing to miss the opportunity to enter the market.

³⁴ De Bondt (1993) study points towards a similar observation: disagreement among investors is stronger in bear markets than in bull markets.

³⁵ Our analysis might be viewed as complementary to Dawson (2015).

³⁶ Recall that the Utility Predatory curve contrasts σ_m and σ_J and includes the constant k = 1.3.

³⁷ At the absolute limit, σ would be over 3.3, but then, at that point, there would be nobody left in the market, and hence, no market at all.

³⁸ For an application of the proposed stylized model, see Appendix.

³⁹ It is based on information’s three fundamental characteristics: time line (horizon and cycles); gamma (γ) and lambda (λ) curves (not discussed in this article – see Mesly 2015); and risk (internal and external). The HPI was calculated for the years ranging from 1971 to 2012 in the US market (see Mesly 2015).

⁴⁰ Note: when testing on the database we used to develop the CMFP, k = 1.35 for some 1700 individual participants; and when taking extremes out, k = 1.13 and the correlation coefficient = 37%.

⁴¹ The mathematical reasoning can be provided upon request.

⁴² We insert a ‘+ ’ sign because J wants to minimize his loss.

⁴³ This analysis reports results that are in line with a recent neurobiological study showing that fear of an unknown predator (chaotic market) elicits stronger reactions than fear of a known predator (see Mesly 2015).

⁴⁴ In fact, based on the HPI, the next extreme financial crisis would be anticipated in 2042–2043.