14.9 Psychology with formal models · M14 Portfolio and going live

Motivation

SEBI's FY26 study found that 87.7% of individual F&O traders lost money (M01 · 1.11 Case 1 has the study and its numbers). Low skill and high costs explain much of it (M01, M04). The rest is behaviour that formal models predict well. Knowing the model does not remove the bias, but it tells you which rule in your plan counters which bias.

14.9.1Prospect theory#

Setup

Kahneman & Tversky ("Prospect Theory: An Analysis of Decision under Risk", Econometrica 47(2), 1979) and Tversky & Kahneman ("Advances in Prospect Theory: Cumulative Representation of Uncertainty", Journal of Risk and Uncertainty 5(4), 1992, 297–323). Outcomes are evaluated as gains and losses $x$ relative to a reference point (often the purchase price), not as final wealth.

Value function

v(x) = \begin{cases} x^\alpha, & x \ge 0,\\ -\lambda(-x)^\beta, & x < 0,\end{cases}

with median estimates $\alpha = \beta = 0.88$ and loss aversion $\lambda = 2.25$ (Tversky & Kahneman 1992, as reported in standard secondary sources). Properties: concave over gains (risk-averse), convex over losses (risk-seeking), steeper for losses (a kink at 0).

Probability weighting

w(p) = \frac{p^\gamma}{(p^\gamma + (1-p)^\gamma)^{1/\gamma}},

with $\gamma = 0.61$ for gains and $\delta = 0.69$ for losses. Small probabilities are overweighted and moderate-to-large ones underweighted: $w(0.01) = 0.055$ , $w(0.05) = 0.132$ , $w(0.5) = 0.421$ , $w(0.9) = 0.712$ . The fixed point $w(p) = p$ is at about $p = 0.34$ . In the cumulative version, weights apply to decumulative probabilities (ranks of outcomes), separately for gains and losses.

Consequences you can compute

Loss aversion. For a 50/50 bet that loses ₹100, the smallest acceptable gain $G$ solves $0.5G^{0.88} = 0.5 \times 2.25 \times 100^{0.88}$ , so $G = 100 \times 2.25^{1/0.88} = \text{₹}251$ . With the weighting function it is ₹274. A trader with these preferences refuses fair and even favourable bets, and, symmetrically, cannot bring himself to take a small certain loss (a stop) when the alternative is a gamble that might get back to even.
Lottery preference. A ₹1 bet paying ₹100 with probability 0.5% has expected value −₹0.50. Its prospect value is about −0.05 (with $v$ and $w$ above), close to indifference: probability weighting makes a deeply negative-EV lottery feel almost fair. Far out-of-the-money short-dated options are such lotteries. In SEBI's FY26 study 59% of index-option turnover was in zero-days-to-expiry contracts (M01 · 1.11 Case 1). Barberis & Huang ("Stocks as Lotteries: The Implications of Probability Weighting for Security Prices", American Economic Review 98(5), 2008) show how this preference leads investors to overpay for positively skewed assets.

14.9.2The disposition effect#

Definition

The tendency to sell winners too early and hold losers too long (Shefrin & Statman, "The Disposition to Sell Winners Too Early and Ride Losers Too Long: Theory and Evidence", Journal of Finance 40(3), 1985).

Proposition 14.15Prospect theory implies disposition

Let the reference point be the purchase price. A position has paper P&L $z$ and will next move $\pm h$ with equal probability, with $0 < h < |z|$ (so the gamble does not cross the reference point). Evaluate with $v$ and equal decision weights. If $z > 0$ the investor strictly prefers to sell; if $z < 0$ he strictly prefers to hold.

Proof

Holding is worth $\tfrac12v(z + h) + \tfrac12v(z - h)$ ; selling is worth $v(z)$ . For $z > h > 0$ both outcomes are gains, where $v$ is strictly concave ( $\alpha < 1$ ); Jensen gives $\tfrac12v(z+h) + \tfrac12v(z-h) < v(z)$ : sell. For $z < -h < 0$ both outcomes are losses, where $v$ is strictly convex ( $\beta < 1$ ); Jensen gives the reverse inequality: hold.∎

The test test_disposition_effect checks this with $z = \pm10$ , $h = 5$ (hold minus sell: −0.11 after a gain, +0.24 after a loss), and that with linear utility and $\lambda = 1$ the investor is indifferent. When the gamble crosses the reference point the kink matters: with $z = -1$ , $h = 5$ the investor prefers to sell, because the chance of a larger loss is weighted by $\lambda$ . Barberis & Xiong ("What Drives the Disposition Effect? An Analysis of a Long-Standing Preference-Based Explanation", Journal of Finance 64(2), 2009) show that in a full dynamic model prospect theory over annual gains does not always produce the effect; "realisation utility" (pleasure or pain at the moment of selling) is an alternative explanation. The behaviour is robust even where the explanation is debated.

Evidence Odean ("Are Investors Reluctant to Realize Their Losses?", Journal of Finance 53(5), 1998, 1775–1798) studied about 10,000 accounts at a large US discount broker. Define

\text{PGR} = \frac{\text{realised gains}}{\text{realised gains} + \text{paper gains}}, \qquad \text{PLR} = \frac{\text{realised losses}}{\text{realised losses} + \text{paper losses}},

counted on days when the investor sells something. He found PGR ≈ 0.148 against PLR ≈ 0.098: winners were realised about 1.5 times as readily as losers. (Secondary sources disagree on whether these are full-year or non-December figures; in December the ordering reverses, PGR 0.108 against PLR 0.128, consistent with tax-loss selling.) He also reports that the winners investors sold went on to do better than the losers they kept, so the behaviour was costly, not informed.

Indian tax angle (as of FY 2026-27, verify) Listed equity with STT paid: short-term gains (held ≤ 12 months) taxed at 20%; long-term at 12.5% above ₹1.25 lakh a year. Realising losses offsets gains; holding losers and selling winners is tax-inefficient as well as behaviourally biased.

Countermeasures (i) Exits are decided before entry (stop and target in the plan), not at the moment of decision. (ii) Review positions as if newly buying them: "would I open this position at today's price?" (iii) Track your own PGR and PLR from the journal.

14.9.3Overconfidence and overtrading#

Model A trader receives a signal and trades if the perceived edge per trade exceeds the round-trip cost $c$ . The true edge is $e$ ; the overconfident trader perceives $\kappa e$ with $\kappa > 1$ (he overestimates the signal's precision). Over a range of signals with $e < c < \kappa e$ , he trades with negative expected net return $e - c$ . Expected net P&L is (number of trades) × (average $e - c$ ), so losses scale with turnover. Indian round-trip costs for intraday equity are about 0.083% before slippage (M01 · 1.7, with a typical ₹20-per-order brokerage; rates as of 6 Nov 2026), so a setup with 5 bp gross edge loses about 3 bp a trade.

Evidence Barber & Odean ("Trading Is Hazardous to Your Wealth", Journal of Finance 55(2), 2000) studied 66,465 US households, 1991–96: the most active traders earned 11.4% a year net against 17.9% for the market. In "Boys Will Be Boys" (Quarterly Journal of Economics 116(1), 2001) men traded 45% more than women, which cut their net returns by 2.65 pp a year against 1.72 pp for women. In Taiwan, fewer than 1% of day traders predictably earned positive abnormal returns net of fees (Barber, Lee, Liu & Odean, Journal of Financial Markets 18, 2014). In Brazil, 97% of individuals who day-traded mini-index futures for more than 300 days lost money (Chague, De-Losso & Giovannetti, 2019/2020). In India, SEBI's FY23 intraday study found that 71% of individual intraday traders lost money, and 80% of those with more than 500 trades a year (M01 · 1.11 Case 1).

Countermeasures A maximum number of trades per day; only pre-defined setups; a cost line in every journal entry; and the statistical graduation test of 14.10, which overconfidence cannot argue with.

14.9.4Douglas and Steenbarger: process over outcome#

Mark Douglas (Trading in the Zone, 2000) argues for thinking in probabilities. His "five fundamental truths", as consistently summarised in secondary sources: anything can happen; you do not need to know what will happen next to make money; there is a random distribution between wins and losses for any given set of variables that define an edge; an edge is nothing more than an indication of a higher probability of one thing happening over another; every moment in the market is unique. In this course's language: each trade is one draw of an R-multiple from a distribution with positive mean (if you have an edge) and large variance. Judging a decision by a single outcome is judging a distribution by one sample. The exercise attributed to him in summaries, taking a fixed sample of trades of one setup at fixed risk without discretion, is exactly the experimental design of 14.10.

Brett Steenbarger is a clinical psychologist and trading coach (described by his publisher as at SUNY Upstate Medical University). His Wiley books include The Psychology of Trading, Enhancing Trader Performance (2006; on a structured process of expertise development), The Daily Trading Coach: 101 Lessons for Becoming Your Own Trading Psychologist (2009) and Trading Psychology 2.0: From Best Practices to Best Processes (2015). The subtitles carry the message used here: the trader studies his own performance data and improves processes, rather than waiting for motivation.

14.9.5Journaling and review#

A journal is a dataset. Design it so that the review questions can be answered by a query.

Per trade, before entry date/time; instrument; setup name (from a fixed list); thesis in one sentence; entry, stop, target; size and 1R in rupees; planned holding period; market regime tag; confidence (1–5); state (sleep, stress, after a loss?). Per trade, after exit: exit price and reason (stop, target, time, discretionary); R-multiple; costs in rupees and in R; slippage versus planned prices; rule adherence (yes/no for each rule); one line on what you would repeat or change.

Weekly review expectancy and its standard error by setup; win rate; average win and loss in R; costs as a fraction of gross P&L; P&L of rule-following versus rule-breaking trades (the most informative split); PGR/PLR; maximum daily loss; number of limit breaches. Monthly review: compare live statistics with backtest statistics (14.10); review the largest three losses and largest three wins for process, not outcome; decide one change, written down, and test it separately.

Separate decision quality from outcome. A trade that followed the plan and lost 1R is a good trade. A trade that broke the plan and made 3R is a bad trade that was rewarded, which is the most dangerous kind because it reinforces the rule-breaking. Annie Duke's Thinking in Bets (2018) is a readable treatment of this distinction.