Behavioural finance

Level 1 Plain words

For every reader: the idea in plain words, no formulas.

Good investors, costly habits

Most money mistakes come from ordinary instincts working in the wrong place. Running from danger helps on a mountain path and hurts in a falling market, where selling after a drop locks in the loss just before a recovery. Following the crowd works for finding a good restaurant and fails when the crowd is buying a stock because its price went up. Intelligence does not protect anyone; Isaac Newton is said to have lost heavily in the South Sea bubble of 1720, though the famous quote attached to the story cannot be traced to him. What helps is a set of rules made in a calm moment and followed in a frantic one.

Losses hurt more than gains please

Offer people a coin toss that wins $150 on heads and loses $100 on tails, and most refuse. The bet is in their favour: on average it pays $25 a toss. They refuse because losing $100 feels worse than winning $150 feels good. Kahneman and Tversky called this loss aversion, and their later estimate is that a loss weighs about 2.25 times as much as an equal gain. For an investor it means a portfolio checked every day feels painful even when it grows, because about half of all days are down days.

Crowds, stories and bubbles

A bubble starts with something real: a new technology, a new market, cheap credit. Prices rise, early buyers make money, and their success becomes a story that draws in people who never cared about the asset before. At some point buyers are paying because they expect someone else to pay more. When the supply of new buyers runs out, prices fall faster than they rose. The pattern has repeated for three centuries with different assets and the same sequence.

Level 2 How it works

For readers who want the mechanism, with the diagrams.

Beginner path stops here

Prospect theory

Classical finance assumes people judge outcomes by their final wealth and dislike risk in a smooth way. Kahneman and Tversky (1979) found four departures in their experiments. People judge gains and losses against a reference point, often the price they paid, and not against total wealth. Losses loom larger than gains. Sensitivity falls with size: the step from $0 to $100 feels bigger than the step from $1,000 to $1,100, which makes people cautious with gains and willing to gamble to avoid a sure loss. And people overweight small chances, which is why lottery tickets and deep out-of-the-money options sell well. In 1992 Tversky and Kahneman put numbers on the curve: curvature of 0.88 for both gains and losses and a loss-aversion coefficient of 2.25.

A field guide to the common biases

Each line has a research literature behind it, and the costs overlap. The disposition effect and anchoring often travel together, since a purchase price serves as both reference point and anchor.

The behaviour gap

Funds report a time-weighted return, what a dollar left alone for the whole period earned. Investors earn a dollar-weighted return, which counts how much money was in the fund when. If people add money after good years and pull it after bad ones, their dollar-weighted return falls short of the fund's. Morningstar measures this every year in a study called Mind the Gap; its 2024 edition put the shortfall near one percentage point a year across US funds over the ten years to 2023. The gap is smallest in plain allocation funds and widest in narrow, volatile ones, which is where people trade most.

How bubbles form

Charles Kindleberger, building on Hyman Minsky, described a sequence that fits most bubbles. A displacement (a new invention, a war's end, a change in policy) opens a real opportunity. A boom follows, usually fed by credit. Euphoria arrives when price gains themselves become the reason to buy and lending standards slip. Insiders and early holders start to sell, a phase of distress. Then a trigger, often small, turns selling into panic and prices overshoot downward. Shiller adds that each bubble carries a story that explains why this time the old valuation rules do not apply.

Why prices can stay wrong

If bubbles are visible, why do professionals not sell them down? Andrei Shleifer and Robert Vishny (1997) called the reason the limits of arbitrage. A short seller who is right about the end can still lose everything before it arrives, because a mispricing can widen first and lenders demand collateral as it does. Fund managers who bet against a bubble lose clients while it inflates. John Maynard Keynes's remark that markets can stay irrational longer than you can stay solvent is widely attributed to him, without a clear source, and states the problem well. So mispricing survives, and individuals face it with less staying power than professionals do.

Guards that work

What helps most is boring. An investment policy statement written in advance sets the mix, the rebalancing rule and the conditions under which the plan changes. Automatic contributions and automatic rebalancing take the decision out of the moment. Checking less often cuts the pain of loss aversion, as Level 3 shows. A broad index fund removes most of the room for overconfidence. Deciding ahead of time to harvest losses each December turns the disposition effect around. None of this makes an investor smarter; it moves the decisions to a time when they are easier.

Level 3 The math

For Series 65 and CFA readers: formulas and worked examples.

Series 65 path stops here

The value function

Tversky and Kahneman (1992) fitted a value function with a kink at zero.

In words, a gain's felt value is the gain raised to a power below one, and a loss's felt value is minus the loss-aversion coefficient times the loss raised to a power below one.

Myopic loss aversion: how often you look

Shlomo Benartzi and Richard Thaler (1995) joined loss aversion to how often investors check their accounts. For an asset with a yearly mean of 10 % and a standard deviation of 20 %, the chance that a single period shows a loss falls as the period lengthens, because the mean grows with time and the standard deviation only with its square root.

In words, the chance of a loss over a period is the normal probability of falling more than the period's mean, measured in the period's standard deviations, below zero.

The last column weights losses 2.25 times and gains once, with no curvature. A daily checker of this asset feels worse off on average with each look, though the asset earns 10 % a year; a yearly checker feels better off. Benartzi and Thaler estimated that investors evaluate their portfolios about once a year, which made the historical equity premium consistent with loss aversion.

Probability weighting and lottery-like assets

Prospect theory also bends probabilities. People treat a 1 % chance as if it were larger and a 99 % chance as if it were smaller. Tversky and Kahneman (1992) fitted a weighting function with one parameter $\gamma$, about 0.61 for gains.

In words, the decision weight of a chance is the chance raised to a power, divided by a scaling term that keeps the weights between zero and one.

The disposition effect in dollars

Odean (1998) measured the habit in about ten thousand accounts at a discount broker from 1987 to 1993. Investors realised 14.8 % of the gains available to them and 9.8 % of the losses, a ratio of 1.5. The pattern reversed only in December, when tax-loss selling peaked. Worse for the habit, the winners investors sold went on to beat the losers they kept over the following year.

Trading, overconfidence and the gap

In words, the yearly return lost to trading is about the share of the portfolio traded in a year times the cost of a sale and a purchase.

Brad Barber and Terrance Odean (2000) found that the fifth of households who traded most earned about 11.4 % a year from 1991 to 1996, against 17.9 % for the market. A behaviour gap of one point a year compounds the same way: $100,000 earning 7.3 % for ten years ends at $202,301, and at 6.3 % it ends at $184,218, $18,082 less.

What a bubble price asks of the future

A price can be tested against what it implies. Suppose a stock trades at 100 times earnings and a buyer wants 9 % a year for ten years, after which the stock trades at a more ordinary 20 times earnings. Ignoring dividends, earnings must grow at $g$ where $(1+g)^{10} \times 20 = 100 \times 1.09^{10}$.

In words, the growth needed is the required return compounded over the years, times the fall in the multiple, taken to the root of the number of years, less one.

At these inputs earnings must grow 28.0 % a year for a decade. Few large companies have ever done that, which is the arithmetic behind most bubble warnings. A crash brings its own arithmetic: after a fall of $d$, getting back to even needs a gain of $1/(1-d) - 1$, so a 50 % fall needs a 100 % gain. Chapter 10 builds the same test from the Gordon model.

Level 4 History, analysed

For readers who want past episodes run through the Level 3 math.

The South Sea Company, 1720

Every phase is there. A scheme to swap government debt for company shares supplied the displacement. Credit fed the boom: the company lent money to buy its own stock and sold new shares in instalments, so buyers paid a fraction up front. Euphoria spread to dozens of other share issues, which Parliament tried to curb with the Bubble Act in June 1720. Insiders sold through the summer, and panic followed in September. An instalment plan works like borrowed money, and a buyer who had paid a fifth of the price lost the whole stake on a fall of a fifth. Run the multiple and the fall through the recovery formula of Level 3 and a buyer at the June price needed the stock to quintuple from its December level to break even, which it never did.

The 1929 crash and the long wait

From the 1932 low the Dow needed a gain of 825 % to return to its peak, and it closed above the 1929 level again only on 23 November 1954, 25 years later. Dividends and the falling price level of the 1930s shorten that wait in real total-return terms, which is a reminder to measure recoveries with the full return. The boom phase ran on credit, with brokers' loans to buy stock on margin growing through 1928 and 1929, and margin calls turned the falls of October 1929 into forced selling.

The dot-com bubble

The displacement was real: the internet did change commerce. The error lay in the price. Many leading stocks traded at 100 times earnings or more, and our bubble formula says that at such a multiple a buyer needed earnings growth near 28.0 % a year for ten years. Recovering from the trough needed a gain of 353 %, and the Nasdaq first closed above its 2000 peak on 23 April 2015, at 5,056.06. Robert Shiller published Irrational Exuberance in March 2000, the month of the peak, which shows that a warning can be right in its timing and still go unheard.

Housing, 2006

Leverage ran the story. A buyer with 5 % down who sees the house fall 10 % has lost twice the down payment. Anchoring kept sellers asking for peak prices while sales dried up, and the disposition effect showed in housing as clearly as in stocks: owners facing a loss held out longer. Chapter 17 follows the losses into mortgage securities.

Meme stocks, 2021

This episode compressed the phases into weeks. Herding ran through social media, call options bought by small investors forced dealers to buy shares to hedge, and short sellers who were right about the business lost billions on their timing, the limits of arbitrage in their sharpest form. Its lesson matches 1720's: a price can move far from value when the buyers' reason is the price itself, and the people who lose most are those who arrive last with borrowed money.