Finance for Normal People

Finance for Normal People
Chapter 7: Behavioral Finance Puzzles: The dividend puzzle, the disposition puzzle, and the puzzles of dollar-cost averaging and time-diversification

Behavioral finance puzzles
Four important financial puzzles: The dividend puzzle is about the preference for spending dividends while refraining from selling stocks and spending their proceeds The disposition puzzle is about the disposition to realize gains quickly but procrastinate in the realization of losses The puzzles of dollar-cost averaging and time-diversification are about their popularity among investors despite faults in the standard arguments that underlie them

The solution to these puzzles combine: 1. Wants for utilitarian, expressive, and emotional benefits, presented in Chapter 2 2. Cognitive and emotional shortcuts and errors in Chapters 3 and 4 3. Tools for correcting errors in Chapter 5 4. Implications of expected utility and prospect theories for life- evaluation, experienced happiness, and choices in Chapter 6

Behavioral finance puzzles The dividend puzzle
”Why do corporations pay dividends? Why do investors pay attention to dividends? ... The harder we look at the dividend picture, the more it seems like a puzzle, with pieces that just don’t fit together” Fischer Black, Journal of Portfolio Management, 1976

Wants for utilitarian, expressive, and emotional benefits Saving provides utilitarian, expressive and emotional benefits and so does spending, but the two wants conflict Distinctions between capital and dividends help us balance our conflicting saving and spending wants and regulate them

Behavioral finance puzzles The dividend puzzle How normal-ignorant investors frame capital and dividends

Behavioral finance puzzles The dividend puzzle How rational and normal-knowledgeable investors frame capital and dividends

Framing and Mental Accounting What is the difference between $1,000 in “homemade” dividends from the sale of shares and $1,000 from a cashed company-paid dividend check?

Self-control How is self control helped by separate mental accounts for capital and income and a rule of “spend income but don’t dip into capital”? How do company-paid cash dividends facilitate exercise of self-control? How do stock dividends facilitate exercise of self-control?

Hindsight, Regret, and Pride What is the regret potential of company-paid cash dividends and homemade dividends?

Framing in prospect and expected-utility theories Choose between: A. $2 today and a chance of $50 or $54 tomorrow B. Nothing today and a chance of $52 or $56 tomorrow

Framing in prospect theory Consider an investor who bought the stock for $40 A. $2 dividend plus a chance for a capital gain of either $10 or $14 B chance for a capital gain of $12 or $16

Figure 7-1a: Comparing prospect theory gain-loss utility with dividends are paid and not paid – The case where the price of the share increased The total gain-loss utility of a $2 dividend gain plus a chance at a $10 or $14 capital gain is 392: 80 + 1/2 ( ) = 392 This is higher than the total gain-loss utility of a chance at a capital gain of $12 or $16. 1/2 ( ) = 335.5

Framing in prospect theory Consider an investor who bought the stock for $70 A. $2 dividend plus a chance for a capital loss of either $16 or $20 B chance for a capital loss of $14 or $18 The prospect theory gain-loss utility of a $2 gain is 80 units. The gain-loss utility of $10, $12, $14, and $16 gains are, respectively, 287, 314, 337, and 357. The total gain-loss utility of a $2 dividend gain plus a chance at a $10 or $14 capital gain is 392: 80 + 1/2 ( ) = 392 This is higher than the total gain-loss utility of a chance at a capital gain of $12 or $16. 1/2 ( ) = 335.5

Figure 7-1b: Comparing prospect theory gain-loss utility with dividends paid and not paid – The case where the price of the share declined The total gain-loss utility of $2 dividend gain plus a chance at a $16 or $20 capital loss is a negative 502.5: - 1/2 ( ) = This is better than the negative 565 total gain-loss utility of a chance at a capital loss of $14 or $18: -1/2 ( ) = -565

Behavioral finance puzzles The Disposition Puzzle
Rational investors are quick to realize losses and slow to realize gains (why?) Yet many normal investors display a disposition to “sell winners too early and ride losers too long” Why do investors display that disposition? This is the disposition puzzle Do you display a disposition to “sell winners too early and ride losers too long”?

Wants for avoiding regret Realizing losses imposes the emotional costs of regret whereas realizing gains yields the emotional benefits of pride

Hindsight shortcuts and errors We bought a share for $100 because we saw, in foresight, its price increasing to $140 But now, in hindsight, we remember all the warning signs displayed in plain sight on the day we bought our share

Hindsight, regret, and responsibility We experience disappointment when a broker who bears responsibility for choosing stocks for us makes a choice that sustains losses But we suffer regret when we ourselves bear responsibility for that choice

Methods for overcoming the disposition effect Transfer your assets Harvest your losses Stop-loss orders

Behavioral finance puzzles The disposition puzzle
Framing in expected-utility and prospect theories You bought a share of stock yesterday for $100 It is selling at $60 today You face a chance that the share’s price would increase by $40 tomorrow to $100 or decline by a further $40 to $20 The capital gains tax rate is 20% Would you realize your loss?

Framing in prospect theory Choose between: A. Sell the share today thereby realizing the $40 loss B. Hold the share for another day, accepting a chance of losing a total $80, or getting-even, losing $0

Figure 7-2a: Gain-loss utility associated with options A and B
Option A imposes on the investor a sure loss of 140 units of gain-loss utility. Option B entails a chance to lose $80, corresponding to negative 175 units of gain-loss utility, and an equal chance to lose $0, corresponding to zero units of gain-loss utility. The expected units of gain-loss utility associated with option B is negative This makes option B better than option

Framing in prospect theory You bought a share of stock yesterday for $60 It is selling at $100 today You face a chance that the share’s price would increase by $40 tomorrow to $140 or decline by $40 back to $60 The capital gains tax rate is 20% Would you realize your gain?

Framing in prospect theory Choose between: C. Sell the share today thereby realizing a $40 paper gain. D. Hold the share for another day, accepting a chance of gaining a total of $80 or gaining $0

Figure 7-2b: Gain-loss utility associated with options C and D
Option D entails a chance to gain $80, corresponding to 95 units of gain-loss utility, and an equal chance to gain $0, corresponding to zero units of gain-loss utility. The expected units of gain-loss utility associated with option D is 47.5, the mean of 95 and zero. This makes option D inferior to option C which is associated with 60 units of gain-loss utility

Countering the disposition effect Rules are a self-control device facilitating the realization of losses

Behavioral finance puzzles The disposition effect
Countering the disposition effect Self-control and outside control “Magic words” such as transfer your assets or harvest your losses The role of December The roles of regret, fear, sadness, and disgust

Behavioral finance puzzles The disposition effect
The disposition effect among corporate managers Corporate managers are disposed to “throw good money after bad” into losing projects Some of the reluctance, but not all, is due to conflicts of interest Project review committees and workout units can counter the disposition effect

Behavioral finance puzzles The puzzles of dollar-cost averaging and time-diversification
The dollar-cost averaging puzzle centers on the argument that utilitarian benefits make investment by dollar-cost averaging better than investment by lump-sum The time-diversification puzzle centers on the argument that the risk of stocks declines as the investment horizon increases

Time-diversification centers on the belief that the risk of stocks declines as the investment horizon increases That belief is shared by amateur and professional investors alike, often accompanied by graphs showing that the probability of stock market gains increases as their holding periods increases

Figure 7-3: Proportion of stock market periods with gains by time horizon (1926-2015)

Behavioral finance puzzles The puzzles of dollar-cost averaging and time-diversification
The solutions to the puzzles combine: Wants for utilitarian, expressive, and emotional benefits Application of expected utility and prospect theories Roles of cognitive and emotional shortcuts and errors Tools for correcting errors

Behavioral finance puzzles The puzzle of dollar-cost averaging
Framing and expected-utility and prospect theories in dollar- cost averaging An investor with $2,000 in cash he has chosen to invest in stocks because stocks are likely to yield higher long-term wealth than cash, even though they also impose higher variance of wealth This choice is consistent with expected-utility theory if the investor’s variance-aversion is not too high

Framing and expected-utility and prospect theories in dollar- cost averaging Loss-aversion, a feature of prospect theory, might deter our investor from buying stocks Dollar-cost averaging overcomes loss-aversion in a frame that highlights gains and obscures losses

Average cost of shares held at the end of the two periods: $2000/100 = $20 Average price at which shares were bought during the two periods: ( )/2 = $31.25 Table 7-1: Dollar-Cost Averaging Period Amount Invested Price per Share Number of Shares Bought 1 2 $1000 50 20 12.5 80 Total $2000 100 Framed the rational way, as in standard finance, our investor started with $2,000 in cash and now, a month later, owns 100 shares worth $12.50 each for a total of $1,250, implying a $750 loss. Framed the normal way, as proponents of dollar-cost averaging do, our investor bought 100 shares at an average cost of $20 per share, while the average price per share on the two dates, $50 and $12.50, was $31.25, implying an $11.25 per-share gain. Indeed, framed the normal way, our investor sees gains in all circumstances except when stock prices never change.

Pride and regret in dollar-cost averaging Investors anticipate the emotional benefits of pride and emotional costs of regret when they make choices Investors mitigate their anticipated emotional costs of regret when they convert only one part of their cash into shares of stock today

Self-control in dollar-cost averaging The strict rules of dollar-cost averaging combat self-control lapses, compelling investors to stick to the stock-buying or stock-selling plan

Reverse dollar-cost averaging An investor with stocks who converts her entire amount into cash today bears less variance-risk and loss-risk tomorrow than when she follows reverse dollar-cost averaging, converting only a portion into cash and keeping the other in stocks Risk reduction cannot be the rationale for both dollar-cost averaging and reverse dollar-cost averaging

Prospect theory The return on cash is zero $2,000 in stocks will, with equal probabilities, either increase by $600 to $2,600 tomorrow or decrease by $280 to $1,720 The reference point of John is $2,000 in cash He frames the choice as between A and B A. Keep in cash: A sure gain of $0 B. Convert cash into stocks: A chance to gain $600 or lose $280

Figure 7-4a: Choice to hold $2,000 in cash or convert it into stocks
The expected units of gain-loss utility of John if he chooses to convert his $2,000 of cash into stocks is a negative 22, the mean of a gain of 80 utility units if he gains $600, and a loss of 124 utility units if he loses $280. These negative 22 units are less than the zero units of gain-loss utility if he chooses to keep his $2,000 in cash, inclining John to keep his $2,000 in cash. Dollar-cost averaging overcomes this inclination, inducing John to buy stocks.

The reference point of Jane is $2,000 in stocks She frames the choice as between C and D C. Convert stocks into cash: A chance for an (opportunity) gain of $280 if the price of shares declines or an (opportunity) loss of $600 if the price of shares increases. D. Keep in stocks: A sure (opportunity) gain of $0

Figure 7-4b: Choice to hold $2,000 in stocks or convert it into cash
The expected units of gain-loss utility of Jane if she chooses to convert her $2,000 of stocks into cash is a negative 56.5 units, the mean of a gain of 47 utility units if she gains $280, and a loss of 160 utility units if she loses $600. These negative 56.5 units are less than the zero units of gain-loss utility if she chooses to keep her $2,000 in stocks, inclining Jane to keep her $2,000 in stocks. Reverse dollar-cost averaging overcomes this inclination, inducing Jane to sell stocks.

Behavioral finance puzzles The puzzle of time-diversification
Framing and expected-utility and prospect theories in time- diversification The time-diversification puzzle is related to the equity premium puzzle $1,000 in Treasury bills at the end of 1925 compounded to a mere $12,720 by the end of 1995, whereas $1,000 in stocks compounded to $842,000 Why are long-term investors reluctant to invest large proportions of their portfolios in stocks when the long-term expected returns from them are so much higher than those of Treasury bills?

Framing and expected-utility and prospect theories in time- diversification Jeremy Siegel and Richard Thaler offered several possible solutions to the equity premium puzzle but favored the “myopic loss-aversion,” rooted in prospect theory’s loss-aversion The frequency of losses varies by the length of periods over which returns are observed Losses are more frequent over short periods than over long periods Investors who observe returns over short periods might exhibit myopic loss- aversion - misled into the belief that losses are more likely over long periods than they truly are

Figure 7-5a: Distribution of returns of stocks and bonds during 1-Year investment horizons (Bond returns in black and stock returns in white) The first bar on the left in Figure 7-5a is the mean return of the lowest 200-bond one-year returns. The bar next to it is the mean return of the lowest 200-stock one-year returns, and so on

Figure 7-5b: Distribution of returns of stocks and bonds during 30-Year investment horizons (Bond returns in black and stock returns in white) The first bar on the left in Figure 7-5b is the mean return of the lowest 200 annualized 30-year bond returns, and so on.

Framing and expected-utility and prospect theories in time-diversification The median allocation to stocks among those who saw the 1-year chart was 40%. The median allocation to stocks among those who saw the 30-year chart was 90% More recent evidence indicates, however, that myopic loss-aversion has little effect on investment choices People invest as much in stocks when they see one-year or long-horizon historical return distributions, but they invest less in stocks when they see no historical return distributions This suggests that lack of knowledge of high historical stock returns rather than myopic loss-aversion makes investors excessively pessimistic about future stock returns

Framing errors in time-diversification Paul Samuelson argued that the advocacy of time-diversification is built on framing errors that mislead investors into an illusory happy ending, as if the probability of losses over the long-run is zero Consider an investor who invests $1,000 in a portfolio with a 50–50 chance to gain 20% or lose 10% each year The investor has a 50% probability of losing money if her horizon is one year, but she has only a 25% probability of losing money if it is two years

Figure 7-6: Probabilities of losing money and amounts of money that can be lost
$1,000 $1,200 $900 $1,440 $1,080 $810 One-Year Horizon (50% chance for a $100 loss) Two-Year Horizon (25% chance for a $190 loss) If risk is framed as the probability of losing money, risk declines as the horizon increases, but if risk is framed as the amount of money that can be lost, risk increases as the horizon increases. The investor might lose $100 after one year, but she might lose more, $190, after two years

Framing errors in time-diversification Many proponents of time-diversification assume, in error, that the probability of losses with stocks held over the long run is zero Yet there is reason to expect a negative return even on the broadest possible stock index in the very long run The error of framing small probabilities as zero probabilities might be described as the illusory-happy-ending error

Regret and Self-Control in time-diversification Time-diversification, like dollar-cost averaging, is useful in bolstering self- control and mitigating fear and regret over losses Time-diversification comes with stay-the-course rules, keeping alive hope of high future gains and countering the urge to sell all stocks, perhaps at the bottom of the market, when extrapolating three bad stock market years into a world-is-coming- to-the-end conclusion

Regret and Self-Control in time-diversification Time-diversification is usually presented in a frame where investment time horizons are fixed, set when investments are made But investors often describe time horizons in a flexible form - simply “the long-run” - rather than in a fixed form – “30 years” An investor with options on time can postpone the realization of paper losses, thereby avoiding closing a mental account at a loss and suffering the accompanying pain of regret

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