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Lecture 38 Choice Bracketing & Dynamic Mental Accounting

Definition

  • Time-series approach to evaluation and decision-making is required (e.g. self-control situations)

Choice bracketing: How people segregate or aggregate choices over time periods.

Prior Outcomes & Risk Choice

  • People make more risky bets on the last race of the day when,
    • Average bettor is losing money
    • Anxious to break-even (don't wanna lose)

  • Sunk cost effect

  • Prior outcome is insignificant if

    • each race were a separate account
    • today's betting combined with rest of bettor's wealth

If a series of gambles are bracketed together \(\{ \}\) then outcome of this one gamble affects later choices…

  • Problem 1: won 30
    • Confidence
    • stimulates risk seeking
    • 'house money': amount won in the casino… is felt more comfortable investing in the.
    • 'own money' is different
  • Problem 2 & 3: lost 30
    • Risk seeking only if offered a chance to break even (chose (30,33%) instead of (10))
    • If the risk is not worth it (then risk averse) cause you are already losing (so avoided (9,50%;-9,50%))

Choice Bracketing - Narrow Framing & Myopic Aversion

  • Day of experiment = natural bracket
  • Gambles/investments over a period of time… then how do you want to calculate gains or losses? (over what period/bracket)
  • Choice of bracket influences individual bets

Illustration by Paul Samuelson
- 200 if won, -100 if lost (coin toss)
- Play only if Willing to play the bet 100 times
- Declined… went home… pair of choices is irrational

  • Reasoning:
    1. Loss of 100 feels more than 200 gain (\(2.25 \times 100 = 225 \gt 200\))
    2. Why series of bets? Mental accounting operation here?
      • Say, utility is piecewise linear: \(U(x)= x\) for \(x \geq 0\) with loss aversion factor of 2.25.
      • Single bet is bad because: (\(2.25 \times 100 = 225 \gt 200\))
      • Two bets? If each bet treated as a separate event, twice as bad (worse!)
      • But if combined. \(\{ 400,0.25; 100, 0.50; -200, 0.25 \}\) yields positive utility… with hypothesized utility function… repetitions increase \(\implies\) portfolio more attractive.

Accept any number of trials \(\geq 2\) as long as he doesn't have to watch!

PT value function… \(r=0, \alpha=\beta=0.88, \lambda = 2.25\)

  • \(r\) is the reference point (random gain)
  • \(\alpha\) and \(\beta\) define the steepness of the gain and loss
\[ v(x) = \begin{cases} x^\alpha & x \geq 0 \\ -\lambda(-x)^\beta & x \lt 0 \end{cases} \]

\((200,0.5,-100,0.5)\) \(\to\) \(V(f) = \lambda \times 100^\beta [w^-(0.5)] + 200^\alpha[w^+(0.5)]\)

  • where \(w^-\) and \(w^+\) are the weighting functions

Loss-averse people are more willing to take risks if they combine multiple bets together.

  • One-bet-at-a-time mental accounting and loss aversion

  • Equity premium puzzle

    • Equity premium = rate of return (stock) - safe investment (t-bill)
    • this difference has historically been too large
      • can be explained by risk: but risk aversion necessary is very implausable
  • how frequently should investors evaluate their investment to make themselves indifferent between two investments?
    • simulation \(\implies\) 13 months
    • if the most prominent evaluation period is once a year = solved!

If the investor has a narrow frame of evaluation: once a year = solved

  • Myopic means short-sightedness = frequent evaluations, preventing investor from adopting long-term strategy.
  • Experiment: More the number of evaluations more risk you are willing to take
    • 8 times a year: 59% assets in bonds
    • once a year: 2/3 funds on stocks
    • once in 5 years: 2/3 founds on stocks
  • Another one
    • shown two charts of stimulated rate of returns
    • one-year rates: majority invested in bonds
    • 30-year rates: 90% in stocks

So that's what is Myopic loss aversion, you will avoid losses in the short-run.

Taxi driver example:
- 12 hour taxi fixed fee
- rest of the earnings are yours
- Each day, demand is different
- Rational: should work longer hours on busy days to max earnings per hour worked

But if earning level is on a per day basis, quit earlier on good days.

  • Elasticity of \(\dfrac{\text{hours worked}}{\text{daily wage (other drivers)}}\) is negative.

Drivers do mental accounting one day at a time.

The Diversification Heuristic

Example of selecting between 6 snacks (for the three class meetings)
- Simultaneous choice = variety-seeking
- Sequential choice = not so much

People diversify when asked to make several choices simultaneously

Diversification Bias

  • Diversification Bias

    • Read & Loewenstein
    • Actually the portfolio in the bag (Halloween trick-or-treaters) that matters, not the portfolio selected at each house as the candy will be consumed later. But the sequential vs simultaneous setting affects that.

  • \(\dfrac{1}{n}\) heuristic

    • Benartzi & Thaler
    • extreme version of this bias
    • Investor is offered \(n\) funds (she will evenly divide among the funds offered)
    • Increase exposure to any particular type of funds

  • Asset allocation choice depends on the array of funds

    • Plan with one stock and one bond fund = 50-50
    • If another stock fund were added = 2/3 stocks
    • Stock for the company they work for in a separate mental account.
      • non-company stock funds are evenly invested on: 29% stocks, 29% bonds