Anchoring and adjustment

in Financial forecasting

Doron Sonsino

School of Business

COMAS- College of Management

Academic Studies

Rishon Lezion, Israel

Framed Field experiment –

with Eran Regev

• Qualified subjects are confronted with binary stock selection problems

• Asked to “take actions” on the Israeli stock market, assuming positions would be closed in 3 months and decisions would be evaluated from actual market dynamics

• Payouts (“consultation fees”) are derived from actual market returns

Stock Sale – Consulting Problem 1

Which of the next two stocks would show lower return in the next 3-months (from the date where the questionnaire is delivered)?

Recall that you are acting as a consultant for an investors holding 100,000 NIS of each stock

OSEM stock id 304014

BAZAN stock id 2590248

PLEASE MARK THE STOCK THAT YOU RECOMMEND SELLING (ONE STOCK ONLY)

Stock Sale – Consulting Problem 1 (continued)

Please provide a 90% confidence-interval for the 3-months return (starting at the questionnaire delivery date) on the stock selected for sale:

Lower bound on return:

With probability 95%, the return on the stock that I selected to sell will be higher than ______

Upper bound on return:

With probability 95%, the return on the stock that I selected to sell will be lower than ______

*please consider your bounds carefully. Recall that accurate, fair prediction could pay an additional bonus of 80 NIS

Questionnaires

• 10 binary choice problems:

5 BUY and 5 SELL

• Random design

• 93 participants. OCTOBER 2010 – APRIL 2011. 55% MBA. Mean EDU 16.5. 40% prof.

- 10 prediction intervals collected from each subject (93X10 intervals).

Results – Calibration Rates

Under perfect calibration- Hit Rate=90%

• Actual HR: mean 27.4%. median 20%

• Informational overconfidence

• In spite of the recent crisis experience – predictions are awfully wrong:

- Unrealistic optimism

- Underestimation of volatility

Mean results

* Most frequent PRED 0 (N=65) 7.5 (N=61)

Unrealistic optimism

Midpoint PRED 5.4

Actual mean return -1.5

ERROR 6.9

Misperception of volatility

LGTH 11.8

LGTH by recent 60 21.5

HIT RATE for

extended intervals 57%

avg

0

10

20

30

40

50

60

70

80

90

100

110

PRED

-30 -20 -10 0 10 20 30 40 50 60

Mean LGTH by mid-point Prediction

avg

0

10

20

30

40

50

60

70

80

90

100

110

PRED

-30 -20 -10 0 10 20 30 40 50 60

Mean LGTH by Mid-point PRED'

Parabolic Approximation LGTH=7.8-0.04*PRED+0.03*(PRED)^2

Mean LGTH by midpoint PRED

abs(PRED) PRED>0 PRED<0

0<|PRED|<5 6.9 (N=233)

9.9 (N=98)

5≤|PRED|<10 8.0 (N=271)

12.7 (N=48)

10≤|PRED| 20.5 (N=198)

24.3 (N=19)

Results for IDS121

0

20

40

60

80

100

120

140

160

0 2.5 5 7.5 15 20 25

Lgth

Pred

Plausible reasons to the increase in LGTH

with extremity of predictions

-Statistical explanation:

Conditionally heteroskedastic expectations Golob (1994); Du and Budescu (2007)

-Technical explanation:

Kahneman and Tversky (1974) Anchoring and adjustment heuristic. If adjustments are proportional to the absolute value of the anchor then LGTH may increase with absolute point predictions Epley and Gilovich (2006) Janiszewski and Uy (2008)

Experiment II:

Technical Prediction from Few Statistics

- Prediction assignments based on realized S&P 500 series

-Subjects are asked to predict MON13 from only 6

statistics regarding performance in 12 preceding months, including STD12

-The identity of stocks and dates of retrieval are concealed. Subjects are discouraged from attempting to recognize stocks from the statistics (Sonsino and Shavit, forthcoming)

Realized annual return (MON1-MON12) -0.3%

Realized return in last 6 months (MON7-MON12) +16.8%

Standard deviation of monthly returns (MON1-MON12) +6.4%

Return in month 10 +3.2%

Return in month 11 -10.0%

Return in month 12 +3.6%

Predictions for month 13

Median prediction: with probability 50% the return in MON13 will be lower or higher than:

Upper 95% limit: with probability 95% the return in MON13 will be lower than:

Lower 95% limit: with probability 95% the return in MON13 will be higher than:

Would you recommend a one month delay in purchase? NO/YES

Experiment II:

The specific series and results (N=46)

ρ(LGTH,|P50|) LGTH STD12

0.02 9.8 4.6 Seq1

-0.01 12.3 6.4 Seq2

0.19* 21.7 12.5 Seq3

0.29** 25.4 18.1 Seq4

Anchoring with Noisy Monotone Adjustments

S – space of information signals

A: S→R+ – Anchor function

Π(S) – similarity partition with σ(A|Si) representing the volatility of the environment where s in Si

ADJ: S →R+ – Expected adjustment function

Ф – independent fixed noise in adjustments

Anchoring with Noisy Monotone Adjustments

If expected adjustments increase with the

anchor within similarity sets and increase

(rapidly enough relatively to the noise)

with the volatility of the environment, then

ρ(LGTH,A|Si)>0 and the correlation

increases with σ(A|Si). In particular, when

perceived volatility is very low (4.6, 6.4) the

the correlation may disappear

Discussion

*If confidence range increases with expected returns,

then overconfidence hazards (e.g., irrational trading)

may instinctively attenuate in extreme market

conditions

*The willingness to pay for a stock may incrementally

decrease with its expected return when agents are

(rational) risk or loss averse (e.g., [5,10] vs. [3,15])