Information and Allocation Synopses



Information and Allocation Synopses

Kroll, Y, H Levy and A Rapoport, 1988, “Experimental Tests of the Separation Theorem and the Capital Asset Pricing Model,” American Economic Review, 78-3, 500-519.

• Subjects make 300 portfolio choices over 3 risky assets (A, B and C) and, in the second 100 choices, a risk free investment/borrowing opportunity. Choices were in sets of 10 trials. Subjects told distributions were A~N(3,3), B~N(5,6) and C~N(7,12). Correlations were ρAB= ρAC=0 for all subjects and ρBC=0, 0.8 or -0.8 depending on treatment group. Subjects had completed a “year long course in statistics,” but their proficiency in understanding the role of correlation in diversification was not assessed. Subjects had participated in a “similar, though considerably simpler, portfolio selection experiment.” Subjects could observe up to the last 60 trials at any time by pressing a button on the computer. Profits were the final portfolio value minus the initial value for each set of 10 trials. Profits from each set of 10 were summed, converted to local currency and paid to subjects. One session average payoffs were $18.91 and, to make it more realistic, one session had average payoffs of $165.

• Different correlations do not seem to affect the average portfolio choices. Nor does the ability to borrow and lend at the risk free rate. Subjects don’t “learn” optimal behavior through time. Heavy investment in asset C.

• They hypothesize that:

o Subjects may not understand the way correlation affects risk.

o Low stakes are address in the second session.

o Investment in C without risk free investing/borrowing may come from the desire to maximize the geometric average return. This gives a higher probability of attaining a higher terminal wealth. This is Mike Stutzer’s (year?) idea. The subjects still do not appear to go to the optimal portfolio when the risk free investing/borrowing opportunity is introduced.

o Maybe “experts” would do better.

o Maybe subjects didn’t believe that returns were distributed as claimed in the instructions.

Notes:

• Rabin argues that subjects should be risk neutral under the level of payoffs in such experiments (even the high payoff session). But, experimentalist frequently observe apparent risk preferences. Maybe these are local, but maybe they can be explained by other things like the “desire to win.” Frequently, risk seeing behavior is observed. Since bankruptcy was possible, this encourages risk seeking behavior. If so, preferences of experimental subjects probably do not accord with those we would expect of investors in large portfolios, especially retirement portfolios. Here, C may be the preferred risky portfolio. Alternatively, approximate risk neutrality may mean that there may be no strong motivation to achieve the efficient frontier. An obvious solution to this problem is to induce risk averse preferences (see Berg, Dickhaut and Rietz, 2003)

• They try to fit a static, single period CAPM to the data…in fact, subject preferences are over final payoffs of a sequence of 10 draws with opportunities to rebalance each period. They address the multiperiod issue and argue the single-stage CAPM optimal choice is a close approximation to optimal behavior in the multi-period setting. We would probably want to come up with optimal strategies for the final stage payoffs (where we would induce preferences) to approximate the retirement or other long-term investment problem.

• I get incomplete diversification in asset markets I’ve run. So, insufficient diversification here is not surprising to me.

• I get hysteresis effects when subjects go through multiple treatments across time. This may explain the lack of reaction to introduction of the risk free asset.

• No study of how information influences choices.

Kroll, Y, and H Levy, 1992, “Further Tests of the Separation Theorem and the Capital Asset Pricing Model,” American Economic Review, 82-3, 664-670.

• Address issues in Kroll, Levy and Rapoport (1988) by:

o Using MBA investments students (before portfolio selection was taught).

o Use grades instead of monetary payments. (The “best” student gets 20 points, the “worst” loses 20 and others are pro-rates. So, your payoff is NOT independent of others’ payoffs. Introduces tournament style incentives.)

o Show all subjects’ performance to all other subjects.

o Losses are possible.

• Results are closer to optimal.

Notes:

• The incentive scheme promotes tournament incentives. While using course grades might promote risk aversion, the tournament nature of the incentives scheme likely promotes risk seeking. It seems like we still don’t know if preference accord with what we expect for natural occurring portfolios.

• Still no work on how information may influence choices.

Levy, H, M Levy and N Alisof, 2004, “Homemade Leverage: Theory versus Experimental Evidence,” The Journal of Portfolio Management, Fall 2004, 84- 93.

• Test whether subjects can identify the most efficient risky investment alternative given a risk free lending and borrowing rate and whether they borrow to increase return or shift to a less efficient portfolio. They use students and practitioners. Sometimes subjects are given the return distributions. Sometimes they are given histories.

• In one treatment, there is a set of 5 risky investments. Subjects have to choose one and can borrow and lend at the risk free rate. The efficient risky investment is the lowest risk and next to lowest expected return (by 0.2%). Given these alternatives, many students and practitioners make suboptimal choices.

• In another treatment, there are 9 risky choices. The 4 additional choices replicate the variances of the 4 suboptimal prior choices with higher expected returns. All of them could have been attained with combinations of the efficient prior choice and borrowing. So, they were attainable before, but not obvious. Now, nearly all subjects choose one of the new 4 choices or the original efficient choice.

• A treatment is to replicate risk of the suboptimal portfolios and a higher return with a portfolio that could be achieved by borrowing and investing in the optimal portfolio.

• No incentives. They argue that it doesn’t matter.

Notes:

• This is an information treatment that affects choice. It may be that simply presenting the Sharpe ratio works, too.

• Again, I’d induce preferences.

• This seems to be along the lines of what you’re interested in, but I’d shoot for more impact.

Benartzi, S, and RH Thaler, 1999, “Risk Aversion or Myopia? Choices in Repeated Gambles and Retirement Investments,” Management Science, 45-3, 364-381.

• They study whether subjects are willing to take single bets, “sequences” of bets or a bet that represents the final distribution of the bet “sequences.”

• There is a long discussion of Samuelson’s paper in 1963. In it, Samuelson proves by backward induction that if you are unwilling to take a 50%/50% bet of winning $200 and losing $100, you wouldn’t take a sequence of 100 such bets.

• Design has people participating in sequences of gambles described in words or in terms of the final distribution. They DO NOT get to opt in or out of a sequence or re-balance.

• They note that some theories say investment mix should be independent of horizon, but cite advice frequently given by investment advisors to change “the asset mix (to more conservative investments) as retirement becomes closer” (p. 366).

• They do a good job of describing the importance of choosing asset allocation.

• Subjects choose between a smaller version of the Samuelson bet or a set of 100 such bets (no opportunity to allocate or re-balance) with the 100 bet sequence described by the single bet outcomes or the distribution of final outcomes. Subjects do not fall into the Samuelson pattern often, but they are affected by how the 100 bet sequence is described. They are much more likely to invest in it when described by the final distribution.

• They have an interesting means of creating the possibility of losses. Students need to work off losses at $5 per hour.

• They have people estimate the distribution of 100 bet sequences and find that subjects underestimate the effects of diversification.

• They survey staff and faculty (in two different studies) and find that summaries of one year returns or 30 year summaries have significant effects on subject’s stated willingness to invest in stock market portfolios. This is an intuitive and interesting result.

Notes:

• I haven’t read the paper, but the argument they cite in footnote 1 seems to rely on being able to choose to be in or out of each of a sequence of bets…not a commitment to taking the outcome of a long bet sequence. Here, the design requires commitment to an entire series. It seems like there is something inconsistent. Need to get Samuelson’s paper to figure it out.

• Good references:

o Coombs and Meyer (1969)

o Lopes (1981, 1996)

o Keren and Wagenaar (1987)

o Keren (1991)

o Montgomery and Adelbratt (1982)

• Again, preferences over these gambles may differ considerably from preferences held by individuals over large or retirement savings plans. Again, I’d induce preferences.

• Interestingly, they seem to make the Samuelson Mistake themselves at the top of column 2 on page 374 (some investments are “bad” for younger workers, but apparently OK for older ones?).

• An obvious feature of retirement investing is the opportunity to re-balance after seeing partial sequences of draws. This would be an obvious, more realistic, extension to their experimental data

• It would also be interesting to combine what they have with the attention span stuff of Hirschleifer and Thoec.

Benartzi, S, and RH Thaler, 2002, “How Much is Investor Autonomy Worth?,” The Journal of Finance, 57-4, 1593-1616.

• Study whether investors who choose their own portfolios are happy with that choice or whether they would prefer the choice made by the average investor.

• They use information from UCLA plan participants. They project the “range” of possible outcomes from the investor’s own portfolio, the average portfolio and the median portfolio and label them generically. Then, they ask which portfolio the investor would prefer. Investor preference over own and average portfolios do not differ considerably. Investors prefer the median portfolio. (Subjects are presented with the 5th, 50th and 95th percentiles of forecast outcomes for each portfolio.)

• Similar results hold for a private company with a professionally managed portfolio choice. Investors who choose their own portfolios would prefer the professionally managed portfolio.

• “One possible solution to the mismatch between individual preferences and portfolio chices is to help people find the ‘right’ portfolio. …we document that this solution is extremely challenging, because people’s preferences are sometimes confused” (p. 1595). These sessions are with hypothetical choices.

• Experimental work is hypothetical choices between four alternatives, two or three of which are present to any given subject at any given time. Portfolios A, B, C and D have increasing risk. When presented with A, B or C, subjects chose C less often relative to B. When presented with B and C, they chose C more often relative to B. When presented with B, C and D, they chose C even more often relative to B.

NOTES:

• Study is not of all investors. They self-select by answering an e-mail solicitation.

• Nice references to the failure of TIAA-CREF plan participants to re-balance. See Ameriks and Zeldes (2000) and Samuelson and Zeckhauser (1988).

• The ABCD thing is a nice framing effect.

Lopes, LL, and GC Oden, 1999, “The Role of Aspiration Level in Risky Choice: A Comparison of Cumulative Prospect Theory and SP/A Theory,” Journal of Mathematical Psychology, 43, 286-313.

• They do a nice job of outlining the differences between expected utility theory, prospect theory, and decumulative weighted utility theories. Deccumulative weighted utlity theories include cumulative prospect theory. They contrast these to their own security-potential/aspiration theory.

• They have subjects participate in a series of hypothetical choices between distributions of gambles. They have gain and loss gambles, shifted gambles (where the outcomes have a constant added or subtracted) and scaled gambles (where the outcomes are multiplied by a constant). The fit cumulative prospect theory and SP/A theory to the aggregate choice fractions (across gambles) in the populations.

• They find that SP/A fits better.

Notes:

• I like they way the present distributions.

• Aspiration level seems like a natural component to investing with a particular goal in mind (e.g., paying for college, retirement, etc.)

• I like they way they couch the debate between psychologists and economists.

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