07. Ambiguity Aversion Flashcards
What is the disposition effect and how can we explain it?
Disposition effect: people hold ‘losers’ too long and sell ‘winners’ too quickly.
Two features of prospect theory can explain this behaviour:
1) The reflection effect: value function exhibits diminishing marginal sensitivity to losses and gains
2) The reference point: outcomes are valued relative to a reference point
Important: so far we have dealth with situations in which probabilities were known.
How do we handle unknown probabilities?
Unknown probabilities = ambiguous situation. In many situations, we do not know the objective probabilities associatew ith outcomes.
Expected utility theory is concerned with situations in which probabilities are objectively known.
Alternative: subjective expected utility (SEU) theory (Savage, 1954) is concerned with situations in which probabilities are not necessarily objectively known.
What is uncertainty and risk?
A situation involves risk if prospects that one has to decides between entail known probabilities.
A situation involves uncertainty if prospects that one has to decide between entail unknown probabilities.
What is Ellsberg paradox?
Let p(r), p(y) and p(b) be the subjective probabilities associated with a certain color.
One prefers Gamble A to Gamble if: p(r)u(100) + (1-p(r))u(0) > p(b)u(100) + (1-p(b))u(0) this implies p(r)>p(b)
Furthermore, on prefers gamble D to gamble C:
P(r)u(100) + p(y)u(100) + p(b)u(0) < p(b)u(100) + p(y)u(100) + p(r)u(0) this simplifies to p(r)<p></p>
What is the sure thing principal?
One of the axioms of SEU
A businessman contemplates buying a certain piece of property. He considers the outocme of the next presidential election relevant. So to clarity the matter to himself, he asks whether he would buy if he knew that the Democratic candidate were going to win, and decides that he would.
Similarly, he considers whether he would buy if he knew that the Republican candidate were going to win, and again finds that he would. Seeing that he would buy in either event, he decides that he should buy, even though he does not know which event obtains, or will obtain.
What are the different models to formalize ambiguity aversion?
1) Utility-based models: a simple way to express ambiguity aversion is to allow the utlities from winning bets on ambiguous and unambiguous events to be different (Karni, 1985)
If the ulitity from winning an ambiguous bet is lower, aversion to ambiguity is consistent with utility maximization (Smith, 1969, Franke, 1978)
2) Max-min preferences: Gilboa and Schmeidler 1989: the subject has too little information to form a prior. Hence he considers a set of priors as possible. Being ambiguity averse, she takes into account the minimal expected utility (over all priors in the set) while evaluating a bet.
What is maxmin expected utlity?
Gilboa & Schmeidler (1989’s model):
A MEU decision maker evaluates a prospect by its least expected utility over a set of possible subjective prior probabilities.
What did Sarin & Weber test?
1993, Sarin & Weber: test the effect of ambiguity aversion on market prices in 2 types of markets:
1) Sealed bid auction
2) Double oral auction
Three studies involving 14 experiments
1) The objective in the first 8 experiments: test whether the individual bids and market prices of ambiguous and unambiguous assets differ in sealed-bid and double-oral auctions
2) Experiments 9 and 10: investigation whether the results would be sustained if experienced executives participated
3) Experiments 11-14: results are robust to a larger number of trading periods.
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What are the findings about the ambiguity in the lab?
The bid price for an ambiguous asset must be at least as much as the bid price for an unambiguous asset.
Findings: individual bid prices as well as market prices for the ambiguous asset were consistently below the corresponding individual bids and market price for the unambiguous asset.
The behaviour of experiences subjects is not different than that of student subjects. Their explanation = people regard an ambiguous asset as more risky.
The ambiguous asset has a potential to induce psychological discomfort = since the nature of the stocastic process is unknown, as well as regret due to hindsight
What are the consequences of the ambiguity aversion?
1) Ambiguity aversion might affect trading volume on organized exchanges:
Eg. US-invasion in Irak in 1991, this created/increased ambiguity about oil prices. Trading volume on stock exchanges went down. Stockbrokers told investors that it was a bad time to buy/sell stocks.
2) Ambiguity might be especially important for certain kinds of assets about wwhich little is known, like shares of smaller firms or IPOs of small privately held companies.
Stock prices of small firms do rise more than prices of large firms and IPOs tend to jump in price about 10% when the market for their shares first opens:
The apparent excess returns to small firms and IPOs might be premiums paid to investors who dislike ambiguity.
3) Another indication of financial ambiguity aversion comes from personal holdings of domestic and foreign securities.
What is the equity home bias?
People in several countries sacrifice about 3M in annual expected returns - a substantial amount, since stocks rise about 8% per year, by holding too many shares of domestic firms and not enough foreign shares = French & Poterba 1991.
Equity home bias puzzle is the term given to describe this fact: individuals and institutions in most countries hold modest amounts of foreign equity.
Why is the home equity bias puzzling?
it is puzzling since observed returns on national equity portfolios suggest substantial benefits from international diversification.
One explanation is that people feel less ambiguity as they have more knowledge about their own country’s economy.
The 3% loss they accept is the premium they pay for avoiding ambiguity about foreign investments.
What conclusions can we draw based on ambiguity aversion?
Many situations involve risk and uncertainty.
It is a persistent finding people shy away from uncertainty = they are ambiguity averse.
This is in contradiction to EUT and SEU.
Ambiguity aversion can psychologically be explained by fear of negative evaluation.
Different models have been proposed to account for ambiguity aversion: eg. MEU.
The consequences of ambiguity aversion are eg. Equity home bias, premiums for smaller firms and IPOs
What is the short introduction on ambiguity aversion?
In many situations, decision makers have only vague infroamtion about the probabilities of potential outcomes of their actions.
Such situations are often called ambiguous (as opposed to risky)
Elssberg (1962) suggested that decsion makers have a preference for risky rather than ambiguous options: ambiguity aversion.
2 different ways to model ambiguity aversion:
(1) Utility based
(2) MaxMin Expected Utility Preferences
Experimental evidence suggest: ambiguity aversion reduces market prices on financial exchanges (Sarin & Weber: 1993)
Individual bids and market prices for ambiguous assets consistently below corresponding individual bids and market price for an unambiguous asset.
Regardless of type of market mechanism (sealed-bid or double-oral)
What is the no trade region
Ambiguity aversion has many implications.
A theoretical example: no trade regions in asset prices: price arease where there’s no trade possible.
Down and Werlang (1992): “Uncertainty Aversion, Risk Aversion and the Optimal Choice of Portfolio”;
