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information from which the investor can infer which secu-
rities are undervalued and which are overvalued. In a fair
game of skill, winners and losers are expected, but trading
on inside information is unfair because it conveys a non-skill-
based advantage to one party in the trade.
5. Suitability regulations: Suitability rules present a clear case
where some fairness rights win over other rights and over
efficiency. A move from a no-paternalism to a full-paternalism
world enhances the right to freedom from cognitive errors and
the right to freedom from impulse. The paternalistic nature
of suitability rules is evident in the incentives they provide
to brokers to err on the side of low risk rather than on the
side of high expected returns.
6. Trading interruption regulations which followed the stock
market crash of 1987: trading halts are detrimental to Pareto
136 Behavioralizing the Approach to Financial Market Regulation
efficiency because they prevent parties from entering into
agreements viewed as beneficial to themselves. A counter-
argument is that trading halts enhance efficiency during a
sharp decline by permitting settling up to ensure that all
parties are solvent. Any impact on informational efficiency
depends on whether such efficiency is achieved in the absence
of interruptions. One critic notes that natural trading inter-
ruptions, such as the closing bell on the exchange, apparently
do not dampen volatility during turbulent periods. As to fair-
ness, the main issues involve coercion, efficient prices (fair
and orderly markets), equal information processing, freedom
from impulse, and equal bargaining power.
7.1.4 Theoretical Example
7.1.4.1 Absence of Constraints
To fix ideas, consider a numerical binomial example, a special case
of the framework described in Section 5, where T = 2. Let aggregate
consumption be equal to 100 units at t = 0. Thereafter the growth rate
of aggregate consumption per period is stochastic, and is equal either
to u>1 or d =1/u
either at 5 percent per period or shrinks at 4.76 percent. Let there be
two types of investors in the model, called type 1 and type 2, with type
1 holding 65 percent of the initial wealth of the economy.
Both types of investors share a common rate of time preference
(´ =0.99). However, the two types of investors differ in their beliefs.
Type 1 investors believe that at t = 1, the probability that u occurs is
0.8, whereas type 2 investors believe that the probability is 0.67. For
t >2, type 1 investors believe that the probability that a u follows a u is
0.95 and that a d follows a d is 0.8. In contrast, type 2 investors believe
that aggregate consumption growth evolves according to a process that
is independent and identically distributed (i.i.d.), with the probability
of u being 0.76 at all dates. For the sake of argument, assume that
type 2 investors are information traders, meaning they possess correct
beliefs. In this case, type 1 investors will be excessively optimistic after
7.1 Dynamic Tug-of-War 137
economic growth has been positive and excessively pessimistic after
economic growth has been negative, reflecting  hot hand fallacy.
At the beginning of each date, investors decide how to divide their
portfolio wealth into current consumption and an end of period portfo-
lio such that the value of consumption together with the end-of-period
portfolio is equal to the value of the beginning of period portfolio.
Because the example is binomial, only two securities are needed
to complete the market, which I take to be the market portfolio and
the one-period risk-free security. In equilibrium, the market portfolio
returns 6.1 percent at t = 1 if the economy has grown and -3.8 percent
if it contracts. At t = 1, the interest rate is 3.5 percent. (Returns are
calculated using Equation (5.1), as the SDF embodies all price informa-
tion. Keep in mind that in this model, the market portfolio corresponds
to unlevered equity, unlike, say, the S&P 500.)
At t = 0, type 1 investors have total wealth equal to $193, and type 2
investors have total wealth equal to $104. Both types save 66.3 percent
of their wealth and consume the remainder. At the end of t =0, type 1
investors borrow $314.6 and hold $442.7 of the market portfolio. Their
equity holdings amount to 346 percent of the value of their portfolios.
Put another way, type 1 investors purchase 71 percent of their equity
holdings on margin. When debt is exclusively used to purchase equity,
the degree of margin corresponds to the debt-to-equity ratio. Type 2
investors hold $314.6 of the risk-free security, and take a short position
of -$245.7 in the market portfolio.
At t = 0, type 1 investors are more optimistic than type 2 investors,
which is why they use leverage to increase their holdings of the market
portfolio. Type 1 investors believe that the expected return on the
market is 4.1 percent, and therefore the equity premium is 0.6 percent.
In contrast, type 2 investors short the market. They believe that the
equity premium is -0.7 percent.
The differences in beliefs at t = 0 lead to an equilibrium with
nonzero sentiment ›. Notably, equilibrium returns are established as if
the market overestimates the probability of an up-move by 12 percent,
and underestimates the probability of a down-move by 31 percent. As
Equation (5.1) indicates, nonzero sentiment impacts the SDF underly- [ Pobierz całość w formacie PDF ]

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