MSC BANKING & FINANCE, MSC FINANCE (ASSET PRICING)
AND MSC FINANCE ANALYTICS
7SSMM716 PRINCIPLES OF BEHAVIOURAL FINANCE
MOCK EXAMINATION SOLUTIONS
Section A
Answer 1
a) FALSE. Uncertainty is the situation where the true probabilities
are not known. On the other hand, it is a feature of Prospect
Theory that true probabilities are known but
over/underweighted.
b) FALSE. It corresponds to risk-averse behavior.
c) TRUE. Under categorical/coarse thinking, investors allocate
stocks to coarse categories and only update allocation when
there is enough data to suggest another category is a better fit.
Thus, if the news under question is that which precipitates a
change in category allocation (e.g., from “medium earnings
growth” to “high earnings growth”), then the stock price will
react disproportionately to the actual fundamental news.
d) FALSE. Attention effects are more likely to affect buying than
selling decisions. On the one hand, people usually sell the stocks
they already own, so they can pay attention to all of them. On
the other hand, people select which stock to buy from a universe
of thousands of stocks, so their buying decision is more likely to
be affected by attention-getting events. Barber and Odean
(2008), “All that glitters: the effect of attention and news on the
buying behavior of individual and institutional investors” tests
and verifies this hypothesis.
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Answer 2
Under exponential discounting, the utility at time from
consumption stream ( , … , ) is given by ( , … , ) =
∑ ()(+)−=0 , where () = with 0 < < 1 is the discount
function. Under hyperbolic discounting, the discount function is () =
1
1+
with > 0, and under quasi-hyperbolic discounting it is () =
�
1 , for = 0
, for > 0 , with 0 < < 1.
[Note: See below in Answer 2 in Section B for detailed advice on
how to enter math during the exam.]
While exponential discounting assumes a constant discount rate,
hyperbolic discounting allows for a decreasing discount rate. As a
result, the latter allows for time inconsistency, and can explain time
preference reversals and the preference for commitment.
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Section B
Answer 1
Own-company-stock bias refers to the phenomenon that a significant
proportion of individuals invest a significant proportion of their wealth
in the stock of the company for which they work.
Evidence on this phenomenon is provided by Benartzi (2001) in
“"Excessive Extrapolation and the Allocation of 401(k) Accounts to
Company Stock.” Benartzi (2001) studies 401(k) plan contributions and
finds that, on average, individuals invest over 30% of their plan
contributions in their employer’s stock.
This phenomenon is puzzling because it implies under-diversification,
both because an individual who over-invests in his employer’s stock
holds an under-diversified stock portfolio, and because the employer’s
stock returns are positively correlated with the individual’s labour
income. While it is conceivable that individuals invest in their
employer’s stock because they have superior information about it, the
data doesn’t support this hypothesis, as it has been found that
allocations to company stock are uncorrelated with its subsequent
returns.
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Answer 2
a) If the individual checks his portfolio at the end of each year,
then his utility is
1,2 = 1 + 2 = () + (1 − )(−) + () + (1 − )(−) = 2[ − (1 − )].
If he checks his portfolio at the end of year 2 only, then his
utility is
2 = 2(2) + 2(1 − )( − ) + (1 − )2(−2) = 22 + 2(1 − )( − ) − 2(1 − )2.
The individual chooses to check the portfolio at the end of year 2
only, if 2 > 1,2. We calculate
2 − 1,2 = 22 + 2(1 − )( − ) − 2(1 − )2
− 2[ − (1 − )] = 2(1 − )( − 1),
which is positive since 1 − > 0 and > 1, by assumption.
[Note: There are multiple options for writing the above during
the actual exam:
1. You can type it nicely, as above, using Microsoft Word’s
Equation Editor. To enter the Equation Editor, press Alt
followed by the = sign (i.e., use the keyboard shortcut Alt+=),
or go to Insert on the Ribbon menu and click on Equation.
2. You can type it crudely (but legibly). For example, you could
type the second equation from above as follows:
U_2 = p^2 v(2G) + 2p(1-p) v(G-L) + (1-p)^2 v(-2L)
= 2p^2 G + 2p(1-p)(G-L) – 2(1-p)^2 lambda L
3. You can write all the equations on a piece of paper, take a
photo using your mobile phone (or scan, e.g., using Microsoft’s
Office Lens app, available for free for both iPhone and
Android), and then transfer this photo to your computer and
insert it into your Word file by going to Insert on the Ribbon
menu, clicking on Pictures, and selecting your picture.
Please ensure that, whichever way you choose, yields a
legible solution, else it will not be marked. It would be worth
trialing each of the above solutions before the actual exam.]
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Thus, the individual chooses to only check his portfolio at the
end of year 2. The intuition is that, checking at the end of the
second year gives a chance for the portfolio to make up for any
losses that might have taken place during the first year. The
probability of ending up with a loss on any given year is 1 − ,
but the probability of ending up with a loss at the end of the two
years is only (1 − )2. Given loss aversion, diminishing the
probability of losses increases the overall utility.
b) The BSV (1998) model explains short-run momentum, long-run
reversals, and the value effect through conservatism and
representativeness. That is, it is a beliefs-based explanation of
these phenomena, according to which they arise due to excessive
optimism/pessimism about future earnings followed by their
correction. If this explanation is correct, then these corrections
should coincide with the release of surprising public information,
which lets investors know that their previous beliefs were too
extreme and the prices were incorrect. This implication (hence
the model) would be verified empirically if a disproportionate
fraction of premia to prior losers (reversal) and to value stocks
(the value effect) was earned around earnings announcements,
which is the statement in (i).
The statement in (ii) is wrong (it is the opposite of the true
empirical observation that value stocks earn more than glamour
stocks, on average); this observation couldn’t verify the BSV
(1998) model as the model tries to explain the opposite.
The statement in (iii) is simply the statement of the value effect;
this is the observation that the BSV (1998) model tries to explain,
but it doesn’t verify the specific explanation offered by this
model.
The statement in (iv) is an empirical observation that relates to
the dispersion-of-opinion explanation of the value effect, not the
BSV (1998) model.
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Answer 3
a) According to the availability heuristic, judgments are made by
remembering related instances or imagining relevant scenarios.
The 2008 financial crisis is an event that many people are
familiar with and something they would quickly bring to mind
when thinking about the market’s returns.
According to the anchoring and adjustment heuristic, individuals
make estimates by starting from an initial value (the anchor) and
making an adjustment.
Combining the above two heuristics, an investor making a
judgment about the market returns in 2010 would anchor his
belief at the 2008 return of -26% and adjust upward (as there was
no crisis in 2010). We don’t know how far he would adjust—this
would indeed depend on his familiarity with the economy in 2010
and/or his personal experiences—but a reasonable guess would
be that his estimate would be some single-digit negative value,
e.g., -5%. Obviously, there is no single correct answer here, but
rather any answer would be judged on how it is argued.
b) One possible explanation is that practitioners learn quickly about
any predictable pattern and exploit it to the extent that it
becomes no longer profitable. Another possible explanation is
that some of these patterns were never sufficiently large or
stable and were simply the result of data mining. It is not
unlikely that the combination of a certain sample and
methodology has produced a statistically significant result that
didn’t really exist.
c) A possible explanation is based on the representativeness bias:
when forecasting the future growth in house prices, home buyers
over-extrapolated the past growth in these prices. This led them
to overpay for their new homes and to take out loans with
excessively high loan-to-value ratios. Furthermore, the rating
agencies may have given AAA ratings to mortgage-backed
securities that did not truly deserve them, because they also
extrapolated the past growth in home prices too far into the
future, which, in turn, led them to severely underestimate the
probability of defaults.
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Answer 4
• Anomalous patterns may not be statistically significant. You need
to make sure that you have used proper econometric analysis and
statistical tests.
• Anomalous patterns may be statistically but not economically
significant. You need to check if the suspected inefficiency is
greater than the transaction costs.
• Data mining. Many analysts search for patterns, therefore some
patterns are bound to be found, even if they are simply sampling
artefacts.
• Strategies that gain excess returns may also be riskier. You need
to have the correct risk adjustment. This is the joint hypothesis
problem.