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Risk Tolerance
Essential, behavioural and misunderstood
Greg B Davies – Barclays; Oxford
Peter Brooks - Barclays
November 2013
ABSTRACT
An understanding of an investor’s risk tolerance is essential to determining investment
suitability and yet there is no universally agreed definition of what risk tolerance is. We discuss
the need for a holistic approach to measuring risk tolerance that provides a consistent
framework for constructing efficient multi-asset allocation and ensuring a suitable aggregate
level of risk and return, given the investor’s personality and financial circumstances. Risk
tolerance is only stable when considered as a personality trait, which can be measured
effectively using holistic psychometric scales. Attempts to measure risk tolerance at lower levels
of granularity are unstable; accentuate, rather than mitigate short-term behavioural distortions;
and cannot be meaningfully aggregated to provide an overall level of risk that is appropriate
given the investor’s risk capacity. This implies that the recent move towards mental accounting,
goal-based, assessments of risk tolerance is misguided and exposes institutions to risks
associated with providing unsuitable advice.
Keywords: holistic risk tolerance, investment suitability, portfolio construction, investing
behaviour
ARTICLE
Whether you are a financial advisor, compliance officer, or regulator, you probably agree that
understanding the risk tolerance of an individual investor is essential to providing good advice.
It is startling, however, that there is no universally agreed definition of what risk tolerance is; let
alone any consensus on how to measure it. This exposes banks to considerable risks: without a
sound assessment of a client’s risk tolerance it is impossible to adequately ensure that
investment advice is suitable to the client, a key regulatory requirement in many jurisdictions
globally. Offering advice that is not suitable for the client’s needs opens the institution to
regulatory risk, reputational risk, and increasingly, conduct risk.
This leads to the very natural question: what are we measuring the investor’s risk tolerance of?
Are we looking at it from the point of view of a single goal or product? Is it being measured at
individual portfolio level (e.g., pension vs. dealing account)? In our view, all of these starting
points are incorrect.
Risk tolerance is essentially the degree to which someone is prepared to trade the chance of
failing to achieve some additional but less-important goals, for the risk of not achieving some
more-important ones. That is, individuals’ willingness to take on additional risk that could
reduce their future wealth (and thus ability to fund important future cash flows), in the pursuit
of greater wealth, which would permit them to both meet these cash flow, but also to engage in
more aspirational, discretionary spending in addition. Risk tolerance is thus about investors’
holistic, broadly framed, thoughtful, and long-term willingness to trade-off potential future
outcomes, not about their immediate inclination to take risk (which we can term risk appetite)
or their perceptions of risk1
Risk tolerance, thus defined, is a broad psychological trait which inheres in the individual as a
whole, considering the trade-offs they’re called to make over their whole wealth, considering all
their future goals. Attempting to measure risk tolerance, or indeed any psychological trait, at
lower levels of portfolio construction, or for a part of an individual, is meaningless: it cannot be
achieved in a stable way and leads to inflexible portfolio construction, which may not aggregate
to an appropriate level of risk.
. These latter two certainly affect observed risk taking, but are
heavily influenced by a whole raft of behavioural biases and short-term, reference-, framing-
and context-dependent considerations that should be excluded from assessments of the
investor’s degree of long-term risk tolerance, not pandered to, and optimized for.
In addition, examining components of wealth at a lower level also forces investors into narrow
framing, which accentuates behavioural distortions of risk attitudes due to loss aversion,
because narrower frames increase the proportion of perceived losses (Thaler[1]). For example,
Rabin[2] shows that observed levels of risk aversion over small gambles, imply absurd levels of
risk aversion for larger amounts. An advisor attempting to assess risk tolerance for multiple
portfolio components simultaneously (often using the same risk questionnaire) is asking too
much of clients, with inadequate tools. This is neither good advice nor efficient portfolio
construction; the result is a muddled construct that can lead to issues of risk capacity being
ignored.
A further concern is that suitability can only be truly determined by considering the combined
effects of risk tolerance and risk capacity. It is not our goal here to clarify the equally
misunderstood notion of risk capacity, but it is crucial to note that it is an inherently holistic
notion. For the sake of context, a simple description might be: if you are likely to need to dip into
capital, or sell investments, to fund any liabilities (current, ongoing or anticipated future
expenditure), then your capacity to take risk is constrained. When all planned expenditures can
be met from anticipated income, we may say that risk capacity is neutral, or high (in cases
where individuals expect to be able to fund all anticipated future expenditure and still
accumulate wealth).
Where risk capacity is neutral, the appropriate level of risk is determined solely by risk
tolerance. Where risk capacity is constrained (for example, by large near term expenditures, or
where the investor has little future income to rely as retirement approaches) investment risk
should be commensurately reduced, and where it is high (e.g., early in life where investors have
many years of anticipated net saving ahead) the investor may comfortably take on more risk.
Since risk capacity considers the totality of all anticipated expenditure, we require a holistic
measure of risk tolerance to match to risk capacity, or else we’re inconsistently combining two
incomparable concepts measured at different levels.
Crucially, the measure also needs to be stable. It is clear that self-reported risk tolerance
measures are inadequate. Wang’s[3] financial interpretation of the famous Asian disease
problem[4], is among the many studies that shows how easy it is to influence financial choice by
changing the way information is framed. Additionally, self-reporting risk tolerance is
susceptible to changes in risk perception through the market cycle. Risk tolerance, as we define
it, is a stable psychological trait, but risk perception is not. Weber et al.[5] provide evidence that
1 In a traditional economic context where we assume that all investors are Homo economicus, and act
according to the economic axioms of rationality, then we may see risk tolerance as being the inverse of
risk aversion that arises from the curvature of their ‘rational’ utility function over total wealth at the
appropriate time horizon.
risk perception, and consequently investing behaviour, changes significantly with market cycles.
This is often associated with a cycle of fear and greed that compels investors to invest more at
the top of the market – when risk is perceived to be low, but is arguably at its highest – and to
sell investments in favour of cash at the bottom of the market – when risk perception is highest.
Asking, often-unsophisticated investors to self-report their risk tolerance is dangerously
unstable and leads to poor advice.
Many advisors have adopted risk tolerance questionnaires, but this does not guarantee that the
result measures risk tolerance at all[6]. Approaches that require numerical trade-offs or
probabilistic reasoning (e.g. willingness to accept percentage losses or hypothetical reactions to
those losses) pick up a great deal of the variance in risk perception and cannot isolate stable risk
tolerance. Indeed, using this method leads to institutionalised procyclical, ‘buy-high, and sell-
low’ behaviour. At the holistic level, we can use psychometric testing to ascertain something
stable and important about the degree to which an investor is comfortable making the trade-off
between more and less achievable goals. Egan et al.[7] make the case for psychometric
assessment being the best approach for such a holistic measurement; and Davies and de
Servigny[8] show how this can be linked directly to portfolio optimisation by using the risk
tolerance score to parameterise a utility function in a generalisation of modern portfolio theory
they call Behavioural Modern Portfolio Theory.
This does not mean that the investor is not willing to risk not achieving certain goals relative to
others – some are less important, further away, or more contingent on what happens in the
future – but assessing this is properly done by adjusting risk capacity for the importance and
timing of the investor's goal structure2
On this point we disagree with the assertion made by Das et al.[9] “that investors are better able
to state thresholds and probabilities for sub-portfolios (e.g. retirement, bequest, education) than
for an aggregate portfolio.” As an assumption of investors’ introspective ability, and of the
accuracy and stability of assessment techniques beyond those measuring holistic psychological
traits, we find this implausible. Establishing stable risk preferences is difficult at any level, but
only at the holistic level can we rely on established psychometric testing techniques to measure
a stable personality trait. At any other level, we can only observe an unstable jumble of risk
preferences and perceptions, which, even if they could be measured adequately, may not
aggregate to anything sensible.
, not by asking investors to separately establish a level of
risk tolerance for many independent goals.
Das et al.[9] show that, under restrictive technical assumptions, mean-variance optimised sub-
portfolios aggregate to a portfolio that itself lies on the efficient frontier. This, however, is only
possible because of a number of assertions regarding the behaviours and abilities of the
investor that we feel cannot be substantiated in the real world. First, psychometric traits are not
valid at the level of individual goals. Second, we know that requiring probabilistic trade-offs as
an assessment method doesn't work – it may be valid to ask individuals to ascribe a level of
priority to goals, but not to ask for precise risk preferences (or, in many cases, even precise
timings or magnitudes). Third, the goals themselves are unstable and contingent. Hard coding
them by separating them into 'pots', each with its own risk tolerance, loses the very valuable
flexibility of being able to adjust goals to circumstances and preferences, thus perpetuating the
status-quo bias in a way that may be harmful to the investor. Fourth, even if it were possible to
adequately establish separate degrees of risk tolerance for separate components of the
2 Considering goals as future expenditures means that goals’ proximity and priority are major
components of determining risk capacity, and so the relative importance of marginal goals should already
be incorporated in the risk capacity. This allows us to use the combination of risk capacity and risk
tolerance directly in establishing the appropriate portfolio.
portfolio, this would still require a holistic assessment of how they work together and whether
the resulting overall risk was appropriate. We have to have some way of assessing how the risks
attributed to each component affect risk in all the other elements; we also need a means of
determining whether the overall effect on the individual's wealth is reasonable. That requires a
holistic measurement of risk tolerance.
Defining risk tolerance at a holistic level is frequently a necessary tool for the financial advisor
wherever assessing investment suitability is important. By combining a stable, holistic and
meaningful measure of risk tolerance with one of risk capacity – to establish the risk profile for
the investor’s total assets – it becomes possible to build an efficient multi-asset allocation that
delivers the optimal aggregate combination of risk and return. Though there is much to this
beyond an accurate risk tolerance assessment, understanding the degree to which investors are
psychologically disposed to trade-off the risk of poor outcomes for the chance of good outcomes
is an essential and core component of providing suitable advice, and thus of mitigating the many
risks of providing poor and unsuitable advice.
REFERENCES
[1] Thaler, R. H. (1999), Mental Accounting Matters. Journal of Behavioral Decision
Making, 12: 183–206.
[2] Rabin, M. (2000), Risk Aversion and Expected-utility Theory: A Calibration Theorem.
Econometrica, 68: 1281–1292.
[3] Wang, X. T. (1996), Framing effects: Dynamics and task domain. Organizational
Behavior andHuman Decision Processes, 68, 145–157.
[4] Tversky, A., & Kahneman, D. (1981), The Framing of Decisions and the Psychology of
Choice. Science, 211, 453–458.
[5] Weber, M., Weber, E. U., and Nosic A. (2013), Who Takes Risks When and Why:
Determinants of Changes in Investor Risk Taking, Review of Finance, 17(3), 847-83.
[6] Financial Services Authority (2011), Guidance Consultation, Assessing Suitability:
Establishing the risk a customer is willing and able to take and making a suitable
investment selection.
[7] Egan, D., Davies, G. B. and Brooks, P. (2011), Comparisons of Risk Attitudes Across
Individuals. Wiley Encyclopedia of Operations Research and Management Science.
[8] Davies, Greg B. and de Servigny, A. (2012), Behavioral Investment Management: An
Efficient Alternative to Modern Portfolio Theory. McGraw-Hill.
[9] Das, S., Markowitz, H., Scheid, J., & Statman, M. (2010), Portfolio Optimization with
Mental Accounts. Journal of Financial and Quantitative Analysis, 45(2), 311.
