Resampled optimisation
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Resampled optimisation is explained further in e.g. Kemp (2010), Michaud (1998),
Scherer
(2002) and Scherer (2007).
In its mean-variance form (and using the relevant tool available through the
Nematrian website for carrying out resampled optimisation) it involves:
(a) Simulating many
different return histories (with number of observations = NoReturns) as
if they were coming from a (multi-variate) normal distribution (with mean,
standard deviations and correlation coefficients equal to the ForecastReturns,
ForecastRisks and ForecastCorrelations respectively).
(b) For each such
simulation set, calculating their mean returns, standard deviations etc. and,
in conjunction with constraints (specified in the same manner as Nematrian’s
traditional mean-variance, i.e. constrained
quadratic, portfolio optimisation engine), identifying portfolios that
efficiently trade-off risk and return given these simulated input assumptions
(c) Calculating the
average of the portfolio mixes identified in (b) and calling this the resampled
efficient portfolio.
It is ostensibly an extreme version of a ‘frequentist’
rather than a ‘Bayesian’ approach to portfolio It is ostensibly an extreme
version of a ‘frequentist’ rather than a ‘Bayesian’ approach to portfolio
construction, i.e. it ostensibly relies exclusively on the contents of the
input dataset rather than imposing any additional ‘prior’ (i.e. subjective,
analyst derived) views about the risks and returns available on different asset
categories.
However, in practice:
i.
In the absence of constraints (other than that weights add to
unity) resampled optimisation (suitably formulated) gives the same result as
more conventional mean-variance, i.e. constrained
quadratic, portfolio optimisation.
ii.
In the presence of additional constraints, resampled optimisation
gives similar results as a more conventional optimisation approach in which a
non-zero penalty is applied to portfolios close to a constraint, the penalty
becoming greater and greater (and reaching infinity) at the point in which the
constraint bites.
The net effect is to smooth out constraints. Depending on
your point of view this may be considered desirable or of limited practical
benefit.
Kemp (2010)
describes one portfolio optimiser selection exercise in which the managers felt
it appropriate to favour greater smoothness in response to small changes in the
input assumptions, which resampled optimisation could achieve. Commonly in
practice, traditional investment managers also operate under a no short-selling
constraint. Resampled optimisation would tend to result in a greater number of
modest positive positions being held than more traditional constrained
mean-variance optimisation, which might also be considered desirable on an
intrinsic diversification arguments.
Conversely, the way in which this smoothing and added
diversification is achieved is arguably largely an accidental outcome of the
methodology. If this sort of behaviour really was important for the optimiser
to exhibit then it could perhaps be achieved more succinctly and in a more
controlled fashion by imposing a more explicit penalty function on portfolios
close to the relevant constraints. Resampled optimisation is also quite time
consuming, involving relatively large numbers of simulations, each one of which
involves a separate portfolio optimisation exercise in its own right. Being a
simulation (i.e. Monte Carlo) based methodology it also does not provide
reproducible answers unless it is seeded with the same random numbers each
time.
Tools that the Nematrian website provides allowing users to
carry out resampled optimisation exercises are set out in Resampled Optimisation
Tools.
References
Kemp, M.H.D.
(2010). Extreme Events. Robust Portfolio Construction in the Presence of
Fat Tails. John Wiley & Sons
Michaud, R.
(1998). Efficient Asset Management: A Practical Guide to Stock Portfolio
Optimization and Asset Allocation. Oxford University Press.
Scherer, B.
(2002). Portfolio Resampling: Review and Critique. Financial Analysts
Journal, November/December 2002, 98-109
Scherer, B.
(2007). Portfolio Construction and Risk Budgeting. 3rd ed. RiskBooks
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