Consistent Multinational Assumptions

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Consistent MultinationalAssumptions

• Stochastic Investment Models
• Working Party

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Working Party Members

• Jeroen van Bezooyen
• Keith Guthrie
• Robert Howie
• Peter Ludvik
• Shyam Mehta
• Andrew Smith

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Challenging Problem

• Investment modelling for portfolio selection
• Individual / fund centric basis
• Split between cash / bonds / equities
• and between eleven possible economies
• How to choose suitable assumptions?
• Lets try historic means and variances

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Compound Returns 8 Years
Dollar investor Source Datastream
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Volatility 8 years, weekly
Annualised vol vs USD Source Datastream
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Optimising Risk / Return

• Construct efficient frontiers
• Or optimise utility
• Result only 5 asset classes feature
• broadly, the historic star performers
• Also observe unpopular assets
• Nobody optimally holds these
• Whatever base currency or risk tolerance
• Or plausible liability structure
• Eg Malaysian equities for our assumptions
• Does this make sense?

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Longer history helps but only a little bit
mean real return (arithmetic)
standard deviation
101 years real annual returns Source Dimson,
Marsh Staunton
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What to do instead?

• Use judgment to select assumed returns
• In our paper, we assumed the volatility and
  correlation estimates were OK
• Possible alternatives
• All equity markets have same return
• Return proportional to local volatility
• Country risk plus asset risk

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Alternative Assumptions
Geometric equity risk premium
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Does this give better results?

• All three alternatives have broadly the same
  effect
• Some unpopular assets remain
• Convenience yields reduced (see paper to last
  years IC for more on convenience yields)
• A step in the right direction
• Makes markets more efficient
• Is there a simple way to quantify how consistent
  assumptions are?

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Quantifying Model Efficiency
mean m
stdev s
Our technique quantifies model efficiency, not
market inefficiency
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Consequences of S
small S
large S
unconstrained optimisation
positive portfolios
value measurement
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Resulting Sharpe Ratios
S

• Assumptions still inefficient
• Using volatility weights did not help
• This is because not all the volatility is
  systematic

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Inefficiency - Recap

• We saw problems with judgmental international
  assumptions
• argued that problems are connected with
  inefficiency
• So we develop an efficiency measure
• then we can trade off model efficiency against
  parameter certainty
• to build a model that is reasonable and whose
  output makes sense

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Systematic Risk

• Important idea in framing EMH
• Measure using CAPM
• Equivalent to minimising S subject to given
  average equity risk premium
• This suggests further alternatives
• Zero premium for cash fixed premium for bonds
  equities can vary by country
• Then minimise S
• Equivalent to APT

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Hoorah!
S
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Assumptions make sense?
Geometric risk premium
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Comments on Assumptions

• Equity risk premiums vary by country
• Lowest is Malaysia
• Could even justify negative RP
• Because these are geometric means
• Arithmetic means higher by s2/2
• ie 8 if s 40
• Switzerland well diversified but leveraged
• Malaysia greater volatility, but Switzerland
  greater systematic risk (as part of portfolio)
• Switzerland merits higher arithmetic risk premium

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Conclusions

• Model building is harder for big models
• Apparently sensible judgmental assumptions may
  conceal problems
• Need a structured approach before ALM to choose
  sensible assumptions
• Good assumptions may require careful explanations
• But at least the results make sense

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Points for Discussion

• ALM exercises seek ever finer decompositions of
  asset portfolios
• Is this a good thing?
• Are we confident of model inputs
• Given extreme output sensitivity?
• Is it cheating to choose inputs by working
  backwards from desired outputs?
• Are there other ways of making international ALM
  sufficiently robust?