Published on October 19, 2007
Consistent MultinationalAssumptions: Consistent Multinational Assumptions Stochastic Investment Models Working Party Working Party Members: Working Party Members Jeroen van Bezooyen Keith Guthrie Robert Howie Peter Ludvik Shyam Mehta Andrew Smith Challenging Problem: 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 Compound Returns: 8 Years: Compound Returns: 8 Years Dollar investor Source: Datastream Volatility: 8 years, weekly: Volatility: 8 years, weekly Annualised vol vs USD Source: Datastream Optimising Risk / Return: 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? Longer history helps – but only a little bit: Longer history helps – but only a little bit 101 years’ real annual returns Source: Dimson, Marsh & Staunton standard deviation mean real return (arithmetic) What to do instead?: 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 Alternative Assumptions: Alternative Assumptions Geometric equity risk premium Does this give better results?: Does this give better results? All three alternatives have broadly the same effect Some unpopular assets remain Convenience yields reduced (see paper to last year’s 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? Quantifying Model Efficiency: Quantifying Model Efficiency stdev s mean m Our technique quantifies model efficiency, not market inefficiency Consequences of S: Consequences of S unconstrained optimisation positive portfolios value measurement small S large S Resulting Sharpe Ratios: Resulting Sharpe Ratios Assumptions still inefficient Using volatility weights did not help This is because not all the volatility is systematic S Inefficiency - Recap: 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 Systematic Risk: 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 Hoorah!: Hoorah! S Assumptions make sense?: Assumptions make sense? Geometric risk premium Comments on Assumptions: 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 Conclusions: 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 Points for Discussion: 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?