Studies into Global Asset Allocation using the Markov Switching Model October 2007

Overview Background Background Aim of thesis Aim of thesis The model The model Results Results Summary Summary

Background

The main question …. Are forecasts of financial markets more powerful if a switching process is incorporated ? Are forecasts of financial markets more powerful if a switching process is incorporated ? This question leads to many issues This question leads to many issues For today just focus on FX – although equities and bonds covered in thesis For today just focus on FX – although equities and bonds covered in thesis Background

Previous studies Forecasting returns for international financial markets (FX, Equities, Bonds) quite common in both practical and academic publications Forecasting returns for international financial markets (FX, Equities, Bonds) quite common in both practical and academic publications Harvey (1994 etc), Ilmanen (1996), Messe & Rogoff (1983) …. Harvey (1994 etc), Ilmanen (1996), Messe & Rogoff (1983) …. But very few “comprehensive” pieces – multiple markets, economic relevance But very few “comprehensive” pieces – multiple markets, economic relevance Background

Theory: Frankel – Froot Model Fair Value Time Cheap, poor momentum Expensive, strong momentum Constant interaction between value and momentum Constant interaction between value and momentum Background

Aim of the thesis

The 5 Questions 1. Is there are predictable component to international investment returns  Linear regressions 2. Is there evidence to support the Frankel – Froot model  Compare linear vs. Switching / Frankel Froot 3. What is the nature of switching in international markets  Conditional switching vs. Markov switching 4. Is there an economic relevance to the modelling  Portfolio simulations 5. Is there a memory of success of styles  Reward models Aim of the thesis

The Model

Currency Model - Value Money Supply Model Money Supply Model Strong theoretical basis Strong theoretical basis Well recognised Well recognised 12m changes for each variable (so no base year issues) 12m changes for each variable (so no base year issues) The model

Currency Model - Momentum Price Momentum & Sentiment Price Momentum & Sentiment Natural extension from Chan, Jegadeesh & Lakonishok (1996) Natural extension from Chan, Jegadeesh & Lakonishok (1996) The model

Results

Regression results 1) Is there are predictable component to international investment returns ?

Can Combine theory with model – The Markov Switching Model Markov Switching model synonymous with works of Hamilton (early 90s) Markov Switching model synonymous with works of Hamilton (early 90s) Commonly accepted non linear model Commonly accepted non linear model Been used in FX markets, very rarely seen in other asset classes Been used in FX markets, very rarely seen in other asset classes In this case – each regime is represented as a “state” In this case – each regime is represented as a “state” 2) Is there evidence to support the Frankel – Froot model

The Two States Value State Momentum State Transition 2) Is there evidence to support the Frankel – Froot model

Log Ratio Tests Not strictly comparable, but evidence quite compelling Not strictly comparable, but evidence quite compelling Frankel Froot structure stronger than 17/20 competing models Frankel Froot structure stronger than 17/20 competing models 2) Is there evidence to support the Frankel – Froot model

Conditional and Unconditional Switching Switching can be naïve and endogenous Switching can be naïve and endogenous Use this to understand the nature of the switching Use this to understand the nature of the switching Use forecast GDP (wealth) and volatility (fear) as influences on switching environment Use forecast GDP (wealth) and volatility (fear) as influences on switching environment Loosely follows a utility function Loosely follows a utility function 3) What is the nature of switching in international markets

Conditional Switching Transition Transition function 3) What is the nature of switching in international markets

Log Ratio Test Not uniformly conclusive, either very powerful or basically noise Not uniformly conclusive, either very powerful or basically noise 3) What is the nature of switching in international markets

Further conclusions Average duration of value regime >6m, while for momentum 6m, while for momentum <2m. Supports Frankel – Froot hypothesis Generally length of both regimes get shorter in volatility – whipsawing of investment styles, while regimes get longer in times of wealth Generally length of both regimes get shorter in volatility – whipsawing of investment styles, while regimes get longer in times of wealth 3) What is the nature of switching in international markets

Economic Relevance 4) Is there an economic relevance to the modelling ?

Economic Relevance Also ran optimised portfolios Also ran optimised portfolios 4) Is there an economic relevance to the modelling ?

Economic Relevance More powerful forecasts from switching More powerful forecasts from switching Other markets show that cross sectional information increases, although time series decreases Other markets show that cross sectional information increases, although time series decreases Money can be made from these models Money can be made from these models 4) Is there an economic relevance to the modelling ?

Is there memory ? “The model of speculative bubbles developed by Frankel and Froot (1988) says that over the period of , the market shifted weight away from the fundamentalists, and towards the technical analysts or “chartists”. This shift was a natural Bayesian response to the inferior forecasting record of the former group, as their forecasts of dollar depreciation continued to be proven wrong month after month” “The model of speculative bubbles developed by Frankel and Froot (1988) says that over the period of , the market shifted weight away from the fundamentalists, and towards the technical analysts or “chartists”. This shift was a natural Bayesian response to the inferior forecasting record of the former group, as their forecasts of dollar depreciation continued to be proven wrong month after month” Frankel, Jeffrey and Froot Kenneth, October 1990, pg 22 Frankel, Jeffrey and Froot Kenneth, October 1990, pg 22 5) Is there a memory of success of styles ?

Test with reward model Reward of 1,-1, based on the success of last month Reward of 1,-1, based on the success of last month Do 5 years of rolling regressions Do 5 years of rolling regressions Test values of λ for relevance Test values of λ for relevance Can also compare against each regime (see who is forgotten quickest) Can also compare against each regime (see who is forgotten quickest) 5) Is there a memory of success of styles ?

Graph of reward model 5) Is there a memory of success of styles ?

Test with reward model Reward of 1,-1, based on the success of last month Reward of 1,-1, based on the success of last month Do 5 years of rolling regressions Do 5 years of rolling regressions Test values of λ for relevance Test values of λ for relevance Can also compare against each regime (see who is forgotten quickest) Can also compare against each regime (see who is forgotten quickest) 5) Is there a memory of success of styles ?

Reward model results Has memory, momentum forgotten quicker (truely short term) Has memory, momentum forgotten quicker (truely short term) 5) Is there a memory of success of styles ?

Summary Markets have some level of predictability Markets have some level of predictability Switching better than linear Switching better than linear Regime switching may lead to less “accurate” individual forecasts – but possibly contain more information Regime switching may lead to less “accurate” individual forecasts – but possibly contain more information Can loose information in time series, but gain cross sectional information. Can loose information in time series, but gain cross sectional information. Summary

Summary Switching in defensive assets more likely to be driven by fear, where in aggressive assets more likely to be driven by greed Switching in defensive assets more likely to be driven by fear, where in aggressive assets more likely to be driven by greed Regime switching portfolios outperform linear counterparts Regime switching portfolios outperform linear counterparts Memory exists – but differs between markets and asset classes Memory exists – but differs between markets and asset classes Frankel – Froot model well supported Frankel – Froot model well supported Summary

Comprehensive Testing Regression results (linear, regime switching) Regression results (linear, regime switching) Forecast analysis (in / out of sample statistical) Forecast analysis (in / out of sample statistical) Simulated portfolios (optimised and naïve) Simulated portfolios (optimised and naïve) 5 currencies, 9 equity markets, 6 bond markets 5 currencies, 9 equity markets, 6 bond markets 10 years data 10 years data Over 10,000 regressions Over 10,000 regressions Summary