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Studies into Global Asset Allocation using the Markov Switching Model October 2007 Overview Background Aim of thesis The model Results Summary Background The main question …. Are forecasts of financial markets more powerful if a switching process is incorporated ? This question leads to many issues 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 Harvey (1994 etc) , Ilmanen (1996), Messe & Rogoff (1983) …. But very few “comprehensive” pieces – multiple markets, economic relevance Background Theory: Frankel – Froot Model Expensive, strong momentum Time Cheap, poor momentum Fair Value Constant interaction between value and momentum Background Aim of the thesis The 5 Questions 1. Is there are predictable component to international investment returns 2. Is there evidence to support the Frankel – Froot model 3. Conditional switching vs. Markov switching Is there an economic relevance to the modelling 5. Compare linear vs. Switching / Frankel Froot What is the nature of switching in international markets 4. Linear regressions Portfolio simulations Is there a memory of success of styles Reward models Aim of the thesis The Model Currency Model - Value Money Supply Model returnt 1 1 (mt m ) 2 ( gt g ) * t * t 3 (it i ) 4 ( t ) * t * t Strong theoretical basis Well recognised 12m changes for each variable (so no base year issues) The model Currency Model Momentum Price Momentum & Sentiment 12MonthConsensusFXra tet-1 Sentiment Spott-1 Spott1 Forward t1,t2 Momentum Forward t1,t2 Natural extension from Chan, Jegadeesh & Lakonishok (1996) The model Results Regression results Table 5.11 Results from OLS Estimation: The table below shows the linear regression results for the model detailed in 5.1.3. Estimation period is from December 1993 – December 2003. Coefficients are given with associated t-statistics in parenthesis Australia Canada Germany Japan UK Constant -0.0168 0.003 0.0103 -0.0069 -0.0014 (-2.3711) (0.6688) (1.4692) (-0.2584) (-0.3064) IP -0.0002 -0.0053 -0.0025 -0.0041 -0.0023 (-0.0555) (-2.0808) (-0.9) (-1.8642) (-1.0539) CPI 0.0052 0.0003 0.0111 -0.0058 0.0117 (1.2051) (0.1116) (1.2337) (-0.5653) (1.3318) Short 0.0085 0.0037 0.003 0.0028 0.0034 (3.9528) (2.6544) (1.452) (1.353) (1.149) MS 0.0006 0.0008 0.0002 0.0012 0.002 (0.4974) (1.5945) (0.2689) (0.853) (2.296) Trend 0.1096 0.0431 0.0784 0.0874 -0.0034 (0.9388) (0.315) (0.7238) (0.6318) (-0.0282) Consensus 0.1443 0.1213 0.0294 0.1084 0.2296 (1.7381) (1.0659) (0.5195) (0.8043) (2.162) R2 Adj R2 Avg Log Likelihood DW F Prob 0.1542 0.110 2.198 0.1452 0.100 2.744 0.1197 0.073 2.202 0.0612 0.012 1.922 0.1023 0.055 2.463 1.9631 0.0035 1.9748 0.0057 1.9971 0.0220 2.021 0.2919 2.0162 0.0514 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) Commonly accepted non linear model Been used in FX markets, very rarely seen in other asset classes 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 d ( yt | st ) 1 Val ( yt Valuet 1 ) exp 2 Val 2 Momentum State d ( yt | st ) 1 mom ( yt Momentumt 1 ) exp 2 mom 2 1 Pu Pu u 1 Q Q Transition u u 2) Is there evidence to support the Frankel – Froot model Log Ratio Tests Switching Model Linear df.=9 Prob Australia 277.73 263.76 27.94 0.10% Canada 335.30 329.28 12.05 21.07% Euro 276.75 264.24 25.02 0.29% Japan 246.25 230.64 31.21 0.03% UK 301.79 295.56 12.45 18.90% Not strictly comparable, but evidence quite compelling 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 Use this to understand the nature of the switching Use forecast GDP (wealth) and volatility (fear) as influences on switching environment Loosely follows a utility function 3) What is the nature of switching in international markets Conditional Switching Transition 1 Pu Pu u 1 Q Q u u Transition function exp( p 0 p1 1) Pt 1(1,1) 1 exp( p 0 p1 1) Pt 1(1,2) 1 Pt 1(1,1) 3) What is the nature of switching in international markets Log Ratio Test Switching s.t. GDP df = 1 Prob Australia 279.16 2.86 90.89% Canada 337.58 4.55 96.71% Euro 270.59 -12.32 0.00% Japan 240.20 -12.10 0.00% UK 301.69 -0.19 0.00% Switching s.t.Vol df =1 Prob 277.99 0.51 52.41% 337.55 4.50 96.61% 269.79 -13.92 0.00% 245.18 -2.13 0.00% 301.25 -1.07 0.00% Markov Model 277.73 335.30 276.75 246.25 301.79 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 <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 3) What is the nature of switching in international markets Economic Relevance Mean Squared Prediction Error Australia Linear 0.11% Switching 0.10% GDP 0.10% Vol 0.10% Canada 0.03% 0.03% 0.03% 0.03% Euro 0.09% 0.08% 0.11% 0.08% Japan 0.09% 0.08% 0.16% 0.17% UK 0.06% 0.05% 0.05% 0.06% Median 0.09% 0.08% 0.10% 0.08% Australia 3.84% -8.47% 6.17% 13.16% Canada 15.21% 18.23% 13.37% 16.00% Euro 23.05% 33.72% 22.24% 29.38% Japan -16.56% 0.66% -12.62% 8.42% UK 2.77% 19.73% 9.25% -4.29% All 8.10% 16.08% 5.59% 11.05% IC's (out of Sample) Linear Model Switching Model GDP Vol Average Rank Information Coefficient Linear Markov Switching Out of Sample Rank IC 9.50% 12.00% St. GDP St. Vol 6.50% 14.50% 4) Is there an economic relevance to the modelling ? Economic Relevance Naïve Portfolios Linear Markov Sw. GDP Vol Full Sample Average 12m Return Risk Info Ratio Success Rate 2.72% 2.52% 1.079 64.17% 2.05% 2.79% 0.734 60.83% 2.67% 2.74% 0.9716 65.83% 2.47% 2.65% 0.9336 67.50% Out of Sample Average 12m Return Risk Info Ratio Success Rate 0.77% 2.23% 0.343 56.67% 1.38% 2.20% 0.625 60.00% 0.53% 2.28% 0.233 60.00% 1.31% 2.21% 0.594 63.33% Also ran optimised portfolios 4) Is there an economic relevance to the modelling ? Economic Relevance More powerful forecasts from switching Other markets show that cross sectional information increases, although time series decreases 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 1981-85, 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 5) Is there a memory of success of styles ? Test with reward model Pmom ,t PrS t j | S t 1 i, Z t 1 exp(a ( m ,t 1 ) 2 ( m ,t 2 ) 3 ( m ,t 3 )...... 6 ( m ,t 6 )) 1 exp( ( m ,t 1 ) 2 ( m ,it 3 ) 3 ( m ,t 3 )..... 6 ( m ,t 6 )) Reward of 1,-1, based on the success of last month Do 5 years of rolling regressions Test values of λ for relevance 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 Do 5 years of rolling regressions Test values of λ for relevance Can also compare against each regime (see who is forgotten quickest) 5) Is there a memory of success of styles ? Reward model results With Memory Australia 134.722 Canada 161.894 Euro 135.561 Japan 134 UK 154.909 No Memory df =1 Prob 134.223 0.997 31.81% 160.551 2.684 10.13% 132.099 6.925 0.85% 131.494 5.012 2.52% 139.861 30.095 0.00% Has memory, momentum forgotten quicker (truely short term) 5) Is there a memory of success of styles ? Summary Markets have some level of predictability Switching better than linear 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. Summary Summary 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 Memory exists – but differs between markets and asset classes Frankel – Froot model well supported Summary Comprehensive Testing Regression results (linear, regime switching) Forecast analysis (in / out of sample statistical) Simulated portfolios (optimised and naïve) 5 currencies, 9 equity markets, 6 bond markets 10 years data Over 10,000 regressions Summary