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2 March 8, 2016 Sakkakom Maneenop, Ph.D. Outline Risk and return of AEC investments Correlation structure and risk diversification Optimal AEC portfolio allocation Modern portfolio theory Correlation and risk reduction Efficient frontier and the Capital Market Line Efficient portfolios based on selected data Topics in portfolio allocation Short-sale constraint Variance-Covariance matrix alternatives Black-Litterman approach Strengths and weaknesses of MPT

3 Notes on data All data are collected from Bloomberg Monthly data from Dec 2007 to Dec 2015, total of 97 observations MSCI equity data (Total return index net dividends) of Thailand (MXTH), Malaysia (MXMY), Singapore (MXSG), Indonesia (MXID), The Philippines (MXPH), Vietnam (MXVI), The U.S. (MSCI Equity), and Japan (MXJP) Exchange rate of USDTHB, USDMYR, USDSGD, USDIDR, USDPHP, USDVND, USDJPY Risk-free rate of Thailand (BOFX1M) Risk & return of AEC investments This section is to introduce that risks/returns from AEC investments depend on both equity and currency components RTHB 1RAEC 1eAECTHB 1 R e R e AEC AECTHB AEC AECTHB Then, the variance of the return can be expressed as: RTHB RAEC eaecthb RAECeAECTHB R e R e R e Var Var Var 2Cov Var Var Var 2Corr Vol Vol Var AEC AECTHB AEC AECTHB AEC AECTHB Positive or negative correlation? If positive capital flows play an important role If negative improvement in competitiveness and profitability

4 Risk & return of AEC investments Decomposition of the return variance Country Var (R_THB) Components of Variance Var (R_XXX) Var (e_xxxthb) 2Cov Delta_Var Malaysia 0.22% 0.14% 66.37% 0.03% 16.13% 0.04% 17.77% 0.00% -0.27% Singapore 0.41% 0.36% 87.51% 0.03% 6.21% 0.03% 6.12% 0.00% 0.16% Indonesia 0.77% 0.51% 66.12% 0.08% 9.72% 0.20% 26.04% -0.01% -1.88% Philippines 0.35% 0.33% 94.43% 0.02% 5.80% 0.00% 0.13% 0.00% -0.35% Vietnam 0.87% 0.85% 97.55% 0.04% 4.74% -0.02% -2.06% 0.00% -0.23% US 0.91% 0.95% % 0.03% 3.33% -0.07% -7.87% 0.00% 0.19% Japan 0.19% 0.36% % 0.09% 48.36% -0.26% % 0.00% 2.02% Thailand 0.45% 0.45% % 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% A large portion of the risk arises from stock volatility Cross-product term contributes less relatively Correlation structure & risk diversification Total risk = unsystematic risk + systematic risk Unsystematic risk: the risk that comes with the company or industry. This risk can be reduced by portfolio diversification Systematic risk: the risk that remains even after investors fully diversify their portfolio as there are systematic sources of variation that affect all stocks in the same way Macroeconomic forces interest rates When foreign stocks are added, these risks can partly be diversified away because Thai monetary policies and business cycles are not perfectly correlated with those of the rest of the world Source: Bekaert and Hodrick (2011)

5 The reduction of unsystematic risk Portfolio risk Total risk Unsystematic risk + systematic risk Unsystematic Risk Thai stocks σ m Systematic Risk Number of securities in the portfolio The reduction of unsystematic risk Portfolio risk σ m Thai stocks σ m AEC stocks Number of securities in the portfolio

6 Correlation structure & risk diversification Stock returns of countries that are in close geographic proximity to one another and have significant exports & imports to one another correlate more highly Trade increases correlations, presumably because importing & exporting firms are affected by the economic factors in the other countries The lowest correlations are observed for Thailand & Vietnam The highest = Thailand & Singapore Industrial structures firms in the same industry are likely to be buffeted by the same shocks affecting CFs and profitability Policies affecting the degree of integration and the independence of business cycles appear to be important determinants of cross-country correlations Contagion phenomenon increased volatility may lead to temporarily increased correlations Source: Bekaert and Hodrick (2011) Correlation structure & risk diversification Corr Thailand Malaysia Singapore Indonesia Philippines Vietnam Mean SD Sharpe Thailand % 6.74% Malaysia % 4.64% Singapore % 6.41% Indonesia % 8.80% Philippines % 5.93% Vietnam % 9.35%

7 Optimal AEC portfolio allocation Modern portfolio theory Correlation and risk reduction Efficient frontier and the Capital Market Line Calculate efficient portfolios based on selected data Modern portfolio theory Investors are risk-averse When two investments have the same expected return, investors prefer the lower risk investment When two investments have the same risk, investors prefer the investment with the higher expected return Investors know expected returns, variances, and covariances for all assets Frictionless markets: No taxes or transactions costs Investors use mean-variance analysis to identify optimal or efficient portfolios

8 Modern portfolio theory Two assets w w, w 1w w w 2w w Three assets p p w w 2w w w w w p w w w 2ww 2ww 2ww p Correlation and risk reduction E(R p ) r 1 100% Stock 1 ρ= +1 r 2 100% Stock 2 Total risk σ 2 σ p w11 w22 2 w1w212(1) Individual asset returns are 2 perfectly correlated, there are no w11 w22 gains from diversification w w p

9 Correlation and risk reduction E(R p ) r 1 ρ= % Stock 1 r 2 100% Stock 2 Total risk σ 2 σ p w11 w22 2 w1w212( 1) Individual asset returns are perfectly 2 (but negatively) correlated, risk can w11 w22 be eliminated via diversification w w p Correlation and risk reduction E(R p ) r 1 ρ= % Stock 1 r 2 100% Stock 2 ρ= +0.4 σ 2 σ 1 Lower correlation greater diversification benefits Total risk

10 Correlation and risk reduction E(R p ) r 1 ρ= -1 ρ= % Stock 1 ρ= +1 r 2 100% Stock 2 ρ= +0.4 σ 2 σ 1 Lower correlation greater diversification benefits Total risk The efficient frontier In the case with two risky assets, the choice of w simultaneously determines portfolio return and standard deviation Adding assets shifts the efficient frontier to the left E(R p ) More assets Fewer assets Total risk

11 The efficient frontier E(R p ) Global Minimum Variance Portfolio Inefficient Portfolios Efficient Froniter Total risk An efficient portfolio: No other portfolio offers higher return with same (or lower) risk Efficient frontier: Set of portfolios with highest returns for each risk level The Capital Market Line An investor can allocate the fraction w of his initial wealth to a portfolio of risky assets and the remaining fraction 1-w to a risk-free asset with return r f The return and standard deviation of the portfolio can be shown as w 1 w r p 1 r 1 f p w1r Combine these 2 equations, we receive the expression r rf p rf p r The relationship between the return and standard deviation is linear The slope is represented by the Sharpe ratio

12 The Capital Market Line E(R p ) CML E(R m ) M E(R m )-r ER ( m) r f tan m f R f M is called the tangency portfolio or market portfolio All investors with mean-variance utility will prefer some combination of the risk-free asset and risk portfolio M to any other portfolio σ m σ The Capital Market Line The derivation of the tangency portfolio w w1 w2 wn 1 2 n n1n n 2n 2 1 n 1n 2 n 2n n The expected return of the portfolio is w T T And the portfolio standard deviation is expressed as w w Investors can solve the following problem: T w r max f 1/2 Subject to w1 w2 w n 1 T w w 1 rf 1 To receive the tangency portfolio wtan T 1 1 r 1 f 1/2

13 Efficient frontier based on selected data 3.00% E(R p ) Efficient frontier 2.50% The tangency portfolio 2.00% 1.50% 1.00% 0.50% Countries AEC portfolio CML (AEC) The tangency portfolio 0.00% 0.0% 2.0% 4.0% 6.0% 8.0% 10.0% 12.0% 14.0% 16.0% σ Efficient frontier based on selected data When adding the U.S. and Japan indices E(R p ) 6.00% Efficient frontier 5.00% 4.00% 3.00% 2.00% 1.00% Countries Incl US & JP AEC portfolio 0.00% 0.0% 5.0% 10.0% 15.0% 20.0% 25.0% σ

14 Selected topics in asset allocation Short-sale constraint Alternatives in building variance-covariance matrix Black-Litterman approach Strengths and weaknesses of MPT Short-sale constraint As the classic theory often leads to extreme long/short positions in each asset In reality, it is not that easy to short in the extreme way as suggested by the model earlier Sometimes, investors are even prohibited to short sell

15 Short-sale constraint E(R p ) 3.00% Efficient frontier 2.50% 2.00% 1.50% 1.00% 0.50% Countries No short-sale AEC portfolio 0.00% 0.0% 2.0% 4.0% 6.0% 8.0% 10.0% 12.0% 14.0% 16.0% σ Alternatives in Var-Covar matrix building By adjusting variance-covariance matrix, an investor can solve the extreme result As shown in the result, the optimal portfolio contains fewer extreme long and short conditions The single-index model assumes that the only sources of variance risk are the market variance and the betas of the assets The constant correlation model assumes the correlation between all asset returns is constant Shrinkage methods assume that the variance-covariance matrix is a convex combination of the sample var-covar and a matrix with variances on the diagonal and zeros elsewhere Option methods use options to derive the standard deviations of returns for the assets Source: Benninga (2014)

16 Black-Litterman approach* MPT produces unrealistic portfolio allocation with extreme long/short positions in stocks With short-sale constraint, this problem can be avoided but this will restrict investors from allocating their positions in asset universe Also, the previous result assumes that past risks/returns represent those of the future By assuming that a given portfolio is optimal then plugging in analysis on each market and confidence level of such analysis to result in an optimal portfolio Step 1: what does the market think? Step 2: incorporating investor opinions * This section follows Chapter 13 of Benninga (2014) Black-Litterman approach Black and Litterman (1991) assume that an investor chooses his optimal portfolio from among a given group of assets This group is defined as a benchmark portfolio which cannot be outperformed BL approach assumes that a given portfolio is optimal and investors can derive the expected returns of the benchmark components Asset returns can be interpreted as the market s information about the future returns of each asset in the benchmark portfolio If the investor agrees with the market, he can buy this benchmark portfolio If not, the investor can incorporate his opinions into the optimization problem to produce a better portfolio

17 Black-Litterman approach Step 1: What does the market think? Recall the previous tangency portfolio formula w w 1 rf 1 rf 1 T T r r and BNorm f, Norm f B Therefore, we can write the expected portfolio returns as w Norm r 1, E B f And it can be shown that T 1 Norm 1 r 1 B B f E T wb rf1 T wbwb B rf, where w, w 1 1, and T w w T T B B B w Expected portfolio returns B Benchmark proportion Benchmark portfolio return Black-Litterman approach Step 1: What does the market think? Expected benchmark return 0.75% Risk-free rate 0.20% Normalizing factor (Norm) 1.68 B Thailand Malaysia Singapore Indonesia Philippines Vietnam Market cap (local currency) 12, ,099,000 7,908 1,082,000 w Market cap (THB) B 12,450 8,283 9,291 13,324 6,075 1,734 Benchmark proportion 24.34% 16.19% 18.16% 26.05% 11.87% 3.39% Average return 0.69% 0.31% 0.32% 0.65% 0.93% -0.25% Benchmark return 0.55%

18 Black-Litterman approach Step 1: What does the market think? Var-covar Thailand Malaysia Singapore Indonesia Philippines Vietnam Thailand Malaysia Singapore Indonesia Philippines Vietnam Benchmark proportion Expected benchmark returns Thailand 24.3% 0.75% Malaysia 16.2% 0.54% Singapore 18.2% 0.74% Indonesia 26.0% 0.97% Philippines 11.9% 0.62% Vietnam 3.4% 0.55% w B E Black-Litterman approach Step 2: incorporating investor opinions Adjust opinion based on expected benchmark return Then calculate the opinion-adjusted optimized portfolio based on the earlier formula 1 E rf1 wbl T 1 1 r 1 E Benchmark proportion Expected benchmark returns Opinion Opinionadjusted optimized portfolio Thailand 24.3% 0.75% 1.00% 89.5% Malaysia 16.2% 0.54% 0.54% 10.1% Singapore 18.2% 0.74% 0.74% -16.7% Indonesia 26.0% 0.97% 0.97% 3.3% Philippines 11.9% 0.62% 0.62% -6.5% Vietnam 3.4% 0.55% 0.70% 20.2% f wb E w tan

19 Black-Litterman approach Step 2: incorporating investor opinions Also, if an investor is not 100% certain of his opinions, he can adjust the optimized portfolio based on degree of his confidence level For simplicity, such proportions can be shown as: Opinion confidence level 75% wadj 1 wb wbl, Confidencelevel Benchmark proportion Expected benchmark returns Opinion Opinionadjusted optimized portfolio Opinionadjusted optimized portfolio wb E w Thailand 24.3% 0.75% 1.00% 89.5% 73.24% Malaysia 16.2% 0.54% 0.54% 10.1% 11.65% Singapore 18.2% 0.74% 0.74% -16.7% -7.96% Indonesia 26.0% 0.97% 0.97% 3.3% 8.97% Philippines 11.9% 0.62% 0.62% -6.5% -1.90% Vietnam 3.4% 0.55% 0.70% 20.2% 16.00% tan Adjusted with confidence level w tan Strengths and weaknesses of MPT Strengths The concept of diversification effect to reduce risk Combination of risk-free and tangency portfolio Foundation to the Capital Asset Pricing Model (CAPM) Weaknesses Either utility must be quadratic or asset returns must be normal Calibration problem as N risky assets implies N(N+1)/2 elements One period framework

20 Summary Risks/returns from AEC investments depend on both equity and currency components AEC diversification should lead to lower risk level Modern portfolio theory leads to gains from AEC allocation compared with investment only in Thailand because efficient frontier moves to the left As the classic theory often leads to extreme long/short positions in each asset and assumes that past risks/returns represent that of the future, investors can: Restrict the short-sale opportunity or Implement the more advanced Black-Litterman approach --> by assuming that a given portfolio is optimal then plugging in analysis on each market and confidence level of such analysis to result in an optimal portfolio References Benninga, S. (2014) Financial Modeling, 4 th edition, The MIT Press Bekaert, G. and Hodrick, R. (2011) International Financial Management, 2 nd edition, Prentice Hall Black, F. and Litterman, R. (1991) Global Asset Allocation with Equities, Bonds, and Currencies, Goldman, Sachs & Co., Fixed Income Research Eun, C. and Resnick, B. (2014) International Finance, 7 th edition, McGraw-Hill Education