Predicting Financial Crisis by Examining Risk-Return Relationship

We test the risk-return relationship in and around the global financial crisis for three market groups namely developed, emerging and frontier markets, from June 2005 to June 2016. Four risk proxies are used viz. Standard Deviation, Semi Deviation, Beta and Downside Beta. We find that the global financial crisis had a de-coupling effect as the return associations between global financial markets declined for the post crisis period. We also observe high positive correlations between alternative risk measures implying that asset pricing tests shall be robust to choice of risk measure. Next, we find that the risk-return relationship is absent in the pre-crisis period while it is significantly negative in the post crisis period using standard deviation based measures. Thus, the breaking down of risk-return relationship may be an important predictor of any forthcoming crisis. Further, global capital markets seem to behave like distressed economies in the post crisis period and, hence, exhibit option like behavior. We re-verify our hypothesis by using data in and around the Asian Crisis Period and confirm the absence of risk-return relationship prior to the crisis period. The study contributes to capital market literature with special emphasis on financial crisis.


Introduction
The relationship between risk and return has been focus of research in contemporary finance literature. The initial theoretical framework for risk-return relationship was provided by Sharpe [1], Lintner [2] and Mossin [3] in which they In the world of DCF, risk being the discounting factor is an adversary whereas in Contingent Claims Approach, risk is an ally for valuation, because as volatility increases, equity value also increases. The sub-prime crisis of 2008 provides an apt situation to test the risk-return relationship for world economies in the pre and post crisis periods.
In the existing literature, the major emphasis has been on cost of equity estimation using CAPM or other asset pricing benchmarks without verifying if such a relationship consistently holds in the real world. If this relationship is negative, then these paradigms will break down and cost of equity estimation will have to be done in a different way. Estrada [4] estimates CAPM based cost of equity for a sample of 28 emerging markets using two measures of risk viz. standard deviation and beta and their two counterpart downsize risk measures viz. semi deviation and downside beta. He finds downside risk to be a better measure for estimating the cost of equity for emerging markets. In continuation to his previous work, Estrada [5] conducts similar study for 23 developed markets and 27 Emerging Markets and shows superiority of downside beta over beta for estimating cost of equity. Collins [6] measures cost of equity using CAPM for 42 emerging economies, using 11 alternative risk measures and suggests that extent of global integration and market development is crucial for determining most appropriate cost of equity measure. Collins and Abrahamson [7] measure sec-S. Sehgal toral cost of equity for African markets and find that cost of equity across sectors and markets declined between mid-1990s to early 2000s. Da, Guo and Jaggannathan [8] justify the continued use of CAPM for estimating cost of capital which is employed as discount factor in project evaluations for capital budgeting projects. Hasan, Hossain, Cheung and Habib [9] investigate the effect of corporate life cycle on cost of capital and find that cost of equity decreases as retained earnings as a proportion of total asset increases after controlling for other firm characteristics and unobserved heterogeneity. Abudy, Benninga and Shust [10] present a method for calculating cost of equity capital for private firms as compared to cost of equity capital of a publicly listed firm.
There have been few international studies which test the risk-return relationship in both linear as well as nonlinear form. Salvador, Floros and Arago [11] analyze risk-return relationship for 11 European stock markets. They find a significant positive non-linear risk return relationship after considering the current state of the sample markets. Chiang, Li and Zheng [12] examine the intertemporal capital asset pricing model for industry portfolio returns of 14 international markets and observe positive risk-return relationship during tranquil period.
Aslanidis, Christiansen and Savva [13] adopt factor models to test intertemporal risk-return relationship for 13 European stock markets and find that such a relationship is generally negative. Wang and Khan [14] re-examine the risk-return relationship for U.S. market and find that risk return tradeoff is strongly time varying with state of the market. Liu [15] empirically estimates risk-return relationship for 12 international markets and finds it to be significantly positive after controlling for higher order moments.
The existing literature has suggested either the best method of finding out cost of equity for various markets or established a positive or negative risk-return relationship using linear or non-linear and static versus dynamic models. However, the literature is almost absent on the evaluation of risk-return relationship in and around the crisis period. Thus, rather than using risk-return relationship to find out cost of equity estimation, we should first test if such a relationship exists using standard asset pricing models. In order to empirically verify the risk-return relationship in and around the crisis period, we conduct the present study for the Global financial Crisis (GFC) 1 period, popularly known as Sub Prime Crisis of 2008, with the following objectives: test the risk-return relationship in pre-GFC period for different types of markets; evaluate the risk-return relationship for the post GFC period; check the robustness of risk-return relationships using alternative risk measures; test if pre crisis risk-return relationship patterns can be used for predicting crisis; draw implications for corporate valuations and cost of equity estimation in the post crisis period.
We test the risk-return relationship in and around global financial crisis for 54 1 The crisis began in 2007 when the sub-prime customers failed in fulfilling their debt obligations and developed into a full blown international banking crisis with the collapse of Investment Bank Lehman Brothers on 15 th September, 2008. Massive bailouts of financial institutions and monetary and fiscal measures were employed to prevent possible collapse of the world financial system. The crisis was followed by a global economic downturn named as Great Recession [21]  This implies that option pricing model may be more useful for business valuation and cost of equity estimations compared to more popular DCF models. We re-verify our hypothesis by using data in and around the Asian crisis period of 1997. The risk-return relationship seems to break down for global financial markets again in the pre-crisis period. This lends support to our argument that an absence of risk-return relationship may be a good predictor of financial crisis.
The paper is divided into five sections including the present one. Data and their sources are discussed in Section 2. In Section 3 we describe the research methodology and estimation procedure. The empirical results are provided in Section 4 and summary and concluding remarks are given in the final section. relationship in and around the Asian Crisis, monthly values of sample country Indices have been taken from June 1994 to June 2003 from Bloomberg. The rationale for taking the above mentioned time period is to divide the total time period of nine years into two equal halves of 4 and a half years (54 monthly observations) of pre(including crisis period) and post crisis period. The pre-crisis period is taken from June 1994 to December 1998 and post crisis period is from January 1999 to June 2003. The length of pre and post crisis periods during the Asian crisis is different from those in case of GFC owing to lack of data for some of the sample countries for the period of early 1990s. The values so obtained have been again converted into percentage returns for further estimations. The sample data of 40 countries out of the originally selected 54 countries has been taken from Bloomberg. The 14 countries were omitted from the sample due to paucity of data for the period under investigation.

Methodology
Since last 50 years the debate is continuing among both, practitioners as well as academics, with regards to the relevance of CAPM as a model to derive the risk Apart from standard deviation and semi-deviation as risk measures, Estrada has proposed to replace the CAPM beta by a measure called downside beta [5].
He finds that cost of equity estimations based on beta for developed and emerging economies gave contradictory results. In his study cost of equity for developed economies came out to be higher than that of emerging economies based on standard CAPM estimations. It is generally believed that emerging markets, being more risky, should have higher cost of equity estimations. On the contrary while using downside beta, he finds that cost of equity of emerging markets is higher than that of developed markets and that is a more realistic depiction considering the risk-return relationship.
Based on Estrada's findings we investigate the risk-return relationship by taking four measures of risk viz. standard deviation, semi-deviation, beta and downside beta. Standard deviation and semi deviation of returns have been estimated using standard statistical formulae, while beta has been estimated as the slope of regression of country returns on global index returns. Downside beta has been estimated as the slope of country returns regressed on All World Index returns using the months for which the All World Index is below its average value.
We estimate the mean correlations of returns for the countries within group as well as pairwise combinations of developed, emerging and frontier markets.
The correlations have been done separately for total period and two sub periods.
The correlations have been estimated to verify how closely related returns of countries are within a group. Further, we also try to see how correlated are developed, emerging and frontier markets, for which we have estimated pairwise correlations of these groups. We have estimated these correlations for total pe- After reporting mean correlations, we also present the mean correlations between 1) returns and the alternative risk measures and 2) between alternative risk measures. We have estimated these correlations for total period as well as two sub periods. The correlations have been estimated to check if risk return relationships have changed for different countries in pre and post crisis period.
Risk return relationships have been explicitly tested using bivariate cross sectional regressions, run for all three market groups taken together as well as separately for both the sub periods.
The equation is given by: where, MR i and RV i stand for mean return and risk measure, respectively, ʎ 0 and ʎ 1 are estimated parameters, U i is an error term, and i indexes markets.
All the regressions have been estimated using Newey West technique in order to take care of heteroscedasticity and autocorrelations.
Finally, to re-verify how risk-return relationships are observed in around financial crisis periods, we investigate these relationships for the sample countries for Asian crisis of 1997. The methodology adopted for constructing the risk factors and establishing the risk-return relationship is similar as used for global financial crisis. We test risk-return relationship using bivariate regressions, firstly by taking a sample of 12 Asian countries out of the 40 countries selected and next by taking a sample of 40 countries (including Non-Asian countries for which data was available) single block. The rationale for taking both Asian as well as Non-Asian countries is that latter may have had exposures in Asian economies owing to international trade and investments, particularly in a world which is highly globalized.

Descriptive Statistics
The first step of the analysis consists of computing the descriptive statistics for both the sub periods of the three market groups under study. We report the descriptive statistics in Table 1. In sub period 1 the average monthly returns given by developed markets is 0.47% (5.64% annually) and the average monthly volatility is 07.3% (87.6% annually). The monthly average skewness and kurtosis measures for developed markets are −0.713 and 4.662 respectively, suggesting these markets are negatively skewed and leptokurtic. The highest and lowest returns among the developed countries have been given by Canada (13.92% annually) and Ireland (−17.28% annually) respectively. The two highest and lowest volatile countries among the developed economies are Austria (124.44% annually) and USA (59.04% annually) respectively. The average monthly returns and volatility measures for emerging markets for sub period 1 are 1.53% (18.36% annually) and 9.51% (114.12% annually) respectively. Their average monthly In terms of returns volatility, Argentina is the most volatile country while Morocco exhibits least volatility.
To sum up, we can say that on the basis of risk-return relationship, emerging markets have performed best in pre-crisis period followed by developed markets.

Return Correlations
Next, we examined the return correlations for countries within each market group as well as across the market groups. The average correlation coefficients are shown in Table 2 for sub periods 1 and 2 separately. In sub period 1, both within group as well as between group mean correlations of returns are above 65% except for frontier markets group where such correlations are relatively lower. Taking the mean of all average correlation coefficients the global financial markets report correlation of 54%. In the post-crisis period, the associations within and between the market group correlations have decreased with the mean of all correlation coefficients to be 40%, thus, the global financial crisis has led to de-coupling effect which is reflected in weaker associations between global financial markets. The lower post crisis period correlations have positive implications for global portfolio diversification.

Measuring Risk-Return Correlations and the Association between Alternative Risk Measures
In the next step, we check the correlations of returns with the four risks measures used for study as well among the four risk measures (see Table 3). Surprisingly, the risk and returns measures exhibit negative correlations both for pre as well as post-crisis period. The findings are robust for alternative risk measures which have strong negative implications for standard asset pricing framework which envisages positive relationship between risk and returns. In terms of correlations among risk measures, we find that by a large risk measures are highly correlated in both the sub periods, although this relationship sobers down in sub period 2. Hence, our risk measures seem to be highly correlated risk proxies. Therefore, the choice of risk measure should not significantly impact our asset pricing analysis. The choice of risk proxy, however, matters more in sub period 2 especially for frontier markets, given lower associations between alternative risk measures.

Regression Analysis
We re-check the risk-return relationship by regressing country returns on MSCI ALL Country World Index returns separately for the two sub periods. The regression results are provided in Table 4. In sub period 1, we find insignificant negative risk-return relationship for developed and emerging markets, while for frontier markets, the relationship is observed to be negative but significant for alternative risk measures. In the post crisis period, we find that relationship between return and risk measures for developed markets remains negative for all risk measures; however, it becomes significant for standard deviation measures.
In case of emerging markets also relationship is negative and significant for all risk measures except downside beta. The interesting observation with regards to frontier markets is that contrary to other market groups, the risk return relationship becomes insignificant, though negative, in post crisis period. On overall basis the risk-return relationship is absent in sub period 1 while it is significantly negative for standard deviation measures in the post crisis period. Unlike Estrada [5], we avoid estimating multi-variate regressions involving alternative risk measures as explanatory variables, given the high empirically observed correlations between these risk measures.
In sum, the risk-return relationship breaks down prior to the crisis period including the crisis phase. Hence, the verification of risk-return relationship can possibly provide us an early warning about the forthcoming crisis. The verification of risk-return relationship may be much easier than computing complex systemic risk measures (see Acharya et al. [17], Chan-Lau et al. [18], Adrian and Brunnermeier [19], WeiB et al. [20]) which are currently in vogue for crisis pre-  This can be clearly seen for developed market group where the average public debt to GDP ratio rose from 51% to 70% from pre to post crisis period, with 9 out of 21 countries reporting Debt to GDP ratio greater than 90% in 2015 (see exhibit 1). Hence, these markets behave more option like and continue to provide better valuations (owing to positive returns) consistent with the Option Greek named as Vega. In contrast, the average public debt to GDP ratio for emerging and frontier markets do not change significantly from pre to post crisis period. Thus, these markets are relatively less distressed. The general decline in GDP, however, stresses all economies. Figure 1 shows the average public debt to GDP ratios for the three market groups.
We recommend that corporate valuations in an around crisis periods (including GFC) must be performed using contingent claims approach instead of standard DCF models. Further the cost of equity estimation using CAPM and other standard asset pricing models makes no sense when the risk-return relationship is empirically negative. Instead the cost of equity should be estimated from the option pricing model by incorporating a risk premium over and above the benchmark risk free rate. Such a risk premia should be a function of the probability of economic default, that is, what is the possibility that a country's GDP is sufficient to honor its public debt. Our findings are strong and have implications for forecasting economic crisis and warrant a re-examination of current asset pricing and cost of equity estimation frameworks beyond the tranquil periods.
However, our conclusions run the risk of being event specific i.e. ensuing to GFC. We are, therefore, motivated to choose another crisis phase in global financial markets. We select the Asian Crisis which started from July 1997 and ended in December 1998.

Risk -Return Relationships in and Around Asian Debt Crisis
In order to check for the robustness of our results, we test the risk-return relationship using the regression analysis separately for sub period 1 and 2 for Asian crisis of 1997. The first sub period named as the pre-crisis period (including crisis months) is from June 2005 to December 2010 and second sub period called as post crisis period is from June 1994 to June 2003. We report the regression results in two parts. In part one we report the results only for Asian economies which belong to the sample used for GFC crisis and which were directly impacted by the Asian crisis. We use data for 12 out of 14 sample Asian countries as sufficient historical market index information is not available for Bangladesh and Vietnam in Bloomberg. In part two, we report regression results using 40 sample markets, including the Non-Asian markets, as these markets may be highly linked to Asian economies owing to international trade and investment flows. 14 countries have been excluded in this phase due to lack of data. The results for Asian economies as well as all economies in and around the Asian Crisis are almost similar. The risk-return relationship is significantly negative using the standard deviation based measures in the sub period 1 while they are significantly positive in the post crisis period. Significant risk return relationship is, however, generally absent both for pre and post Asian crisis periods using beta based measures. These results are reported in Table 5. In other words the risk-return relationship as confirmed by standard asset pricing models like CAPM breaks down in and around the crisis period, thus reconfirming the power of these simple tests in diagnosing crisis. The world economies seem to recover quickly from the Asian crisis as compared to GFC given the regional nature of economic stress which did not have long reaching implications for most global financial markets.
Thus, by taking an out of the sample study for an alternative crisis period, we show that by verifying a simple risk-return relationship, using bivariate regressions, one can get an indication about a prospective financial crisis. Hence, an absence of risk-return relationship may be a good indicator of global economic health rather than using more computationally expensive econometric  Table 5. Tests of risk-return relationships using regression analysis in and around the Asian crisis period. The table provides the regression results using the alternative risk measures for Asian Financial Crisis divided into four panels. The first two panels include the results of pre and post crisis period for the 12 Asian countries while the last two panels provide results of pre and post crisis period for all the countries (which includes 40 countries out of the total 54 selected for global financial crisis).

Summary and Conclusion
The risk and return relationship has been a prominent subject of research in contemporary finance and there have been divergent findings with regards to the direction of this relationship. The seminal research work of Sharpe [1] has established a positive relationship between the two parameters, more popularly Frontier countries, and MSCI ALL Country World Index, representing global market index, has been taken from Bloomberg to conduct the study. The period under study has been taken from June 2005 to June 2016 which has been divided into two equal halves of 5 and half years each to perform pre-and post-crisis analysis.
We investigate the risk-return relationship by taking four measures of risk viz. standard deviation, semi-deviation, beta and downside beta. We find that the associations between returns within different market groups have weakened from sub period 1 to sub period 2. We further find the negative correlations between risk and return among the three market groups because both the sub periods and the results are similar for alternative risk measures. We also, observe that many risk measures are highly correlated to each other in both the sub periods, although this relationship sobers down in sub period 2. Therefore, the choice of risk measure should not significantly impact our asset pricing analysis.
Finally, we re-check the risk-return relationship by regressing country returns on MSCI ALL Country World Index returns separately for the two sub periods.
We report either the absence or negative relationship between risk and return for the three market groups taken separately. On overall basis, the risk-return relationship is absent prior to the crisis period including the crisis phase while it is found to be negative in the post crisis period, thus implying that the shadow of GFC still looms large on global financial markets. Hence, the verification of are generally recommended for crisis forecasting. The negative risk-return relationship reported for global financial markets imply that these markets exhibit an option like behavior around the crisis phase as well as the post crisis period.
The option like behavior is on account of the fact that these economies are "relatively distressed" in and around the post crisis period owing to declining GDP, shrinking world trade and rising public debt to GDP ratios.
We recommend that corporate valuations in an around GFC must be performed using contingent claims approach instead of standard DCF models.
Further, the cost of equity estimation using CAPM and other standard asset pricing models makes no sense when the risk-return relationship is empirically negative. Instead the cost of equity should be estimated from the option pricing model by incorporating a risk premium over and above the benchmark risk free rate. Such a risk premium should be a function of the probability of economic default that is what is the possibility that a country's GDP is not sufficient to honor its public debt. Our findings have strong implications for forecasting economic crisis and warrant a re-examination of current asset pricing and cost of equity estimation frameworks beyond the tranquil periods.
In order to check for the robustness of our results, we re-test the risk-return relationship for the Asian crisis of 1997 for the period from June 1994 to June 2003 divided into two equal periods of 4 and a half years each for our analysis. In conformity to our findings for GFC, we find absence of risk-return relationship prior to crisis period. Thus, we infer that examination of the risk-return relationship and confirmation of its absence may be an early warning system for diagnosing possible financial crisis.
Our results have implications for asset pricing, portfolio construction and valuations. It can be clearly seen in our study that over well as academic point of view, contingent claim approach to equity valuation seems to be more appropriate compared to standard DCF models in and around the crisis period. The cost of equity also needs to be measured using option S. Sehgal, A. Pandey