Dominique Guegan
email: dguegan@univ-paris1.fr

Bertrand K Hassani
email: bertrand.hassani@santander.co.uk

Xin Zhao

Dominique Guégan

Documents de Travail du

Keywords: Credit Risk, Rating, Panel Model, Multi-factor regression, Credibility Theory

Assets, debts and other financial products issued by emerging countries are usually considered more speculative than those issued by developed economies. Therefore, relying on traditional rating agencies to invest in these countries is problematic as the information used to assess the economic and market condition in these economies is quickly outdated. Consequently, both the investment opportunities and the necessity to clear particular positions may be missed, respectively resulting in potential significant costs of opportunity or losses. Therefore, an approach taking into account the latest information displayed by financial markets may enable us bypassing the traditional limits. As a result, this chapter proposes a creditworthiness evaluation methodology based on adjusting ratings obtained from macroeconomic fundamentals (GDP growth rate, inflation, external debts, etc.) and financial market movements (bonds, equity volume, volatility, etc.). In the first step, a general panel model is applied on country-specific information to generate fundamental ratings. In the second step, applying a multi-factor model to market indicators and breaking down long-term sovereign bond yields into different risk premia, market implied ratings are obtained. Finally, the rating to be considered (denoted "δ-Rating") for investment purposes is a combination of fundamental ratings and market implied ratings carrying out an adapted Bühlmann-Straub method (Credibility Theory). Then, emerging countries "δ-Rating" will be compared to those obtained from developed countries and discussed against financial institutions risk appetite.

Introduction

The term of emerging markets or emerging economies refers to the nations with social or business activity in the process of rapid growth and industrialization. Within these class of economies, it is possible to differentiate different families, as for sure Morroco and China do not have the same profile despite the fact that they are both emerging countries. The seven largest emerging economies according to nominal gross domestic product (GDP) are Brazil, Russia, India, China (the BRICs), Mexico, Indonesia, and Turkey. S&P/IFC index1 considers a market to be emerging if it satisfies at least one of the criteria:

1. It is in a low-or middle-income country, as defined by the World Bank, and 2. Its investable market capitalization is low relative to its most recent GDP figures.

In contrast, S&P/IFC defines a market as developed if it is in a country where gross national product (GNP) per capita exceeds the World Bank upper income threshold for at least three consecutive years and the investable market capitalization-to-GDP ratio is in the top 25% of the emerging market universe for more than three consecutive years.

Regarding the risks for investor, emerging markets are usually considered relatively riskier than developed countries as they carry additional political, economical and currency risks. Investing in emerging markets may lead to volatile returns, i.e. the probabilities of both large profits and large losses are high. The upside of investing in emerging markets is that their performance is considered usually less correlated with developed markets. As a result, these may be good investments for diversification purposes. Consequently, nowadays developing countries are major investments targets, and these fast growing economies are usually a growth relay for major banks. The second criterion highlights the fact that these economies are growing so fast that the information characterizing them is rapidly outdated as their structure is quickly evolving. Therefore, relying on the traditional rating agencies (e.g. Fitch, Moody's and S&P's) to evaluate the risk of investing in these economies may be misleading, especially when the investment horizon is short or medium term. Indeed, by not integrating the latest information contained in the market, they may not provide the freshest point of views. It is important recalling that the rating is suppose to reflect the credit worthiness of a country, i.e. its probability of default. The consideration of fast growing economies allows us assuming that the related quickly growing cash flows generated decrease the probability of default of these country on a constant basis.

Although there are papers doubting the quality of evaluations provided by rating agencies, investors keep relying them. The problems of their evaluations have been largely unveiled during the East Asian Crisis and the recent European Sovereign Debt Crisis. Regulators and market practitioners have acknowledged the problems caused by external analysis, and as a consequence financial institutions developed internal rating methodologies 2 . External ratings, however, are still used as benchmark or important input of inside rating models. Possible explanations are that ratings provided by the major agencies are widely spread, easy to understand, and as a result contribute to limit information bias. Moreover, discussions concerning the problems of rating system and propositions of new rating methods in recent literature have not reached any consensus. There are two school of thoughts: the first states that the credit of a country is determined by its fundamental economic condition, therefore, ratings should rely on country-specific fundamentals; the second argues that economic fundamentals are insufficient to model sovereign credit risk and they propose to use market information.

In order to construct a rating methodology, the causal factors of sovereign default need to be analyzed, and these are different from the determinants of corporate defaults [START_REF] Duffie | Modeling Sovereign Spreads: A Case Study of Russian Debt[END_REF] [START_REF] Duffie | Modeling Sovereign Spreads: A Case Study of Russian Debt[END_REF]). The risk of investing in a country is linked to its economic condition. Therefore, it is natural to start analyzing the credit quality of a country using its fundamental indicators. Literatures discussing relationship between country fundamentals and ratings include [START_REF] Cantor | Determinants and Impact of Sovereign Credit Ratings[END_REF] [START_REF] Cantor | Determinants and Impact of Sovereign Credit Ratings[END_REF], [START_REF] Ferri | The Procyclical role of rating agencies: Evidence from the east asian crisis[END_REF] [START_REF] Ferri | The Procyclical role of rating agencies: Evidence from the east asian crisis[END_REF], [START_REF] Mellios | Which Factors Determine Sovereign Credit Ratings?[END_REF] [START_REF] Mellios | Which Factors Determine Sovereign Credit Ratings?[END_REF], and many others. [START_REF] Cantor | Determinants and Impact of Sovereign Credit Ratings[END_REF] [START_REF] Cantor | Determinants and Impact of Sovereign Credit Ratings[END_REF] have shown that Moody's and S&P's ratings can be explained by a number of well-defined economic criteria. [START_REF] Ferri | The Procyclical role of rating agencies: Evidence from the east asian crisis[END_REF] [START_REF] Ferri | The Procyclical role of rating agencies: Evidence from the east asian crisis[END_REF] used these indicators to compare the ratings pre-and post-East Asian crisis. They reached the conclusion that rating agencies failed predicting the emergence of the East Asian crisis and attributed worse ratings than what the countries' fundamental economic condition deserved. They also argued that this undervaluation amplified the East Asian crisis. To solve the problems engendered by the previous approach, [START_REF] Mellios | Which Factors Determine Sovereign Credit Ratings?[END_REF] [START_REF] Mellios | Which Factors Determine Sovereign Credit Ratings?[END_REF] suggested to add other indicators, through which they emphasized the importance of political variables. However, the second school of thoughts claims that sovereign risk cannot be fully explained by country-specific fundamentals, especially for the risk in emerging market, as market opinions may influence the perception of a country credit quality up to a certain extent. This argument partially explains the inertia of agencies' rating. It is generally accepted that markets react faster than agencies to evaluate the credit worthiness of sovereigns. [START_REF] Hettenhouse | An Analysis of the Information Value of Bond Rating Changes[END_REF] [START_REF] Hettenhouse | An Analysis of the Information Value of Bond Rating Changes[END_REF] and Weinstein(1977) [23] have shown that bond prices are systematically reacting to the signals implying a credit quality variation before agencies modify the ratings. Ederington et al.(1984) [START_REF] Ederington | The information content of bond ratings[END_REF] stated that market practitioners evaluate issuer's creditworthiness according to their expectations and the market risk perception, and these are not considered by rating agencies. To capture market's attitude towards sovereign risk, [START_REF] Cunningham | Analysing yield spreads on emerging market sovereign bonds[END_REF] [START_REF] Cunningham | Analysing yield spreads on emerging market sovereign bonds[END_REF] discussed the relationship between government bonds yield spreads and the corresponding default risks on emerging market, where they claimed that information contained in yield spreads are multi-faceted. They mentioned the importance of investors' appetite for risk evaluation and the value of liquidity for specific instruments. Perraudin and Taylor(2004) [22] have shown that sovereign bond valuations are inconsistent with their ratings. They claimed that the inconsistency can be eliminated by adjusting the prices for the effects of taxes, liquidity and other risk premiums. They also proved the inconsistencies between ratings and spreads are naturally eliminated over time. Mainstream discussions concerning market evaluated sovereign risk focus on detecting determinants of risk proxy from market, such as bond yields and credit default swaps. [START_REF] Baek | Determinants of market-assessed sovereign risk: Economic fundamentals or market risk appetite[END_REF] [START_REF] Baek | Determinants of market-assessed sovereign risk: Economic fundamentals or market risk appetite[END_REF] claimed that risk appetite can explain the movement of bond yields. They further proved that investors' risk attitude was not considered in public ratings. [START_REF] Longstaff | How Sovereign Is Sovereign Credit Risk?[END_REF] [START_REF] Longstaff | How Sovereign Is Sovereign Credit Risk?[END_REF] decomposed credit spreads into several risk premiums. They found that sovereign credit risk was more driven by market factors, risk premiums and investment flows than by country-specific fundamentals. Moreover, they found strong relationship between credit spreads and VIX index. In summary, movements of market indicators are closely related to agencies' ratings, but ratings issued by agencies are not consistent with investors' perceptions as fundamental indicators cannot fully explain the part of sovereign risk nested in market sentiments.

Therefore, this chapter presents a methodology to combine information obtained from macroeconomic indicator (fundamental rating) on the first hand and financial market (market implied rating) on the other hand in order to construct a rating reflecting both the targeted state's economic health and the global market evaluation of the sovereign's creditworthiness. This approach is referred as the δ-rating approach in the following. By means of this hybrid approach, it is possible to offer more timeless ratings compared to agencies' valuations and provide prompt signals for investment opportunities or necessity to sell. Therefore, this approach enables improving the investment strategy in emerging countries as being a more reality and reactive methodology comparing to the traditional approach.

To create the δ-ratings, three steps are required. In a first step, country-specific fundamental information is modeled using a general panel model to obtain a basic long-term country-specific implied rating. In a second step, a multi-factor model is applied to decompose bond yields into different risk premiums. Then, market implied ratings are computed from the stripped credit risk premium. In a final step, the δ-rating is evaluated applying a simplified version of the Bühlmann-Straub credibility theory [START_REF] Bühlmann | A Course in Credibility Theory[END_REF] [START_REF] Bühlmann | A Course in Credibility Theory[END_REF]) which may be summarized by the following formula:

δ-Rating = ω • Fundamental Rating + (1 -ω) • Market Implied Rating,
where, ω is the credibility weight calculated by Bühlmann-Straub method. This chapter proposes a method which systematically matches low-frequency macroeconomic data with high-frequency financial market data in the modeling of sovereign rating, it analyzes how market demands and risk appetite affect market implied rating, and their impact on financial institutions' investments in developing countries 3 . The novelty of our hybrid methodology stands in the combination information from data having different frequencies. Therefore, the next section introduces the methodology, the third section presents our results and a last section concludes.

The δ-rating methodology

This section details how a fundamental rating and a market implied rating are combined. In a first step, the next subsections present the methodologies carried out to evaluate each component. The third subsection outlines the credibility theory approach used to bring together the two elements.

Country-Specific Fundamental Rating

Sovereign credit risk can be captured by a relative small number of economic variables. These do not dramatically differ among studies [START_REF] Cantor | Determinants and Impact of Sovereign Credit Ratings[END_REF] [START_REF] Cantor | Determinants and Impact of Sovereign Credit Ratings[END_REF], [START_REF] Ferri | The Procyclical role of rating agencies: Evidence from the east asian crisis[END_REF] [START_REF] Ferri | The Procyclical role of rating agencies: Evidence from the east asian crisis[END_REF], Mellios and Paget-Blanc(2006) [START_REF] Mellios | Which Factors Determine Sovereign Credit Ratings?[END_REF], etc.). Table 1 summarizes these macroeconomic variables.

Variable

Corr. * Economic Principal Literature

Per capita income + [START_REF] Cantor | Determinants and Impact of Sovereign Credit Ratings[END_REF] The increase of the per capita income implies Cantor and Packer (1996) use the notation external balance refer to the current account deficit. * "Corr." refers to the correlation between the variable and the creditworthiness of the government. "+" means the bigger the variable the higher the credit. "-" means the lower the variable the higher the credit. ** The literature are not the complete review, we only give relevant references.

Nonetheless, the model used to analyze these variables varies among the studies. [START_REF] Cantor | Determinants and Impact of Sovereign Credit Ratings[END_REF] [START_REF] Cantor | Determinants and Impact of Sovereign Credit Ratings[END_REF] tested the variables with cross-sectional data 4 . [START_REF] Ferri | The Procyclical role of rating agencies: Evidence from the east asian crisis[END_REF] [START_REF] Ferri | The Procyclical role of rating agencies: Evidence from the east asian crisis[END_REF] applied panel data 5 and did regression analysis with random effect. [START_REF] Mellios | Which Factors Determine Sovereign Credit Ratings?[END_REF] [START_REF] Mellios | Which Factors Determine Sovereign Credit Ratings?[END_REF] used a principal component analysis (PCA) method, a linear regression and an ordered logistic modeling to analyze the indicators. The relationship between explanatory variables and historical ratings on a special day is not the focal point of this paper, whereas we are interested in the explanatory power of fundamental economic indicators during a relative long period, and panel analysis is more appropriate for this purpose. Therefore, a general panel model is applied to regress fundamental economic indicators on the numerical mappings of agencies' historical rating, which can be expressed by equation [START_REF] Badaoui | Do sovereign credit default swaps represent a clean measure of sovereign default risk? A factor model approach[END_REF].

S t = α 0 + β 1 • X t + t (1)
where α 0 is an intercept vector, β 1 is the coefficients of explanatory variables, t is a white noise residual, and X t is a matrix of economic indicators listed in Table 1. S t represents the rating of each sovereign. Parameters and vectors are real numbers. The techniques of analysis used in the empirical study include PCA and panel regression methods. To explore the fittest regression method of equation ( 1), the pooling regression has been tested against random and cross-sectional effects using Breusch-Pagan Lagrange Multiplier Test [START_REF] Breusch | The Lagrange Multiplier Test and Its Applications to Model Specification in Econometrics[END_REF] [START_REF] Breusch | The Lagrange Multiplier Test and Its Applications to Model Specification in Econometrics[END_REF]). Fixed effect against random effect of the selected data will be analyzed using the Hausman Test [START_REF] Hausman | Specification Tests in Econometrics[END_REF] [START_REF] Hausman | Specification Tests in Econometrics[END_REF]). The time-fixed effect are tested using both the F-test and the serial correlation using Breusch-Godfrey/Wooldridge test(Godfrey (1996) [START_REF] Godfrey | Misspecification tests and their uses in econometrics[END_REF]).

Market Implied Rating

In this study, government bond yields are used as a representation of market perceptions of the risk. Government bonds are a publicly traded financial product. Their prices are related to a government's creditworthiness. Though many papers use credit default swap (CDS) as the proxy of credit risk, these are less resourceful data of CDS than bonds, especially for emerging countries. Secondly, sovereign bond spreads are less subject to liquidity frictions than CDS, therefore they provide a better representation of sovereign risk [START_REF] Badaoui | Do sovereign credit default swaps represent a clean measure of sovereign default risk? A factor model approach[END_REF] [START_REF] Badaoui | Do sovereign credit default swaps represent a clean measure of sovereign default risk? A factor model approach[END_REF]). Moreover as highlighted by Hull et al.(2004) [17] bond yield and CDS contain almost the same information, government bond yield is a good proxy of sovereign risk.

Generally, the higher the rating of a sovereign, the lower the bond yields, and vice versa, therefore, bond yields movements can reflect the shift of market attitude towards credit quality of a sovereign. On the other hand, the movements are influenced by other factors than only government repayment capability. When an investor lends money to a government by buying bonds, he exposes himself to many risks, such as credit risk, market risk and liquidity risk. Perraudin and Taylor(2004) [22] have shown that the inconsistencies6 between credit ratings and corporate bond yields come from non-credit-related factors of spreads such as tax, liquidity and other risk premia. [START_REF] Ejsing | Liquidity and credit risk premia in government bond yields[END_REF] [START_REF] Ejsing | Liquidity and credit risk premia in government bond yields[END_REF] discussed liquidity and credit premia for the Euro Zone sovereign bonds. Bonds are traded in the secondary market which simultaneously reflect the market risk perception and deliver timeless information to evaluate the credit risk. Agencies, however, evaluate countries' credit quality on a frequency from quarterly to annually. Hence, some discordances are observed between agencies' ratings and bond yields primarily. Rating agencies advocate that they provide less precise point-in-time measures of risk since the ratings reflect the credit quality in the long term. However, and despite the fact that the previous statement is questionable, market practitioners may be more interested in a short to medium term investments. The inconsistence comes from non-credit reasons rather than only horizon difference.

To improve the analysis, a multi-factor approach is carried out. It is commonly accepted in the literature that credit spreads can be expressed as a linear combination of default-related components and other associated risk premiums (Longstaff and Pedersen(2011) [START_REF] Longstaff | How Sovereign Is Sovereign Credit Risk?[END_REF], Collin-Dufresne et al.(2001) [START_REF] Collin-Dufresne | The Determinants of Credit Spread Changes[END_REF], Beber et al.( 2009) [START_REF] Beber | Filight-to-Quality or Flight-to-Liquidity? Evidence from the Euro-Area Bond Market[END_REF], etc.). Accordingly, the non-credit-reasons are considered as liquidity risk premium, market demands and investors' risk appetite. Then, yield spreads are decomposed into credit, liquidity, market demand premia and risk appetite using a multi-factor model:

y i,t = a i,0 + a i,1 L i,t + a i,2 M P i,t + a i,3 RA i,t + ε t (2)
where y i,t refers to yield spreads of bond i at time t, a i,0 represents the averaged credit risk premium, L i,t is the sign of liquidity risk and M P i,t represents the market demand of government bonds and denotes the market appetite, RA i,t measures investors' risk appetite, and ε t is a standard white noise which is independent from other explanatory variables. Proxies of each indicator in equation ( 2) are as follow:

1. Bid-ask spreads for liquidity risk, 2. FTSE-Index for the market demand of government bonds 3. Implied volatility of S&P 500 index options (VIX) for the global risk aversion.

Credible Weights

The "δ-Rating" is obtained through the average of fundamental ratings and market implied ratings using the credibility weight ω. Bühlmann-Straub method7 , the most extensively used and important model in credibility theory, is applied to compute the weight ω (Bühlmann and Alois(2005) [START_REF] Bühlmann | A Course in Credibility Theory[END_REF]).

Theorem 1 (Bühlmann-Straub). The credibility estimator µ in the simple Bühlmann-Straub model:

A.1 The random variables X kj (j = 1, . . . , n) are, conditional on Θ k = ϑ, independent with the same distribution function F ϑ and conditional moments

µ(ϑ) = E[X kj |Θ k = ϑ], σ 2 (ϑ) = V ar[X kj |Θ k = ϑ].
A.2 The pairs (Θ 1 , X 1 ), . . ., (Θ K , X K ) are independent and identically distributed.

is given by

µ = ωX i + (1 -ω)X (3)
where

ω = n n + σ 2 τ 2 , σ 2 = E[σ 2 (Θ)], τ 2 = V ar(µ(Θ)). (4)
X i = 1 n n j=1 X i,j X = 1 Kn K i=1 n j=1 X ij
Practically, in our case, X j is the rating implied by the specific market information and X is the long-term fundamental rating estimated through country-specific economic data. Moreover ω is the weight given to market implied rating and lead to the "δ-rating", as it is the weighted average of the two previous components.

3 Rating Evaluation: Carrying out the methodology

Country-Specific Implied Rating

The data used to estimate country-specific rating has annual frequency and belong to the period between 2001 and 2012. Historical rating scores are derived from Fitch Sovereign HistoricalRatings8 using the mapping exhibited in Table 14. Economic indicators, except for the "corruption index", are collected from the International Money Fund (IMF) WEO Database. Corruption Perceptions Index (CPI) has been obtained from Transparency International 9 . The sample includes 20 advanced countries and 8 emerging countries, according to the IMF classification 10 .

Statistics of data are presented in Table 8. The rating of advanced economies are higher than emerging economies'. Advanced economies usually have smaller GPD growth rate, larger external debts, higher per capita income, lower inflation rates, greater fiscal balance, better current account balance and higher corruption perceptions index than emerging economies.

In a first step, the multicollinearity and the correlation of the indicators with the ratings have been analyzed. There is no sufficient evidence supporting a linear relationship between indicators (Figure 1). Moreover, the value of correlations and variance inflation factors (VIF) presented in Table 6 shows that there is no significant multicollinearity. The cumulative explanatory proposition of indicators are given in Table 7 and computed implementing a principal component analysis. The results indicate that the first seven components can explain up to 99% of the information. The fittest regression method of equation ( 1) is obtained using the tests introduced in section 2. The tests are implemented on both subgroups of countries and the whole data set. Results are presented in Table 9. The p-values of Breusch-Pagan and Breusch-Godfrey/Wooldridge tests indicate that there are cross-sectional dependencies and serial correlations in the advanced economies data set, emerging economies data sets and the whole sample, therefore an OLS regression is not reliable. This is confirmed by using a F-statistic to test fixed effects against the OLS, and Breusch-Pagan LM test of the random effects against the OLS. The p-values of Hausman tests reveal that a fixed effect model is more appropriate. The p-values of the F -tests reject time-fixed effect. Thus, the fixed-effect approach is the best regression method for fundamental rating model (equation 1). The results are presented in Table 2.

External debt (ED) and current account balance (CAB) are significant factors and exhibit negative effects considering advanced economies, emerging economies and the whole data set. The negative effect of ED is consistent with the discussion in Section 2. Indeed, higher external debt causes higher debt burden and leads to lower creditworthiness. A possible explanation of negative CAB is that domestic investments are financed by foreigners' savings, and this implies a higher confidence in sovereigns' creditworthiness.

Although the averaged CAB of advanced countries is higher than of emerging economies, the regression results suggest that the CAB indicator alone is not sufficient to characterize a country credit quality.

Secondly, the inflation rate (denoted as Inf.) factor is significant for both the whole sample and the emerging economies subsample. It has a negative sign, as a high inflation rate is a negative indicator for the economic development of a country. Investing in countries where the inflation rate is uncontrolled is highly risky. Nevertheless, the causal factor of inflation is ambiguous, especially for the developed countries. It could be the result of a monetary policy aiming at improving the economic condition of a country rather than deteriorating it. However, GDP growth rate, fiscal balance (FB) and Corruption Perceptions Index (CPI) factors are not statistically significant. As a result, the GDP growth rate is not a suitable explanatory variable for rating scores, although it is an important index to characterize the development speed of a country. This result is not entirely counter intuitive as reviewing international GDP growth rate during 2012, we observed that most countries with high GDP growth rate, such as Qatar, Ghana, Turkmenistan, etc., are countries with poor credit quality. On the contrary, countries with good ratings, such as Germany, Finland or Canada, have GDP growth rate under the world average. However, sovereigns with negative growth rate (recession) such as Sudan, Andorra, Syria, etc., are very The regression is implemented with the data set of all countries, advanced countries and emerging countries respectively. In this table, the coefficient estimate of the corresponding variable is provided in the column labeled "Estimate" along their standard errors in brackets. The p-values are given on the right of each estimate. The symbols "***", "**", "*" and "." refer to the significance level 0.001, 0.01, 0.05 and 0.1.

Table 2: Fix-Effect Regression Results for Country-Specific Model risky investment choices, as these countries are not creating any value. Consequently, the influence of GDP growth rate on a country credit quality is not linearly related. Though these high scored countries generally have high and positive FB, the difference is not significant in our sample. Regarding the CPI, contrary to the results obtained by Mellios and Paget-Blanc (2006) [START_REF] Mellios | Which Factors Determine Sovereign Credit Ratings?[END_REF], this factor is positively significant for the whole sample at a 90% confidence level. Our results indicate that the PCI factor is appropriate to explain the rating scores if the countries are not split in different subsets. Finally, R 2 and Adjusted R 2 lie between 0.23 and 0.68 for the estimation of equation ( 1) on the three data sets. Moreover, R 2 and adjusted 11 R 2 cannot be improved by changing regression methods. It indicates that using these indicators cannot fully explain the ratings issued by agencies during the recent 10 years. These statistics suggest that during the selected time period some macroeconomic indicators which were explanatory variables in previous analysis cannot explain the rating in ours. This intermediate conclusion should be related to the fact that our analysis is performed during a global downturn and this affects the data. But this support the paper's objective of adjusting this fundamental rating using the market information.

Market Implied Rating

The data used in market implied rating analysis characterized by (2) include bond yields, bid-ask spreads of bond, FTSE-Global Index, and VIX index. These contain the market related information of 20 advanced countries and 8 emerging countries and start from 01/01/2001 to 30/09/2012 on a daily basis.

Concretely, the government benchmark bond index provided by Reuters EcoWin with a 10 years maturity, along their local currencies are used to capture bond yields movements. The two main advantages of using this index than computing the term structure of a specific bond are the following. Firstly, it is much easier to match other market indicators with the selected bond yields. Secondly, this bond index is a reference to which investors benchmark the performance of individual market sectors as it is neither polluted by coupons nor taxes. Most bond yield indexes are provided by Reuters EcoWin, however, for some emerging economies, the data have been obtained from Datastream. The bid-ask spreads of bonds have been obtained from Bloomberg. The FTSE-Global Index for each sovereign provided by Reuters EcoWin is used as a proxy for the variation of market demands. VIX indexes obtained from Datastream is used as a measure of the market risk appetite.

Statistics of government benchmark bond index of the selected sovereigns with 10-years maturity are given in Table 10. To facilitate the comparison, a dichotomic approach has been undertaken, splitting advanced and emerging countries into two sub-groups. In average, higher rating leads to lower yields. Consequently, means of high rated sovereigns' bond yields are generally lower than means of those from low rated governments, however, the watershed is not clearly identified. There are intersections of the averaged yields between the high and low rated sovereigns' bond yields. For example, average yields of Thailand who has the highest rating of A/Stable is lower than the mean yields of Australia who are rated AAA/Stable in the period of analysis. Moreover, among the high rated bonds, the movements are not uniform. Figure 2 represents the time series of the government benchmark bond yields of eleven countries whose ratings remained AAA/Stable during the considered period. Although, they hold the same rating during the same period, the movements and ranges of their yields were varying. Switzerland bonds moved relatively smoothly during the observed period, however, on the same period Norway's government bonds fluctuations were significant. Moreover, all bond yields show clear upward movements from 2007 to 2009 except for Canada. Figure 3 exhibits the remaining nine advanced economies' government bond yields. These nine time series show more divers features, since their ratings were varying during this period.

Portugal government bond yields experienced the most prominent increase during the last two years. An identical phenomenon has been observed for the government bonds of Belgium, Italy and Spain. However, these countries have been dramatically impacted by resent European Sovereign Debt Crisis (Movements of emerging countries' bond yields are plotted in Figure 4). Though there is no tendency for these bond yields behaviors, they are more volatile than those of advanced economies.

Chicago Board Options Exchange Volatility Index (VIX) of the same period is presented in Figure 5.

Statistics of bid-ask spread of bonds and market capitalizations of FTSE-Global Equity Index are given 11 Here we assume the linear relation among the variables as model 1 the lower the transaction costs, the lower the risk, and consequently the lower the return. However, a negative bid-ask spreads has been observed in the result of the regression regarding emerging economies. A possible interpretation of this result is that the liquidity factor for emerging market 12 works in a different way than for the intuitive approach. When investing in emerging markets, which are relatively riskier than advanced markets, investors may hold more active and sensitive investment strategies than investing in advanced economies. Therefore, even though investors prefer to choose more liquid bonds, they are more sensitive to losses than in advanced market such that they actively trade the bonds. Active trading contributes to a higher liquidity and the yields generated by these bonds are not necessarily very high. Secondly, the market requirement indicator (FTSE-Global Market Capitalization Index) is significant in both regressions with negative signs. This indicates that when investors are willing to invest but are "disappointed" by equity markets, they turn to other markets such as the bonds. Similarly, investors will leave bond market if it becomes depressed. The p-values of the t-tests confirm that this indicator has a significant influence for the bond yields. While, comparing coefficients of the FTSE Market Cap. in the two regressions, we observe that the influence of market requirements is more significant for the emerging economies than for advanced markets. Finally, the VIX index which measures the risk appetite of market practitioners has a significant positive coefficient in both regressions. This is consistent with the fact that investors tend to be more conservative when the markets are turbulent, i.e. they tend to demand higher returns for the same level of risk under a volatile market than under bullish market conditions. Moreover, the influence of this indicator is stronger for emerging markets than for advanced economies, as people have usually more confidence in advanced economies during crisis (e.g. "fly to quality" behaviors).

Implied Ratings and Credibility Weights

Here, we give the two implied ratings and the δ-ratings in the standard alphabets fashion so that to compare the results with agency's ratings. Country-specific implied rating and market implied rating are derived from previous results listed in Table 2, 3 and 4. The two ratings are both calculated from an ordinal scale method 13 with the inputs of the previous obtained implied credit premium. The outcomes are credit scores showed in the first two columns of Table 13. Credibility weights, i.e. ω in equation 4, are listed in the fifth column of Table 13 14 . Alphabets given in Table 5 are the scaled results according to the mapping given in Table 14.

Firstly, fundamental ratings listed in the second column of Table 5 are compared with Fitch's ratings, the last column. Rating agencies tend to rate the advanced countries higher than what is implied by the related economic data, except for the countries affected by crisis like Belgium, Italy, Portugal and Spain. However, this optimistic attitude is not observed evaluating the ratings of emerging countries. Emerging countries with higher agency's ratings than fundamental ratings are usually believed to have good economic perspectives, while those with higher fundamental ratings than agency's ratings usually recently experienced an economic turmoil.

Secondly, we compared market implied ratings and agency's ratings (third and last column in Table 5). Similarly, Fitch gave better ratings to advanced economies than the ratings implied by their market indicators except for the countries believed in trouble, such as Italy, Spain and Portugal. However, this tendency is not particularly clear in the emerging group. Comparing fundamental and market implied ratings, we found that market implied ratings are lower than their fundamental ratings for advanced economies, except for Czech Republic, Portugal and Switzerland. For emerging economies, however, market implied ratings are higher than country-specific implied ratings except for India and South Africa.

Credibility weights are given in Table 13, applying the algorithm expressed in equation ( 4) and the bootstrapping results of E(σ 2 ). Market implied ratings bear lower weights for the states with stable ratings through years and higher weights for the countries with volatile ratings. The δ-rating provided in the fourth column, are obtained using the credibility weights between the fundamental ratings and the market implied ratings. Comparing the δ-ratings and Fitch's ratings, we observe that the adjusted ratings are usually lower than agency's ratings for advanced economies, but they exhibit different aspects whether the countries are facing financial or economic trouble. This phenomenon indicates that rating agencies may overreact to these countries problems than what their economic and financial indicators imply. For emerging countries, rating agencies give higher ratings to the countries which are believed having better economic perspectives than the averaged ratings we proposed and lower ratings to these countries facing or under economic or financial difficulties. Therefore, we believe ratings agencies are driven by public belief or mass media and partially lose their objectivity. Combining the two implied ratings using credibility weights enables assessing the underlying credit risk of the sovereign. In the first two columns, the country-specific ratings and the market implied ratings of both the 20 advanced economies and the 8 emerging economies are provided using the regression results obtained in the previous section. The weighted averaged ratings obtained using the credibility theory are listed in the third column. The fitch's history rating is given at the last column.

Discussion and Conclusion

As investment opportunities become more global and diverse, it is important to decide which countries represent good investment opportunities. There are advantages to invest in foreign markets, but the risks associated may be considerably higher when investing in emerging economies. To secure the advantage of foreign investment, investors should ensure that the return generated is sufficient to offset the risk they are taking. Measuring the ability of a country to face its financial commitments, i.e. its debts, ratings are essential tools to support investment decisions. Traditional ratings are issued by credit rating agencies (CRAs) which are painfully recovering their credibility after the crisis. The recent remedial regulations such as the Sarbanes-Oxley Act or the Code of Conduct for CRAs15 cannot solve the problems completely. Hence, it is necessary to challenge CRAs' fundamental methodologies. In this paper, we proposed an hybrid method using public information to evaluate sovereign's credit. We find several interesting results supporting the idea that investors should rethink the credibility or the objectivity of the ratings issued by CRAs.

Firstly, some macroeconomic indicators which have proved to be useful (indeed used by CRAs in their quantitative models) do not really explain the ratings issued by them nowadays. As mentioned above, ratings are a combination of quantitative and qualitative evaluation approach, but the results of countryspecific implied rating in section 3.1 tend to show that agencies' models tend to improve the ratings of advanced economies and lower the ratings of emerging economies. While, it is interesting to notice that there are three exceptions, Italy, Portugal and Spain, who have the agencies' ratings lower than both their country-specific ratings and market implied ratings. This finding confirms the belief that CRAs tend to become more conservative during the crisis and by the way, may adopt a pro-cyclical attitude toward these economies. This attitude justifying the need of alternative approach. Indeed, they tend to give conservative ratings to the countries who are "believed" in trouble even though both economic indicators and market perceptions do not acknowledge them. On the other hand, fundamental rating obtained in our study offers investors an overview of sovereigns credit risk implied by their economic profile. Therefore, an investor holding a long-term investment project may rely more on the fundamental ratings in order to screen the subjective biases released in agencies' ratings.

Secondly, market implied ratings are generally lower than country-specific implied ratings for advanced economies, but higher than the corresponding fundamental ratings for emerging markets. This finding indicates that market has different opinion concerning the difference of credibility between developed and developing sovereigns. Besides, the influence of bond liquidity exhibits different roles in advanced and emerging economies. This outcome suggests that in practice, investors use different trading strategies for emerging markets than for developed economies, since these markets work in another way than the traditional ones. This finding shows that investors who are attracted by the advantages of investing in emerging countries should consider alternative trading strategies than traditional developed markets'. Therefore, investors having a more complex business model should pay more attention to the market implied ratings approach which allows quicker updates regarding the tendency of the uncertain markets. Moreover, the overvalued risk of investing in emerging countries according to CRAs' ratings may offer arbitrage opportunity to short-term oriented investors.

Additionally, the δ-rating approach proposed in this paper gives a weighted average of the long-term fundamental ratings and the updated market implied ratings through credibility weight. We believe the δ-rating can provide better information to investors to make investment decisions. The pure quantitative approach combine the information contained in the low frequency macroeconomic data which provide a long-term through-the-cycle credit evaluation and the timeless market cognition of the risk of investing in the country. The credibility factor grants higher weight to market implied rating when the market is facing turmoil and less weight when the market is stable. We believe the quantitative adjustment from market implied rating is more objective than the qualitative adjustment implemented by rating agencies, and therefore provide better ratings to investors. Accordingly, the δ-rating can correct the subjective biases of agencies' ratings and offer better information to investors to make their investment decision. This statement is even more important, as to optimize a portfolio allocation considering the financial assets issued by the fast growing emerging countries, a more reactive analysis is required.

Furthermore, having used a data set from 2001 to 2012 which covers the turmoil period of the recent European Sovereign-Debt Crisis, our results show that CRAs cannot justify themselves by claiming that they focus on a long-term horizon in using a through-the-cycle rating methodology. Their ratings seems distorted by certain subjective decisions which may be questionable. The statement that they aim to respond only to the perceived permanent component of credit-quality changes is suspect as well since they gives the ratings to Italy, Portugal and Spain lower than the ratings implied by their economic and market indicators. The debt problem experienced by the PIGS (Portugal, Italy, Greece and Spain) justify the concerns, but the pressures from public opinions seems aggravating their predicaments. It is interesting noticing that according to CRAs the PIGS are not investment grade while considering our analysis they are. Consequently, from a credit point of view, the PIGS are ranked among emerging economies. Relying on CRAs may lead to arbitrage opportunities as the yield of bonds issued by the new pool of emerging countries (i.e. PIGS and traditional emerging countries) are too high considering the inherent risk highlighted by our study, therefore, it could be very interesting to invest in these countries, as the bonds are under-priced according to our analysis. The crisis of these sovereigns, however, could be chances for investors, since hidden opportunities during crises discovered and highlighted by alternative risk evaluation may be the way to the success. Emerging Markets today will become tomorrow' developed countries. From a credit point of view, without considering any political aspects, these changes may come faster than expected. Besides, considering that some developed countries may do a backward journey toward uncertainty, the definition of emerging countries should be revised, and should be disconnected to the definition underlying investment/ non-investment grade assets.

These results stimulate further interests in studies. Firstly, we have not discussed the problem of forward looking ratings which could be achieved by a quantitative analysis. Since the macroeconomic forecasts for the coming five years from are available from worldwide banks and IMF, we are able to derive a forward looking perspective of country-specific implied ratings. Difficulty may arise from forecasting the market information. Secondly, the correlations between the ratings and the loss given defaults have not been dealt with. We believe these ratings combined practitioners' expectations of the two important factors of counterpart risk. It could be interesting to study the implied default probability and loss given defaults using public available information which is more practicable for investors and risk managers.

Lastly, our studies is limited by the availability of market data for emerging markets. The study will be extended considering a larger group of emerging countries when there are more resourceful data for emerging markets. Furthermore, as some non-linearity in both the fundamental and the market implied models' factors, it will be interesting to extend the methodology to non-linear approaches.

[22] Perraudin, W. and Taylor, A. P. ( 2004 In this table, the implied credit ranks of the 20 advanced economies and the 8 selected emerging economies have been provided.

The number in the first column is the country-specific ranks computed from the results of Table 2. The market implied ranks are listed in the second column calculated from the implied credit premium in Table 3 and 4. In the last column, the differences between the two ranks have been provided. . The δ-score listed in the last column are the weighted averaged scores of fundamental and market credit score using the credibility weights.

Ferri et al. (1999) 1 a

 1 larger tax base and stronger ability to Mellios and Paget-Blanc (2006) honor the debt obligation. Gärtner et al. (2011) GDP growth rate + Cantor and Packer (1996) The higher growth rate of GDP indicates a Ferri et al. (1999) better ability of the country to facing their Mellios and Paget-Blanc (2006) debt burden. Gärtner et al. (2011) Inflation -Cantor and Packer (1996) High inflation rate indicates government Ferri et al. (1999) financial structure problem and low Mellios and Paget-Blanc (2006) creditworthiness. Gärtner et al. (2011) Fiscal balance + Fiscal surplus indicates the government has the Cantor and Packer (1996) financial capacity to pay their debts. Fiscal Ferri et al. (1999) 2 deficit indicates less capital to pay the debts.

2 Ferri

 2 et al. (1999) use the notation of budget deficit instead of fiscal balance.

3 Ferri

 3 et al. (1999) use the notation of development indicator instead of economic development.

4

 4

  default history) and the rating scores. The upper, medium and lower plots are respectively, the score plots of the variables of all the sovereigns, the advanced economies and the emerging economies.

Figure 1 :

 1 Figure 1: Score Plot of Economic Indicators 24

Figure 2 :

 2 Figure 2: Government Benchmarks 10 Year Bond Yields of the Advanced AAA/Stable Rated Countries 25

Figure 3 :

 3 Figure 3: Government Benchmarks 10 Year Bond Yields of the Downgraded Advanced Countries

Figure 4 :

 4 Figure 4: Government Benchmarks 10 Year Bond Yields of the Emerging Countries

Figure 5 :

 5 Figure 5: 10 Year Government Bond Yields of Brazil with rating announcements and VIX Index

Table 1 :

 1 Fundamental Explanatory Variables introduced in Literature

	Gärtner et al. (2011)

Table 11 .

 11 Statistics of these two market indicators are presented in two groups following the country's economic development level. Italian, Portugese and Spanish bonds are relatively more liquid than others among the advanced economies. Meanwhile, the Hungarian, Philippians and Polish bonds are more liquid compared to others emerging countries. The interesting observation in the results presented in the Tables This table presents the result of the regression of the market implied rating model with the data of 20 advanced economies.Credit risk premia of each country are given in the second column. *** refers significant level 0.001.

		Estimates (Coefficients)	Std.Error	t-value	P r(> |t|)
	Ask-Bid Spread	-1.5303	0.0098 -155.5998	< 2.20E -16 ***
	FTSE Maket Cap.	-0.0006	0.0001	-7.9346	2.15E-15 ***
	VIX	0.0018	0.0004	4.8693	1.12E-06 ***
		Estimates (Credit Risk Premiums)	Std.Error	t-value	P r(> |t|)
	Australia	5.5258	0.0183	301.8760	< 2.20E -16 ***
	Austria	3.9067	0.0173	226.4240	< 2.20E -16 ***
	Belgium	3.9839	0.0173	230.1640	< 2.20E -16 ***
	Canada	4.1206	0.0186	221.4800	< 2.20E -16 ***
	Czech	4.3676	0.0172	253.2900	< 2.20E -16 ***
	Denmark	3.9283	0.0173	226.6980	< 2.20E -16 ***
	Finland	3.8605	0.0173	222.5650	< 2.20E -16 ***
	France	3.9276	0.0196	200.7410	< 2.20E -16 ***
	Germany	3.7990	0.0187	203.4140	< 2.20E -16 ***
	Italy	4.1761	0.0179	233.5370	< 2.20E -16 ***
	Netherland	3.8647	0.0177	218.3950	< 2.20E -16 ***
	New Zealand	5.8735	0.0173	340.2560	< 2.20E -16 ***
	Norway	4.5459	0.0173	262.0960	< 2.20E -16 ***
	Portugal	4.4751	0.0182	246.5230	< 2.20E -16 ***
	Singapore	2.7923	0.0173	160.9860	< 2.20E -16 ***
	Spain	4.1114	0.0179	229.8260	< 2.20E -16 ***
	Sweden	3.7717	0.0175	215.3550	< 2.20E -16 ***
	Switzerland	2.5913	0.0185	139.7220	< 2.20E -16 ***
	United Kingdom	4.3938	0.0251	175.2200	< 2.20E -16 ***
	United States	4.6549	0.0867	53.6620 < 2.20E -16 ***
		R-Squared: 0.2849			Adj R-Squared: 0.2848

10 Documents de Travail du Centre d'Economie de la Sorbonne -2013.34 in

Table 3 :

 3 Fixed-Effect Regression Results of Market-Implied Rating Model of Advanced EconomiesThis table presents the results obtained from the regression of the market implied rating model with the data of 8 emerging economies. Credit risk premia of each country are given in the second column. *** refers significant level 0.001.

		Estimates (Coefficients)	Std.Error	t-value	P r(> |t|)
	Ask-Bid Spread	2.8778	0.0686	41.9800	< 2.20E -16 ***
	FTSE Maket Cap.	-0.1210	0.0011 -107.7100	< 2.20E -16 ***
	VIX	0.0344	0.0013	27.1910	< 2.20E -16 ***
		Estimates (Credit Risk Premiums)	Std.Error	t-value	P r(> |t|)
	Brazil	9.7298	0.0628	154.8320	< 2.20E -16 ***
	Hungary	6.7608	0.0692	97.6460	< 2.20E -16 ***
	India	7.5942	0.0457	166.2740	< 2.20E -16 ***
	Philippines	9.1144	0.0492	185.4130	< 2.20E -16 ***
	Poland	6.0675	0.0428	141.8240	< 2.20E -16 ***
	Russia	9.2199	0.0501	184.1090	< 2.20E -16 ***
	South Africa	10.8099	0.0484	223.4070	< 2.20E -16 ***
	Thailand	4.1275	0.0429	96.1070	< 2.20E -16 ***
		R-Squared: 0.3505			Adj. R-Squared: 0.3503

Table 4 :

 4 Fixed-Effect Regression Results of Market-Implied Rating Model of Emerging Economies

3 and 4, is that the liquidity have different impact on the ratings depending on the group the country belongs to. The results show that liquid bonds issued by advanced economies, i.e. characterized by low bid-ask spreads, bear lower yields. This result is consistent with the fact that the more liquid the asset, 11 Documents de Travail du Centre d'Economie de la Sorbonne -2013.34

Table 5 :

 5 Fundament Implied Rating, Market Implied Rating, Adjusted Rating and Agency Rating

  ) On the Consistency of Ratings and Bond Market yields, Journal of Banking & Finance, 28[START_REF] Ejsing | Liquidity and credit risk premia in government bond yields[END_REF], 2769 -2788. PCI is per capita income; Inf. means inflation; FB refers to fiscal balance; ED indicates external debt; CAB is the abbreviation of current account balance; CPI is the Corruption Perceptions Index published by Transparency International; DH denotes default history; Score is the numerical value of the corresponding rating. The correlations are computed for all the sovereigns, advanced economies and emerging economies and listed in the three sub-tables.

	[23] Weinstein, M. (1977) The Effect of a Rating Change Announcement on Bond Price. Journal of
	Financial Economics, 5, 329-350.
				Advanced Economies
		GDP	PCI	Inf.	FB	ED CAB	CPI Score
	GDP	1.00 -0.09	0.11 -0.25 -0.15	0.23	0.18	0.13
	PCI -0.09	1.00 -0.14	0.29 -0.02	0.46	0.44	0.41
	Inf.	0.11 -0.14	1.00 -0.09 -0.11 -0.29 -0.12 -0.13
	FB -0.25	0.29 -0.09	1.00 -0.05	0.08	0.01	0.02
	ED -0.15 -0.02 -0.11 -0.05	1.00	0.19 -0.30 -0.23
	CAB	0.23	0.46 -0.29	0.08	0.19	1.00	0.48	0.33
	CPI	0.18	0.44 -0.12	0.01 -0.30	0.48	1.00	0.69
	Score	0.13	0.41 -0.13	0.02 -0.23	0.33	0.69	1.00
	VIF	1.29	1.57	1.14	1.20	1.53	2.32	1.91
				Emerging Economies
		GDP	PCI	Inf.	FB	ED CAB	CPI Score
	GDP	1.00 -0.36	0.08 -0.30	0.02	0.09 -0.32 -0.12
	PCI -0.36	1.00 -0.11	0.81 -0.15 -0.29	0.52	0.41
	Inf.	0.08 -0.11	1.00	0.16 -0.20	0.30 -0.22 -0.45
	FB -0.30	0.81	0.16	1.00 -0.09 -0.21	0.50	0.23
	ED	0.02 -0.15 -0.20 -0.09	1.00 -0.34	0.20 -0.37
	CAB	0.09 -0.29	0.30 -0.21 -0.34	1.00 -0.73 -0.46
	CPI -0.32	0.52 -0.22	0.50	0.20 -0.73	1.00	0.54
	Score -0.12	0.41 -0.45	0.23 -0.37 -0.46	0.54	1.00
	VIF	1.23	3.84	1.38	3.89	1.28	2.60	3.21
				All Sovereigns
		GDP	PCI	Inf.	FB	ED CAB	CPI Score
	GDP	1.00 -0.35	0.30 -0.41 -0.16	0.12 -0.28 -0.32
	PCI -0.35	1.00 -0.50	0.56	0.11	0.37	0.77	0.75
	Inf.	0.30 -0.50	1.00 -0.29 -0.20 -0.10 -0.56 -0.66
	FB -0.41	0.56 -0.29	1.00	0.04	0.08	0.48	0.50
	ED -0.16	0.11 -0.20	0.04	1.00	0.12	0.02	0.02
	CAB	0.12	0.37 -0.10	0.08	0.12	1.00	0.29	0.16
	CPI -0.28	0.77 -0.56	0.48	0.02	0.29	1.00	0.88
	Score -0.32	0.75 -0.66	0.50	0.02	0.16	0.88	1.00
	VIF	1.38	3.26	1.63	1.63	1.13	1.37	2.95

*

Table 6 :

 6 Correlation among Economic Indicators and Rating Scores (2001-2012) This table gives the principle component analysis results of the economic indicators listed in Table 1 with the three sample sets. Here PC1 to PC8 refers to Rating Scores, GDP growth rate, Per capita income, inflation rate, fiscal balance, external debts, current balance accounts, and corruption perceptions index.

	Importance of components:
				All Economies
		PC1	PC2	PC3	PC4	PC5	PC6	PC7	PC8
	Standard deviation	1.9281 1.0897 1.0377 0.8948 0.71550 0.62213 0.46419	0.3213
	Proportion of Variance	0.4647 0.1484 0.1346 0.1001 0.06399 0.04838 0.02693	0.0129
	Cumulative Proportion 0.4647 0.6131 0.7477 0.8478 0.91178 0.96017 0.98710	1.0000
				Advanced Economies
		PC1	PC2	PC3	PC4	PC5	PC6	PC7	PC8
	Standard deviation	1.5973 1.2271 1.1086 0.9247 0.86485 0.68678 0.63403 0.48714
	Proportion of Variance	0.3189 0.1882 0.1536 0.1069 0.09349 0.05896 0.05025 0.02966
	Cumulative Proportion 0.3189 0.5071 0.6607 0.7676 0.86113 0.92009 0.97034 1.00000
				Emerging Economies
		PC1	PC2	PC3	PC4	PC5	PC6	PC7	PC8
	Standard deviation	1.7672 1.2814 1.1289 0.9353	0.7818	0.46764 0.37059 0.34435
	Proportion of Variance	0.3904 0.2053 0.1593 0.1094	0.0764	0.02734 0.01717 0.01482
	Cumulative Proportion 0.3904 0.5956 0.7549 0.8643	0.9407	0.96801 0.98518 1.00000

Table 7 :

 7 Principle Component Analysis of Economic Indicators(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)

		GDP	PCI *	Inf. *	FB *	ED *	CAB *	CPI *	DH *	Score *	Rating
					Advanced Economies
	Min	-8.3540	6270	-0.903 18.01	9.709	-12.638	3.700	0.0	49.00	AA-/stable
	1st Qu	0.7505	27146	1.575 36.47	42.511	-3.201	7.100	0.0	99.00	-
	Median	1.9195	37293	2.184 43.58	58.422	1.012	8.500	0.5	100.00	-
	Mean	1.7465	38335	2.180 42.60	60.735	1.847	7.921	0.5	96.72	-
	3rd Qu.	3.0595	46329	2.784 49.59	77.138	5.788	9.000	1.0	100.00	-
	Max. 14.7630	99665	6.612 58.53 123.357	25.813	9.900	1.0	100.00	AAA/stable
					Emerging Economies
	Min.	-7.800	467.2	-0.846 17.00	7.876	-8.4270	2.300	1	26.0	BBB-/negative
	1st Qu.	2.851	2118.7	3.703 20.28	40.096	-3.3453	2.700	1	54.0	-
	Median	4.325	5080.5	4.944 31.84	50.806	-0.2730	3.500	1	62.5	-
	Mean	4.194	5861.7	5.871 30.27	51.529	-0.1983	3.652	1	61.8	-
	3rd Qu.	6.118	8768.7	7.099 38.58	66.929	2.8727	4.525	1	74.0	-
	Max.	10.623 15354.3 21.461 52.40	84.300 11.0690	5.500	1	80.0	A/stable
						All Countries
	Min.	-8.3540	467.2	-0.903 17.00	7.876	-12.638	2.300	0.0000 26.00	BBB-/negative
	1st Qu.	0.9423 11248.1	1.780 33.78	41.700	-3.248	4.600	0.0000 75.00	-
	Median	2.5165 30152.8	2.479 39.34	55.836	0.285	7.300	1.0000 100.00	-
	Mean	2.4459 29056.8	3.234 39.08	58.105	1.262	6.701	0.6429 86.75	-
	3rd Qu.	3.9000 43394.7	3.814 47.68	72.164	4.697	8.800	1.0000 100.00	-
	Max. 14.7630 99664.5 21.461 58.53 123.357	25.813	9.900	1.0000 100.00	AAA/stable
	* In this table, PCI is the per capita income; Inf. means inflation; FB refers to fiscal balance; ED indicates external debt; CAB
	is the abbreviation of current account balance; CPI is the Corruption Perceptions Index published by Transparency International;
	DH denotes default history; Score is the numerical value of the corresponding rating. It includes 20 advanced economies: Australia,
	Austria, Belgium, Canada, Czech, Denmark, Finland, France, Germany, Italy, Netherland, New Zealand, Norway, Portugal, Singa-
	pore, Spain, Sweden, Switzerland, United Kingdom, United States; and 8 emerging economies: Brazil, Hungary, India, Philippines,
	Poland, Russia, South Africa and Thailand. The data is from 2001 to 2012, annually.

Table 8 :

 8 Market capitalizations of the country's equity market issued by FTSE-Global Equity Index for each sovereign are normalized into the common scale as bond yields and liquidity spreads. Statistics of two market indicators of the 28 economies. The Bid-Ask spread is calculated using the following formula: Ask-Bid Ask × 100% using data collected from Bloomberg. The equity market capitalizations of sovereign is measured by the FTSE-Global market cap index. Std means standard deviation. These data start from Jan. 2001 to Sep. 2012. The data of Philippine and Russia follow the same period as the data of their government benchmark bond yields. They are all daily data.

					Ask-Bid Spreads			FTSE Global Market CAP
			Min	Median Mean Max	Std	Min	Median	Mean	Max	Std
	1	Australia 0.99	1.09	1.10	1.32	0.04	20.42	61.88	63.07	111.28	27.34
	2	Austria	0.61	1.02	0.99	1.12	0.08	0.75	3.40	3.61	8.90	2.12
	3	Belgium 0.31	1.01	0.94	1.08	0.15	3.59	7.83	8.04	12.11	1.86
	4	Canada	0.87	1.07	1.08	1.24	0.05	26.92	78.68	74.44	134.39	28.98
	5	Czech 0.78	1.00	1.02	1.42	0.13	0.17	1.41	1.24	3.24	0.77
	6	Denmark	0.97	1.08	1.09	1.54	0.08	3.80	8.55	9.17	16.29	3.29
	7	Finland 0.84	1.03	1.03	1.27	0.04	6.58	11.75	12.62	26.39	3.85
	8	France	0.62	1.03	1.00	1.12	0.08	46.85	100.92	104.75 179.16	31.70
	9	Germany 1.02	1.07	1.09	1.39	0.90	28.60	75.69	76.89	138.34	24.65
	10	Italy	0.06	0.99	0.86	1.04	0.24	19.24	35.54	38.37	65.67	12.21
	11	Netherland	0.84	1.03	1.03	1.15	0.04	15.80	35.90	36.31	57.24	8.77
	12	New Zealand	0.92	1.09	1.08	1.22	0.06	0.79	1.63	1.63	2.55	0.42
	13	Norway	1.02	1.12	1.15	1.60	0.11	2.58	7.52	7.61	16.34	3.58
	14	Portugal	0.00	1.01	0.82	1.06	0.35	1.88	3.52	3.76	6.87	1.10
	15	Singapore	0.75	1.00	1.00	1.18	0.01	4.14	10.13	12.10	23.00	5.66
	16	Spain 0.04	1.02	0.89	1.09	0.27	16.35	39.96	39.71	73.11	14.21
	17	Sweden	0.75	1.01	1.00	1.24	0.03	9.39	25.73	25.44	43.04	8.43
	18	Switzerland 1.00	1.14	1.17	1.69	0.10	34.96	72.44	70.89	101.92	17.67
	19 United Kingdom	0.94		1.08	1.28	0.04	118.8	224.4	225.0	345.1	48.68
	20	United States	0.95	1.10	1.10	1.22	0.04	642.3	1142.8	1131.3 1513.1 196.30
	1	Brazil	1.16	1.72	1.74	2.13	0.16	3.12	27.15	32.04	75.75	23.44
	2	India 2.72	2.72	2.72	2.72	5.70E-07	3.68	27.23	24.63	46.10	12.06
	3	Hungary	0.69	0.96	0.95	1.16	0.08	0.36	1.65	1.65	3.60	0.82
	4	Philippine 0.38	0.73	0.73	1.08	0.16	0.34	1.00	1.16	3.38	0.73
	5	Poland	0.72	0.98	0.96	1.13	0.06	0.64	2.68	2.78	6.44	1.65
	6	Russia 0.49	1.23	1.23	1.80	0.15	2.59	20.10	17.66	40.29	10.35
	7	South Africa 0.91	1.00	1.01	1.15	0.04	4.41	22.34	20.89	38.52	10.21
	8	Thailand	0.61	0.99	1.00	1.50	0.13	0.59	3.30	3.53	8.86	2.12

Statistics of Economic Indicator Data (2001-2012) 18 Documents de Travail du Centre d'Economie de la Sorbonne -2013.34

*

Table 11 :

 11 Statistics of Market Indicators(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)

	Country-Specific Rank Market Implied Rank Rank Splits
	Advanced Economies
	Australia	17	19	2
	Austria	5	7	2
	Belgium	6	10	4
	Canada	8	12	4
	Czech Republic	20	14	-6
	Denmark	12	9	-3
	Finland	14	5	-9
	France	2	8	6
	Germany	4	4	0
	Italy	7	13	6
	Netherlands	9	6	-3
	New Zealand	18	20	2
	Norway	3	17	14
	Portugal	19	16	-3
	Singapore	1	2	1
	Spain	16	11	-5
	Sweden	11		-8
	Switzerland	10	1	-9
	United Kingdom	15	15	0
	United States	13	18	5
	Emerging Economies
	Brazil	7	7	0
	Hungary	3	3	0
	India	4	2	-2
	Philippines	5	6	1
	Poland	2	4	2
	Russia	6	8	2
	South Africa	8	5	-3
	Thailand	1	1	0

20 Documents de Travail du Centre d'Economie de la Sorbonne -2013.34

Table 12 :

 12 Country-Specific Implied and Market Implied Ranks The advanced and emerging economies are listed in the first column separated by a horizontal line. The upper 20 countries are the advanced economies considered in our study and the lower 8 countries are the emerging countries. Fundamental credit scores and market credit scores are given in the second and the third column. The Fitch's scores are the score obtained from Fitch's rating using the mapping given in Table14. Weights are the credibility weights (ω in Equation (4)) computed by

	Country	Fundamental Score	Market Score Averaged Scores Fitch's Score δ-Socre	Weight
	Australia	0.83	0.82	0.83	1.00	0.83	0.311901195
	Austria	0.97	0.87	0.92	1.00	0.97	0.039688222
	Belgium	0.96	0.87	0.91	0.89	0.96	0.003523232
	Canada	0.96	0.86	0.91	1.00	0.95	0.056833804
	Republic	0.76	0.84	0.80	0.85	0.76	0.007325898
	Denmark	0.94	0.87	0.91	1.00	0.94	0.050539811
	Finland	0.93	0.87	0.90	1.00	0.93	0.057606644
	France	0.99	0.87	0.93	0.99	0.98	0.023910266
	Germany	0.98	0.89	0.93	1.00	0.98	0.019197356
	Italy	0.96	0.85	0.90	0.69	0.90	0.529180125
	Netherlands	0.95	0.87	0.91	1.00	0.95	0.044894827
	New Zealand	0.83	0.81	0.82	0.95	0.82	0.122773553
	Norway	0.98	0.83	0.91	1.00	0.97	0.104713107
	Portugal	0.80	0.84	0.82	0.49	0.83	0.851728728
	Singapore	1.00	0.99	1.00	1.00	1.00	1.23082E-06
	Spain	0.87	0.86	0.87	0.59	0.86	0.736500433
	Sweden	0.94	0.89	0.92	1.00	0.94	0.028099158
	Switzerland	0.95	1.00	0.97	1.00	0.95	0.00088457
	United Kingdom	0.91	0.84	0.88	0.99	0.91	0.091735941
	United States	0.94	0.83	0.89	0.99	0.93	0.095308758
	Brazil	0.56	0.62	0.59	0.60	0.56	0.002671929
	Hungary	0.68	0.7	0.69	0.54	0.69	0.626134691
	India	0.72	0.67	0.69	0.54	0.69	0.644876707
	Philippines	0.62	0.64	0.63	0.55	0.62	0.113775216
	Poland	0.67	0.73	0.70	0.75	0.68	0.027353724
	Russia	0.52	0.63	0.57	0.60	0.52	0.051003205
	South Africa	0.66	0.61	0.64	0.74	0.65	0.276121817
	Thailand	0.74	0.86	0.80	0.70	0.76	0.159453856
						2
						2+ σ 2 τ 2

21 Documents de Travail du Centre d'Economie de la Sorbonne -2013.34

*

Table 13 :

 13 Fundamental and Market implied Ratings Scores 22 Documents de Travail du Centre d'Economie de la Sorbonne -2013.34 This table shows the mapping from numerical credit score between 0 to 1 to the standard alphabets ratings from D watch negative to AAA stable.

	1	AAA	Stable	0.67 BBB+ Watch Positive 0.34	B+	Negative
	0.99 AAA	Negative	0.66 BBB+	Positive	0.33	B+	Watch Negative
	0.98 AAA Watch Negative 0.65 BBB+	Stable	0.32	B	Watch Positive
	0.97 AA+ Watch Positive 0.64 BBB+	Negative	0.31	B	Positive
	0.96 AA+	Positive	0.63 BBB+ Watch Negative 0.3	B	Stable
	0.95 AA+	Stable	0.62	BBB	Watch Positive 0.29	B	Negative
	0.94 AA+	Negative	0.61	BBB	Positive	0.28	B	Watch Negative
	0.93 AA+ Watch Negative 0.6	BBB	Stable	0.27	B-	Watch Positive
	0.92	AA	Watch Positive 0.59	BBB	Negative	0.26	B-	Positive
	0.91	AA	Positive	0.58	BBB	Watch Negative 0.25	B-	Stable
	0.9	AA	Stable	0.57 BBB-	Watch Positive 0.24	B-	Negative
	0.89	AA	Negative	0.56 BBB-	Positive	0.23	B-	Watch Negative
	0.88	AA	Watch Negative 0.55 BBB-	Stable	0.22 CCC Watch Positive
	0.87 AA-	Watch Positive 0.54 BBB-	Negative	0.21 CCC	Positive
	0.86 AA-	Positive	0.53 BBB-Watch Negative 0.2 CCC	Stable
	0.85 AA-	Stable	0.52	BB+	Watch Positive 0.19 CCC	Negative
	0.84 AA-	Negative		BB+	Positive	0.18 CCC Watch Negative
	0.83 AA-Watch Negative 0.5	BB+	Stable	0.17	CC	Watch Positive
	0.82	A+	Watch Positive 0.49	BB+	Negative	0.16	CC	Positive
	0.81	A+	Positive	0.48	BB+	Watch Negative 0.15	CC	Stable
	0.8	A+	Stable	0.47	BB	Watch Positive 0.14	CC	Negative
	0.79	A+	Negative	0.46	BB	Positive	0.13	CC	Watch Negative
	0.78	A+	Watch Negative 0.45	BB	Stable	0.12	C	Watch Positive
	0.77	A	Watch Positive 0.44	BB	Negative	0.11	C	Positive
	0.76	A	Positive	0.43	BB	Watch Negative 0.1	C	Stable
	0.75	A	Stable	0.42	BB-	Watch Positive 0.09	C	Negative
	0.74	A	Negative	0.41	BB-	Positive	0.08	C	Watch Negative
	0.73	A	Watch Negative 0.4	BB-	Stable	0.07	D	Watch Positive
	0.72	A-	Watch Positive 0.39	BB-	Negative	0.06	D	Positive
	0.71	A-	Positive	0.38	BB-	Watch Negative 0.05	D	Stable
	0.7	A-	Stable	0.37	B+	Watch Positive 0.04	D	Negative
	0.69	A-	Negative	0.36	B+	Positive	0.03	D	Watch Negative
	0.68	A-	Watch Negative 0.35	B+	Stable

*

Table 14 :

 14 Ratings and Corresponding Scores

23 Documents de Travail du Centre d'Economie de la Sorbonne -2013.34 * This figure presents the economic indicators exhibited in

Table 1 except for the two dummy variable (economic development and

S&P using data acquired from International Finance Corporation, produces a number of capitalization weighted indexes to measure emerging securities market including: S&P/IFCG (Global) Indexes and S&P/IFCI (Investable) Indexes

Basel II/III: banks meeting certain conditions are allowed to use internal risk parameters calculating regulatory capital.

Our empirical analysis covers an extent range of countries and time period which includes the peaks of recent crisis. 5 Documents de Travail du Centre d'Economie de la Sorbonne -2013.34

Data of forty-nine countries at September 29, 1995

10 years time period (1989-1998) data of seventeen countries

The term "inconsistencies" refers to the disordered ordering classification of average price of bond according to ratings. 6 Documents de Travail du Centre d'Economie de la Sorbonne -2013.34

This approach is also called empirical Bayesian method

http://www.fitchratings.com/web content/ratings/sovereign ratings history.xls. The annual minimum ratings have been used when there were multiple rating assignments during one year.

Transparency International (2010) Corruption Perceptions Index 2010. Retrieved 24 Aug 2011

Documents de Travail du Centre d'Economie de la Sorbonne -2013.34

Though there are plenty of macroeconomic data available for a larger number of countries, it is difficult to collect the market information for the same group of countries. The sample used in this part of analysis is in line with the sample used for the market implied rating. Thus, whether a country is selected in our sample depends on the limit of our access to its pertaining market indicators. Therefore, some interested candidates, such as Greece, China and Argentine are missing.

Or the emerging markets in our sample.

The scales are different since the difference of models of the two ratings. We separate the two economies groups to compute market implied ratings since the different sign of liquidity. Credit rankings are given in Table12.

The value of σ 2 are calculated by bootstrapping.12 Documents de Travail du Centre d'Economie de la Sorbonne -2013.34

The code published by the International Organization of Securities Commissions 13 Documents de Travail du Centre d'Economie de la Sorbonne -2013.34


Daniel Fouomene Pewo

Romain Rouvoy

Lionel Seinturier

Snapshot Provisioning of Cloud Application Stacks to Face Traffic Surges

Keywords: IaaS, Slashdot effect, Traffic surge, Forecast

Traffic surges, like the Slashdot effect, occur when a web application is overloaded by a huge number of requests, potentially leading to unavailability. Unfortunately, such traffic variations are generally totally unplanned, of great amplitude, within a very short period, and a variable delay to return to a normal regime. In this report, we introduce PeakForecast as an elastic middleware solution to detect and absorb a traffic surge. In particular, PeakForecast can, from a trace of queries received in the last seconds, minutes or hours, to detect if the underlying system is facing a traffic surge or not, and then estimate the future traffic using a forecast model with an acceptable precision, thereby calculating the number of resources required to absorb the remaining traffic to come. We validate our solution by experimental results demonstrating that it can provide instantaneous elasticity of resources for traffic surges observed on the Japanese version of Wikipedia during the Fukushima Daiichi nuclear disaster in March 2011.

Approvisionnement de piles logicielles pour les applications dans les nuages informatiques pour faire face aux pics de trafic

Résumé : Les pics de trafic, tels que l'effet Slashdot, apparaissent lorsqu'une application web doit faire face un nombre important de requêtes qui peut potentiellement entraîner une mise hors service de l'application. Malheureusement, de telles variations de traffic sont en général totalement imprévues et d'une grande amplitude, arrivent pendant une très courte période de temps et le retour à un régime normal prend un délai variable. Dans ce rapport, nous présentons Peak-Forecast qui est une solution intergicielle élastique pour détecter et absorber les pics de trafic. En particulier, PeakForecast peut, à partir des traces de requêtes reçues dans les dernières secondes, minutes ou heures, détecter si le système sous-jacent fait face ou non à un pic de trafic, estimer le trafic futur en utilisant un modèle de prédiction suffisamment précis, et calculer le nombre de ressources nécessaires à l'absorption du trafic restant à venir. Nous validons notre solution avec des résultats expérimentaux qui démontrent qu'elle fournit une élasticité instantanée des ressources pour des pics de trafic qui ont été observés sur la version japonaise de Wikipedia lors de l'accident nucléaire de Fukushima Daiichi en mars 2011.

Mots-clés : IaaS, Effet slashdot, Pic de trafic, Prévision.

Introduction

Traffic surges, like the Slashdot effect, occur when a web application is overloaded by a huge number of requests, potentially leading to unavailability. Unfortunately, such traffic variations are generally totally unplanned, of great amplitude, within a very short period, and a variable delay to return to a normal regime, as illustrated in Figure 1 1 . A Slashdot effect is characterized by a sudden rise of traffic occurring when a site attracting many Internet users publishes a link for its visitors to a less known or smaller site that will barely be able to take into account this peak audience and that will cause it to slow down its functioning or even to become temporarily unavailable. This phenomenon has been observed when the Slashdot2 site, wellknown in the Linux community, publishes articles with links referring to more marginal sites. This is the origin of the term Slashdot effect. This has a major impact on communications because the saturation of the site can saturate the server and deprive all users from the possibility to communicate with the site. Moreover, with the generalization of broadband access, many users join the Internet through mobile devices and computers, which suggest an increase in the frequency of the Slashdot effects and more generally in traffic surges. In this context, it is legitimate to ask the following questions: from the history of the number of requests received in the last seconds / minutes / hours, how to detect if we are facing a traffic surge, and how to predict the upcoming traffic?

In order to address this challenge, we propose an elastic IaaS management solution, that can (i) detect traffic surges in less than 60 seconds, (ii) predict the upcoming traffic using a forecasting model with an acceptable precision, and (iii) estimate the number of resources needed to absorb this traffic surge, by adding or removing, quickly and automatically, resources within a virtual infrastructure.

The remainder of this paper is organized as follows. We present a case study (see Section 2) and our contribution, PeakForecast, by describing its various components (see Section 3) and then validate with experimental results (see Section 4). Finally, we discuss related work (see Section 5) in this domain before concluding (see Section 6).

Case study

Figure 2 depicts the traffic traces that were collected on the Japanese version of Wikipedia, days before and after the tsunami on 11 March 2011. We can observe that between 12:49 and 12:50 a traffic surge occurred. In this case, how to detect if we are facing a traffic surge caused by a Slashdot effect or not, and predict the upcoming traffic?

Detecting the traffic surges

Detecting a traffic surge requires to monitor the number of incoming requests within a period of a reasonable length in order to get enough confidence in the actual occurrence of such an event. To detect the nearest second, we collect the number of requests per interval of 30 seconds (see Figure 3). Then, we plot the curve of variations multiplier coefficients between two intervals of 30 seconds (Figure 4). We note that the multiplier coefficient is still substantially 1 and at time

Inria

RR n°8299
T, the curve is more than tenfold. This multiplier coefficient thus allows us to detect the start of the peak, in this case 30 seconds.

Forecasting traffic surge coming from the Slashdot Effect

After detecting the traffic surge, we need to predict the upcoming traffic. To do this, we consider the prediction method simple exponential smoothing for time series. The simple exponential smoothing model is one of the most popular forecasting methods. Its principle is to give more importance to recent observations. It is more reactive than moving averages or regression models because it takes into account a rapidly changing trend. It is a method of forecasting t + 1. It does not extend a series, unlike a simple regression, but seeks to obtain a smoothed value for t refers simply t + 1. The forecasting formula is the basic equation:

ŷi+1 = αy i + (1 -α)ŷ i , 0 < α < 1, i > 0 (1)
Where y i is the actual known series value for time period i, ŷi is the forecast value of the variable Y for time period i, ŷi+1 is the forecast value for time period i + 1 and α is the smoothing constant.

(1) can be written as:

ŷi+1 = ŷi + αe i (2)
where residual e i = y i -ŷi is forecast error for time period i. We choose α minimizing e 2 i . This model is described comprehensively in [START_REF] Brown | The fundamental theory of exponential smoothing[END_REF].

We have applied the simple exponential smoothing method on the number of requests in a time interval containing the traffic surge (see Table 1).

Inria

Table 1: Values of the number of requests per interval of 30 seconds on 10-03-2011 between 12:46:30 and 12:53:30 Due to the recurring formula of simple exponential smoothing, we must choose a value from which forecasts can be made. This value is of little importance if the series is long. It often takes the average of the two or three first observations but this choice is arbitrary. In our case (see Table 1), we chose the first observation, i.e. the number of requests for the interval #1 [START_REF] Gandhi | SOFTScale: Stealing Opportunistically for Transient Scaling[END_REF]981). Concerning the choice of the smoothing constant α, which directly affects the results, no direct mathematical method gives its optimum value. For this, it is obviously necessary to rely on data stored and therefore in our case (see Table 1), based on request history. Thus, we have chosen three values of α, 0.4, 0.1 and 0.9, and then calculated prediction using the formula forecasts recurring simple exponential smoothing. By summing the differences between predicted and real number of requests per interval of 30 seconds (first column), squared for each smoothing constant, we note that the one that minimizes this sum is α = 0.9. Therefore the smoothing constant gives estimates with an acceptable precision when it is α = 0.9. This can be confirmed in Figure 5. With this value of 0.9, the constant smoothing, when we detect that we face a traffic surge at the interval #6 (see Table 1), it predicts 11,504 upcoming requests during the next period (see Table 1). Adding this estimated traffic to previous requests, we obtain a forecasted traffic of 23,560 requests from the 30 th second of the minute marking the traffic surge, as shown in Figure 6. This prediction is close to the peak of real traffic, which reached 27,405 requests per minute (adding the interval number 6 and 7 of Table 1), with an average of 457 requests per second. From the estimated traffic, loading time of a cloned virtual appliance, the time to install an application (e.g., MediaWiki takes 10 seconds on average), a server or middleware (e.g., MongoDB takes 11 seconds on average) on a virtual machine, we can estimate the number of virtual machines needed to absorb a peak by taking into account their deployment time. In particular, we use the following formula where the number of virtual machines to deploy N is estimated as:

N = S t -Y t X
Where S t is the estimated value of the traffic at time t, Y t is the value of the traffic at time t, X is the number of requests that can support a virtual machine, about 600 requests per second in our case (estimation based on benchmarks).

Contribution

In a virtual infrastructure (see Figure 7), PeakForecast is the solution we have developed to automatically respond to scalability issues not only by adding resources to absorb traffic surges, but also to release resources when the load decreases. Adding more resources mainly concerns instances of virtual machines (VMs) hosting the presentation layer and the business logic tier of the website, because they are usually the bottleneck caused by traffic surges. After adding its instances of VMs, the load balancer (NGINX3 ) is responsible for the load balancing. Finally, FABRIC4 is a Python library and command-line tool for streamlining the use of SSH for application deployment or systems administration tasks. In this section, we provide a detailed overview of our tool PeakForecast in virtual web infrastructure (see Figure 7). PeakForecast is an SCA distributed system (see Figure 8). The Service Component Architecture (SCA) standard is a set of specifications for building distributed application based on Service-Oriented Architectures (SOA) and Component-Based Software Engineering (CBSE) principles [START_REF] Merle | A Reflective Platform for Highly Adaptive Multi-Cloud Systems[END_REF]. As illustrated in Figure 8, in SCA the basic construction blocks are software components, which have services (or provided interfaces), references (or required interfaces) and expose properties. The references and services are connected by means of wires. SCA specifies a hierarchical component model, which means that components can be implemented either by primitive language entities or by subcomponents. In the latter case the components are called composites. Both component references and services can be exposed at the composite level by means of promotion links. SCA is designed to be independent from programming languages, interface definition languages (IDL), communication protocols, and non-functional properties. We use the FraSCAti5 [3] middleware platform, which enables the development and the execution of distributed SOA applications based on SCA. Beyond the support of standard SCA features, FRASCATI brings reflection to SCA-i.e., introspection and reconfiguration capabilities, via a specialization of the Fractal component model [START_REF] Bruneton | The Fractal Component Model and its Support in Java, Software Practice and Experience[END_REF].

To make our distributed system efficient, so that it can respond with the highest reactivity as possible to scalability, we built PeakForecast with the event-driven middleware framework Akka. Akka6 is a toolkit and runtime for building highly concurrent, distributed, and fault tolerant event-driven applications on the JVM. Akka implements a programming model based on actors (Actor ). The strength of Akka lies in impressive digits its performances: 50 million messages processed per second on a single machine, and small memory footprint; 2.7 million actors per GB of heap. As illustrated in Figure 8, PeakForecast is composed of two SCA composites:

• The first composite exposes a web service to manipulate and perform operations on VMs of the virtual web infrastructure (see Fig. 7). It contains two essential components "ControllerSoftware" and "ControllerVM ". The component "ControllerSoftware" provides, services such as install, uninstall, status, reconfigure, stop, start, restart a component representing a server or an application on one or more VMs. In case the service must be running on multiple VMs, execution is performed by actors "Worker n" operating in parallel and coordinated by the supervisor actor "Con-trollerSoftware". The component "ControllerVM " meanwhile, provides services, such as start, restart, pause, resume, clone, create, delete one or more VMs. Similarly, in case the service must be running for multiple VMs, the execution is performed by the actors "Worker n" operating in parallel and coordinated by the supervisor actor "ControllerVM ".

• The second composite allows PeakForecast to monitor HTTP traffic, detecting traffic surges and reacting accordingly by consuming the services provided by the first composite. It contains a single component "Monitor ". The component "Monitor " is mainly composed of four actors: "Collect", "Analyse", "Decide", "Action", communicating with each others by exchanging messages. The actor "Collect" collects traffic information per time interval, for example the number of requests per second, 15 seconds, 30 seconds, or minute. The number of requests collected by the actor "Collect" are sent as a message to the actor "Analyse". The actor "Analyse" analyzes the number of requests to detect when we are facing a traffic surge (see section 2.1), or prediction gives an estimate of upcoming traffic (see section 2.2). It is within this actor that we have implemented the recurrent formula simple exponential smoothing. With this prediction of the traffic, it estimates the number of VMs to absorb traffic surge (see section 2.3). The actor "Analyse" sends the number of VMs as a message to the actor "Decide". Based on a user profile, the latency of VMs in use, the actor "Decide" determines the exact number of VM instances to deploy in order to absorb the traffic surge, and then sends this number to actor "Action", which takes care of making available the requested VM instances, allowing the virtual web infrastructure to anticipate the traffic surge ahead. As a matter of validation, the virtual web infrastructure (see Figure 7) has been developed. The physical machine uses Virtual Box as an hypervisor and has the following characteristics: Dual Core CPU 2.50GHz, RAM 2000 MB and for each virtual machine (VM): CPU 1 GHz, RAM 500 MB.

In this virtual web infrastructure, a VM front-end hosts the load balancer NGINX responsible for distributing incoming HTTP requests among the VMs hosting the MediaWiki website (the business logic tier of the website). While another VM contains the MYSQL load balancer responsible for distributing SQL queries to the VMs hosting the database (the data layer of the website). As illustrated in Figure 7, MYSQL Proxy redirects read SQL queries to MYSQL server master and slaves, while write queries are processed by the MYSQL server master before forwarding the master replica to slaves.

For the purpose of this validation, adding additional resources mainly concerns instances of VMs containing MediaWiki, because they are considered as the bottleneck in traffic surges. To perform our benchmark, we use the tool SIEGE 7 . It can stress test a single URL with a user-defined number of simu-lated users, or it can read many URLs into memory and stress them simultaneously. The program reports the total number of hits recorded, bytes transferred, response time, concurrency, and return status. Siege supports HTTP/1.0 and 1.1 protocols, the GET and POST directives, cookies, transaction logging, and basic authentication. For example, the following command: siege -d1 -r600 -c200 http://192.168.0.6/mediawiki/index.php/Accueil, simulates the connection of 200 users, each running 600 requests, spaced a second (d1). That makes approximately 120,000 requests.

For the first test without PeakForecast: we have a single VM (apache1) containing MediaWiki and thus treating all HTTP requests sent by the NGINX load balancer. After some minutes, the web site becomes overloaded and causing it to slow down or even temporarily becomes unavailable, as illustrated in Figure 9.

For the second test with PeakForecast: In Figure 10 There is a lot of prior work that deals with dynamic capacity management [START_REF] Gandhi | SOFTScale: Stealing Opportunistically for Transient Scaling[END_REF]. These works can be classified into reactive [START_REF] Julius | Stochastic approximation control of power and tardiness in a three-tier web-hosting cluster[END_REF][START_REF] Nathuji | Q-clouds: Managing performance interference effects for qos-aware clouds[END_REF][START_REF] Padala | Automated control of multiple virtualized resources[END_REF], predictive [START_REF] Krioukov | Napsac: Design and implementation of a powerproportional web cluster[END_REF][START_REF] Horvath | Multi-mode energy management for multi-tier server clusters[END_REF] and mixed [START_REF] Urgaonkar | Dynamic provisioning of multitier internet applications[END_REF][START_REF] Gmach | Adaptive quality of service management for enterprise services[END_REF][START_REF] Gandhi | Minimizing data center sla violations and power consumption via hybrid resource provisioning[END_REF] approaches. While these approaches can handle gradual changes in load, they cannot abrupt changes, especially load spikes that occur almost instantaneously [START_REF] Gandhi | SOFTScale: Stealing Opportunistically for Transient Scaling[END_REF]. This claim was also verified by other authors [START_REF] Chandra | Effectiveness of dynamic resource allocation for handling internet flash crowds[END_REF].

In order to handle traffic surges, the authors advocate either having spare servers that are always available (over-provisioning), or finding a way to lower setup times. This is the case in [START_REF] Gandhi | SOFTScale: Stealing Opportunistically for Transient Scaling[END_REF], which considers that the architecture of the datacenter includes a tier "caching" consisting of machines that are always available. They then temporarily use the resources of these machines to respond to requests as long as new servers are deployed in the tier application. The elastic part is limited to the tier application which is the tier largest consumer of CPU resources. If the load is high, [START_REF] Gandhi | SOFTScale: Stealing Opportunistically for Transient Scaling[END_REF] needs of being coupled with techniques like those in [START_REF] Urgaonkar | Cataclysm: Scalable overload policing for internet applications[END_REF][START_REF] Adya | Load management in a large-scale decentralized file system[END_REF][START_REF] Voigt | Kernel mechanisms for service differentiation in overloaded web servers[END_REF][START_REF] Cherkasova | Session-based admission control: A mechanism for peak load management of commercial web sites[END_REF] to minimize the damage caused by load spikes. However, by using PeakForecast, we do not have to pay for any additional resources, which is not the case when over-provisioning via spare servers. Furthermore, Inria we used mixed approaches (reactive and predictive), which allows us to detect traffic surge in less than 60 seconds, be to predict the up-coming traffic using a forecasting model with an acceptable precision, as Lassettre et al. [START_REF] Lassettre | Dynamic surge protection: An approach to handling unexpected workload surges with resource actions that have lead times[END_REF], allowing to estimate the number of resources needed to absorb traffic surge, by adding or removing it quickly, automatically, resources within a virtual web infrastructure in order to respond with the best reactivity as possible to user demands and maintaining the quality of service online site continuously.

There is also works, such as [START_REF] Lim | Automated control for elastic storage[END_REF][START_REF] Trushkowsky | The scads director: scaling a distributed storage system under stringent performance requirements[END_REF], which address elastic control for multitier application services that allocate and release resources in discrete units, such as virtual server instances of pre-determined sizes. It focuses on elastic control of the storage tier, in which adding or removing a storage node or "brick " requires rebalancing stored data across the nodes, and are not the focus of our paper.

Conclusion

In this paper, we have presented an elastic IaaS management solution capable named PeakForecast. From a trace of requests received in the last seconds, minutes or hours, PeakForecast detects if the underlying system is facing a traffic surge or not, and then predicts the upcoming traffic using a forecast model with an acceptable precision, thereby estimating the number of resources required to absorb the remaining traffic to come. We have evaluated our solution using MediaWiki and web application traffic traces that were collected on the Japanese version of Wikipedia some days before and after the tsunami on 11 March 2011, in an interval where the Slashdot effect PeakForecast. The experimental results confirm that our solution can provide instantaneous elasticity of resources during traffic surges.

Figure 1 :

 1 Figure 1: Graph from some Web server statistics showing a moderate Slashdot effect in action in 2005.

Figure 2 :

 2 Figure 2: Graph of requests by minute interval of 10-03-2011

Figure 3 :

 3 Figure 3: Graph of requests by intervals of 30 seconds on 10-03-2011

Figure 4 :

 4 Figure 4: Graph of the multiplier coefficient between two intervals of 30 seconds on 10 March 2011

Figure 5 :

 5 Figure 5: Graph of requests by intervals 30 seconds on 10-03-2011 between 12:46:30 and 12:53:30

Figure 6 :

 6 Figure 6: Graph of requests per minute on 10-03-2011

Inria

2. 3

 3 Estimating the number of resources required to absorb the traffic surge

Figure 7 :

 7 Figure 7: Virtual Web Infrastructure

Figure 8 :

 8 Figure 8: PeakForecast architecture

  (a), we also have a single VM (apache1) containing MediaWiki and thus serving all HTTP requests sent by NGINX load balancer. After a few minutes, PeakForecast detects that we are facing a traffic surge, predicates the future traffic, estimates the number of VMs required to absorb the traffic surge (2 VMs: apache 2 & 3) and starts the process of provisioning these VMs. In Figure 10(b), PeakForecast installs MediaWiki on VMs apache 2 & 3 (in approximately 10 seconds), then add the VMs in the configuration file of the NGINX load balancer to make them visible to NGINX. Figure 10(c) reports treatments, such as requests sent by VMs apache 2 & 3, which explains the evolution of CPU and RAM in VM apache 1. In Figure 10(d), PeakForecast removes the VMs apache 2 & 3 after the traffic surge has been absorbed.

Figure 9 :

 9 Figure 9: Benchmark 1 without PeakForecast.

Figure 10 :

 10 Figure 10: Benchmark 2 with PeakForecast

http://en.wikipedia.org/wiki/Slashdot_effect

http://slashdot.org RR n°8299

RR n°8299

http://wiki.nginx.org

http://fabfile.org RR n°8299

http://frascati.ow2.org Inria

http://Akka.io RR n°8299

http://manpages.ubuntu.com/manpages/hardy/man1/siege.1.html Inria

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