Measuring liquidity risk in Social Security using VaR technique

Article history: Received October 15, 2012 Received in revised format 4 December 2012 Accepted 8 December 2012 Available online December 9 2012 Measuring liquidity risk plays an important role on any business unit especially financial organizations. Social security systems in most countries around the world are responsible to provide necessary requirements in many countries such as health care, pension plans, etc. Therefore, it is necessary to reduce any risk associated with these systems as much as possible. In this paper, we study liquidity risk in Iranian social security using VaR technique. The proposed model of this paper uses historical information for a fiscal year of 2008-2011. We first divide the information of each year into two groups of first and second half and using VaR technique analyzed whether there was any trend change in these two groups. The results of our survey indicate that the mean of VaR in the second half of the year is greater than the first half of the year. Therefore, we can confirm that VaR maintains an increasing trend over the time horizon. We also study the trend in liquidity using regression analysis for each year, separately and the results of our survey confirm that there was an increasing trend in liquidity over time. © 2013 Growing Science Ltd. All rights reserved.


Introduction
Measuring liquidity risk plays an important role on any business unit especially financial organizations.Social security systems in most countries around the world are responsible to provide necessary requirements in many countries such as health care, pension plans, etc.During the past few years, there have been tremendous efforts on measuring risk using value at risk (VaR) techniques.Ourir and Snoussi (2012) investigated the impact of negligence of dependency in liquidity extreme risk assessment of Tunisian stock market.They used returns dependency to evaluate market risk based on Time series-Extreme Value Theory combination.They compared VaRs estimated under independency relatively to the VaR when dependence was considered.The efficiency of those methods was examined and compared using the backtesting tests.They reported the adequacy of the recent extensions of liquidity risk in the VaR estimation and proved a performance improvement of VaR estimates under the assumption of dependency across a significant reduction of the estimation error, particularly with AR (1)-GARCH (1,1)-GPD model.Brana et al. (2012) studied the impact of global excess liquidity on commodities and asset prices for a set of emerging market countries by investigating a panel VAR framework.They defined first global liquidity and reported that excess liquidity at global level had spillover impacts on output and price levels in emerging countries.According to their investigation, the effect on real estate, commodity and share prices in emerging countries was less clear.Bracke and Fidora (2012) reported that (US) monetary policy shocks could explain the largest part of the variation in imbalances and financial market prices.They also reported that savings shocks and investment shocks could explain less of the variation.Niu et al. (2012) developed an improved portfolio optimization framework by developing the endogenous and exogenous liquidity risk and the corresponding indexes were designed to compute the endogenous/exogenous liquidity risk, respectively.Härdle et al. (2012) modeled the dynamics of ask and bid curves in a limit order book market based on a dynamic semiparametric factor model.The shape of the curves was captured by a factor structure, which is estimated nonparametrically.Chadha et al. (2010) decomposed broad money into primitive demand and supply shocks and reported that supply shocks had played an important role in the time series in each of the USA, UK and Eurozone in the short to medium term.

The proposed study
The proposed model of this paper uses value at risk (VaR) to measure the risk of liquidity.There are literally two methods for measuring VaR, which are simulation based method and parametric method and the proposed model of this paper uses simulation based method.In this method, we use historical data to predict future value.VaR describes the maximum loss on portfolio associated with assets for a specified period of daily, weekly or monthly.More specifically, according to VaR, we are X percent sure that the loss will not exceed more than a specified value, V.In other words, V is the actual value of, which is subject to risk including two parameters of time horizon (N) and level of confidence (X).Fig. 1 shows details of VaR.When daily information changes are normally distributed with mean of zero, Eq (1) is precisely correct, otherwise, this formula is approximately correct.This ratio provides a number, which incorporates all associated risk components and a manager can make appropriate decision based on this value.This value also helps to design appropriate budget and different monitoring agencies such as Federal Reserve or insurance firms could determine risk associated with a budget.For instance, if we are about to measure risk for 292 business days, we can consider the following information,

The results
Based on the results of Table 1, the means of liquidity were in different range from 220.26 to 338.02.Skewness of the time series seemed to be more than normal and details of time series can be verified in Fig. 1 to Fig. 4.     The proposed study of this paper considers whether there is any change in VaR as the time goes on.In other words, the main hypothesis of this paper is to know whether VaR increases over the time.In order to test this hypothesis, we have divided the information into two groups of the first and second groups in each four year.Table 3 shows details of our findings for two groups.As we can observe from the results of Table 3, the mean of VaR in the second half of the year is greater than the first half of the year.Therefore, we can confirm that VaR maintains an increasing trend over the time horizon.In order to compare VaR in different years, we have chosen ANOVA test and the results are presented in Table 4 as follows, According to the results of Table 4, there is a meaningful difference among the mean of all four groups.In other words, VaR was different in various years.In order to understand which years maintained big changes we have used Post Hoc Tests, Tukey HSD and LSD tests.The results have indicated that there was not any significant difference between mean of VaR in 2008 and 2009 but there was a meaningful difference in other years.There are also four sub-hypotheses associated with the proposed study of this paper, which are as follows,

The first sub-hypothesis: Increasing trend in VaR in 2011
The first sub-hypothesis of this paper is associated with an increasing trend in VaR during the year of 2011.We use the following regression analysis to test the results.
where LVAR is the logarithm of VaR, t is the time, 0 β and 1 β are coefficients, which are estimated using least square technique and ε is the residual.
Table 5 shows details of implementing regression analysis for the data in this year.β means as time increases VaR increases in this year.In addition, the high value of F statistics explains that the relationship is linear, indeed.

The second sub-hypothesis: Increasing trend in VaR in 2010
The first sub-hypothesis of this paper is associated with an increasing trend in VaR during the year of 2010.Again, we use Eq. ( 2) to fit the regression for year 2010.Table 6 shows details of implementing regression analysis for the data in this year.β means as time increases VaR increases in this year.In addition, the high value of F statistics explains that the relationship is linear, indeed.

The third sub-hypothesis: Increasing trend in VaR in 2009
The first sub-hypothesis of this paper is associated with an increasing trend in VaR during the year of 2009.Again, we use Eq. ( 2) to fit the regression for year 2009.Table 7 shows details of implementing regression analysis for the data in this year.

Conclusion
In this paper, we have performed an empirical investigation to study liquidity risk in Iranian social security using VaR technique.The proposed model of this paper has gathered historical information for a fiscal year of 2008-2011.The study first divided the information of first and second half of each year into two groups and, using VaR, technique analyzed whether there was any trend change in these two groups.The results of our survey have indicated that the mean of VaR in the second half of the year was greater than the first half of the year.Therefore, we could confirm that VaR maintains an increasing trend over the time horizon.We also studied the trend in liquidity using regression analysis for each year, separately and the results of our survey confirmed that there was an increasing trend in liquidity over time.

Fig. 4 .
Fig. 4. Liquidity change for 1235 days As explained earlier, we use 291 days of information using simulation technique to estimate VaR for the social security organization of Iran.Since there are 290 different observations, we have 290 Fig. 6 to Fig. 9 demonstrate details of price change in these years.

Fig. 7 .Fig. 9 .
Fig. 7. VaR change for 281 days in 2009 Fig. 6.VaR change for 274 days in 2008 Let v i be liquidity in day i and m be the number of days where statistics are observed.Therefore, the liquidity can be predicted by .In our survey, we have collected daily information of liquidity over the period 2008-2011.Table1demonstrates details of our statistical observation in terms of min, median, standard deviation, skewness and Kurtosis.
As we can observe from the results of Table2, mean of VaR has been changed significantly in different years.

Table 3
The results of comparing VaR in the first and the second group of each year

Table 4
The results of ANOVA test

Table 5
The results of VaR trend in Year 2011

Table 6
The results of VaR trend in Year 2010

Table 7
The results of VaR trend inYear 2009As we can observe from the results of Table 7, all t-student values are statistically meaningful.The positive coefficient of 1 β means as time increases VaR increases in this year.In addition, the high value of F statistics explains that the relationship is linear, indeed.The fourth sub-hypothesis of this paper is associated with an increasing trend in VaR during the year of 2008.Again, we use Eq.(2) to fit the regression for year 2008.Table8shows details of implementing regression analysis for the data in this year.As we can observe from the results of Table8, all t-student values are statistically meaningful.The positive coefficient of 1 β means as time increases VaR increases in this year.In addition, the high value of F statistics explains that the relationship is linear, indeed.

Table 8
The results of VaR trend in Year 2008