Historical Simulation Method involves the application of asset returns of a time series of past 250 days to the current portfolio weights (Bolgün & Akçay, 2009) .

W: Current weight of the risk factors in a portfolio

R: Change in returns

Probable portfolio value is estimated using the changes in return for w weights and a time period of t, and VaR is calculated for a confidence level of 95% or 99%. The full valuation method involves the whole set of prices while Historical Value at Risk requires efficiency curves which proves the realism inherent for this method.

Thus, the model risk decreases while it is fully eliminated when not available in the data. Therefore, this method can be used as both linear and nonlinear investment tools (Manganelli & Engle, 2001) .

The criticism about this method focuses on the disadvantage arising from ignoring some risks by failing to consider possible future changes as the method focuses on the changes in the sample being based on historical data (Pallotta & Zenti, 2000) .

Monte Carlo Simulation requires the generation of various random numbers in order to reach the correct VaR. Random number generation should be increased by 100-fold in order to increase the accuracy of VaR by a digit (Glasserman, 2004) . Nevertheless, Monte Carlo Simulation is commonly used in stress testing (Guo, 2008) .

Parameters Used in the Value at Risk Measurement.

VaR calculations depend on a number of parameters. These are holding period, confidence level, sampling period and calculation of capital requirement.

Considering Value at Risk is based on the measurement of the price changes of a portfolio or an individual asset

in a “certain time period”, the holding period is a parameter concerning the time period in which assets will be held in the portfolio. In other words, the holding period is the time horizon in which the change in the portfolio value is to be calculated (Assaf, 2015) .

The holding period is calculated by taking the square root of the period as part of the VaR calculations (Iglesias, 2015) .

1 day holding period = = 1

10 days holding period = = 3.162278

21 days holding period = = 4.582576

252 days holding period = = 15.87451

The VaR calculated for a holding period is multiplied with the square root of that holding period which VaR is to be calculated for. Therefore, the result obtained for a holding period of 10 days is higher than the result obtained for a holding period of 1 day. The VaR increases as the holding period increases.

Confidence interval should be estimated beforehand in VaR calculations. The confidence level is determined based on the company’s risk appetite and its economic capital stock (Yildirim, 2012) . Standard VaR calculations aim to measure potential future losses in a specified confidence level (commonly 95% or 99%) (Bolgün & Akçay, 2009) .

Confidence level when defined as 99% for VaR estimation means that the probability of the maximum loss for a day exceeding the VaR level is only at 1%. The VaR value calculated increases with the increasing confidence level.

Another parameter of the Value at Risk (VaR) measurements is the determination of past observation periods for which the volatility and correlations will be calculated and price changes will be observed.

The success of VaR calculations depends on the dataset to be used in volatility and correlation calculations. Volatility values calculated for different sampling periods will give different results therefore resulting in different VaR values. The Basel Committee defined a minimum of a year (252 working days) as the sampling period and obliged companies to update their dataset in specific intervals and to calculate VaR according to the new dataset (Basel Committee on Banking Supervision, 2009, 13) . The sampling period shall be no less than a year (250 working days).

Capital requirement calculation is not a primary parameter of VaR calculations. However, capital requirement will be calculated for the market risk following the VaR calculation. In other words, risk exposure should be stated in capital in order to make it possible to compare capital costs of all risks in a common plane. Therefore, Bank for International Settlements (BIS) set the capital coefficient to be 3 at a minimum. This value alternates between 3 and 4. The BIS is subject to serious criticism on this subject. Some claim that this capital coefficient lacks the necessary basis. Actors of the market find this coefficient higher than it should be (Bolgün & Akçay, 2009) .

It is a common practice for banking organizations to associate VaR results with their capital adequacy by multiplying the VaR results with the capital coefficient, 3 as part of the capital requirement calculations. Yet, there are no standards defined for the insurance companies.

Insurance companies included in this study and their exchange rate positions are shown in Table 1 and Table 2.

This study analyzes 7 insurance companies operating in Turkey listed in Borsa Istanbul. 6 of these insurance companies focus their activities in fields other than life insurance while 1 of them operates in life insurance. It was not required to calculate the risks life insurance companies and others are exposed to separately as financial risks were in question. Exchange rate positions of the insurance companies included in the analysis are given in Table 2.

6 of the insurance companies have a positive foreign exchange position. In other words, they do not have a

foreign exchange deficit. Only Aviva insurance had a negative foreign exchange position. USD and Euro were included in the study in terms of foreign exchange positions of the companies. Other currencies which account for small amounts were not included in the foreign exchange positions of insurance companies. In addition, amounts which were listed under the “other” option were not included in the portfolio.

Net positions of the insurance companies in USD and Euro as stated in their balance sheets were calculated in Turkish Lira dividing the amounts by the average exchange rates issued by the Central Bank of Turkey for the date of 31.12.2014 (USD = 2.1343; Euro = 2.9365).

The analysis was based on the daily exchange rates for 252 working days between 01.01.2014 and 31.12.2014. It is required to take data for at least 252 days into account when calculating the VaR. Figure 2 shows the value of the Euro and USD against Turkish Lira.

The analysis involved the value of the Euro and USD for 252 days. According to the increases and decreases in the value of the USD (Figure 2) it was found that the maximum increase in the value accounted for 5% while the maximum decrease in the value accounted for 4%. The Euro, on the other hand, suffered a value loss by 6% against the Turkish Lira in 2014 while increasing by over 4% for the same period.

Results of the Historical Simulation Method give the maximum expected loss for a time interval of 252 days under normal market conditions with a confidence level of 99%. The results obtained from the Historical Simulation Method against Foreign Exchange risk are shown in Table 4.

When the Historical Simulation results of the insurance companies were analyzed it was found that their daily losses ranged between 0.59 and 1.75. Halk Insurance suffered the greatest loss with 1.75%. The losses insurance companies suffer increased with the increasing holding periods. Losses calculated for a holding period of 10 days range between 1.86% and 5.54%.

Monte Carlo Simulation Method reveals the most unfavorable conditions insurance companies may face under normal market conditions with a confidence level of 99%. Results of the Monte Carlo Simulation against the Foreign Exchange risk are shown in Table 5.

When the results given in Table 5 are analyzed it was found that daily losses ranged between 0.35% and 0.93%. Güneş Insurance suffered the greatest daily loss with 0.93%, while Ak Insurance suffered the lowest daily loss with 0.35%. According to the VaR results obtained from a holding period of 1 day using the Monte Carlo Simulation, Ak Insurance suffered the second greatest loss with 0.90%.

When the Value at Risk positions were calculated using the Monte Carlo Simulation is proportioned to their current values; daily losses with respect to a holding period of 10 days was found to be in a range between 1.10% and 2.95%. Güneş Insurance suffered the greatest loss with 2.95% according to the Monte Carlo Simulation results obtained from a holding period of 10 days. The lowest loss, on the other hand, was 1.10% in the case of Ak Insurance. Halk Insurance suffered the second greatest loss with 2.85% according to the results obtained from a holding period of 10 days.

VaR results obtained using the Historical Simulation Method for holding periods of 1 day with a confidence level of 99% were higher than those calculated using the Monte Carlo Simulation. Similarly, the results obtained for a holding period of 10 days is higher than the results obtained for a holding period of 1 day.

Capital adequacy correlation is a necessary process in order to determine the impact of the VaR results on the capital adequacy of insurance companies. Especially the regulatory and auditing authorities will be interested to see the erosion in the capital adequacies of insurance companies caused by the VaR results.

We have mentioned that the Bank for International Settlements (BIS) identified a capital coefficient at a minimum of 3 for the calculations of capital adequacy according to the Value at Risk (VaR) results. However, several authorities claim that this capital coefficient lacks the necessary basis. In fact, when the capital coefficient is taken 3 in the correlations between the VaR results and capital adequacies it would take the capital adequacy ratios to a lower level. Banking Regulatory and Supervisory Agency also recommends the capital coefficient to be taken 3. Yet, there are no standards defined for the insurance companies in Turkey in this respect. This study used the capital coefficient of 3 in the correlations between the VaR values of insurance companies and their capital adequacy ratios.

Table 6 shows the current capital adequacy ratios of insurance companies as of 2014.

Insurance companies operating in Turkey calculate their capital adequacy ratios by dividing their capitals by their minimum required capital. According to the capital adequacy ratios obtained, capital adequacy ratio of Aviva Insurance is found to be below 100. Anadolu Life Insurance was found to be the insurance company with the greatest capital adequacy ratio.

The required capital is most commonly calculated using two methods in Turkey. According to the first method, the capital is calculated separately for fields such as insurance other than life insurance, life insurance and pension. This method involves the use of the highest of the two amounts found based on the premium and dam-

^*Capital/Minimum Required Capital. Source: 31.12.2014 Balance Sheet Annotations.

^*1-day VaR results are multiplied by 3 capital factor.

ages for insurance other than life insurance and the use of the total amount for results related to obligation and risk for life insurance. According to the second method, required capital equals to the sum of active risk, reassurance risk, risk of overly increased premiums, risk of provision for outstanding claims, notation risk and foreign exchange risk.

Insurance companies operating in Turkey most commonly prefer the first method when calculating the minimum required capital. The minimum required capitals included in this study are directly taken from the balance sheet annotations of the insurance companies in question.

The impacts of the Historical and Monte Carlo Simulation Methods on the capital adequacy ratios were found at different levels (Table 7). Values obtained from the Historical Simulation Method have taken the capital adequacy ratio to a point lower than the ones obtained from the Monte Carlo Simulation Method. However, this decrease was not significant. The VaR results obtained appears to have no adverse impact on the capital adequacy ratios.