78 ANÁLISIS FINANCIERO Fangyuan Yan y José Miguel Rodríguez-Pardo Asset Liability Management –ALM in Life Insurance Risk Management Gestión de Activo y Pasivo –ALM en Gestión de Riesgo del Seguro de Vida ABSTRACT In the insurance sector, the risk management of asset and liability (ALM) is more and more important by the effect of economic crisis. For an insurance company, how can it reduce the risk of insolvency when it invests its capital to the financial market; a traditional method of Cash-Flow Matching, Duration Matching, or we need some models more dynamic and predictable? After discussing these traditional models of ALM, this paper will show us a view of a new dynamic measure of ALM - the Value at Risk (VaR). A research of the index of IBEX-35 with a period from November of 2012 to February of 2013, which is included the Bootstrap Simulation, can reveal us the ascendancy of the VaR in the risk of loss management. Key Words: Asset Liability Management, Cash-Flow Matching, Duration Matching, Value at Risk (VaR), Bootstrap JEL Classification: G11, G22 RESUMEN En el sector del seguro, la gestión del riesgo de los activos y pasivos (ALM) es cada vez más importante por el efecto de la crisis económica. ¿Cómo puede una compañía de seguros reducir el riesgo de insolvencia cuando invierte su capital en el mercado financiero?, ¿utiliza un método tradicional de correspondencia de flujos, coincidencia de duraciones, o se necesitan algunos modelos con mayor capacidad de predicción?. En este artículo, presentamos un modelo mas dinámico de ALM: el Valor en Riesgo (VaR). Se ha realizado una investigación sobre el índice IBEX-35 desde noviembre de 2012 a febrero de 2013, que nos revela la importancia del VaR en la gestión del riesgo de pérdida en las inversiones financieras. Palabras Clave: Gestión de Activo y Pasivo, Casamiento de flujos, casamiento de duración, Valor en Riesgo (VAR), Bootstrap Códigos JEL: G11, G22 Recibido: 20 de abril de 2015 Aceptado: 9 de mayo de 2015 Universidad Carlos III. email: linda [email protected] y [email protected] Fangyuan Yan y José Miguel Rodríguez-Pardo: Asset Liability Management –ALM in Life Insurance Risk Management Gestión de Activo y Pasivo –ALM en Gestión de Riesgo del Seguro de Vida Análisis Financiero n° 128. 2015. Págs.: 78-91 ASSET LIABILITY MANAGEMENT –ALM IN LIFE INSURANCE RISK MANAGEMENT INTRODUCTION Asset and Liability Management (ALM) is a concept using in the banks, funds and insurance companies, to whom we can understand from twofold meanings. One is the financial strategy to maintain the balance among the liquidity, security and profitability; the other is a method for avoiding the effect of interest fluctuation by adjusting the duration of assets and liabilities or by Cash-Flow matching. The Society of Actuaries definite ALM as following: ALM is the ongoing process of formulating, implementing, monitoring and revising strategies related to assets and liabilities to achieve an organization’s financial objectives, given the organization’s risk tolerance and other constraints. For any investment that uses to balance liabilities, ALM is an important and applicable financial management tools. The asset and liability management bases on “two symmetrical principles”: duration symmetry and interest symmetry between the asset and the liability, which we can extend to four branches. 1. The Scale Symmetry Principle, which refers to the symmetry between the scale of asset and liability, while the scale is a dynamic scale with the oscillation of financial market. vestment with different levels of financial product should be designed to disperse the risk of loss. There are many methods for ALM, the Efficient Frontier, Duration Matching, Cash Flow Matching, Multicriteria Decision Models, Stochastic Control and Dynamic Financial Analysis. Most common ones are the Efficient Frontier Simulation, Duration Matching and Cash Flow Matching. In this paper, we mainly talk about Cash-Flow Matching, Duration Matching and VaR Model. MACAULAY DURATION AND MODIFIED DURATION The concept of Macaulay duration is a financial asset comprises of one or more cash flows with various maturities, as bonds, stocks, foreign exchanges… In the insurance investment, to compare their present value, we should discount all the flows to a same point of time. In general, the duration measures the sensitivity of the asset prices to the interest rate risk, is to say that, when the asset is considered as a function of interest yield, and the change in price can be explained as the sensitivity of yield. The most important factor of Macaulay duration is the period of each payment of the cash flows, which are weighted by the present value of the coupon of bonds: 2. The Structure Symmetry Principle, known as the symmetry of repayment period with comparing the average the maturity date of asset and liability, to obtain the average turnover ratio. If more than one, we have overspent the asset, otherwise we have underutilized it. B is the present value of future coupon 3. The Complementary Principle, in the real market, a perfect balance does not always exist among the liquidity; security and profitability, so we can reduce liquidity and security in order to archive more profits. 4. The decentralization of Asset Principle, don’t put all your eggs in one basket! A portfolio of in- 79 D is the duration Macualay T is the period of time Xt is the payment of coupon of each period r is the interest of bond F is the nominal value of bond Fangyuan Yan y José Miguel Rodríguez-Pardo: Asset Liability Management –ALM in Life Insurance Risk Management Gestión de Activo y Pasivo –ALM en Gestión de Riesgo del Seguro de Vida Análisis Financiero n° 128. 2015. Págs.: 78-91 80 ANÁLISIS FINANCIERO The Modified Duration is another sensitivity of interest rate, which is the first derivative of the function of the present value of all asset flows with interest rates. DM is the modified duration To explain this concept with a simple example, we can find that for 1.00% change of interest, the change of the price of: Bond A is 16.82 euro, Bond B is 18.50 euro, and Bond C is 16.58 euro. The Bond B is more sensitive about the change of interest, so the more coupons have the bond, the larger change has its price accompanying with the interest rate volatility. The Bond C, who has the highest interest, the change of interest rate affects its price less than others. It means that a higher interest can protect the value from the volatility of interest. Calculate all the flows of these three bonds, while Bond A and Bond C are similar because they have the same annual coupon, but their duration Macaulay; the Bond C recovers 0.02 years (7 days) before the Bond A. Although the Bond B has an annual coupon 5 euro more than the bond A, considering to its duration Macaulay, it will be recovered 0.18 years (65 days) later than the Bond A. With the hypothesis of same maturity, the duration indicates the risk between the variation of interest rate and the insolvency of capital, so it´s significant to manage the assets and liability at the same duration. In insurance law, requests a continuous of the same duration between assets and liabilities, which also is meaningful for the financial immunization. Convexity analysis is the standard financial tool, when the interest rate curve shocks heavily, the Macaulay Duration is not a good model for measuring the sensitivity of the financial instruments, so we need the second derivative of the bond price to instead the duration. Fangyuan Yan y José Miguel Rodríguez-Pardo: Asset Liability Management –ALM in Life Insurance Risk Management Gestión de Activo y Pasivo –ALM en Gestión de Riesgo del Seguro de Vida Análisis Financiero n° 128. 2015. Págs.: 78-91 ASSET LIABILITY MANAGEMENT –ALM IN LIFE INSURANCE RISK MANAGEMENT Xt is the coupon I is the interest rate F is the nominal value of bond From the formula above, the convexity has three properties: 81 2. When amplify the period of investment, the convexity reduces. 3. If we have the modified duration and the interest rate, the more coupon we have, the larger convexity we obtain. 1. When increases the interest rate, the convexity decreases. A bond of nominal value 1.000 euro, annual coupon 5.00%, maturity 10 years and interest rate annual 6.50%. To discount its nominal value to the present value, the price is 892.17 euro, then discounting all the future cash flows; we compare the Macaulay Duration, Modified Duration and Convexity. Fangyuan Yan y José Miguel Rodríguez-Pardo: Asset Liability Management –ALM in Life Insurance Risk Management Gestión de Activo y Pasivo –ALM en Gestión de Riesgo del Seguro de Vida Análisis Financiero n° 128. 2015. Págs.: 78-91 82 ANÁLISIS FINANCIERO From the table, when the interest rate rises 1.00%, the price of bond reduces 66.84 euro, to say that a loss of 7.49% of the initial price. ities can be estimate by the mortality rate. So these portfolios always invest in low-risk investment grade to make sure the security of the capital. En the graph, a green tangent line is added on adjusting the convexity curve: To comply with the regulations referred to in Article 33.2 Regulation and Supervision of Private Insurance: It should prove that payment flows of the asset allocated to comply with the derivate obligations for one policy or a homogeneous group policy. The payments and collections flows have to coincide sufficiently of time and amount, the balance after operation should be maintained positive or 0. where % r is the change of interest rate With the tangent line, the calculation will be easier than the curve. The adjustment modifies the convexity about 3.18 euro, 0.36% of the initial price. Now the change of price is 63.66 euro, and the new price is 828.51 euro that decreased 7.14% than before. Convexity is the marginal sensitivity, which is the weighted average of the durations of the bond. It´s used to adjust the estimation of duration when the interest rate has greater variation. The greater dispersion has the financial period, the larger the convexity is. Generally, the relationship between the maturity and the duration is positive where can well present the figure of convexity. If the duration is not acceptable for the variation of interest rate, the convexity is a better measurement for correcting and improving the valuation. CASH-FLOW MATCHING AND MATHEMATICAL PROVISION It is defined Cash flow Matching as a process of hedging in which a company or other entity matches its cash outflows (i.e. financial obligations) with its cash inflows. It also called dedicating a portfolio, which is an alternative to multi-period immunization for managing the maturity of liability and asset streams. The practice of matching returns on a portfolio to future capital that involves investing in certain securities with a certain expected return for the future paying of liabilities. In the life insurance, pension funds and annuities perform the most cash flow matching, because that the future liabil- In the life insurance, for the cash flow matching, we need considering about an important factor, the mortality. The mortality table shows us the probability of death for people of different age which is the risk of the probable payment for the future claim. To manage this risk, the insurance company always calculates an amount of capital as the mathematical provision of payment. The phase of this calculation is: Phase 1: IRR for each periodic payment CFji: the collection flow for each period NPVj: the present value of the collections N: the maturity of asset investment IRRj: the internal interest of the asset Phase 2: Reduced IRR Coefj: the reduced coefficient of asset for several reasons Fangyuan Yan y José Miguel Rodríguez-Pardo: Asset Liability Management –ALM in Life Insurance Risk Management Gestión de Activo y Pasivo –ALM en Gestión de Riesgo del Seguro de Vida Análisis Financiero n° 128. 2015. Págs.: 78-91 ASSET LIABILITY MANAGEMENT –ALM IN LIFE INSURANCE RISK MANAGEMENT Phase 3: Actual Value of Asset of the Reduced IRR* 83 Rate: the factor of the mathematical provision calculation As determined the assets and liabilities have to maintain the same flows of collection and payment. It´s said that the present value of assets and the present value of liabilities should be equal. We use the internal interest rate to discount the present values of all cash flows. Phase 4: The implicit calculation of provision Phase 5 Mathematical Provision PM: Mathematical Provision m: the number of asset titles n: the maturity of asset s: the maturity of insurance operation PFi: the flows of payment in the time zone i In this phase, the factor of mathematical provision is exactly the internal interest rate IRR, the present value of collection is the PM, because that the PM is calculated by the net value of the cash flows. Finally, the difference between the asset and the PM is a part of liability. COLLECTION & PAYMENT WITH TAIL 2.500.00 2.000.00 1.500.00 collection 1.000.00 payment 500.00 1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151 161 171 181 191 201 211 221 231 241 251 261 271 281 291 301 311 321 331 341 351 - Fangyuan Yan y José Miguel Rodríguez-Pardo: Asset Liability Management –ALM in Life Insurance Risk Management Gestión de Activo y Pasivo –ALM en Gestión de Riesgo del Seguro de Vida Análisis Financiero n° 128. 2015. Págs.: 78-91 84 ANÁLISIS FINANCIERO In the life insurance, especially for a pension plan, the longest period for an investment is less than 30 years, but in the real situation, a person can live more years after the last payment of the financial investment. For calculating the possible flows of payment, we need the dead probability from the Mortality Table, while the hypothesis of a probable living life till 120 years old. Then the number of future contract NF DYNAMIC FINANCIAL ANALYSIS – VALUE AT RISK (VAR) From the graphic, we can see that the duration of payment flow is much longer than the duration of collection flow. So in this situation, we suppose that the last payment ending at the same time as the last collection, than all the payment flows after this date are discounted by an interest DGS(1.50%) to an amount of value. Now we obtain the collection and payment flow with the same duration, recalculating these flows and finding a proper spread rate to match the collection flows and payment flows for each period. DURATION MATCHING The Duration Matching whose function is based on the internal rates of return, coupon and maturity, can immunize the risk of investment between the asset and liability by denominating different future interest rates. The value of a future contract is also dependent of the present value of asset and liability which are calculated by their determinate interest rates. With this method we can lengthen or shorten the duration of the investment portfolios by buying or selling future contracts, while the gained or lost positions are compensated with an opposite result of the real derivatives market. DA PA = DL PL + DF FP NF DA = asset duration The dynamic Financial Analysis (DFA) originated from the field of operation research and mainly uses simulation techniques for problem analysis. For this approach, the insurance company is modeled a large number of possible scenarios for the simulation. The Value at Risk (VaR) method is one type of simulation for the future provision of earning and loss in the investment event. A part of premium of life insurance is always invested to different financial products. In the previous paragraph, we have already talked about the product with low risk as bond, now; we will discuss another product that has a higher risk, the security, where the management of risk is really important. In the financial crisis, we know that the stock market is a soft market, meanwhile a fluctuant market. So all the 35 listed stocks of IBEX 35 are chosen for this experiment, and the period of the investigation is divided to two periods, the first one is from 26/11/2012 to 23/01/2013 ( experimental period), the other one is from 24/01/2013 to 25/02/2013 ( observed period). The observed period is for certifying the conclusion of our investigation origin by the experimental period. the To explain the function of VaR model, we calculated the increased return rate of the trade date for these 35 stocks in these two periods. PA = present value of asset DL = liability duration PL = present value of liability DF = duration of future contract FP = the price of future NF = the number of future contract • Risk- Expected (Mean – variance) for Data Grouping A mostly traditional method to evaluate the stock risk and return is the famous “Mean – Variance” that is based by the efficient frontier theory. Fangyuan Yan y José Miguel Rodríguez-Pardo: Asset Liability Management –ALM in Life Insurance Risk Management Gestión de Activo y Pasivo –ALM en Gestión de Riesgo del Seguro de Vida Análisis Financiero n° 128. 2015. Págs.: 78-91 ASSET LIABILITY MANAGEMENT –ALM IN LIFE INSURANCE RISK MANAGEMENT The efficient frontier is a concept introduced by Markowitz, “efficient” is referred to a best expected return for its level of risk. With ever possible combination of risky asset, can be plotted in risk-expected return space, and the collection of all such possible portfolios defines a region in this space. The unward-sloped part of the left boundary of this region is called “efficient fron- 85 tier”. The pursue of this theory is “earning highest expected return with determined level of risk.” By using the efficient frontier theory, we can obtain the expected increased returns, variance of our research data, and compare the result with the market level. EX MARKET 1 2 3 4 5 6 7 8 9 10 avorage 0,34% 0,28% 0,44% 0,67% 0,18% 0,28% 0,15% 0,39% 0,75% 0,19% 0,28% variance 0,0004 0,0010 0,0002 0,0004 0,0003 0,0003 0,0001 0,0003 0,0014 0,0003 0,0001 11 12 13 14 15 16 17 18 19 20 average 0,91% 0,46% 0,60% 0,27% 0,29% 0,43% 0,20% 0,52% 0,13% 0,43% variance 0,0008 0,0002 0,0004 0,0007 0,0003 0,0002 0,0002 0,0007 0,0003 0,0002 21 22 23 24 25 26 27 28 29 30 average 0,05% 0,47% 0,02% 0,12% 0,39% -0,03% 0,15% 0,77% 0,42% 0,35% variance 0,0001 0,0006 0,0002 0,0003 0,0004 0,0005 0,0005 0,0007 0,0002 0,0003 31 32 33 34 35 average 0,08% 0,82% 0,15% 0,15% 0,01% variance 0,0002 0,0006 0,0002 0,0001 0,0004 If the expected increased return is higher than the market level, we mark it to the color green, and if the variance (risk) is higher than the market level, the color is red. To separate these 35 stocks to three Groups: Group A (7 stocks), which has higher expected increased returns but lower variance stocks; Group B (9 stocks), which has the highest expected increased re- EX PERIOD µ turn and highest risk stocks; Group C( 21 stocks), the others stocks. After grouping, the expected increased return ( ) and deviation ( ) for the experimental period (EX PERIOD) and the observed period (OB PERIOD) are as the following table: OB PERIOD µ EX PERIOD σ OB PERIOD σ MARKET 0.34% -0.12% 0.0196 0.0202 GROUP A 0.42% -0.01% 0.0145 0.0171 GROUP B 0.62% -0.27% 0.0258 0.0231 GROUP C 0.15% -0.08% 0.0169 0.0195 From the result, we may notice that the “efficient frontier” is what was explained. The “expected-risk” method can help us find the homogeneous portfolio to invest. Although the Group B complies with this theory, the Group A has an expected increased return much higher than the Group C, and a lower risk. The Group A could Fangyuan Yan y José Miguel Rodríguez-Pardo: Asset Liability Management –ALM in Life Insurance Risk Management Gestión de Activo y Pasivo –ALM en Gestión de Riesgo del Seguro de Vida Análisis Financiero n° 128. 2015. Págs.: 78-91 86 ANÁLISIS FINANCIERO be defined as a group of Blue-Chip Stocks are more stable while having more returns. The stocks of Group C maybe are junk stocks. In the experimental period, the expected increased returns are positive. On the tape means a Bullish trend. But in the observed period, the market is in a Bearish situation because of that the expected return is negative. For the Group A, it has the lowest loss and risk, while the Group B the highest loss and risk. Furthermore it can prove that our homogeneous portfolios are reasonable. For the average of these returns, the empirical mean can be computed. For the standard deviation, a double-sided risk measure should be considered, especially the risk of potential downside of the target, whose loss will catch a ruin of insolvency of asset. • Value at Risk ( VaR ) Value at Risk (VaR) is used in risk measure of the risk of loss on a specific portfolio of financial assets. For a given portfolio, probability and time horizon, VaR is defined as a threshold value such that the probability that the mark-to-market loss on the portfolio over the given time horizon exceeds this value with the given probability level. The common level is 1% or 5% for a hypothetical profit-and-loss probability. For the p-quartile of distribution, we can design a level to suit the own necessary of solvency, for example 68%, 95%, 99.5%... In this research, we defined the p as the expected returns of market value for the bullish market, while the p as 0% for the loss of bearish market. The VaR model has some assumptions: If we trust the “expected-risk” method, why we need the VaR? Compared to the traditional risk measure, VaR focus on considering the loss risk of asset, is said that the size of the loss can be calculated in a default confidence interval before the real loss happening. The provision of loss is of prime importance in the insurance risk management, particularly, for the life insurance that has a long period risk of investment. 1. The effective market assumption 2. The volatility of market is random without autocorrelation In order to illustrate the feasibility of this experiment, the trend of increased returns for these two periods as the following graphics, which can display the random of the volatility of market: For a model of N variables, the function of increased returns of stock (y), the accumulated probability for each y is same to 1. Fangyuan Yan y José Miguel Rodríguez-Pardo: Asset Liability Management –ALM in Life Insurance Risk Management Gestión de Activo y Pasivo –ALM en Gestión de Riesgo del Seguro de Vida Análisis Financiero n° 128. 2015. Págs.: 78-91 ASSET LIABILITY MANAGEMENT –ALM IN LIFE INSURANCE RISK MANAGEMENT 87 EXPERIMENTAL PERIOD 0.06 0.05 0.04 0.03 0.02 0.01 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 -0.01 0.02 -0.03 MARKET GROUP A GROUP B GROPU C OBSERVED PERIOD 0.03 0.02 0.01 0 -0.01 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0.02 -0.03 -0.04 -0.05 MARKET GROUP A • Bootstrap Estimation for Simulating the VaR Model Due to the volatility of the stock market, the experiment period should be short-term that has a problem of insufficiency of data. For constructing a better VaR model, a Bootstrap Estimation is demanded to obtain more random variables. The Bootstrap Estimation is a linear regression model, y = BX + å where y is a vector of dependent variable, X is a matrix of independent variables, B is the regression GROUP B GROPU C coefficient and, å is the error that is expected with a normal distribution , whose variance is (ó2) and covariance is zero, å ≈ N(0, ó2In). The least squares estimate of the coefficient vector is given by b = (X’X)-1X’y and the residual corresponds to e = y-Xb. The advantage of Bootstrap Estimation is to find random variable from the taken portfolios. In this investigation, 5000 actual parameters are simulated for the three groups with the program @RISK to modify their functions. Fangyuan Yan y José Miguel Rodríguez-Pardo: Asset Liability Management –ALM in Life Insurance Risk Management Gestión de Activo y Pasivo –ALM en Gestión de Riesgo del Seguro de Vida Análisis Financiero n° 128. 2015. Págs.: 78-91 88 ANÁLISIS FINANCIERO 0,35 0,30 0,25 0,12 0,10 0,08 0,06 0,02 0,04 0,00 -0,02 -0,04 -0,06 -0,10 -0,08 0 0,20 5 0,15 10 0,10 15 0,05 20 -0,00 25 20 18 16 14 12 10 8 6 4 2 0 -0,05 30 -0,10 35 0,35 0,30 0,25 0,20 0,15 0,10 0,05 -0,00 -0,05 -0,10 EX GROUP B Log Logistic (-,14395,.14777,10.644) 0.1050 0.1650 99,6% 0.39% 0,0% 99,6% 0.39% 0,0% -0,15 20 18 16 14 12 10 8 6 4 2 0 EX GROUP B Log Logistic (-,14396,14777,10.644) 0,0034 0.1650 49,3% 50,7% 0,0% 49,3% 50,7% 0,0% 0.1050 0,0% 0,0% -0,15 EX GROUP A Log Logistic (-,083027,.08579,10-733) 0,0034 52,0% 48,0% 52,0% 48,0% In the experimental period, the expected increased return of market is 0.34%, of Group A is 0.42%, and of Group B is 0.62%. But the result of VaR simulation shows that 50.7% of the increased returns of Group B is higher than the expected return of the market level, eventhough is 2.7% higher than the result of the Group A. The highest increased return of Group B is 16.5%, and 0.3% of its increased returns is more than the highest return of Group A(10.5%). Fangyuan Yan y José Miguel Rodríguez-Pardo: Asset Liability Management –ALM in Life Insurance Risk Management Gestión de Activo y Pasivo –ALM en Gestión de Riesgo del Seguro de Vida Análisis Financiero n° 128. 2015. Págs.: 78-91 ASSET LIABILITY MANAGEMENT –ALM IN LIFE INSURANCE RISK MANAGEMENT 0,35 0,30 0,25 0,12 0,08 0,10 0,06 0,04 0,02 0,00 -0,02 -0,04 -0,06 -0,08 -0,10 0 0,20 5 0,15 10 0,10 15 0,05 20 -0,00 25 20 18 16 14 12 10 8 6 4 2 0 -0,05 30 -0,10 35 0,35 0,30 0,25 0,20 0,15 0,10 0,05 -0,00 -0,05 -0,10 EX GROUP B Log Logistic (-,14395,.14777,10.644) 0.1050 0.1650 99,6% 0.39% 0,0% 99,6% 0.39% 0,0% -0,15 20 18 16 14 12 10 8 6 4 2 0 EX GROUP B Log Logistic (-,14396,14777,10.644) 0,0034 0.1650 49,3% 50,7% 0,0% 49,3% 50,7% 0,0% 0.1050 0,0% 0,0% -0,15 EX GROUP A Log Logistic (-,083027,.08579,10-733) 0,0034 52,0% 48,0% 52,0% 48,0% 89 In the observed period, the expected increased return of market is -0.12%, of Group A is -0.01%, and of Group B is -0.27%. But the result of VaR simulation shows that 53.6% of the increased loss of Group B is larger than 0, eventhough is 5.5% higher than the loss rate of the Group A. The largest increased loss of Group B is 9.75%, and 1.1% of its increased loss is more than the largest loss of Group A(-5.80%). 1. In a bearish market ( =0.0202), the volatility of stock price is higher than the bullish market ( =0.0196). The using of traditional method “media-variance” may not satisfy the fluctuation of market, but the estimate function with VaR simulation can reduce the effect of random uncertainty of the price by demonstrating a proper function for invested portfolio. To discuss the significance of VaR for the insurance risk OB GROUP A management: Weibu (5.0701,.082115, RialShifd (-.075574) 2. For the insurance company, to avoid the ruin of OB GROUP A insolvency of asset, an amount of capital reserve logistic (-001795,.012667) -0.0580 00,0% 00,0% 25 20 15 10 48,1% 48,1% 0.0000 51,9% 51,9% -0.0975 00,9% 00,9% 0.0000 53,69% 53,69% 25 Fangyuan Yan y José Miguel Rodríguez-Pardo: Asset Liability Management –ALM in Life Insurance20Risk Management Gestión de Activo y Pasivo 15 del Seguro de Vida –ALM en Gestión de Riesgo Análisis Financiero n° 128. 2015. Págs.: 78-91 10 46,4% 46,4 90 ANÁLISIS FINANCIERO as the provision of solvency is always required. The VaR value estimates the loss probability and the probable loss by different risk levels for the company’s own needs, so the VaR is much more dynamic and adjustable than other traditional method. Couceiro Rodríguez, Adrián, ¨Inversiones en el seguro de vida en la actualidad y perspectivas de futuro¨, Fundación MAPFRE, 2009. Cuesta Aguilar, Francisco, ¨El riesgo de tipo de interés experiencia española y Solvencia II¨, Fundación MAPFRE, 2011. 3. The VaR model is also a challenge of the low risk portfolio for the insurance investment. Because for the security of asset, the most of the traditional invested portfolio for premium is included the low risk product as the bonds, deposit of risk free rate. By the estimation of VaR, we can predict the probable loss, while investing more assets to a higher risk product, such as stocks, future contract… Today we are in a financial market filling with sundry financial derivatives, the more risk we face to, the more returns we will have. If we can control the loss risk to an acceptable level, the portfolio of investment may change a lot in the future. Eling, Martin Parnitzke, Tomas, “Dynamic Financial Analysis: Classification, Conception, and Implementation”, December 2005. Fernández Palacios , Juan, ¨Tendencias del seguro de vida¨, ICE 833. H. 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