Asset Liability Management –ALM in Life Insurance Risk Management

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. Panning, William, “Managing Interest Rate Risk: ALM,
Franchise Value, and Strategy”.
J.Iñaki de La Peña, ¨Provisión Matemática a tipos de interés de
mercado¨, artículo publicado.
Kaufmann, Roger Gadmer and Ralf Klett, Andres, “INTRODUCTION TO DYNAMIC FINANCIAL ANALISIS”.
Lozano Aragués, D.Ricardo, ¨Análisis de la regulación re-
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Gestión de Activo y Pasivo
–ALM en Gestión de Riesgo del Seguro de Vida
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