Liability driven investment asset liability management optimisation

LDIOpt:
Asset – Liability Management
Software Demo

 LDIOpt – An integrated solution
 Insurance ALM problem considered
 LDIOpt Demo
 Pre Analysis window
 Optimization window
 Post Analysis Window
 Performance Measure Window
 Chart Viewer
 Solver Options

• An integrated solution - considers Assets and Liabilities
together.
• Advanced stochastic models with real world constraints.
• Incorporates Uncertainties in decision models
• Based on most recent and effective approach to
overcome interest rate risk.
– minimize the Present value (PV) deviation of asset and
liability at each time step over the planning horizon.
• Considers overlay strategies to make the results robust.

LDIOpt :From Historical data to
Optimum ALM decisions

Platform and technical aspects
• The LDIOpt is currently in development stage
• It runs under windows, XP and Vista.
• The optimization models are constructed using AMPL
modelling tool and the embedded application with GUI and
solver is constructed using AMPL NET.
• LDIOpt uses FORTSP as solver engine which in turn is
built around CPLEX and FORTMP solvers which are
embedded within the systems as an alternative

Insurance Product Considered for
this Prototype
• Liabilities of one of the most popular and conventional
life insurance products, Annuity is considered.
• The individual is supposed to pay a fixed amount, once
while buying the Annuity Policy.
• The annuitant will get the coupon value at every six
month on the decided pay-out(Interest Rate).
• Policy maturity is till death of the annuitant and on the
death of the annuitant, the nominee receives the ‘sum
assured and the pay-out’.

Getting Started With Prototype: LDIOpt
LDIOpt Prototype is in Development stage
ICON OF LDIOpt

Getting Started With Prototype: LDIOpt
LDIOpt Prototype is in Development stage
ICON OF LDIOpt
The Introduction Page
Default page opens when you click on the LDIOpt icon

The Pre-Analysis window: LDIOpt
Window to Analyze the Current Portfolio.
Screen shot of
Pre-Analysis
window

Browse to
insert the Asset
, Liability and
current holding
data

Two TAB
1.Universal Set: Shows all assets considered for the
portfolio rebalancing.
2.Portfolio Allocation: Shows the current holdings of the
client portfolio

Shows the break-up
based on risk rating
of bonds available
for rebalancing.

Display clients current bond/fixed
income portfolio by

The Optimization window: LDIOpt
• To fix the optimization model

• To Input the Interest rate values for PV calculation

• To Fix the Bond Rating and Sector constraints

• To choose the asset classes/indices/swap

• To solve the model click “Solve”To solve the model click “Solve”

• To create the Efficient Frontier click “Solve”To create the Efficient Frontier click “Solve”

The Optimization window After filling
the data: LDIOpt

The Post- Analysis window : LDIOpt
• Screen shot of Post Analysis window when you just
start

start
Efficient Frontier:
A graph shows
tradeoff between
Initial Injected Cash
and Total Deviation

start
Initial Injected Cash:
Additional cash requirement,
at present, to buy Assets to
meet all liabilities in future.

start
Total Deviation:
Sum of
deviations of PV
(Asset PV – Liability PV)
at each time step.

The Post- Analysis Page : LDIOpt
• Screen shot of Post Analysis Page when you click on
any efficient frontier point

Selected Efficient
Frontier Point

The value of total deviation for
that particular efficient frontier
point

The value of Initial Injected cash
for that particular efficient frontier
point

Four Tabs
1.Allocation Chart
2.Allocation Data
3.NPV Matching
4.NPV Asset and NPV
liabilities

1. Allocation Chart:
A. Allocation in various
assets by volume.
B. Allocation in various
assets by value.

2. Allocation Data:
A.Allocation by volume
( # of units per
bond )
B. Allocation by value
( rupee value
investment per bond )

3. NPV Matching:
A Bar chart shows
Asset PV and Liability PV
on each time step

4. NPV Assets and
NPV Liabilities:
A.PV of Assets at
each time period
B. PV of Liabilities at
each
time period

The Performance Measure Page : LDIOpt
• Screen shot of Performance Measure Page when you
just start

• Screen shot of Performance Measure Page when you
just start
Efficient
Frontier
Performance
Measures from
Industries &
academia.

• Chosen Solvency Ratio and any of the efficient
frontier point

frontier point
Efficient Frontier
Point Selected
Point - 11
Performance
Measure/Ratio
Selected

frontier point and “Graph” tab.

Every insurance
company is required
to maintain solvency
margins based on its
volume of business
and as per the
guidelines stipulated
by the IRDA.

Ratio of Excess value
of Assets over
insurance liabilities
(furnished by IRDA) by
value of insurance
liabilities is called
SOLVENCY RATIO

The solvency of an insurance
company corresponds to its
ability to pay claims.
An insurer is insolvent if its
assets are not adequate
[over indebtedness] or
cannot be disposed of
in time {illiquidity} to pay
the claims arising.

frontier point and DATA TABLE TAB

TIME STEP
FRONTIER
POINT 11
FRONTIER
POINT 11

FRONTIER
POINT 11
Solvency Ratio is
calculated using
Asset PV and Liability
PV.
= (Asset PV –
LiabilityPV) / Liability
PV

From the shown
solvency ratio value it
can be concluded that
at any time period of
planning horizon; if all
the liabilities come due
suddenly than
insurance company
can easily pay back by
liquidating its asset
without any delay or
loss.

• Chosen Funding Ratio and any of the efficient frontier
point

point
Efficient Frontier
Point Selected
Point - 11
Performance
Measure/Ratio
Selected

point and GRAPH TAB

point and GRAPH TAB
Ratio of value of
Assets and the value
of insurance liabilities
(furnished in IRDA)
called FUNDING
RATIO

point and GRAPH TAB
Ratio of value of
Assets and the value
of insurance liabilities
(furnished in IRDA)
called FUNDING
RATIO
The Funding of an
Insurance company
corresponds to its
ability to pay claims.
Funding ratio is similar
to solvency ratio. An
insurer is not enough
Funded if its assets are
not adequate or cannot
be disposed of in time
{illiquidity} to pay
the claims arising.

point and DATA TABLE TAB
FRONTIER
POINT 11

TIME STEP
FRONTIER
POINT 11
FRONTIER
POINT 11

Funding Ratio is
calculated using
Asset PV and Liability PV.
= Asset PV / LiabilityPV

From the shown
Funding ratio value it
can be concluded that
at any time period of
planning horizon; The
Insurance provider is
funded enough to
overcome any liability
that comes at any time
period.

• Chosen Sharpe Ratio and any of the efficient frontier
point

point
Efficient Frontier
Point Selected
Point - 11
Performance
Measure/Ratio
Selected

point and GRAPH TAB

point and GRAPH TAB
Sharpe ratio was
derived in 1966 by
William Sharpe, it has
been one of the most
referenced risk/return
measures used in
finance.

point and GRAPH TAB
The ratio describes how
much excess return
(AssetPV return – LiabilityPV
Return)
You are receiving for the extra
volatility (SD of AssetPV
return – LiabilityPV Return)
that you endure for holding a
riskier asset.

TIME STEP
FRONTIER
POINT 11
FRONTIER
POINT 11

Sharpe Ratio is calculated using
(Asset PV return and Liability PV return)

It is the measure of excess
return you receive at each
time period with
unpredictability.

FRONTIER
POINT 11
An investor choose to
invest in a portfolio with
higher value of Sharpe ratio.
A positive value and upward trends
of Sharpe ratio always attracts the
investor.
Here, we suggest clients to choose
the frontier point with maximum
value of Sharpe ratio and do the
investment as per that point.

• Chosen Sortino Ratio and any of the efficient frontier
point and GRAPH TAB

point and GRAPH TAB
A ratio developed by
“Frank A. Sortino” to
differentiate between
good and bad volatility
in the Sharpe ratio.

point and GRAPH TAB
The ratio describes how
much excess return
(Asset return – Liability
Return)
You are receiving for the
downwards volatility
(Downside Deviation of Asset
return – Liability Return) that
you endure for holding a
riskier asset.

TIME STEP
FRONTIER
POINT 11
FRONTIER
POINT 11

• The Sortino ratio measures the
return to "bad" volatility.
• This ratio
allows investors to assess risk in
a better manner than simply
looking at excess returns to total
volatility (Sharpe ratio),
• Since such a measure does
not consider how often
the price of the security rises as
opposed to how often it falls. A
large Sortino Ratio indicates a low
risk of large losses occurring.

An investor choose to
invest in a portfolio with
higher value of Sortino ratio.
Here, we suggest clients to
choose the frontier point
with maximum value of
Sortino ratio and do the
investment as per that point.

• Chosen Modigliani M2 ALPHA and any of the
efficient frontier point and GRAPH TAB

Modigliani Risk-
Adjusted
Performance(RAP) or
M2 is a measure of the
risk-adjusted return of
a investment portfolio.

It measures the return of the
portfolio, adjusted for the risk
of the portfolio, relative to that
of some benchmark (e.g., the
market). In our case, the
benchmark is the liability
return.

• Chosen Modigliani or M-Square Measure and any
of the efficient frontier point and DATA TABLE TAB

TIME STEP
FRONTIER
POINT 11
FRONTIER
POINT 11

The Modigliani Risk-Adjusted
Performance measure is used
to characterize how well a
ALM Model rewards an
investor for the amount of risk
taken, relative to that of
Liability retrun.

The Modigliani or M-Square
Measure (see Modigliani and
Modigliani (1997))
is given as the following:
RAPA(F) = Sharpe ratio *
standard deviation of liability
return ( Benchmark portfolio)

• Chosen Jensen Index and any of the efficient
frontier point and GRAPH TAB

The Jensen Index
measures the
performance against
the market
index(Liability Return).
A high Jensen Index is
interpreted as higher
return given a risk level
on the portfolio.

The Jensen index uses
the capital asset pricing
model(CAPM) as its basis for
determining whether or not
a ALM manager outperformed
a market index (or
outperformed its liability
Portfolio).

• Chosen Jensen Index and any of the efficient frontier

TIME STEP
FRONTIER
POINT 11
FRONTIER
POINT 11

The CAPM determines
the required rate of return, and
the Jensen index helps
investors see if the calculation
yielded expected results.
In our present case Jensen’s
alpha would be
Jensen's alpha = Asset
Return − Asset Beta *
(Liability Return)

A high Jensen index
suggests a high level of
return given the level of risk
(systematic or market) on
the investment. A low
Jensen index, such as a
negative number, indicates
inferior performance when
compared to the risk.

• Chosen Treynor Ratio and any of the efficient

The Treynor ratio
relates Asset PV return to
the risk taken; however,
systematic risk is used
instead of total risk. The
higher the Treynor ratio, the
better the performance of
the ALM implementation.

Also known as the
"reward-to-volatility ratio".
The Treynor ratio is
calculated as:
Treynor ratio = Asset
Return / Asset Beta

• Chosen Information Ratio and any of the efficient

A ratio of portfolio returns
above the returns of a
benchmark (presently Liability
return) to the volatility of those
returns. The information ratio
(IR) measures a portfolio
manager's ability to generate
excess returns relative to a
benchmark, but also attempts
to identify the consistency of
the investor. In our case
benchmark is Liability Return.

This ratio will identify
if a manager has
beaten the benchmark
by a lot in a few time bucket
or a little every time bucket.
The higher the Information
Ratio the more consistent a
Manager is and consistency
is an ideal trait.

• Chosen Tracking Error or Standard deviation of
excess return and any of the efficient frontier point
and GRAPH TAB

and GRAPH TAB
The standard deviation
of the difference between
the funds return
(Asset PV return ) and a
benchmark return
(liability PV return) is also
called the tracking error.

and GRAPH TAB
The Tracking error
represents the volatility in
the excess return and
successfulness of the
optimization function. The
value should be close to
zero. The tracking error
plotted against planning
horizon represent the
movement (upper or lower)
of the total PV deviation.

This Page is to help user to compare
different models with their efficient frontiers
The Chart Viewer Page: LDIOpt

Here you can
see the
comparison of
EVLP model and
SP model for two
conditions
1.With bonds
only portfolio
2. With all asset
class

Whereas when we
include the market
indices it reduces
the initial inject cash
significantly. The
efficient frontier is
very steep for this
case which means
for small reduction in
deviation, fund
manager will require
more cash in
comparison to “Bond
Only Portfolio”

This Page helps users to choose the
solver to solve the optimization model
The Solver Option Page: LDIOpt

LDIOpt has two solvers CPLEX and FortMP
embedded into the solver options

CPLEX is developed and marketed by IBM ILOG
It is very efficient and solve the problem very fast
For large scale problem we prefer the use of CPLEX

FortMP is developed and marketed by
OptiRisk Systems, UK and It is good for small scale
problems and can be easily used for the
Small scale ALM problem.

LDIOpt: Tailoring as per
client requirement

Asia Pacific, Africa, Australia &
Middle East:
Europe & America:
No 12, 25th Cross Street
Thiruvalluvar Nagar ,
Thiruvanmiyur,
Chennai –600041, India
OptiRisk R&D House,
One Oxford, Uxbridge,
Middlesex, UB9 4DA,
United Kingdom
Contact
Bala. Padmakumar
Ph: +91 98406 18472 / +91 44 4501 8472
Email: optimize@optiriskindia.com
Web: http://www.optiriskindia.com/
Thank you

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