Portfolio VaR Estimation_Final1leen

8/9/2019 Portfolio VaR Estimation_Final1leen

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PORTFOLIOVAR

ESTIMATION

Husam Sawalha Muna GhoshehLeen Bargouth Flora Mansour


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INTRODUCTION

A portfolio was built by choosing the following stocks

from Amman stock exchange :

Jordan Ahli Bank. The Jordan Cement Factories. Jordan Poultry Processing & Marketing. Jordan Diary.

The historical data of those stocks was collected for themost recent 501 days


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INTRODUCTION

Our Companies Value of investment

AHLI 4000

JO CEMENT 3000

JO POULTARY 2000

JO DAIRY 1000

Total 10,000

J.D 10,000 was invested in this portfolio allocated

as follow :


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INTRODUCTION

Portfolio VaR was estimated according to the

following approaches:Standard Approach.

Historical Simulation Approach :Basic historical simulation approach.

Adjusted weighting historical simulation approach.

Volatility Adjusted approach ( EWMA & GARCH Models).

Model-Building Approach :

Equal-WeightsEWMA


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METHODOLOGY OF WORK

First of all, the normality of stocks returns was tested,

to ensure returns are normally distributed, so that no

out layer number that may effect our estimation of VaR

.

Secondly, VaR was estimated based on standardapproach.

Thirdly, under the Historical Simulation Approach, 500

alternative scenarios was built based on 501 returns of

stocks, to estimate the probability distribution of the

change in the value of the current portfolio

Finally, under the Model-Building Approach, the

covariance matrix between stocks returns was built

and used in estimation.


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NORMALITY TEST

All portfolio stocks returns are normally

distributed or semi normally.

The descriptive analysis of returns was made,

and the values of Kurtosis and Skewness was

checked as follow:

Skewness Kurtosis Stock

0.304856 8.884672 AHLI

-0.331869 0.617962 JOCM

0.591727 1.772698 JPPC

-0.189063 3.460736 JODA


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STANDARD APPROACH

Based on returns of portfolio, the

mean and standard deviation was

calculated.

The following formula was used to

estimate VaR :

)(

1XNVaR

=


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HISTORICAL SIMULATION

APPROACH

Basic Historical Simulation:According to Basic historical simulation approach:

VaR is based on historical scenarios of losses .we collect the historical data on their

returns over a set observation period Each scenario -or day outcome- is given equal

weight, which is 1/number of scenarios .

for each asset and each t in the observation period, we generate scenarios by

calculating the return (% change) on each of the assets. Here is the formula to

calculate the percentage price changes: (price t - price t-1) / price t-1 or (ln t) .

For 500 scenarios , the one-day 99% VaR can be estimated as the fifth-worst loss.

no of observations=500, 1-.99=10% ,10%*500=5 Then we find mean and standard deviation and according to the equation: Mean-Z(n)*standard deviation Wefind the historical var


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HISTORICAL SIMULATION

APPROACH

We suggest that more recent observations should be given more weights because theyare more reflective of current volatilities and current macroeconomic conditions .

We calculate the weights by choosing lambda = 0.94

and our formula .

n-i(1-)

1-n

Where

n: number of observation .

i : scenario number,

i=1 is the scenario that calculated from the most distant data.

: can be chosen by experimenting to see which value back-test best .

As approaches 1, the relative weights are approach the equal weight. Then we do a cumulative weight column for our weights

Starting at the most worst observation sum weight until the required quintile of

distribution is reached( we are calculating VaR with 99% confidence level) , so we

continue summing weight until the cumulative weight is just greater that 0.01 .


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CALCULATING VAR USING THE HISTORICAL

SIMULATION VOLATILITY-ADJUSTED

APPROACH (EWMA)

In this part volatility of each scenario

was taken into consideration .

This approach will produce VAR

estimation that incorporate the

volatility of current information


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PROCEDURE OF VOLATILITY

ESTIMATION USING EWMA

Calculate daily varianceThe following equation used to produce new variance

Then we find standard deviation which is the

Square root of variance Then we make volatility multiplier:Last sd/1stsd, last sd/2ndsd Then we multiply volatility*lossesVar=1-95%=5% we will find the 5thloss from the

bottom

assumed to be .94Adjusted prices are then calculated using the followingformula :

2

1

2

1

2 )1( += nnn u

1

111

/)(

+ +

i

iniii

n

v

vvv

v


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MODEL-BUILDING APPROACH

The main alternative to historical

simulation is to make assumptions

about the probability distributions of

the returns on the market variablesThis is known as themodel

building approach(or sometimes

the variance-covariance approach).


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Daily changes in the value of a portfolio equal the

total daily changes in the values of individual

stocks.

This approach based on the assumption that daily

changes of the values of individual stocks are

normally distributed and so daily changes in the

value of the portfolio are normally distributed.

The variance of the daily changes of portfolio value

is given by:

j

n

i

n

j

iijP = =

=1 1

2cov

MODEL-BUILDING APPROACH


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PROCEDURE OF ESTIMATING VAR

IN MODEL-BUILDING APPROACH

Calculate daily returns for each stock.

Based on the following equation, the

variance of portfolio is calculated

j

n

i

n

j

iijP = =

=1 1

2 cov

Then VaR of the portfolio is estimated.


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USING EWMA IN MODEL-

BUILDING APPROACH

Instead of using equal weights, Exponentially

weighted average method with certain value could

be used.

Firstly, calculate variance of each stocks returnsusing .

Secondly, calculate covariance for each pair of stocks

using .

Finally, build the variance-covariance matrix tocalculate portfolio variance

Then VaR of the portfolio can be estimated.

Portfolio VaR Estimation_Final1leen

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