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Value at Risk 1
VALUE AT RISK
(An Approach to Risk Management)
Value at Risk 2
Introduction
A dynamic financial globalized environment, where economies of all countries in the
world are going through a major risk of unexpected change in stock prices. Market risks play a
major role in deciding the extent of investment to be made and whether or not investment is to be
made by investors. A rational investor will always want to reduce the risk to which he is exposed
and and will always want to maximize its return on the stock prices he is holding. Due to world-
wide famous financial and economy disasters such as Barings‟s fall, VaR method was
developed in 1993.VaR is considered as a risk management tool, Banks, financial institutions
and Non-Banking Financial Corporations use it more, often. VaR is an important and commonly
used tool to, estimate; exposure to market risks as well as it measures the expected loss in the
worst situation. The key quantitative factors which are defined and presented in VaR method are,
namely, the confidence level c and the time horizon τ .
One important and peculiar, purpose and task for VaR method is to manage and mitigate
the risk. Therefore, besides computing the Var of entire portfolio, investor has to know which
asset, contributes most to the total risk, what, the effect is if delete or add an asset, and so on. In
this section, a detailed analysis of VaR tools is introduced, to control and manage the portfolio
risk.
According to Philippe Jorion,
“VaR measures the worst expected loss over a given horizon under normal market
conditions at a given level of confidence. For instance, a bank might say that the daily VaR
of its trading portfolio is $1 million at the 99 percent confidence level. In other words,
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under normal market conditions, only one percent of the time, the daily loss will exceed $1
million.” (Jorion 2001, p. xxii)
Background
The basic theory behind evaluating, risk is to protect ourselves from the future loss due
to market risk, credit risk, investment risk etc. Even if a person tries to create a portfolio of its
various assets, hence, there is always a probability of, risk and What if a person faces, a worst
situation. Such questions and situations are considered in VaR theorem.
The market risk of, a portfolio refers, to the, possibility, of financial ,loss due to the
changes of different systematic economic variables such, as rate of interest, and Foreign
exchange rates. In assessing solvency and and in allocating scarce capital, determination of
market risk is most important. Moreover, financial risk faced by financial institutes is market
risk. The basic and absolute method in measuring the central financial risk place a narrow,
conservative Confidence interval, on, portfolio losses for short forecast, ,horizons. This, limit on,
losses is often called capital-at-risk or central risk (VAR). VaR can be of following types:
Marginal Value-At-Risk
The basic method for measuring risk exposure and management and assessment is
marginal value at risk, as the Partial derivative, in respect of the component weight, it measures,
the difference in the VaR calculated from, adding additional dollar to, a component.
Portfolio VaR
VaR or Value at Risk measures maximum, potential loss in value, of an asset or portfolio
over a defined period, at a given confidence interval. In an investment to estimate the downside
risk to its maximum, VaR is used. ΔP is the difference between Pt+1 and Pt, i.e. ΔP =Future
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Price – Current Price, difference in value of portfolios at different at current time t and future
time t+1, where Pt is the value at current time t and Pt+1 is the value at the future period. Rate to
be taken is arithmetic & geometric as same.
Computation
If the VaR, of an asset is Rs. 10 lakh for, a week at 95% confidence level, then it means Rs. 10
lakh is the maximum, potential loss expected during any given week, in that asset at 95%
confidence level. There is, however, a 5% chance that, the value of the asset will change by more
than Rs. 10 lakh during, a week.
Most popular & traditional measure of risk is volatility. VaR statistic has three, components:-
(a) A time period
(b) A confidence level
(c) Loss amount ( or loss percentage)
Underlying formula is used for computation of VaR:
Market Value, of the Asset * Confidence Factor * Volatility, of the Holding Period
There are three methods of calculating VaR are:-
(a) The historical method or non-parametric method.
(b) The Variance- Covariance, Method
(c) Monte Carlo Simulation.
Detailed explanation for each method is enumerated below:
(a) The historical method or non-parametric method.
Historical data is required by historical method. Main assumption of the model is that
future will emulate past, which is not always true. It is good practice to use, as much data as
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is reasonably possible, when using nonparametric models to incorporate as many "black
swans" as possible. Hence following will give you more realistic data explanation.
The graph shown below is the, daily % periodic returns as per, S&P TSX Composite,
Index from the period from January 2000 to November 2000. 2988 data points are enumerated.
The three tiny, bars on the left indicate, the number of days where the, TSX saw
declines of between 9.8% -8.1%, 8.1%-6.4% and 6.4%-4.8%; the days are labeled, above the
bars. We have a total of 2988 data points, and 21/2988 = 0.00703. That means, less, than
1% of the time over the past 11 years, (or 0.703% of the time to be exact) the TSX saw,
losses in excess of 4.8%. In, other words, we can say with 99% confidence, that the worse
daily loss will not exceed 4.8%.
Parametric approach or the Variance – Covariance Method.
The approach requires only two variables, the variance and the mean. It is not difficult to
estimate the confidence, levels in the parametric approach of VaR. The basic assumption of this
approach is that it uses normal distribution. Normal distributions are terrible at, predicting black
events.
The TSX daily return, since 2000 data set had a mean of 0.013% and a variance, of 1.5%.
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Using this model, we can say, the daily VaR with 95% confidence, is -2.5% and with
99% confidence is -3.5%. In other words, we are 95% confident, daily losses will not be in
excess of 2.5% and 99% confident that maximum daily loss is of 3.5% daily;
Now let's compare the results of parametric approach from the non-parametric,
model. The historical model indicates that 99% VaR was, 4.8% compared to the parametric,
3.5% (a difference of 37%). This difference, are due to periodic returns being not, normally
distributed. Therefore, if any person wishes to use the variance-covariance method firstly
performs a test to check whether data is normally distributed. In Excel, use the skew and
kurtosis functions and select the data set. Normal distributions have a skew of zero and a
kurtosis of 3. No wonder the VaRs don't match up.
Monte Carlo approach
To actual predictions, Monte Carlo Simulation uses random numbers and probabilities. It
involves inputting known pertinent variables, selecting, the type of simulation, and then letting
the computer run the simulation hundreds, or thousands of times. The data is further analyzed to
determine the worst 1% or 5% of the results, our 99% Var and 95% Var. Most enterprise
resource planning software, such as SAP, contains Monte Carlo applications.
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There are various, types of Monte Carlo Simulations : lognormal or positively skewed,
normal or bell curve, triangular and PERT, uniform or equal chance where most of the
parameters are discrete and user defined where the user inputs the likelihood of occurrence and
defines each value. Given the accurate and proper data, it, is the most time consuming and most
accurate method.
Following is the calculation of VaR of Copper, which shows $ 8909 is the maximum loss
which an investor can face in the worst situations.
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Uses of Value at Risk (VaR)
VaR is clearly a useful risk measure for banks and financial institutions that are involved
in regular trading activity, but it is tempting to dismiss VaR as having limited relevance
to...