Application of Statistical Theories Assessment 2022

Application of Statistical Theories 1
APPLICATION OF STATISTICAL THEORIES
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Application of Statistical Theories 2
a) VaR
Value at Risk, VaR is a statistical metric which utilizes the normal distribution
knowledge to estimate the expected minimum loss of value a company with a given probability
for a specific period (Hartmann, 2016). VaR is widely utilized in the financial industry for
budgeting and risk mitigation purposes. The risk management statistical concept introduced in
the 1980s has many advantages.
The major advantage of VaR is its wide application in the financial industry. The
application of VaR statistical concept for risk estimation is not limited to any industry. VaR is a
standard metric applicable across various industries in an attempt to estimates the potential
financial risk exposure for institutions, companies, and parastatals (Davies, 2017; Zax, 2011).
Moreover, VaR calculation is easy; therefore, managers, senior managers, and company's
directors who are not experts in statistics easily understand and interpret the concept. Besides the
minimum loss of value estimation, VaR is a very useful tool in risk budgeting and capital
allocation factoring the minimum expected loss of value for every business units in a company or
institution. Hochkirchen (2011) highlighted VaR as a very important tool for risk budgeting and
capital allocation for different business units in cases where a company utilizes a central process
of capital allocation.
Even though VaR has many advantages and wide application, it has a weakness in its
application. VaR measure of risk estimates the minimum loss of value but does not estimate the
expected maximum loss of value in the risk estimation process (The Financial Applications of
Mathematical Statistics, 2014). Estimating the maximum expected loss of value enables the
managers of companies to factor in the resultant financial loss from company activities.
Practically, VaR measure of risk underestimates the frequency and magnitude of losses resulting

Application of Statistical Theories 3
from the assumptions made during VaR calculation. Additionally, VaR utilizes historical data to
predict expected losses in the future. Past data may not be a good predictor of futures events,
especially for black-swan events. Moreover, VaR assumes that the distribution of returns is
normally distributed and follow a bell-shaped graph. Normality assumption is only applicable for
periods of normal market conditions but abnormal market conditions.
VaR Calculation
VaR is measured using three different approaches; the historical simulation, Monte Carlo
simulation, and variance-covariance method. The variance-covariance VaR measure of risk
assumes that the portfolio values follow the normal distribution. The normal distribution is
motivated by the famous central limit theorem. Therefore, a randomly sampled portfolio data is
independent and identical regardless of the distribution of data sample, thus normally distributed
(Notz, 2012). Variance-variance VaR method calculates the standard deviation of price
movements of a security. The calculated expected value (Mean) and the standard deviation
values are used to plot a normal distribution curve against actual data.

Application of Statistical Theories 4
Plotting a normal curve gives an advantage is easy identification of the worst 5% and 1%
on the curve. For instance, a one-security portfolio of $500 is invested in a stock market F, and
the standard deviation is approximately 4% per annual, and the stock price movement is assumed