Introduction
Traditional theories, models and techniques continue to be remodified in an effort to come up
with new methods of estimating market risks. Empirical models and techniques for determining
risks continue to be re-engineered by researchers and other financial actors to capture the
realities of market volatilities. Value at Risk is one such development in financial which has
proved vital in risk management. VaR is a method provided by statistics used to make prediction
in finance on the maximum possible loss that can occur over a given period of time. (Happer,
2022). This style of examining market risks is widely used in banking sector and other financial
institutions when conducting analysis on their investments. VaR applies probabilistic methods in
determining the value of likely losses that a bank or other business organization can suffer incase
of worse case situation.
Properties of Value at risk (VaR)
Market risk are normally examined based on volatility of market prices. VaR utilize three
variables in estimating this volatility, that is the size or extent of value that will be lost,
confidence level and the time period of investment. Time period can be daily, monthly quarterly
or annually, while confidence level can be 95% or 99% while possible loss is the value of loss
for instance in US dollars. Loss can also be measured in terms of percentages. This paper used 2-
year daily share price data for Lenovo and Alibaba companies between October 15 2018 and
October 15 2019. It will examine maximum possible loss in the value of the shares at 90%,
95% and 99% confidence level.
Techniques of calculating VaR
There are three techniques or methods of calculating value at risk. These methods are variance-
covariance method, historical simulation method and Monte Carlo simulation method.
Methodologies, advantages, disadvantages and application of these methods are explained in the
next section.
1.Variance-covariance method
This method uses expected returns of stock and the standard deviation to calculate value at risk.
It further assumes normal distribution of the expected returns. The confidence level and the
corresponding z-score is used in this method.
The first step in this technique is to derive or to calculate expected return from the share prices of
the two companies. The expected price is determined by finding the natural logarithm of array of
change in share price. The formula for this step is In (P 1 -P 2 )/P 2 multiplied by 100. In represent the
natural logarithm, P1 the price of share at a particular point in time and P2 the preceding share
price. The natural logarithm is used as it takes into account cumulative changes in rate of return.
The table of share prices and expected returns obtained for Lenovo and Alibaba is given below.
Share prices Expected Returns
Date Lenovo Alibaba Lenovo Alibaba
10/15/2018 12.48 144.16
10/16/2018 12.84 149.6 2.884615 3.773586
10/17/2018 12.9 148.14 0.46729 -0.97594
10/18/2018 13.2 142.02 2.325581 -4.13122
10/19/2018 13.03 142.93 -1.28788 0.640747
10/22/2018 12.93 148.8 -0.76746 4.106913
10/23/2018 12.34 146.65 -4.56303 -1.4449
The summary statistics for the returns obtained for the two companies are given below. The most
important statistics applicable in VaR calculation using this technique is the standard deviation
and the mean or average return. The rest statistics are used in examining the distribution of the
returns and making inference on the kind of distribution.
Descriptive statistics
Lenovo Alibaba
Mean 0.062998 0.097899
Standard
Error 0.140131 0.137936
Median 0.074738 0.121945
Mode 0 #N/A
Standard
Deviation 2.220091 2.185315
Sample
Variance 4.928802 4.7756
Kurtosis 3.028095 0.420932
Skewness 0.502303 0.027514
Range 17.83147 13.64852
Minimum -5.86057 -6.6424
Maximum 11.9709 7.006121
Sum 15.81257 24.57255
Count 251 251
From the descriptive statistics expected returns for Lenovo and Alibaba are 0.063 and 0.08
respectively. Their median is 0.14 and 0.13 respectively. Under normal distribution conditions
the mean of variable is zero. These values do not deviate more from this assumption and the little
deviations are attributed to chances. This means that the distributions of expected returns are
normally distributed. The skewness is 0.5 and 0.02 which again supports the assumption of
normal distribution. Kurtosis for the two sets of returns does not exceed 3 meaning there are few
extreme values in expected return or the prices. Normal distribution can be visualized in the
histograms below.
The correlation between the expected returns for the two companies is 0.368, meaning there is
weak association between the prices of the two shares.
Correlation
Lenovo Alibaba
Lenovo 1
Alibaba 0.368341 1
Lenovo Alibaba
Lenovo 4.909166
Alibaba 1.779923 4.756574
Lenovo
Confidence level 90% 95% 99%
Average rate of
return
0.062998 0.062998 0.062998
Probability 10% 5% 1%
Standard
deviation
2.220091 2.220091 2.220091
z -1.645 -1.96 -2.576
z*Standard
Deviation -3.6534 -4.3514 -5.0107
Value of asset(V)
Alibaba
Confidence level 90% 95% 99%
Average rate of
return
0.097899 0.097899 0.097899
Probability 10% 5% 1%
Standard
deviation
2.185315 2.185315 2.185315
z -1.645 -1.96 -2.576
z*Standard
Deviation -3.5948 -4.2832 -5.6294
Value of asset(V)
The formula for determining Value at risk is given by
VaR= [Rp – (z) (SD)] *V
Where Rp is the rate of return, z is the z-score for a given confidence level, SD is the standard
deviation and V is the value of the shares. In this paper we have not been given the value of the
shares hence the final value will represent VaR in percentage form. The VaR for the two
companies at 95% confidence level are;
VaR(Lenovo) = [6.3%- 4.3%] =2%
VaR(Alibaba) = [9.8%-5.6%] = 4.2%
The interpretation of the results means that Lenovo shares will loose 2% of its value at 95%
significance level at a given risk probability. Alibaba on the other hand will lose 4.2% of its
shares at the same confidence level and risk.
2. Historical simulation technique
Historical simulation method of estimating VaR assumes that the occurrence of risks in the
future follows historical pattern of risk. This means that there is strong association between the
occurrence of risk in the past in the future. It is considered the easiest technique of determining
market risk. Based on this method expected returns for the two companies were also calculated
using historical daily share price given. The returns were then arranged from the lowest value to
the highest. Based on confidence level VaR was determined at a particular percentile. Histogram
for the sorted expected returns are given below.
At 95% confidence level it means that the VaR will be equal to VaR of 5 th percentile of historical
data according to historical simulation method.
3. Monte Carlo Simulation Technique
This method calculates VaR through the use of computer software which simulates or generate
expected returns of a financial asset. In the software the values of expected returns depend on the
inputs that are fed into the system, that is the share prices and the standard deviation. In this
technique several simulations are performed in an effort to capture various situations in the
market. This results in different expected returns according to the variations in the inputs of the
simulation process. The advantage of this method unlike the historical method is that it attempts
to capture all the possible circumstances which might occur in the market. The historical method
assumes that the past occurs of risks are the same with the expected risks in the future which
might not be the case. The limitation of this method is that it is based on several assumptions are
use of varied inputs hence it is cumbersome.
In conclusion Value at risk is useful in making comparisons of various stock for example from
the analysis using variance-covariance method it was found that Alibaba has a higher VaR
compared to Lenovo meaning it will lose a higher value of its shares in the event of occurrence
of risks.
References
Alexander C. Shhedy E. (2008) The assessment of market risks in the context of the current
financial crisis.
Ahmed N.H and Ariff M. (2007). Multi-country study of bank credit risk determinants.
International journal of banking and finance, 5 (1/6)
Aruwa, S.A. S, and Musa, A.O. 2014.Risk components and the financial performance of deposit
money banks in Nigeria. International journal of social sciences and entrepreneurship.
Namasake N. (2016). The effect of market risk on the financial of commercial banks in Kenya
Mugenda, D.M and Mugenda, A. G (2003). Research Methods. Qualitative and Quantitative
Approaches
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