Computing Value at Risk Using Descriptive Statistics

...

ONGC

[pic 2]

Data from Table in page 11

Frequency Distribution Table of ONGC:

Frequency distribution

Bins

Frequency

-8 to -7

0

-7 to -6

1

-6 to -5

2

-5 to -4

3

-4 to -3

13

-3 to -2

23

-2 to -1

30

-1 to 0

50

0 to 1

59

1 to 2

37

2 to 3

23

3 to 4

8

4 to 5

6

5 to 6

2

6 to 7

1

7 to 8

1

VALUE AT RISK

Value at Risk has been used in finance industry to precisely define risk. There are three methods to compute it.

- Historical

- Model building approach

- Monte Carlo Simulation

Here, we have used Model Building Approach to compute the same, which assumes that over a long period, the population of stock returns follows normal distribution. Based on this approach, we have computed Value at Risk at 99% confidence interval for both stocks.

As the sample data size is large and also frequency distribution curve looks normally distributed, it will be a good assumption that we compute value-at-risk at 99% confidence interval. Hence,

Assumptions:

- Sample is normally distributed

- Sample standard deviation is given

Tata Motors:

Mean: 0.18%

Standard Deviation: 2.14%

At 99% confidence interval:

Z=2.58

X = Mean – z-value*(std. deviation) = 0.18 – 2.58*2.14 =

-5.34%

ONGC:

Mean: 0.05%

Standard Deviation:2.11%

At 99% confidence interval:

Z=2.58

X=Mean – z-value*(std. deviation) = 0.05 – 2.58*2.11 =

-5.394%

Hence, Value at risk at 99% confidence interval for Tata Motors is -5.34% and for ONGC is -5.394%, which implies that ONGC is more potential to losses than Tata Motors, although variability of Tata Motors is more compared to ONGC.

CORRELATION ANALYSIS

[pic 3]

The regression equation is:

Y = 0.3373X – 0.0001

The equation shows that returns of both the stocks are positively correlated over last one year. The correlation is 0.3373, which is not a strong correlation though.

CONCLUSION

Tata Motors and ONGC stocks have been selected from different industries based on the market capitalization. Both are one of the biggest market capitalized companies of that sector. Their correlation and analysis suggests us a decent interpretation about the whole sector.

Here are our conclusions, that we draw from above analysis:

First, the correlation coefficient between the two companies suggests that if we add oil stock in automobile portfolio or do vice versa, it is not going to reduce our risk.

Secondly, although variability of Tata Motors stock is more, still value at risk for ONGC comes to be more. Also, even though risk is high in ONGC, still it’s mean returns are less that let’s us to assume, that in any case, Tata Motors is a better stock to invest in, both for risky as well as risk averse investor.

The Sharpe ratio of Tata Motors is more compared to ONGC, which further reiterates our idea that Tata Motors is better stock to invest into compared to ONGC.

...