Value–at–Risk (VaR) Methodologies: Measuring the financial risk of an FMCG stock portfolio (HUL, Nestle, Dabur, Godrej & ITC)

Risk and Return are the main parameters of all investment processes. Many investors desire to know how much money they can lose for example in a day, ten days or over a year. One of the key concepts of risk measurements in the financial sector and industrial sector is the probability-based risk measurement method known as Value-at-Risk or VaR. It is a widely used measure of financial risk, which provides a way of quantifying and managing the risk of a portfolio. The results produced by a VaR model are simple for all levels and that is why it has been adopted so rapidly.

Present here three methods for computing the VaR of 5 major FMCG stocks (HUL, Nestle, Dabur, Godrej & ITC) for the last 5 years.

1. Variance/ Covariance simulation
2. Historical simulation
3. Monte Carlo simulation

1. Variance/Covariance (Var-Covar) Simulation Method:

Variance– covariance approach (also known as delta normal) depends on correlation and covariance matrices to estimate the variance and standard deviation of a risky asset. This method assumes that stock returns are normally distributed. In other words, it requires that we estimate only two factors—an expected (or average) return and a standard deviation

Analysis/ Findings:

• The value at risk (VaR) at a 95% confidence level is -176.93, implying that 95 times out of 100, the one-day loss of this portfolio will be within Rs. 176.93 and would not surpass that. Whereas, the Risk(VaR) at a 99% confidence level is -250.23, which means that 99 times out of 100, the one-day loss of this portfolio will be within Rs. 250.23 and would not surpass that.
• As per the backtesting, out of?370 testing data samples, 86 data points are exceptions for the 95 % confidence level bracket, while 47 data points are exceptions for the 99% confidence level bracket. For a 95 % confidence level, the ideal no. of exceptions?is?18.85, and for a 99%?confidence level, it was 3.7. Thus, Var-Covar simulation is not coming as a very good model, as calculated & ideal values are too far from each other.?
• The calculated Z-Values at 95 % confidence level, i.e. 0.03, fall between the critical Z-Values of -1.64 and 1.6. In contrast, for?a 99%?confidence level, it is not lying between the critical Z-Values. As a result, we can deduce that the Var-Covar model is suited for a confidence level?of 95%, but should be avoided for 99%.

2. Historical Simulation Method:

The historical simulation method provides a straightforward implementation of full valuation. The key assumption in historical simulation is that the set of possible future scenarios is fully represented by what happened over a specific historical window. This methodology involves collecting the set of risk factor changes over a historical window: for example, daily changes over the last five years. The set of scenarios thus obtained is assumed to be a good representation of all possibilities that could happen between today, tomorrow or in future. The instruments in the portfolio are then repeatedly re-valued against each of the scenarios.

Analysis/ Findings:

• The value at risk (VaR) at a 95% confidence level is -269, implying that 95 times out of 100, the one-day loss of this portfolio will be within Rs. 269 and would not surpass that. Whereas, the Risk(VaR) at a 99% confidence level is -591, which means that 99 times out of 100, the one-day loss will be within Rs. 591 and would not surpass that.
• As per the backtesting, out of?370 testing data samples, 42 data points are exceptions for the 95 % confidence level bracket, while 02 data points are exceptions for the 99% confidence level bracket. For a 95 % confidence level, the ideal no. of exceptions?is?18.85, and for a 99%?confidence level, it was 3.7. Thus, Historical simulation is not coming as a very good model for a 95% confidence level, as calculated & ideal values are too far from each other in that case.
• The calculated Z-Values at 95 % confidence level, i.e. 1.34, fall between the critical Z-Values of -1.64 and 1.6. Added, for?99%?confidence level, it is also lying between the critical Z-Values i.e 2.32 > -0.46 > -2.32. As a result, we can deduce that the Historical Simulation model can be suited for both the confidence level?of 95% and 99%.

3. Monte Carlo Simulation Method:

Monte Carlo simulation techniques are by far the most flexible and powerful as it involves developing a model for future stock price returns and running multiple hypothetical trials through the model. Here, through this simulation model, we generated trials and probabilistic outcomes on the HUL, Nestle, Dabur, Godrej and ITC stock data for the last 5 years based on its historical trading pattern.

Analysis/ Findings:

• The value at risk (VaR) at a 95% confidence level is -767.91, implying that 95 times out of 100, the one-day loss of this portfolio will be within Rs. 767.91 and would not surpass that. Whereas, the Risk(VaR) at a 99% confidence level is -592.85, which means that 99 times out of 100, the one-day loss of this portfolio will be within Rs. 592.85 and would not surpass that.
• As per the backtesting, out of?370 testing data samples, 19 data points are exceptions for the 95 % confidence level bracket, while 04 data points are exceptions for the 99% confidence level bracket. For a 95 % confidence level, the ideal no. of exceptions?is?18.5, and for a 99%?confidence level, it was 3.7. As a result, it's easy to deduce that the number of exceptions is nearly equal to what's calculated as ideal, and therefore the Monte Carlo simulation model is correct.
• The calculated Z-Values at 95 % confidence level, i.e. 0.02, fall between the critical Z-Values of -1.64 and 1.6. Added, for?99%?confidence level, it is also lying between the critical Z-Values i.e 2.32 > -0.08 > -2.32. As a result, we can deduce that the Monte Carlo Simulation model is best suited for both the confidence level?of 95% and 99%.
• Also, 20 iterations were examined from a verification standpoint, demonstrating that with any random values of Simulated VaR at 95%?and 99%?confidence levels, the number of exceptions does not change in any case, which is undoubtedly a good thing for any investment. Furthermore, the calculated Z-Score values for each of the 20 iterations were 0.03@95% confidence and 0.08@99% confidence, respectively, and all of them fall within the critical Z-Score Values range. In light of these findings, it can be concluded that the Monte Carlo Simulation model is best suited for both 95%?and 99%?confidence levels.

Thus, we can deduce that the Monte Carlo simulation technique is by far the most flexible and powerful, since they are able to take into account all non-linearities of the portfolio value with respect to its underlying risk factor and incorporate all desirable distributional properties, such as fat tails and time-varying volatilities.