Measure and Manage Risk of your Equity Portfolio: Value-at-Risk (VaR) Approach

Article by Santosh Adhikari

There is one golden investment rule that you should always keep in mind: never invest money that you can’t afford to lose. Like a drunk driver who’s begun to believe the speed limit no longer applies until the inevitable smash-up. Similar provisions apply to the stock market so never violate it, otherwise be prepared something potentially catastrophic occurs like bankruptcy, the wipe-out of your lifetime savings, and ultimately mental illness, to name a few.

For any type of investment, of course, there will always be some risk involved. Therefore there is a common narrative that investment is a tradeoff between risk and return. It is true, but it’s only theoretical. And people tend to look at investment in the two-dimensional traditional sense.

In reality, investment is actually subjective to your own personal situation. What do I mean by that? Let’s just look at two people in very different financial situations and looking at the same financial risks. Let’s say there is an equity investment opportunity of Rs 5 lakh and you can make on the upside Rs 25k in a month so that you can make 20% on return. Think about it this way, a person that saves Rs 1 lakh per year is going to see that risk very differently to somebody who saves Rs 10 lakh per year. Imagine further that person that saves Rs 1 lakh per year took additional Rs 4 lakh personal loan to invest in the equity and market moves against your position and for a prolonged period. To invest with clarity, risk IQ is really important.

In recent years in Nepal, the interest in equity investment is growing. It can be a good investment opportunity in the current market so long as detailed research is undertaken. But it is also true that naive investors are getting dangerously caught up in a speculative bubble. Everyone is talking about the stock market and it had become trendy to invest in the share market, encouraging even more naive investors to concentrate their personal savings in the stock market- and leaving them dangerously exposed to risk.

Therefore, the objective of this article is to show you how to measure and manage the risk of your investment portfolio, particularly Equity Portfolio using the Value-at-Risk(VaR) technique. Of course, sigma (s) and beta (b) of the portfolio do tell about risk. But the main problem with sigma and beta, however, is that it does not care about the direction of an investment’s movement: stock can be volatile. For investors, the risk is about the odds of losing money, VaR answers the question, “What is my worst-case scenario?”.

Let’s get specific. VaR is a statistical technique to estimate how much an investment might lose over a given period of time and at a pre-defined confidence level. For example, if a portfolio of stocks has a 95% 1-month Value-at-Risk (VaR) is Rs 1 lakh. This means that there is a 95% probability that over the next months, the portfolio will not lose more than Rs 1 lakh. Let me put it another way, there is a 5% chance that the portfolio losses will be Rs 1 lakh or more. 

For demonstration purposes, six companies of different sectors of Nepal are covered. Note that the chosen company and amount of investment in the analysis were selected randomly. The data were retrieved from the Nepal Stock Exchange (NEPSE) from the period of 01-05-2020 to 27-05-2021 that we consider reliable. The dataset is analyzed using Python specialized libraries (Pandas, Numpy, and Matplotlib).

More details are given in the table below:

Historical VaR

As an example, here are the steps needed to calculate the VaR using Historical Simulation. Historical simulation base your result on the past performance of your portfolio and make the assumption that the past is the good indication of the future.

Step 1: Calculate the returns ( or price changes) of all the assets in the portfolio between each time interval.

The daily return is calculated as today’s price, minus yesterday’s price, all divided by yesterday’s price.

Step 2: Sort your results of the portfolio-simulated P&L from the lowest to the highest value.

After applying these price changes to these assets, we end up with 223 simulated values for the portfolio and thus P&Ls. Since historical VaR calculated the worst expected loss over a given horizon at a given confidence level under normal market conditions, we need to sort these 223 values from the lowest to the highest as VaR focuses on the tail of the distribution.

Step 3: Set the desired confidence level.

In statistics, every confidence interval has a percentage associated with it, called a confidence level. This percentage represents how confident you are that the results will capture the true population parameter. The choice of confidence level depends on your field of study or research, however, 95% is the most common confidence level being used.  Let us choose 95% for this demonstration.

Step 4: Pick the simulated value that corresponds to the desired confidence level.

The last step is to read the corresponding value in the series of the sorted simulated P&Ls of the portfolio at a 95% confidence level. In our case, there are 223 observations in total, and if we are interested in the 95th percentile. For example,  95th percentile = 223 x 0.05 = 11.5 (value between 11th and 12th observations). Therefore, the value that represents between 11th position and 12th position is -0.0239851.

Notice the red bars that compose the ‘left tail’ of the histogram. These are the lowest 5% of daily returns (since the returns are ordered from left to right, the worst are always the “left tail”). Because these are the worst 5% (1-95)% of all daily returns, we can say that 95% confidence that the worst daily loss will not exceed 2.3%. Let’s re-phrase the statistic into rupees terms:

As calculated above, with the portfolio standard deviation of 1.887% and an average return rate of 0.38%, the average expected return of the portfolio was usually between -1.505% and 2.267% for each day.

Note:  In order to calculate Parametric VaR, the returns from the portfolios should be normally distributed. Otherwise, the result makes no intuitive sense.

 To recap briefly, Let’s look again at our calculations using two different methods for the same portfolio.

For example, the share prices of Mega Bank and Lumbini Bikash Bank tend to move in the same direction. The reason for this is both are operated in the banking industry. Likewise, the stock prices of Asian Life Insurance and Everest Insurance tend to move in the same direction as well. However, there is a negative correlation between Mega Bank and Taragaon Regency Hotel, as such, share price moves in the opposite direction. I am not commenting further since the data speaks for itself.

Conclusion

When deciding how to invest in your portfolio, your first goal should always be to avoid major losses. To avoid major losses, remember the golden rule “Never invest money that you cannot afford to lose”. Keep in mind that as an investor, even if you have limited capital, you live in a time where there are many strategies and investment alternatives. One way to do this is to choose the path of diversification. What do I mean by that? Well, “Don’t put all your eggs in one basket”.

Own stocks from several different industries to protect yourself in the case of a market crash. Last but not the least, a smart investor always profits handsomely from the portfolio, say, by optimizing the portfolio. Optimizing a portfolio is selecting asset classes to which you wish to allocate resources and then you can decide to include the weight of each asset class in the portfolio.

Adhikari is a Risk Analyst, Alpha Analytics Operations, State Street Bank International GmbH. He can be contacted at santosh-adhikari@outlook.com.