# What is volatility and how is it interpreted?

DATE

09.27.2022

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We find a lot of information on social media about what volatility is, but often by trying to summarise it too much, it is not explained enough to be used in making investment decisions. This is especially true for an investor who wants to advance their knowledge without having to delve into terms too complex for their purpose.

## Volatility and uncertainty

Historical volatility is the most popular statistic for estimating the market risk of a financial asset (fluctuations in that asset in the market). While there are other more appropriate and understandable statistics, historical volatility is the most familiar indicator for an individual investor.

In reality, it is a statistic that measures uncertainty and is used as an approximation to the historical market risk of a financial asset.

## How volatility is calculated

Historical volatility is calculated based on the historical behaviour of an asset by measuring the intensity of the price changes of an asset between two determined dates for a given time. It is usually expressed in annual terms. The information it gives us is the dispersion of historical returns around the average return of a financial asset. It is also applied for a portfolio or set of assets or a stock market index.

In order to calculate it, certain assumptions are made about market behaviour such as, for example, that the returns of an asset behave according to a normal distribution (with the symmetry in behaviour that assumes normality in the distribution of returns).

Therefore, it informs us of both positive and negative deviations around the historical average profitability by assuming symmetry in the dispersion of the results. It is for this reason that it is an indicator of uncertainty as it indicates the degree of variation both positive and negative. From the point of view of risk, we would only be interested in the negative side, but in this article we will give it a practical meaning to be applied in risk decision making.

## How to interpret volatility

Like many of the statistics we use, historical analysis is used to try to characterise an asset, and we also use it to make investment decisions in the future.

In the case of volatility it is used to measure the degree of uncertainty. With the information that an individual investor normally has at his disposal, which is the volatility data expressed in a percentage, it serves only to identify and rank assets according to their uncertainty. The higher the volatility, the greater the uncertainty.

But volatility can provide us with more information to help us understand the behaviour of an asset for investment decision making.

First of all, we should know that volatility informs us of the dispersion of returns around the average return in a year, taking into account 68% of the possible cases. This means that, if we are interested in using volatility as a measure of risk, there are 32% of cases that are not covered by the volatility statistic (16% for positive cases and 16% for negative cases).

If we know the historical average return on a financial asset, volatility can be translated and can help us better understand the uncertainty implicit in this asset.

For example, if we are informed that the volatility of a share is 20%, and its historical average return is 8%, we can say that in 68% of the cases observed, returns on this asset have been between -12% (8% – 20%) and +28% (8% + 20%).

For investment decision making purposes, if we assume that the factors that have caused historical fluctuations in an asset are going to be replicated in the future, we could say that there is a 68% chance that the return on that asset in the future will be between -12% and 28%.

## Conclusion

For an investor with a long-term investment time horizon, taking into account that only 68% of possible cases are considered and that in situations of stress in the markets downturns can occur outside this range of probabilities, volatility can help us understand uncertainty:

1. Factors that have caused market fluctuations in the past under normal market conditions tend to be reproduced in the future.
2. Assuming that returns in financial markets behave like a normal distribution, although not entirely true, is a simplification that does not lead to relevant changes for long-term investment decision-making.

It is important to know that there are risk indicators that are more appropriate for measuring market risk and, in any case, are complementary to characterising the market risk of a financial asset, which we will address in other articles. Some of them are:

• Expected loss in monetary terms (Value at Risk or VaR). That allows us to estimate statistically, as we do for the calculation of volatility, but in this case analysing only the possible losses and in monetary terms. VaR allows us to estimate expected losses with probability levels for risk measurement that are more demanding than volatility.
• The maximum historical drawdown (MDD)  of an asset in a given analysis period.
• The number of times an asset dropped below a given threshold for a given analysis period.
• Time takes an asset to recover losses.

Finally, it should be noted that investment decisions on assets or financial products cannot be based solely on expected returns.

Risk is the basis for investment decision making and, in any case, if we want to make decisions based on expected returns, it would be necessary to have the profitability information in relation to the risk you are willing to take. This is where all risk-adjusted return ratios come in. For example the ratios of Sharpe, Sortino, Treynor, Information…

José Luís Álvarez – CEO HollyMontt

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