**Volatility definition – What is volatility?**

**In math, volatility is a measure of how much the numbers are spread out around the mean. Volatility in Layman’s definition is how fast a certain financial asset’s price moves around its average price or mean.** You can think of it like this, for each time the price of a financial asset moves, you can imagine that the asset will also have its highest and lowest potential price to reach based on statistical values.

The common practice in the industry is that it is used as a risk indicator by analysts because they use them to determine the possibilities of the price of the financial asset to deviate from its average price. Although there are a lot of other ways to compute volatility, the standard deviation is the most commonly used. Suppose that we have two securities, A and B, each having a standard deviation of 2.5 and 3.0, respectively. If we compare the standard deviation of both securities, we can say that security B is riskier than A because it has a higher chance to deviate from its mean price. Therefore, the higher the volatility, the more risky that security is.

**Difference between risk and volatility**

**Volatility is not a risk. In finance, the risk is defined as the chance that a projected outcome will differ from an expected outcome. Sometimes volatility market can give the opportunity to the trader to make a profit and can be a positive influence. **

However, conventionally financial wisdom indicates that one of the major risks of investing money is that the market is very volatile. However, there are some investors, especially value investors do not believe in this conventional logic. These investors think that if the capital is permanently lost, it is the biggest risk. However, both these perspectives are not fully correct.

Investment performance is often judged assuming that the risk involved is linked to how volatile the portfolio is. Some of the metrics for measuring the returns like information ratio, tracking error, and Sharpe ratio compare the return with the volatility of the portfolio, measured with reference to the benchmark or absolutely. Since the investors are usually only thinking in the short term about the returns on their investment, they will usually avoid volatility under all conditions. These conventional investors will be very happy with a return rate which is below the average if there is very little volatility.

**In trading, volatility risk meaning has a different explanation. When traders analyze risks, volatility risk represents the type of risks that can decrease the profitability of the trader if unexpected high volatility occurs. Mitigation of volatility risk is that traders need to decrease the trading position size or stop trading or change stop loss and targets based on the Daily Average true range (include volatility to calculate stop loss or target).**

Let us see an example.

April 2018 is a good example where volatility is not a risk and an excellent opportunity. The euro weakness in April 2018 was brought about by the fact that the ECB kept the rates on hold and also refused to give a timeline for the tapering and ending of the QE. So from April and several next weeks and months, volatility increased every day, EURUSD went down more and more. Bad news for EUR, increase volatility, strong bearish trend were great opportunities for traders.

Now let us see, opposite example. In spring 2020, because COVID 19 forex and the stock market were volatile markets. Now volatility is not an opportunity for trading, it is a more unexpected event (like an earthquake) that hurt the economy, and consequences can not be measured, the ending is unknown.

**Risk and volatility measurement**

As mentioned earlier, the common measure for volatility is the standard deviation. There are other methods of determining volatility such as computing for the beta coefficient of the asset but it requires more data than computing for the standard deviation.

In computing for the volatility, we will need to determine the financial asset’s mean price; it can also be called the mean return because in order to compute for the mean we will have to compute for its average arithmetically or geometrically. However, in our example, we will show it arithmetically because it is more simple. In basic finance, it is also called as the expected return of the asset.

The formula for computing for the mean return:

Mean = (P1 + P2 + P3 + ….. + Pn) / n

where P = price and n = number of values used.

After we compute for the mean price of the asset, we can now compute its variance. Variance is the measurement of how the data is spread. It determines how far each price went when compared to its mean.

The formula for computing for the variance:

Variance = (mean – P1)2 + (mean – P2)2 + (mean – P3)2 + … + (mean – Pn)2

where Mean = average price, P = price, and n = number of values used.

The last step in computing for the standard deviation is simple, we square root the variance.

The formula for computing for the standard deviation:

Standard Deviation = (variance)1/2

We can also express the exponent as 1/2, it has the same meaning as rooting the value with a square.

Therefore, the complete formula in computing for the standard deviation is:

Standard Deviation = ((mean – P1)2 + (mean – P2)2 + (mean – P3)2 + … + (mean – Pn)2)1/2

where Mean = average price, P = price, and n = number of values used.

For a practical application, assume that we will analyze stock A. It’s 5 most recent closing prices are $10, $20, $30, $40, $50, respectively.

In computing for the mean, we will have a value of $30.

Mean = (10 + 20 + 30 + 40 + 50) / 5

Mean = 30

This means that the arithmetic average of the price of stock A for the past 5 trading days is $30.

Now, we need to compute for the variance which is getting the deviation first then squaring it. When the mean is subtracted to its price, it is called deviation. Below is the solution.

Variance = (30 – 10)2 + (30 – 20)2 + (30 – 30)2 + (30-40)2 + (30 – 50)2

Variance = (20)2 + (10)2 + (0)2 + (-10)2 + (-20)2

Variance = 1000

Since we got the variance, we can get its squared root to determine the standard deviation of the stock.

Standard Deviation = (1000)1/2

Standard Deviation = $31.62

The standard deviation of stock A is $31.62. This means that the future price of the stock may deviate by 31.62 upwards or downwards. This helps analysts and traders in making trading decisions through risk management. Keep in mind, that this measure of risk is an absolute risk of the company and it is based on historical prices of the stock.

**Other Methods of Determining Volatility**

As mention earlier, one method of computing for the volatility of an asset is computing for its beta coefficient (?). Its difference from the standard deviation is that the beta is compared with the aggregate market or index. In the United States, we use the S&P 500 as a benchmark for future returns in the equities market. Therefore, if we were to compute for the beta of the stock, we will have to compare the performance of the stock to the S&P 500. The values of beta coefficients are usually expressed as a whole number with a decimal. For example, a beta of 1.35 means that for each 1% increase of the S&P 500 index, the stock moves 1.35 times that S&P. Therefore, we can say that a higher beta is riskier because it will be labeled as more unpredictable or its deviation from the market is huge.

Volatility is also an important variable in valuing option contracts. Since these derivatives derive their prices from a specific underlying asset, in order to value the option price, incorporating volatility is important. Moreover, since the future is hard to predict, a lot of analysts and traders rely on historical data to potentially have an idea of where the market might be in the future.

**Volatility and value investors**

Most value investors do not consider market volatility to be a risk. One of the most famous value investors Warren Buffett is quoted as claiming he would rather get 15% returns in the long term in lumps rather than 12% smoothly. Using this logic many of the value investors at present are not worried about volatile markets. Their risk management strategy involves focussing on preventing capital loss permanently. These investors believe that they are emotionally strong enough to tolerate any kind of fluctuation in the short term if their strategy is proper and they get the desired result in the long term.

**Investor profile linked to risk of volatility**

The risk caused due to volatility is not fixed, it depends to a large extent on the profile of the investor. Some of the different investor profiles and the effect of volatility on the results from the investment are discussed

**Long term investors with high-risk tolerance:** These investors are looking at returns over a longer time period like ten years since they wish to save money for their retirement or college expenses for children. Due to their behavior, these investors are not affected by volatility. These will persevere with their plan for investment, though the market is volatile. These investors do not consider volatility as a risk. They are more concerned about the annual returns on their investment in the long term, and ensure that there no loss to their capital permanently during this period

**Short term investors** will typically plan to use a major part of their investment portfolio within three years of investing. For these investors the market volatility is a major risk, since withdrawing the capital at the end of the period, will be affected by the results in the short-term. These investors are closely monitoring the volatility, since it will force them to sell their investment at prices that are low, resulting in losses.

**Long term investors with low-risk tolerance.** Due to their personal behavior, these investors are affected by market volatility. Though these investors have long term goals, they may take investment decisions that act against these goals because of market news, volatility in prices, or other short term conditions. These investors do not behave rationally when they hear negative news, and so they sell at lower prices, though this is not required. This investor category should consider the risk due to volatility since having an investment that is more volatile will result in low financial returns.

**Long term investors who spend a small amount of their portfolio consistently:** These investors include individuals who use a small part of their investment portfolio for their expenses every year or endowments, charities, which spend 5% of the investment portfolio to cover their operational expenses annually. Though volatility matters to some extent, it is not the main risk involved.

Historical Volatility and Implied Volatility for determining option prices

Historical volatility takes the data of the underlying asset historically. This type of volatility takes into effect the historical performance of the underlying asset and measures the fluctuations that happened during the data series. In practice, historical volatility is not used in forecasting the prices of options contracts because it reflects past values. However, the use of historical volatility can provide traders valuable insight into how the underlying security is performing presently when compared to the past.

Implied volatility, on the other hand, incorporates the expectations of the analyst in order to determine the potential price of the underlying asset in the future. However, it cannot be also regarded as a “forecast” because volatility looks at the probability of how much will price deviate from its average. But in the case of implied volatility, it is looking forward to the future and does not incorporate historical values in computing it.

**Conclusion**

Hence while choosing the investment, it is important to understand the client profile well to determine what portfolio volatility will be most suitable. It is always better to advise the client to invest for longer terms and tolerate any fluctuate in the value of the portfolio. This will help the investment manager to maximize the long-term returns, without bothering about volatility, so that the client will have a major advantage over other investors.

Volatility is not a risk but sometimes it can be, and then we talk about risk volatility. It looks complicated but it is not. Let we see what Warren Buffett said about volatility and risk:

“Volatility is not a measure of risk. And the problem is that the people who have written and taught about volatility do not know how to measure — or, I mean, taught about risk — do not know how to measure risk. And the nice about the beta, which is a measure of volatility, is that it’s nice and mathematical and wrong in terms of measuring risk. It’s a measure of volatility, but past volatility does not determine the risk of investing.”

*Warren Buffett*