The term "volatility" enjoys success in the analyzes and comments on the performance of the financial markets and therefore deserves some attention, so that the concept remains adequately "stable". Clearly the term was borrowed from physics, where it indicates the property of a liquid to pass into a vapor state, and it came to the Italian language as a translation of volatility from the vast Anglo-Saxon financial literature of the 60s and 70s. last century.
The potential investor of a sum of money usually has the choice between alternative investments, from each of which a certain profit is expected, let's say a certain "return", referring, as usual, the profit to the sum of 100 monetary units invested. But then, if he behaves rationally, he must contextually make his choice by also considering the second horn of the dilemma, the risk he can expect to run as a result of that investment. In fact, return and risk must be weighed together, as elements each placed on one of the pans of the scale so that this remains in balance.
The term "volatility" refers precisely to an indicator provided by the technical-statistical tools, the one most used to measure this risk. Both the expected return and the risk associated with it are variables seen in the future investment horizon of which there is no experience yet and, therefore, the risk too must cover that time horizon. But the “volatility” we will deal with here instead, it is a statistical measure of risk related to a past experience, the series of observed prices, and therefore qualifies as "historical".
This emphasis seems appropriate because there is a tendency to consider the riskiness of investing in the future as a characteristic permanently connected to that certain type of investment which is experienced because it was found and measured instead in the past. The placement of the securities subject to investment in different volatility ranges responds yes to a commonly confirmed observation; however it should not be stated so unconditionally, because different market situations can show significant changes in the reciprocal positioning of the risk ranges. The purpose of this note is to provide a precise idea of the concept of price volatility and the different levels of risk typically associated with the main categories of financial assets with public prices.
Volatility and variability
We are considering variable quantities especially over time. Their variability in geographical space is now a very limited fact, given the speed of communications which contributes to the almost instantaneous leveling of prices in the various financial markets. The "volatility of prices" as a measure of investment risk should be seen in the broader concept of statistical "variability". Precisely, the best-known aspect is that of "dispersion", ie the difference between individual data and a central "pole". This concept, originally developed in other fields, has been very useful in the more recent context of the analysis of the prices of financial assets that concern us here. It is known that these prices are in fact typically variable and therefore require suitable methods of measuring this characteristic. The term volatility refers to a specific form of price variability, that of "returns", calculated as relative differences - in practice, percentages - between the prices of a security in successive periods. More precisely, the term volatility refers to the statistical measure of the variability of returns calculated as the standard deviation of the same. Volatility, generally expressed as a percentage, is therefore calculated on pure numbers and is therefore indifferent both to the unit of measure of the prices (euros, dollars...), and to their scale (small prices, large prices)
This makes this measure particularly useful for any type of financial investment that you want to compare with others. It is not difficult to calculate volatility according to current financial analysis practice. The procedure is this:
– for each day the daily return is calculated, usually on the closing prices, determining the percentage variation between one day and the next; in practice, the price is divided by the previous one, 1 is removed and the result is multiplied by 100;
– for yield data over a certain period, for example 15 or 45 days, the standard deviation is calculated, and this can be repeated for each day, scrolling forward. Thus we have the daily volatility, expressed as a percentage and, if the latest figure is today's, volatility is also qualified with the adjective "current". At this point, a useful measure of daily volatility is already available. Here is an example in the chart relating to the Generali stock for the days of January 2010.
Note that volatility is higher when calculated on end-of-day data, the reference prices, than the official average price data: in fact in the latter case the average of the day's prices has the effect of appreciably flattening the differences between one day and the next. However, the practice then "normalizes" this measurement by bringing it back to the annual equivalence by means of a suitable coefficient. This coefficient, which is calculated as the square root of the ratio 252/1, assuming that 252 are precisely the trading days of the year, in practice is equal to 16 4 . Thus, if a security has a current historical volatility (the latest figure is today's) equal to 1%, it is declared that its one-year volatility is precisely equal to 16%. In the case of the transformation applied to the data of the previous graph, it can be seen that the profile of the graph remains identical and that the only effect is to alter the vertical scale of representation.
Obviously, for the calculation of the yield it would make sense to assume periods that may be different from the day, such as the week or the month, but this is not the current practice.
Different financial assets compared by degree of volatility
It is important to show how some categories of financial assets differ more or less in terms of price volatility. We will do this with the aid of some graphs relating both to the prices of some individual stocks, and to synthetic index numbers, those representing the stock market, stock and bond lists. Also considered are two currencies and some important goods or commodities with an international market. The graphic 1 again for the period December 2009-January 2010, it shows the trend of the basic data, prices or indices, recorded daily on the Italian Stock Exchange or on other official markets. The calculation of the volatility as a standard deviation of 21 days will naturally reduce the period of actual availability of the results by the same amount.
to the evidence, the movement of securities and stock indexes is decidedly more marked than that of bonds; however the different level of values prevents a clear vision of the phenomenon. Therefore, it is better to look at the yields.
Il next graph shows the trend of the daily percentage returns, which are obtained for each series from the previous ones. In particular, we highlight i greater movements of the Fiat share compared to those of the Generali share. Furthermore, among the indices shown, those calculated continuously show higher returns with the closing data, more or less, than those of the only index for the session, the historic Mib, which is notoriously calculated only once a day based on official average prices. But the comparisons stand out better by calculating, for each series, its volatility. The results are highlighted by the following graphs.
We have divided the various financial activities into two groups, for greater clarity.
For the first group, the greatest volatility is still recorded for the equity sector: in order, Fiat ref. price, Fiat PMU, Generali ref. price, Generali PMU, FTSE It. All Share and historic Mib.
For the second group, the price of oil and that of gold shine for their volatility. The Nikkei Tokyo, Paris CAC, Frankfurt DAX and London FTSE 100 indices follow.. The continuous closing index of the Borsa Italiana in this period appears the least volatile. Of the two currencies, the Yen is significantly more volatile than the US dollar. Obviously, the bond sector is characterized by the lowest volatility, which here is represented solely by the MTS index.
This results from an average of the price indices of a large number of bond securities; therefore, obviously, the volatility of this index is an average of the volatilities of the individual stocks. Note then that MTS not only detects prices, but also the accumulation of interest, being a capitalization index, and which, therefore, necessarily shows a slight increasing underlying trend, which is reflected in generally positive returns. This "historical" volatility of bonds obviously depends on the actual price trend and should not be confused with the "ex ante" volatility, which is also calculable. In fact, for the specific case of bonds, an ex ante volatility is defined by precise mathematical formulas, a close relative of the "financial duration of the bond" (duration) and its actual ex ante return; financial measures, all of these, in which various certain elements converge, such as duration, coupon flows and market rates. Volatility is also variable From what has just been highlighted, it appears that the volatility of each security or even of each investment class can change depending on certain factors, which can be summarized in the shift of market interest from one investment class to another.
Typical is the market reaction to the changed expectations of interest rate levels that will prevail in the near future as a result of changes in the monetary and credit policies implemented by the central banks. These changes are capable of weighing more or less on the various categories of securities, both equity and bond ones. Here is a comparison of the volatility of the types of investments already considered in two different periods, November 2007 and January 2010. In the following bar chart we can see that volatility generally decreased more or less for all stocks, but instead increased for the two currencies and for gold and for crude oil; in the meantime, interest rates have undergone strong variations: the official ECB rate has dropped from 4% to 1%.
The volatility indicator
Volatility is a tool widely used as an indicator in technical analysis of the stock market, useful for signaling particular situations of market uncertainty. In particular, the volatility indicator finds estimators to identify the turning points of the market, from upwards to downwards or vice versa, on the basis of the assumption that, near the turning points, volatility also takes on particular values. But it is not an axiom.
For example, according to Gabriele Belleli "there is no fixed rule to state that the maximum peaks of volatility correspond to the tops (maximums) of the market and the minimum peaks of the indicator correspond to a bottom (minimum) of the prices." After having also excluded the validity of the statement "that an increase in volatility, continued for a short period of time, always signals a minimum or that a low level of the indicator identifies a maximum", the same Author then states that the indication more reliable remains, in fact, that the peaks of the indicator, maximums or minimums, serve to signal points of possible market reversal.
Here it should be added that the "historic volatility" mentioned above is contrasted with an "implicit volatility". Specifically for the case of shares, it is a measure that can be obtained using mathematical-statistical formulas from the prices of derivative contracts, in particular the "options", of which the share constitutes the underlying security. Naturally, just as from stock prices it is possible to pass to the calculation of compound index numbers of stock prices, so by means of measurements of the implied volatility calculated on a group of stocks on which option contracts take place it is possible to compose synthetic indexes of the implied price volatility of the shares. These indicators obviously have greater validity – compared to the corresponding historical volatility data – in the sense of signaling the forecast attitude of the market, at a precise moment incorporated in the price of those contracts. However, looking to the future must not deceive: it remains clear that these are still current judgments on future trends.
