# Volatility

Volatility is the relative rate at which the price of a security moves up and down. The more the price moves up and down, the more volatility it is considered to have.

### Eric asks:

Eric, Jill and John decided to have a picnicon a green, flower-filled meadow.

#### Prof. Jill, the Investor

#### John, the Trader

#### Eric, the Beginner

#### John, the Trader

#### Prof. Jill, the Investor

#### John, the Trader

#### Eric, the Beginner

#### John, the Trader

#### Eric, the Beginner

#### Prof. Jill, the Investor

#### John, the Trader

After a couple of pancakes…

#### Prof. Jill, the Investor

#### Eric, the Beginner

#### John, the Trader

#### Eric, the Beginner

#### John, the Trader

#### Eric, the Beginner

#### Prof. Jill, the Investor

#### Eric, the Beginner

**Definition**

Volatility is a very important measure in evaluating the risk of an investment. It shows how the prices fluctuate in a given period of time. The greater the volatility, the wider the range of prices. High volatility means that the price of the asset can change dramatically over a short time period of time in either direction. A lower volatility means the asset's value does not fluctuate as dramatically.Instead its value tends to change at a steady pace.

**Volatility of Gold and Silver**

First of all, notable fluctuations of the price of a security make long-term investors more nervous. They cannot be sure if the rate of return comes back to its average.

Please, look at the chart below.

The chart presents two hypothetical gold stocks: the “First Gold Stock” and the “Second Gold Stock.”.Which is more volatile? The answer is quite simple – the “First Gold Stock”. Why? Its price fluctuates more than the price of the “Second Gold Stock”. If you try to predict the prices of these two stocks you will conclude that it is easier to predict the price of the “Second Gold Stock” as it does not diverge significantly from the $30 level. The “First Gold Stock” also fluctuates around this level but its moves are far more rapid and therefore it is considerably more difficult to anticipate future price levels of this stock.

Volatility is not just a theoretical concept. Please, take a look at the charts (charts courtesy of http://stockcharts.com) below.

The upper chart presents gold’s price path during a given period while the lower chart presents silver’s price path during the same period. You can easily notice that the two metals have different volatility. If you calculate (more on that in the following part of this page) the relative volatility of gold in this period, it will turn out to be smaller than the corresponding relative volatility of silver. You can spot that the price moves in the upper chart are not as dramatic as those in the lower chart.

**Volatility's Implications for Gold & Silver Investors **

First of all, notable fluctuations of the price of a security make long-term investors more nervous. They cannot be sure if the rate of return comes back to its average.

Secondly, **gold price volatility** and **silver price volatility** presents opportunities for traders to buy assets cheaply and sell them when they are overpriced. In the above example, silver gives you a greater chance to earn more when compared to gold (silver’s price changes more dramatically), but investing in the white metal is more risky. (In the modern portfolio theory volatility = risk, however we believe that there are some exceptions.)

**Volatility and Forecasts**

Let’s use a hypothetical example to explain the concept of volatility. Assume that we have two weather forecasts for tomorrow.The first forecast suggests an average temperature of 68 °F with a volatility of 3.6 °F, and the second implies the same average temperature of 68 °F, however with a volatility of 10 °F.

Which forecast is better for us?

The answer is clear: the forecast with lower volatility. It provides us with a hint that the temperature changes would not be as huge as in case of the second forecast, and allows us to be better prepared.

If we consider the second forecast, we are not so sure about the weather. The temperature in the morning might be 68 °F and then it might drop to 58 °F, so we are not quite sure if to pick a jacket or just a sweater.

To illustrate the main idea more clearly let us show you some real life example.

Assume that we have been forecasting the weather again. We used satellite photos and measurements from weather research stations to make our forecast. We predicted that the next day the temperature would be at the level of 68 °F (20 °C) during the day. These had been our expectations but in reality the temperature next day was 65 °F at 8 a.m. 72 °F at midday and 67 °F at 6 p.m. These changes in the temperature during the day are used to calculate the volatility of the temperature. We can predict the average or the most probable temperature, but our forecasts rarely hit their precise targets – it is more likely that the actual temperature will be in the range based on the forecast +/- the implied volatility.

**Volatility – Examples**

Consider a security with an expected rate of return of 10% and with an annual volatility of 5%.

This means that the average return is 10%, and using the volatility we can calculate the range of possible return. Thanks to statistical measures (and the assumption that the data is normally distributed), we may estimate our range with 95% confidence at 0% to 20%. It means that 95 times out of 100 our rate of return will be a value between 0% and 20%. This helps us to estimate whether it makes sense to invest in this particular security.

Let’s now consider a security with the same rate of return but with a volatility of 10%.

The estimated range is now at -10% to 30%, with 95% confidence.

We can clearly see that **higher volatility gives us a wider range**, which means that we can possibly earn or lose more – so in a way more volatility means more risk.

Below you will find a chart showing how the annual **volatility of the rate of return of gold** has been changing over the years.

**Volatility and Options**

Volatility is extremely important if you are planning to trade in options. All other things being equal, **an option’s value tends to rise along with the volatility of the underlying asset **and decline when this volatility decreases. There is a special coefficient called Vega (sometimes referred to as Kappa or Tau), which tells you how much (in dollar terms) the price of a given option will rise, when the implied volatility of the underlying security rises by one percentage point, and nothing else (interest rate, time, price of the underlying security) changes. Although at first glance this might seem complicated, we will show you that it is really intuitive.

Remember our chart with the “First Gold Stock” and the “Second Gold Stock”? Take a look at it once again. The last price for both stocks is $30, and this is also the average value of each of the stocks in the analyzed time frame.

Which stock is more likely to surpass the level of $35? Of course, the “First Gold Stock”. Since its daily trading range is so wide, it would be surprising not to see this stock occasionally getting past this level. The “Second Gold Stock”, on the other hand, would most likely need to rise consecutively for a few days before it would have a chance to get beyond $35. As you see, the probability for the stock price to go above a certain level is higher if this stock is highly volatile. Now imagine that the$35 level represents the strike price of a particular option. If we’re not taking time into, the call option’s value is the difference between the current price of the underlying security and the strike price. If the “First Gold Stock” has a greater chance of going above the strike price than the “Second Gold Stock, all other things being equal, than options on the “First Gold Stock” should be worth more than options on the “Second Gold Stock”.

To sum up, options on stocks that are less volatile are cheaper than options on more volatile stocks. If a particular company’s shares suddenly become more volatile, then options on this company will become more expensive. And, if these shares calm down and trade in a close range, then the value of options will decrease (all other things being equal).

**Drawbacks of Volatility**

Though volatility is very useful and important in evaluating the risk, it has one significant weakness. Namely, it does not take into consideration the way the price moves. High volatility can occur both when prices are flying high and when they are taking a nosedive.From an investor’s point of view, the first situation may be desirable,while the latter one in most cases is not. That means that analyzing volatility should be supported by analysis of other risks in the market e.g. the fundamental factors driving it.

**Calculating Volatility**

To explain how the volatility is calculated we have to provide you with a simple formal definition.

In the financial markets, volatility refers to the standard deviation of a financial instrument and is normally expressed in annualized terms, and it may either be an absolute number ($5) or a percentage (5%).

The **standard deviation** shows how much variation or dispersion there is from the average (mean or expected/budgeted value). A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.

Let’s get back to our temperature example.

Our average was 68 °F. The standard deviation is calculated as follows.

First, we compute the difference between every single observation and the average. In our case the results are: (65 - 68) = - 3, (72 - 68) = 4 and (67 - 68) = - 1.

We square our results: (- 3) ^ 2 = 9, 4 ^ 2 = 16 and (- 1) ^ 2 = 1.

We add our squared results up: 9 + 16 + 1 = 26.

Now, we divide our sum by the number of our observations less one which in our case is 2 (3 - 1 = 2). Our result after this operation is 13 (26 / 2 = 13).

Let’s take a square root of our result: sqrt(13) = 3.6.

Our standard deviation is 3.6 °F.

We hope you enjoyed reading the above definition. If you'd like to **learn more about gold and silver and how to profit from their volatility**, we invite you to sign up for our gold newsletter. It's free and if you don't like it, you can easily unsubscribe. Sign up today.