How To Calculate Volatility
Question
A low level volatility means a stock will stay fairly ___________ and we can be pretty sure of the type of return we would get.
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Hi, my name is Grant Hobson. I work as a finance analyst and today, I'm going to talk you through some business math, calculations and ratios. How to calculate volatility. Volatility is used to assess how much variance there is in a data point or a piece of data around a mean. So in terms like investment, we use that to determine the risk element there is in investment. So if we've got a highly volatile say, stock, which is really vastly dispersed over a period of time around its mean, it shows that it could fluctuate rapidly, so we might get high gains, but alternatively we could have high losses. Whereas if it's low level volatility, that means that it stays fairly stable, so we can be pretty sure of what type of return we're going to get. And so there's smaller risk involved in that. In terms of manual calculation for volatility, we'll run through this now in an example. So for the calculation, there are three steps that we should follow. So first, we need to calculate the mean. The mean being the average of the data set. Then calculate the variance to this mean. And we're going to take the square of this variance from the mean. And then at the end, for step three, is to take the square root of the total variances, divided by the number of months. So, for the example, we're going to use the price of petrol to fill up your car over a period of six months. So, in this example, we'll start off in month one, fifty pounds, month two at forty-eight pounds. Month three, forty-seven pounds, month four, forty-nine. Month five, fifty-three and month six is fifty-seven. So basically, what we're trying to show here is the fluctuations in the price it costs us to fill up. And you might want to start at a general investment place. You see the risk of this sample investment from a personal perspective, it is the price to fill up your car. You might be thinking, well, prices are quite volatile, getting more expensive, it's a low price. So you buy a bit of fuel to reduce the impact of price increases. So step one is calculating the mean. So basically, to calculate the mean you need to take the sum of these six pieces of data, and divide them by the total number of data. So we got six pieces of data, so it's the sum of this, and divided by the six pieces of data gives you the mean. So that's going to be consistent for each cell. Then you calculate the variance to the mean. Which is quite simple, take your amount from there over, so we do the price, plus the mean, and just follow that down. And then we want to square this. So we square nine point-six-seven. So we simply do that, to the power of two, gives us point-four-four, and again, we just copy that down for the rest of the data set. Then we need to complete the final step of the data, which is basically, we're summing it all up. And again, we then divide it by the number of months. It's going to be eleven point-five-six. So, it equals the sum of your squared variances, divided by the number of data sets which is six, its eleven point-five-six. And then the final bit in the calculation wants you to take the square roots of these variances. So you can insert the square root formula, and that gives you a square root of three point-four. Alternatively, you might not be on Excel, so you can get the square root function on your scientific calculator to calculate that. Then we can say that the volatility of that set of data is three point-four. So, just as a quick example, I'm just going to change some of the prices here, just to show if they are more volatile, how that gets reflected. So we're going to start from the same base, but then we're going to say that, we actually got a bigger decline, an even bigger decline. And then because there was a problem with the supply, for example, of oil, some sort of conflict, it was an instant big hike in the price, so it went up to fifty-three, up to fifty-eight. And then it started getting really e