Averages, spread and volatility

In simple terms

An average summarises a list of numbers with one number. A measure of spread says how far the numbers wander from that average. Investors need both: an average return tells you what an investment earned typically, and the spread tells you how bumpy the ride was.

Volatility is the investing word for spread. A volatile share's price swings a lot; a steady one moves little.

Mean and median

• The mean is what most people call the average: add the values and divide by how many there are.
• The median is the middle value when the list is put in order (or the mean of the two middle values if the count is even).

When a few values are extreme, the two can be very different.

Standard deviation

The standard deviation measures how far values typically sit from the mean. To calculate it for a list:

Volatility

When people say a share or fund is volatile, they usually mean the standard deviation of its returns is high, often measured on daily or monthly returns and scaled to a yearly figure. Higher volatility means a wider range of likely outcomes in any period, including bigger falls.

Volatility is useful, but it is not the whole of risk:

• It treats rises and falls alike, while most investors care far more about falls.
• It says nothing about permanent loss, such as a company going bankrupt.
• Real markets produce extreme days and years more often than a simple bell-shaped pattern of outcomes would suggest, so the worst outcomes can be worse than volatility implies.

Why swings reduce compound returns

Investments A and B have the same mean return, 8% a year. But money does not grow by the mean; it grows by multiplying each year's return in turn, as the compounding and CAGR lesson showed.

B ends with about ₹7,500 less despite the same average return, because its losses had to be recovered from a lower base. The more an investment swings, the more its compound growth falls below its simple average. This gap is sometimes called volatility drag.

Why it matters

Averages are quoted everywhere: average returns, average incomes, average fund performance. Knowing whether a figure is a mean or a median, and how much spread sits around it, tells you whether the average describes anything typical. Understanding volatility explains why steadier investments can grow faster than their averages suggest, and why a high-return, high-volatility investment may be unsuitable for money you need soon.

Limitations

• Standard deviation calculated from past returns describes the past. Volatility changes, often rising sharply in a crisis.
• Short histories give unreliable estimates of volatility.
• Comparing volatilities is only meaningful for returns measured over the same frequency and period.

Common mistakes

• Trusting a mean dominated by one extreme value. Check the median.
• Treating low volatility as no risk. A steady price can still fall a long way when conditions change.
• Using the average return to project growth. Use the compound growth rate.
• Comparing a daily volatility with a yearly one.

Try it yourself

1. Write down five yearly returns for any index or fund. Calculate the mean, the median and the standard deviation.
2. Work out what ₹1,00,000 would have become by multiplying the five yearly returns in turn, and compare the CAGR with the mean.
3. Do the same for a made-up list with the same mean but bigger swings. How much lower is its CAGR?