Risk in an investment is often thought of as volatility. This would be considered as the risk of losing value in an investment. It should be more correctly viewed as the probability that prices will fluctuate.
Volatility of returns is most commonly measured as standard deviation. Standard deviation measures how widely the actual returns on an investment varies when compared to the average or mean return. As standard deviation rises, the more risky an investment is seen to be. As a measurement tool, standard deviation is useful in identifying the range of potential returns that an investment might generate in the future. It also helps us to understand the risk being taken to create those returns.
Investment theory presumes that returns are normally distributed. This means that they are spread symmetrically around the average return. When data is normally distributed, returns can be expected to fall within one standard deviation of the average return two-thirds of the time. During the remaining one third of the time, returns would be expected to fall outside of these boundaries.
To explain this a little more clearly: if an investment has an average return of 8% and a standard deviation of 5%, then two thirds of the time returns can be anticipated to fall in a range of between 3% and 13%.
However, standard deviation does not provide a measure of performance in relation to other companies, funds, benchmarks or the maket.
Relative to the market as a whole, the volatility of a security is known as beta. The market has a beta of 1.
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Needless to say, in an area like finance, there are a great many people looking for a slight advantage. This has lead to many different types of tools and forumulas.
A great example of this is the VIX (that is the ticker symbol) which measures the implied volatility of index options on the S&P 500.
There are a number of models used to forecast volatility and this one has it's pros and cons like the others. It is however, widely referred to as a way to measure the fear in the market in the short term (on Wall Street, everything can be measured).
The reality, of course, is that these mathematical models have been shown to be flawed. While your author is not clever enough to prove it with a formula, there have been a number of times where the movements on the stock exchanges of the world have defied probability. At the time of the 2008 Wall Street crash, the 'quant quake', the collapse of Long Term Capital Management and others, events that were only believed to be possible once per century or more happened several days in a row.
These events are known as fat tails because they exist at the far end of the distribution curve. Famed author Nassim Nicholas Taleb has written and spoken about such events frequently in books such as The Black Swan.
So far, everything above has been quite academic and it's use for a beginner to investing (information here) might be limited.
Instead, it might be better to think of risk this way:
If the money invested in a security or bond were to be lost completely, what impact would that have on the lifestyle of you and your family?
While this has no mathematical basis, giving thought to this question will hopefully make it easier to decide whether to invest and if so, how much, in a real-world way. Mathematical formulas and investment theories are very nice and all, but if you need money fast they will not pay the rent or put food on the table!
Understanding what an investment means to you and your finances is how to really gauge the risks in your portfolio.
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Learn How Beta And Volatility Impact Your Investment Portfolio
Why Low Risk Can Be Good
How To Use Risk Analysis To Make You A Better Investor
How Do Different Types Of Risk Influence A Portfolio?
Does Correlation Influence Portfolio Diversification?
What Is A Stop-Loss?
Understanding Gearing And Borrowed Money
What Does The Return On Capital Employed (ROCE) Tell Us?
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Understanding A P/E Ratio (Price To Earnings Ratio)