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6th June 2019 | Michał Karol Ejdys | Portfolio Quantitative Analyst

# What is the volatility and what is its link with customer risk?

## Market volatility should be intuitively understood as an answer to the question ‘by how much the market used to move on an average day?’. It is inherently linked with risk – it makes all the difference whether the hundred dollars’ worth of stock one has, has a volatility of five or fifty.

#### A bit of math

Historical volatility is measured by the standard deviation of returns. Simplifying this as much as possible, think about the daily percentage changes in price of something – its daily returns. Get a mean of those and subtract it from each such return. Square each of them and average the results. This is the variance. Get a square root of that – that’s the standard deviation.

Assuming asset returns are normally distributed (which is a common and useful, albeit technically incorrect, approximation), 68% of the time the daily return should be within one standard deviation range. If we extend if to two standard deviations, the probability of the return falling within it rises to 95%, which is fairly large by anyone’s standards.

#### Betting high vs playing it safe

Coming back to our examples, to visualise what is at stake in each: suppose you have \$100 invested. First scenario: your volatility is 5%. Assuming it ‘sticks’ (and it does, as first observed by Mandelbrot in 1963), with 68% probability you should have between \$95 and \$105 tomorrow. You can also bet it will be between 90 and 110, and you would be wrong only once in 20 times (95% probability). Second scenario (50% volatility) makes you 95% sure that you will have… something between 0 and 200 tomorrow.

Now you probably cannot help but notice it seems implicitly fair (still, assuming a normal distribution, caveats above apply): risk a little (5%), and you get equal chance for an upside. Risk a lot (50%), and you get a chance to double your wealth. This is exactly why volatility, and its measure – the standard deviation of returns – is a common proxy of risk.

#### Why do we care so much?

Because risk is the fundament of financial markets. At least since in 1990 Sharpe, Markowitz and Miller got their Nobel Prize for their contribution to finding out the relationship between the risk of an asset and the return it is expected to yield, we became able to theoretically calculate it, provided we knew the asset’s risk. Risk was then approximated by the asset’s volatility, which can in turn be measured by the standard deviation of returns, as introduced in the paragraphs above. Thus, we have come a full circle.

Volatility enables us to estimate the degree of certainty for the future value of assets and portfolios. It has many interesting properties that managers exploit to enhance desirable characteristics of portfolios. To give a few: volatility of a 50:50 mix of two assets will usually be lower than the average of their volatilities – that’s diversification. High volatility of an asset today suggests that tomorrow the volatility should be higher as well – that’s volatility clustering.

#### Our approach to volatility

In Golden Sand Bank, we take advantage of all the above. Volatility, as the only predictable (to some extent, at least) characteristic of financial time series, is in the centre of our attention. We look closely at volatility to manage and limit the risk of your portfolios, whether it is our Shelter or Aggressive strategy, in order to provide you with sustainable risk-adjusted returns.

Golden Sand Bank ("Bank") exercised due diligence to ensure that the information contained in this publication was not incorrect or untrue as at the date of publication.

All Investment products are at risk, as their value can go down as well as up. The tax treatment of your investment will depend on your individual circumstances and may change in the future. If you are unsure about whether investing is right for you, please seek financial advice. This publication is not an investment recommendation or investment advice in connection with any services provided by the Bank to the Client.

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