11th June 2019 | Michał Karol Ejdys | Portfolio Quantitative Analyst

What is the Value-at-Risk?

Value-at-Risk is one of several indicators of asset or portfolio risk that have been developed in the last decades, arguably the one that caught the most traction. Popular with practitioners and regulators alike, it serves as an easily understandable, intuitive risk metric.

How is it supposed to work?

VaR is always defined with two parameters. One is the time horizon (usually annual) and the other – the certainty level (usually 5% in market-related activities, 1% in regulatory requirements in banking). Now, a 5% annual VaR would be the dollar value of a portfolio below which there is only 5% probability that the actual value will be in a year’s time. Conversely, there is 95% chance the portfolio value will be above the 5% annual VaR. 

How does it really work?

VaR defined in the way above is like a goal we can pursuit in many ways, but never reach. We can get closer to it, yes, but the real value is always seen through a layer of fog, thinner or thicker. Why? Because the task is inherently about predicting the future, which cannot be done without error. Hence, we use estimates and proxies. 

Looking back…

First and most popular one is to use historical data – the historical VaR. Gather one year of daily returns, sort the in ascending order and cut off the first 5% of sorted observations (days with lowest returns). What is now first in the row, is the percentage loss the asset (or portfolio) has suffered in the last year, so to get the dollar value of loss it has to be multiplied by the portfolio value. The resulting number is the 5% daily VaR, meaning there was only 5% chance the portfolio would have lost more than that much on any given day last year. Curious readers will now see the problem, that without assuming that the past will repeat itself perfectly, this VaR tells us about the past rather than the future. 

…or looking forward?

But the past does not repeat itself, never, at least not perfectly. To decrease the dependence on past outcomes when it comes to the calculation of VaR, models have been developed that rely on volatility to estimate the distribution of daily returns that is forward-, rather than backward-looking. These models rely on the empirical fact, first observed by Mandelbrot in 1963, that volatility is autocorrelated – high volatility today, suggests high volatility tomorrow, and vice-versa. A family of these models, called ARCH (Auto-Regressive Conditional Heteroskedasticity), was brought to the main stream when Robert Engle received a Nobel prize in 2003 for their development.

With the help of models like these, we can calculate a forward-looking volatility and plug it into some theoretical distribution of returns, e.g. a normal one. We introduced some probability concepts together with their theoretical assumptions in a previous article. Then, the procedure is the same – cut the left (lowest) 5% of the distribution, and what is left, is the 5% VaR – the parametric one. Parametric VaR avoids the unrealistic assumption that the past repeats itself perfectly, which troubles the Historical VaR. Instead, it makes the assumption on volatility and on the shape of distribution of returns. But we cannot avoid making assumptions at all. This time, however, they are more realistic and well-proven, respectively by empirical research and theory of statistics. 

What to do with all this knowledge?

Manage the risk of the investments, of course. Every investor has a different propensity for taking on risk. Meanwhile, the risk of assets and portfolios changes. VaR serves as the common ground for aligning the requirements of the investors with the risk of financial assets and portfolios. If the investor feels like a loss of 10% in a year is palatable, then a portfolio with an annual VaR of 10% should be constructed. As circumstances change, some assets that have e.g. increased in volatility should be sold, and safer ones bought to realign the portfolio with the desired 10% VaR. The portfolio should always be kept suitable and appropriate for a given investor (in terms of risk), and, theoretically, close to the risk limit when the outlook is good, and de-risked in bad times. Why high returns are deemed achievable only when taking on high risk, and why high risk does not automatically mean high return – well, that is a topic for another article.

Notice: 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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