![]() To convert this into a monthly value at risk, we will need to 1) adjust the return by using simple division, 2) convert the standard deviation by dividing by the square root of time, and 3) feeding it back into the VAR equation. In our example, we started with data that was based on annual return figures of 10% and a standard deviation of 6%. When dealing with investment portfolios, some of the common time periods to know off hand are that there are 20 trading days in a month, 250 trading days in a year, and of course, 12 months in a year. The mathematics to make this conversion are based off the idea that standard deviation of returns increase/decrease with the square root of time. To make this data more relevant and to answer various risk management questions, we can convert this data for different time periods. Often we have data for average returns and standard deviations that have been collected over a specific period of time. This conversation signifies that the return data was not normally distributed having fat or long downside tail ends which were not properly taken into account when calculating risk of the portfolio. Fans of the movie Margin Call, about the 2008 financial crisis, would recall the opening scene where analysts are huddled around a computer anxiously talking about recent data in the markets falling outside their model predictions. Confidence Levels (One-tail):Ĭautious Side Note: Value-at-risk is a good estimation of risk but is far from perfect and has significant flaws in assuming that return distributions are normal. As mentioned previously, these Z-Scores or standard deviations stay constant under a normal distribution. And, at 99% confidence level, we are 2.33 standard deviations away from the average. At a 95% confidence level, we are 1.65 standard deviations away from the average. As can be seen below, a 90% confidence level (could also be referred to as 10% VAR) will be 1.28 standard deviations away from the average expected portfolio return. Value-at-Risk-Calculator-VAR-from-IFB Downloadīecause this is a risk analysis (and not an upside return analysis), we are only concerned about the lower part of the normal distribution curve. Assuming a normal distribution curve as can be seen below, the percent of portfolio return scenarios which fall outside specific standard deviations away from the average portfolio return stays constant. ![]() ![]() The Z-Score is a statistical measure for a normal distribution curve of the number of standard deviations (#) away from the expected portfolio return (the average) that a certain percentage of calculated returns will fall under. The confidence intervals represents how sure an analyst wants to be that portfolio losses will not exceed a certain percentage or dollar value of the portfolio. = $1,000 Confidence Intervals for Value-at-Risk Value-at-Risk ($) = Value-at-Risk (%) x Portfolio Value ($) The VAR formula can then be manipulated algebraically to solve for any of the independent variables in an analysis. To get this amount into dollar terms, we simply multiply the outcome of this formula by the value of the portfolio, as can be seen below. For example, this formula would spit off the calculation that at a 95% confidence level, portfolio returns will be greater than 0.1% in a one year period and a 5% probability they will be less than 0.1%. ![]() The above formula will give the value-at-risk in percentage terms. The Z-Score is a statistics term for a normal distribution which we will discuss in more detail next, but there are common Z-Scores that can be remembered for each confidence interval. 10%) and then subtracts off the standard deviation of the portfolio (the risk) which is multiplied by the Z-Score of the confidence interval we are looking to analyze. The value-at-risk formula starts by looking at the expected return of the portfolio over the time period (ex. ![]() For our ongoing example throughout this reading, we will look at a hypothetical $1 million portfolio with annual expected returns of 10% and a standard deviation of 6%. This article will teach analysts and investors how to calculate value-at-risk, convert VAR for different time periods and confidence levels, as well as walk readers through examples with a sample portfolio. The end goal of doing a VAR calculation is being able to make a statement such as there is 5% probability in any given year that the loss of the portfolio will exceed $100,000 and a 95% probability the loss will be less than that. ![]()
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