What Is Value at Risk (VaR)?

Value at Risk (VaR) has been called the "new science of risk management," and is a statistical technique that can be used to predict tღhe greatest potential loss of aღn investment over a specific time frame.

Commonly used by financial firms and commercial banks in 澳洲幸运5官方开奖结果体彩网:investment analysis, VaR can determine the extent and probabil💃ities of potential losses in portfolios. 💞Risk managers use VaR to measure and control the level of risk exposure.

In Part 1, let's calculate VaR for the 澳洲幸运5官方开奖结果体彩网:Nasdaq 100 index (QQQ) and establish that VaR answers a ꦫthree-part question: "What is the worst loss that I can expect during a specified period with a certain confide💟nce level?"

Elements of Value at Risk (VaR)

The traditional measure of risk is 澳洲幸运5官方开奖结果体彩网:volatility, and an investor's main c🌃oncern is the odds of losi☂ng money. The VaR statistic has three components: a period, a confidence level, and a loss amount, or loss percentage, and can address these concerns:

• What can I expect to lose in dollars with a 95% or 99% level of 澳洲幸运5官方开奖结果体彩网:confidence next month?
• What is the maximum percentage I can expect to lose with 95% or 99% confidence over the next year?

The questions include a high level of confidence, a period, and an estimate of investment loss.

Methods for Calculating VaR

Let's evaluate the risk of a single index that trades like a stock, the 澳洲幸运5官方开奖结果体彩网:Nasdaq 100 Index, which is traded through the Invesco QQQ Trust. The QQQ is an index of the largest non-financial stocks that trade on the Nasdaq exchange.

There are three methods of calculating Value at Risk (VaR), 澳洲幸运5官方开奖结果体彩网:including the historical method, the variance-covariance method, and the 澳洲幸运5官方开奖结果体彩网:Monte Carlo simulation.

1. Historical Method

The historical method simply re-organizes actual 澳洲幸运5官方开奖结果体彩网:historical returns, putting them in order from worst to best. It then assumes that history will repeat itself, from a risk perspective. Let's look at the Nasdaq 100 ETF, which trades under the symbol QQQ.

In calculating each daily return, we produce a rich data set of more than 1,400 points. Let's put them in a 澳洲幸运5官方开奖结果体彩网:histogram that compares ꦛthe frequency of return "buckets."

At the highest bar, there were more than 250 days when the daily return was between 0% and 1%. At the far right, a tiny bar at 13% represents the one single day within five-plus years when the daily return for the QQQ was 12.4%.

2. Variance-Covariance Method

This method assumes that stock returns are normally distributed and requires an estimate of only two factors, an expected return, and a 澳洲幸运5官方开奖结果体彩网:standard deviation, allowing for a 澳洲幸运5官方开奖结果体彩网:normal distribution curve. The normal curve is plotted against the same 澳洲幸运5官方开奖结果体彩网:actual return data in the graph above.

The variance-covariance is similar to the historical method except it uses a familiar curve instead of actual data. The advantage of the normal curve is that it shows where the worst💯 5% and 1% lie on the curve. They arᩚᩚᩚᩚᩚᩚ⁤⁤⁤⁤ᩚ⁤⁤⁤⁤ᩚ⁤⁤⁤⁤ᩚ𒀱ᩚᩚᩚe a function of desired confidence and the standard deviation.

The curve above is based on the actual daily standard deviation of the QQQ, which is 2.64%. The average daily return happened to be fairly close to zero, so it's safe to assume an 澳洲幸运5官方开奖结果体彩网:average return o𒅌f zero for illustrative purposes. Here are the results of using the actual standard deviation in the formulas above:

3. Monte Carlo Simulation

A 澳洲幸运5官方开奖结果体彩网:Monte Carlo simulation refers♏ to any method that randomly generates trials, but by itself, does not tell us anything about the unde🐎rlying methodology.

For most users, a Monte Carlo simulation amounts to a "black box" generator of random, probabilistic outcomes. This technique uses computational models to simulate projected returns over hundreds or thousands of possible iterations.

𓆏 I𝓡f 100 hypothetical trials of monthly returns for the QQQ were conducted, two of the worst outcomes may be between -15% and -20%, and three between -20% and 25%. That means the worst five outcomes were less than -15%.

The Monte Carlo simulati🌳on, therefore, leads tꦆo the following VaR-type conclusion: with 95% confidence, we do not expect to lose more than 15% during any given month.

Explain Like I'm 5

Value at Risk (VaR)can help investors answer the question: "What's the potential maximum loss I could expect from this investment within x days/weeks/months?". In other words, VaR is a statistical method that can be used to estimate the worst-case loss of an investment over a specific period of time, considering a certain probability of that loss occurring (which is called "confidence level"). For example, if an investment's one-day VaR is $5,000 at a 95% confidence level, it means there's a 5% (100% - 95%) chance the investment could lose more than $5,000 in a single day.

The Bottom Line

Value at Risk (VAR) 澳洲幸运5官方开奖结果体彩网:calculates the maximum loss expected on an investment over a given period and given a specified degree of confidence. We looked at three methods commonly used to calculate VAR. 澳洲幸运5官方开奖结果体彩网:In Part 2 of this series, we show you how to compare different 澳洲幸运5官方开奖结果体彩网:time horizons.