Here we explain how to convert one value at risk (VAR) of one time period into the equivalent VAR for a different time period and show you how to use VAR to estimate the downside risk of a single stock investment.
Converting One Time Period to Another
In Part 1, we calculate VAR for the Nasdaq 100 index (ticker: QQQ) and establish that VAR answers a threepart question: "What is the worst loss that I can expect during a specified time period with a certain confidence level?"
Since the time period is a variable, different calculations may specify different time periods  there is no "correct" time period. Commercial banks, for example, typically calculate a daily VAR, asking themselves how much they can lose in a day; pension funds, on the other hand, often calculate a monthly VAR.
To recap briefly, let's look again at our calculations of three VARs in part 1 using three different methods for the same "QQQ" investment:
* We do not need a standard deviation for neither the historical method (because it just reorders returns lowesttohighest) or the Monte Carlo simulation (because it produces the final results for us). 
Because of the time variable, users of VAR need to know how to convert one time period to another, and they can do so by relying on a classic idea in finance: the standard deviation of stock returns tends to increase with the square root of time. If the standard deviation of daily returns is 2.64% and there are 20 trading days in a month (T = 20), then the monthly standard deviation is represented by the following:
To "scale" the daily standard deviation to a monthly standard deviation, we multiply it not by 20 but by the square root of 20. Similarly, if we want to scale the daily standard deviation to an annual standard deviation, we multiply the daily standard deviation by the square root of 250 (assuming 250 trading days in a year). Had we calculated a monthly standard deviation (which would be done by using monthtomonth returns), we could convert to an annual standard deviation by multiplying the monthly standard deviation by the square root of 12.
Applying a VAR Method to a Single Stock
Both the historical and Monte Carlo simulation methods have their advocates; but the historical method requires crunching historical data, and the Monte Carlo simulation method is complex. The easiest method is variancecovariance.
Below we incorporate the timeconversion element into the variancecovariance method for a single stock (or single investment):
Now let's apply these formulas to the QQQ. Recall that the daily standard deviation for the QQQ since inception is 2.64%. But we want to calculate a monthly VAR, and assuming 20 trading days in a month, we multiply by the square root of 20:
* Important Note: These worst losses (19.5% and 27.5%) are losses below the expected or average return. In this case, we keep it simple by assuming the daily expected return is zero. We rounded down, so the worst loss is also the net loss. 
So, with the variancecovariance method, we can say with 95% confidence that we will not lose more than 19.5% in any given month. The QQQ clearly is not the most conservative investment! You may note, however, that the above result is different from the one we got under the Monte Carlo simulation, which said our maximum monthly loss would be 15% (under the same 95% confidence level).
Conclusion
Value at risk is a special type of downside risk measure. Rather than produce a single statistic or express absolute certainty, it makes a probabilistic estimate. With a given confidence level, it asks, "What is our maximum expected loss over a specified time period?" There are three methods by which VAR can be calculated: the historical simulation, the variancecovariance method and the Monte Carlo simulation.
The variancecovariance method is easiest because you need to estimate only two factors: average return and standard deviation. However, it assumes returns are wellbehaved according to the symmetrical normal curve and that historical patterns will repeat into the future.
The historical simulation improves on the accuracy of the VAR calculation, but requires more computational data; it also assumes that "past is prologue". The Monte Carlo simulation is complex, but has the advantage of allowing users to tailor ideas about future patterns that depart from historical patterns.
To read more on this subject, see Continuously Compound Interest.

Investing
How ETFs May Save You Thousands
Being vigilant about the amount you pay and what you get for is important, but adding ETFs into the investment mix fits well with a valueseeking nature. 
Stock Analysis
The Biggest Risks of Investing in Netflix Stock
Examine the current state of Netflix Inc., and learn about three of the major fundamental risks that the company is currently facing. 
Mutual Funds & ETFs
3 Fixed Income ETFs in the Mining Sector
Learn about the top three metals and mining exchangetraded funds (ETFs), and explore analyses of their characteristics and how investors can benefit from these ETFs. 
Bonds & Fixed Income
High Yield Bond Investing 101
Taking on highyield bond investments requires a thorough investigation. Here are looking the fundamentals. 
Retirement
How RoboAdvisors Can Help You and Your Portfolio
Roboadvisors can add a layer of affordable help and insight to most people's portfolio management efforts, especially as the market continues to mature. 
Mutual Funds & ETFs
Top 3 Muni California Mutual Funds
Discover analyses of the top three California municipal bond mutual funds, and learn about their characteristics, historical performance and suitability. 
Investing Basics
What Does In Specie Mean?
In specie describes the distribution of an asset in its physical form instead of cash. 
Economics
Calculating Cross Elasticity of Demand
Cross elasticity of demand measures the quantity demanded of one good in response to a change in price of another. 
Mutual Funds & ETFs
Mutual Funds Are Not FDIC Insured: Here Is Why
Find out why mutual funds are not insured by the FDIC, including why the FDIC was created and how to minimize your risk with educated mutual fund investments. 
Professionals
How to Sell Mutual Funds to Your Clients
Learn about the various talking points you should cover when discussing mutual funds with clients and how explaining their benefits can help you close the sale.

Why have mutual funds become so popular?
Mutual funds have become an incredibly popular option for a wide variety of investors. This is primarily due to the automatic ... Read Full Answer >> 
What licenses does a hedge fund manager need to have?
A hedge fund manager does not necessarily need any specific license to operate a fund, but depending on the type of investments ... Read Full Answer >> 
Can mutual funds invest in hedge funds?
Mutual funds are legally allowed to invest in hedge funds. However, hedge funds and mutual funds have striking differences ... Read Full Answer >> 
When are mutual funds considered a bad investment?
Mutual funds are considered a bad investment when investors consider certain negative factors to be important, such as high ... Read Full Answer >> 
What fees do financial advisors charge?
Financial advisors who operate as feeonly planners charge a percentage, usually 1 to 2%, of a client's net assets. For a ... Read Full Answer >> 
Can your car insurance company check your driving record?
While your auto insurance company cannot pull your full motor vehicle report, or MVR, it does pull a record summary that ... Read Full Answer >>