Clearwater VaR User Guide
S O LU T I O N S
Value at Risk (VaR) User Guide Clearwater Analytics offers dynamic and interactive investment risk reporting backed by daily reconciled portfolio data. ®
The Value at Risk (VaR) report is contained within the Clearwater Risk module. VaR is an effective way to show an aggregate risk over an entire portfolio. It aims to calculate a value that, with a given confidence, the portfolio will not fall more than on a particular day. VaR assumes normal market conditions and no trading in the portfolio. Consider the following example: A 95% VaR of $10,000 would indicate that 95% of the time, the portfolio should not lose more than $10,000 on a day, or equivalently that 5% of the time the portfolio is expected to lose at least $10,000 on a day. If the portfolio loses more than the VaR calculated, a VaR break has occurred. VaR breaks are not uncommon and a 5% VaR is expected to have a VaR break roughly 15-20 times a year.
clearwater’s var methodology High-Level Overview Clearwater’s VaR methodology determines parameters from historical data and infers a distribution. We calculate the mean (μ) and standard deviation (σ) of security price changes based on our recorded price history, with the assumption that the data is distributed normally.
A security level VaR is calculated by moving a number of standard deviations away from the mean based on the desired confidence. When calculating portfolio level VaR, securities are combined using correlation to quantify the tendency for securities to move in price together or in opposition to each other. Each pair of securities is combined with their correlation and summed to create a portfolio level VaR.
accounting. compliance. performance. risk.
www.clearwateranalytics.com
S O LU T I O N S
Details Weighting VaR uses weighted calculations. Weighted mean and weighted variance are used for security level VaR, while weighted correlation is used for portfolio level VaR. Historical events are only a faint indicator of how a security will perform in the present, whereas recent fluctuations due to events like market trends, changes in interest rates, and announcements of the company’s quarterly profits have a more profound impact on present performance. Due to this, weight is a simple decaying factor which is 1 for the most recent date and multiplied by 0.94 for each subsequent price point. For example, consider the following price history:
The weighted mean of this is -0.1935% (compared to the mean of -0.1732%), and the weighted standard deviation is 0.6020% (compared to the standard deviation of 0.5734%).
Confidences For the confidences, the number of standard deviations from the mean result in the following:
An alternative method to generate the number of standard deviations for other confidence levels is to use =NORM.INV(, 0, 1) in Excel.
Security Calculations Percent VaR = (Number of Standard Deviations) x (Weighted Standard Deviation) + Abs(Weighted Mean) Dollar VaR = (Percent VaR) x (Security Market Value)
Amount of Data Clearwater uses 100 data points of pricing data (100 prices). If less data is available, current data is utilized to fill the remainder of this history with the last available price. This will lower both the standard deviation and the mean percentage change but allows the applications of the heaviest weights to actual price changes, making it an ideal solution under the given circumstances. Circling back to the example introduced above, the 95% VaR threshold equals 1.65 x 0.6020% + 0.1935% = 1.187%, and the 99% equals 2.33 x 0.6020% + 0.1935% = 1.596%. If the current market value of the position is $10,000, then the 95% VaR would be $118.68, and the 99% VaR would be $159.62.
accounting. compliance. performance. risk.
www.clearwateranalytics.com
S O LU T I O N S
Correlation Correlation is a statistical measure for how two random variables change in respect to each other. Clearwater utilizes the Pearson product-moment correlation coefficient, which equals -1 if when one of the variables increases, the other always decreases, and 1 if when one increases, the other also increases. This allows the combination of many risks from individual securities to arrive at an overall portfolio risk. Portfolio Risk = sqrt((Security Risk) x (Correlation Matrix) x (Security Risk)T) Where the ith entry of the Security Risk vector is the risk for the ith security in the portfolio, and the (i, j)th entry of the Correlation Matrix is the correlation between the ith and jth security in the portfolio. Consider two stocks for Alice Corp and Bob LLC. If they are perfectly correlated, the Portfolio Risk is: Portfolio Risk =
sqrt( A B 1 1 A ) = sqrt(A^2+2*A*B+B^2) = sqrt((A+B)^2) = |A+B| 1 1 B
That is, if they are perfectly correlated, the Portfolio Risk is the sum of the risks. Likewise, if they are perfectly negatively correlated: Portfolio Risk =
sqrt( A B 1 -1 A ) = sqrt(A^2-2*A*B+B^2) = sqrt((A-B)^2) = |A-B| 1 -1 B
That is, if they are perfectly negatively correlated, the Portfolio Risk is the difference of the risks. If they are between these two extremes, a portion of B’s risk will be added to A or removed from A depending on the sign of the correlation. Similar results are achieved with more than two securities. Three perfectly correlated securities have an account risk of |A+B+C| and so on. See the Risk User Guide for more information about the Clearwater Risk Module. Please contact your Clearwater Account Manager with any questions or for more information.
accounting. compliance. performance. risk.
www.clearwateranalytics.com
Value at Risk (VaR) User Guide Clearwater Analytics offers dynamic and interactive investment risk reporting backed by daily reconciled portfolio data. ®
The Value at Risk (VaR) report is contained within the Clearwater Risk module. VaR is an effective way to show an aggregate risk over an entire portfolio. It aims to calculate a value that, with a given confidence, the portfolio will not fall more than on a particular day. VaR assumes normal market conditions and no trading in the portfolio. Consider the following example: A 95% VaR of $10,000 would indicate that 95% of the time, the portfolio should not lose more than $10,000 on a day, or equivalently that 5% of the time the portfolio is expected to lose at least $10,000 on a day. If the portfolio loses more than the VaR calculated, a VaR break has occurred. VaR breaks are not uncommon and a 5% VaR is expected to have a VaR break roughly 15-20 times a year.
clearwater’s var methodology High-Level Overview Clearwater’s VaR methodology determines parameters from historical data and infers a distribution. We calculate the mean (μ) and standard deviation (σ) of security price changes based on our recorded price history, with the assumption that the data is distributed normally.
A security level VaR is calculated by moving a number of standard deviations away from the mean based on the desired confidence. When calculating portfolio level VaR, securities are combined using correlation to quantify the tendency for securities to move in price together or in opposition to each other. Each pair of securities is combined with their correlation and summed to create a portfolio level VaR.
accounting. compliance. performance. risk.
www.clearwateranalytics.com
S O LU T I O N S
Details Weighting VaR uses weighted calculations. Weighted mean and weighted variance are used for security level VaR, while weighted correlation is used for portfolio level VaR. Historical events are only a faint indicator of how a security will perform in the present, whereas recent fluctuations due to events like market trends, changes in interest rates, and announcements of the company’s quarterly profits have a more profound impact on present performance. Due to this, weight is a simple decaying factor which is 1 for the most recent date and multiplied by 0.94 for each subsequent price point. For example, consider the following price history:
The weighted mean of this is -0.1935% (compared to the mean of -0.1732%), and the weighted standard deviation is 0.6020% (compared to the standard deviation of 0.5734%).
Confidences For the confidences, the number of standard deviations from the mean result in the following:
An alternative method to generate the number of standard deviations for other confidence levels is to use =NORM.INV(, 0, 1) in Excel.
Security Calculations Percent VaR = (Number of Standard Deviations) x (Weighted Standard Deviation) + Abs(Weighted Mean) Dollar VaR = (Percent VaR) x (Security Market Value)
Amount of Data Clearwater uses 100 data points of pricing data (100 prices). If less data is available, current data is utilized to fill the remainder of this history with the last available price. This will lower both the standard deviation and the mean percentage change but allows the applications of the heaviest weights to actual price changes, making it an ideal solution under the given circumstances. Circling back to the example introduced above, the 95% VaR threshold equals 1.65 x 0.6020% + 0.1935% = 1.187%, and the 99% equals 2.33 x 0.6020% + 0.1935% = 1.596%. If the current market value of the position is $10,000, then the 95% VaR would be $118.68, and the 99% VaR would be $159.62.
accounting. compliance. performance. risk.
www.clearwateranalytics.com
S O LU T I O N S
Correlation Correlation is a statistical measure for how two random variables change in respect to each other. Clearwater utilizes the Pearson product-moment correlation coefficient, which equals -1 if when one of the variables increases, the other always decreases, and 1 if when one increases, the other also increases. This allows the combination of many risks from individual securities to arrive at an overall portfolio risk. Portfolio Risk = sqrt((Security Risk) x (Correlation Matrix) x (Security Risk)T) Where the ith entry of the Security Risk vector is the risk for the ith security in the portfolio, and the (i, j)th entry of the Correlation Matrix is the correlation between the ith and jth security in the portfolio. Consider two stocks for Alice Corp and Bob LLC. If they are perfectly correlated, the Portfolio Risk is: Portfolio Risk =
sqrt( A B 1 1 A ) = sqrt(A^2+2*A*B+B^2) = sqrt((A+B)^2) = |A+B| 1 1 B
That is, if they are perfectly correlated, the Portfolio Risk is the sum of the risks. Likewise, if they are perfectly negatively correlated: Portfolio Risk =
sqrt( A B 1 -1 A ) = sqrt(A^2-2*A*B+B^2) = sqrt((A-B)^2) = |A-B| 1 -1 B
That is, if they are perfectly negatively correlated, the Portfolio Risk is the difference of the risks. If they are between these two extremes, a portion of B’s risk will be added to A or removed from A depending on the sign of the correlation. Similar results are achieved with more than two securities. Three perfectly correlated securities have an account risk of |A+B+C| and so on. See the Risk User Guide for more information about the Clearwater Risk Module. Please contact your Clearwater Account Manager with any questions or for more information.
accounting. compliance. performance. risk.
www.clearwateranalytics.com
