ChartsPortfolio analysis and optimizationPortfolio Management

# Efficient Frontier Using Excel (With Marketxls)

Written by Priya Kumar
Mon Aug 17 2020
See how MarketXLS helps you take advantage in the markets.

The Efficient frontier using excel is one of the most important financial tools that help an investor compose an investment portfolio with the maximum returns and minimum amount of risk. This article will discuss what it is, how it is then calculated, and how MarketXLS calculates it of your Portfolio.

Contents:

1. What is Efficient frontier
2. Importance of Efficient frontier
3. Optimal Portfolio by Efficient frontier
4. How MarketXLS Calculates Efficient frontier of Portfolio

### What is an Efficient frontier?

The Efficient frontier, also known as the portfolio frontier, represents the set of efficient portfolios that will give the highest return at each level of risk or the lowest risk for each level of return. The set of efficient portfolios is produced by the combination of different weights to get maximum expected return.

The Efficient frontier is a curve representing a combination of various securities to produce a different level of return.This frontier is formed by plotting the expected return on the y-axis and the standard deviation as a measure of risk on the x-axis.

For building the frontier, there are three crucial factors to be taken into consideration:

1. Expected Return
2. The covariance of one asset’s return to that of another asset.
3. Variance/ Standard Deviation as a measure of the variability of returns known as risk.

The efficient frontier allows investors to understand how a portfolio’s expected returns vary with the amount of risk taken.

### Importance of Efficient frontier

This tool helps investors get the most from their investment by analyzing the risk and returns associated with an investment portfolio and assisting them in adjusting their asset allocation accordingly.

It can also help determine if an investor should pull their funds from an investment with a certain amount of risk and return for a similar investment with less risk and the same return. The efficient frontier is important as it minimizes risk while maximizing rewards or returns.

### The Optimal Portfolio by Efficient frontier

An optimal portfolio would offer a perfect balance between risk and return. The optimal portfolio contains:

1. Securities with the highest potential returns with an acceptable degree of risk.
2. It features securities with the lowest degree of risk for a certain level of return.
3. Optimal returns tend to lie along the efficient frontier.

A risk-ready investor could choose securities right end of the efficient frontier. Those would likely have a high degree of risk coupled with high potential returns. Meanwhile, securities on the left end of the efficient frontier would be suitable for more cautious investors.

### How MarketXLS Calculates Efficient frontier of your Portfolio

MarketXLS® completely automates the process of calculating the Efficient frontier using excel to get the optimal portfolios which tend to lie along the efficient frontier.

The following inputs are required to be entered by the investor:

1. Symbol of the asset: Enter the ticker under which the security in your Portfolio is traded.
2. Weight of the asset in your Portfolio: Enter the percentage weight of each security, as shown below.

Input:

Output:

Optional Fields:

Risk-free-rate(Rf):

To account for individuality in investor outlook, we make sure to give you the flexibility of determining what Mar/Rf you think is most viable. Default value: MarketXLS assumes a Mar/Rf of 0% by default to calculate the ratio.

Months under observation:

To determine how many months you want to utilize retrospectively to arrive at your calculation, you may input the number of months you feel best, given that all the securities in your Portfolio have existed long enough to have data for those periods. Default Value: In the absence of any user input, MarketXLS uses the data for the preceding 12 months from the date of the query.

Number of Points:

This refers to the number of points for which data is calculated for plotting the frontier. Default Value: MarketXLS calculates 100 points of data by default.

The  GMV Portfolio:

The global minimum variance portfolio (GMV portfolio), is the portfolio with the lowest possible standard deviation (risk) out of all possible levels of expected return.

Calculation:

The following is how the MarketXLS add-in calculates the Efficient frontier for your Portfolio, one may note, that this also serves as an explanatory step-by-step guide for an n-asset portfolio as to how to calculate the Efficient frontier.

Method to calculate average monthly return is same for both types as follows:

1. Monthly Return Calculation for Each Asset in Portfolio:

Where:

Note: To maintain consistency with theory in this regard, Close Price is a security’s Adjusted Close (Close prices adjusted for dividends and splits) of the last day of a given month, and the Open Price is the Adjusted Close price for the last day of the previous month.

1. Portfolio Monthly Return Calculation:

Portfolio return for a given month is calculated as follows:

Where:

This is repeated for all the months under consideration.

1. Determining Highest and Lowest Possible Expected Return on a Portfolio:

The individual return of every asset in the portfolio is determined by taking the mean of periodic returns for every asset and annualising the same to arrive at the expected return for every asset in the portfolio.

For MarketXLS as monthly data is utilized, the no. of periods in a year are taken as 12.

The lowest value among this is the lowest possible return of the portfolio and similarly as the highest.

1. Determining Weights for Every Level of Return in Between:

Quadratic Linear Programming is utilised to minimize portfolio volatility for all different levels of return subject to the constraint that sum of weights equals one. Herein, the optional input regarding the number of data points determines how many points in between the data is calculated for.

1. Covariance of Portfolio is Calculated:

The covariance matrix is calculated for the portfolio:

Note: This is a two and three asset example and can be done for as many assets as a portfolio might have.

1. Standard Deviation of Portfolio:

The portfolio’s standard deviation is calculated below:

Where:

1. Standard Deviation of Portfolio is Annualized:

To maintain consistency in periodicity of different parameters, standard deviation is annualised as follows:

Annualizing Factor = SQRT(Number of Periods a Year)

Note: Since MarketXLS uses monthly values, the annualizing factor is sqrt(12)

For instance, if taking daily data, seeing as a trading year has 252 days, multiply the ratio with the square root of 252.

Similarly,

• for yearly returns, annualizing factor = SQRT(1)
• for monthly returns, annualizing factor = SQRT(12)
• for weekly returns, annualizing factor = SQRT(52)
• for daily returns, annualizing factor = SQRT(252)
1. Plotting the Efficient Frontier:

This results to derive the Efficient frontier plotted with standard deviation (risk) on x-axis and expected return on y-axis.

The portfolio with lowest risk is plotted as the GMV portfolio.

The portfolio with the highest Sharpe Ratio is used to plot the Capital Market line as a segment starting at the risk-free-rate of return on the y-axis and extending to the portfolio with the maximum sharpe ratio.

The investor can use the Efficient frontier of Portfolio excel formula to get a combination of assets that has the optimal level of expected return for a given level of risk as all the portfolios on the line are efficient. An investor can choose a suitable portfolio anywhere on the Efficient Frontier depending on his individual preferences and investment timeframe using MarketXLS.

Interested in building, analyzing and managing Portfolios in Excel?

#### Top 100 Gainers Today

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AEY
AEY
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Manufacturing10.3026.85%612 M-3.20-2.5532.005.5227.95%-49.01%
AAOI
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ABVC
ABVC
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AAMC
AAMC
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AGEN
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Agenus Inc.
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ACCD
ACCD
Information12.9110.06%782 M-1.90-6.0649.474.619.50%-51.02%
ACLS
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ACB
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AEHR
AEHR
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ACVA
ACVA
ACV Auctions Inc
Professional, Scientific, and Technical Services3.996.40%418 M-6.70-3.0778.822.411.53%-45.04%
Healthcare2.376.28%399 M-4.30-0.502.481.0114.49%68.09%
ACST
ACST
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AFRM
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ACIU
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AC Immune SA
Healthcare3.414.92%279 M-3.10-1.0212.612.067.23%-31.11%
AERI
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Healthcare16.404.19%2,618 M-12.50-1.3328.0612.24-1.32%-29.73%
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Industrials50.464.13%11,271 M-13.30-3.3071.3837.2011.42%-22.87%
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Consumer Cyclical38.553.60%3,266 M4.108.4350.9627.1512.10%-19.49%
ABST
ABST
Absolute Software Corp
Information10.843.53%509 M-23.20-0.4412.626.795.76%15.20%
AEO
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American Eagle Outfitters Inc.
Consumer Cyclical12.853.13%1,946 M7.302.1334.2210.821.74%-49.25%
AFYA
AFYA
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Educational Services12.333.09%1,041 M22.400.5322.808.736.66%-21.51%
AEM
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ABM
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ABM Industries Incorporated
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ACR
ACR
ACRES Commercial Realty Corp
Finance and Insurance9.712.97%83 M19.800.4717.207.784.30%-22.13%
AG
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Archer-Daniels-Midland Company
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ABIO
ABIO
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Healthcare2.472.92%35 M-2.00-1.183.171.713.78%14.88%
Industrials8.252.74%7,155 M-266.70-0.0410.396.003.13%-1.90%
Analog Devices Inc.
Technology179.262.70%88,559 M53.303.56191.95138.501.93%1.99%
Automatic Data Processing Inc.
Industrials256.782.62%103,796 M35.507.03257.16192.263.29%4.14%
AAP
AAP
Consumer Cyclical202.532.59%11,629 M21.609.05244.55164.004.24%-15.57%
AEP
AEP
American Electric Power Company Inc.
Utilities103.782.55%51,666 M19.705.09104.8180.223.70%16.65%
Autodesk Inc.
Technology233.012.53%47,396 M99.902.23344.39163.205.58%-17.13%
Technology445.672.48%199,635 M42.4010.31699.54338.002.61%-21.41%
ABNB
ABNB
Airbnb Inc.
Administrative and Support and Waste Management and Remediation Services124.512.48%68,252 M62.601.99212.5886.717.50%-25.21%
Manufacturing0.172.46%9 M-0.10-1.663.950.126.46%-67.43%
ABCL
ABCL
AbCellera Biologics Inc
Manufacturing13.682.40%3,161 M18.300.7222.635.4216.33%-4.34%
AGE
AGE
AgeX Therapeutics Inc - Ordinary Shares
0.692.39%26 M-2.70-0.251.390.520.56%-37.07%
ACCO
ACCO
Acco Brands Corporation
Industrials6.992.34%632 M5.801.259.766.36-2.65%-15.38%
ACGL
ACGL
Arch Capital Group Ltd.
Financial Services47.042.31%16,482 M10.804.1950.7337.446.55%5.83%
AFL
AFL
AFLAC Incorporated
Financial Services64.032.22%38,180 M9.006.6767.2051.287.47%9.66%
AES
AES
The AES Corporation
Utilities24.892.22%15,924 M-42.60-0.5326.5218.624.27%2.43%
ACM
ACM
AECOM
Industrials76.572.16%10,279 M49.001.4779.9760.747.88%-1.01%
ACNB
ACNB
ACNB Corporation
Financial Services36.012.16%298 M11.103.1136.1427.153.87%15.12%
AAPL
AAPL
Apple Inc.
Technology172.102.14%2,859,274 M27.306.10182.94129.044.39%-3.08%
ABOS
ABOS
Acumen Pharmaceuticals Inc
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ACN
ACN
Accenture plc Class A (Ireland)
Technology320.441.91%195,957 M30.1010.47417.37261.773.26%-22.70%
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ABC
ABC
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ACA
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AAL
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ACMR
ACMR
ACM Research Inc.
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ABCB
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ABTX
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ACOR
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Aethlon Medical Inc.
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AFG
AFG
American Financial Group Inc.
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ACHC
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AFMD
AFMD
Affimed N.V.
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Healthcare94.411.31%1,502 M33.802.81108.1168.571.09%0.96%
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ABR
ABR
Arbor Realty Trust
Real Estate15.741.22%2,701 M7.902.0820.7412.18-1.81%-14.08%
ABUS
ABUS
Arbutus Biopharma Corporation
Healthcare2.501.21%369 M-4.20-0.606.501.930.00%-35.73%
A
A
Agilent Technologies Inc.
Healthcare133.551.21%38,497 M32.004.19179.57112.520.78%-16.35%
Alliance Data Systems Corporation
Financial Services56.801.16%2,932 M3.50106.0853.30-15.65%
AAON
AAON
AAON Inc.
Basic Materials61.721.10%3,176 M55.701.1583.7947.50-0.10%-22.30%
AAU
AAU
Basic Materials0.241.08%33 M-10.20-0.030.490.211.25%-18.63%
AEVA
AEVA
Aeva Technologies Inc
Manufacturing4.031.00%891 M-7.60-0.5910.752.47-9.64%-46.69%
ABMD
ABMD
ABIOMED Inc.
Healthcare293.590.91%12,807 M61.804.79379.30219.85-0.06%-18.26%
ABT
ABT
Abbott Laboratories
Healthcare111.480.90%188,974 M22.804.84142.60101.242.28%-20.79%
ACRE
ACRE
Ares Commercial Real Estate Corporation
Real Estate13.810.88%736 M12.101.1116.4811.181.54%-5.02%
AEE
AEE
Ameren Corporation
Utilities94.830.85%24,147 M23.603.9299.2080.273.20%6.54%
AAT
AAT
American Assets Trust Inc.
Real Estate30.430.83%1,790 M44.900.6740.8328.382.77%-18.92%
ACTG
ACTG
Acacia Research Corporation
Industrials4.870.83%222 M1.903.627.543.30-2.60%-5.07%
ACT
ACT
26.960.82%4,240 M6.404.0627.0018.763.93%30.43%
Healthcare8.220.74%376 M-4.80-1.708.254.02
AGCO
AGCO
AGCO Corporation
Industrials112.700.61%7,949 M10.2010.59150.2888.555.19%-2.86%
Agree Realty Corporation
Real Estate78.970.59%6,213 M41.001.8979.9861.621.94%10.66%
Healthcare0.580.44%15 M-0.70-0.885.080.45-3.08%-78.70%
AEZS
AEZS
Aeterna Zentaris Inc.
Healthcare4.990.40%24 M-2.40-2.1224.384.11-1.19%-43.82%
ABBV
ABBV
AbbVie Inc.
Healthcare142.600.37%247,976 M19.907.11175.91105.561.61%5.32%
AAN
AAN
Aaron's Inc.
Industrials14.600.34%429 M8.301.7931.6911.980.00%-40.77%
ACEV
ACEV
ACE Convergence Acquisition Corp
Manufacturing10.240.10%143 M18.9010.259.630.20%2.81%
AAC
AAC
AAC Holdings Inc.
Healthcare9.880.00%1,235 M91.800.119.909.660.00%1.44%
AAIC
AAIC
Arlington Asset Investment Corp
Finance and Insurance3.390.00%100 M-11.00-0.294.042.882.73%-3.14%
ACC
ACC
American Campus Communities Inc
Real Estate65.420.00%9,125 M130.700.5165.4648.010.08%14.19%
ACIW
ACIW
ACI Worldwide Inc.
Technology26.130.00%2,949 M19.901.3136.0123.630.81%-24.70%
ACRS
ACRS
Aclaris Therapeutics Inc.
Healthcare16.800.00%1,177 M-13.40-1.3419.979.26-6.67%15.54%
AESE
AESE
Allied Esports Entertainment Inc
Arts, Entertainment, and Recreation1.570.00%61 M1.001.562.501.201.30%-8.19%
AFIB
AFIB
Acutus Medical Inc.
Manufacturing1.660.00%43 M-0.30-4.5013.800.487.79%-51.32%

#### Top 100 losers Today

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APTX
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AUD
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ABEO
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AIT
AIT
Applied Industrial Technologies Inc.
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ACXP
ACXP
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AMC
AMC
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Consumer Cyclical24.44-3.97%11,603 M-15.50-1.5952.799.702.00%-10.15%
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ACHV
ACHV
Achieve Life Sciences Inc.
Healthcare5.00-3.85%48 M-1.30-3.8010.094.780.32%-35.73%
AE
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AEHL
AEHL
Antelope Enterprise Holdings Ltd
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ATNX
ATNX
Athenex Inc.
Healthcare0.52-3.33%134 M-0.60-1.723.910.41-52.73%-61.76%
ARAV
ARAV
Aravive Inc.
Healthcare0.90-3.22%29 M-0.50-2.124.400.80-10.45%-59.11%
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ALOT
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AINC
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ASUR
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Asure Software Inc
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ATRI
ATRI
Atrion Corporation
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ARLO
ARLO
Arlo Technologies Inc.
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ALRN
ALRN
Aileron Therapeutics Inc.
Healthcare0.21-2.08%16 M-0.70-0.291.270.136.05%-62.34%
AC
AC
Associated Capital Group Inc.
Financial Services39.68-1.93%903 M-25.60-1.5947.5033.69-2.36%-7.72%
ACET
ACET
Aceto Corporation
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AJX
AJX
Great Ajax Corp.
Real Estate10.16-1.65%234 M23.800.4714.748.68-2.87%-22.80%
AGFS
AGFS
AgroFresh Solutions Inc.
Basic Materials1.84-1.60%97 M-2.20-0.822.441.520.00%-7.54%
AGLE
AGLE
Aeglea BioTherapeutics Inc.
Healthcare0.49-1.58%25 M-0.30-1.268.500.3715.22%-89.64%
APTO
APTO
Aptose Biosciences Inc.
Healthcare0.82-1.57%77 M-1.40-0.633.130.71-4.43%-39.12%
AREC
AREC
American Resources Corporation
Basic Materials2.52-1.56%165 M-5.00-0.502.741.200.00%40.00%
ASPS
ASPS
Altisource Portfolio Solutions S.A.
Industrials11.21-1.49%180 M7.401.5814.588.07-4.60%-0.09%
AHPI
AHPI
Allied Healthcare Products Inc.
Healthcare2.10-1.41%9 M-5.40-0.4712.151.55-16.67%-63.92%
ATY
ATY
Information2.83-1.39%151 M36.700.078.691.657.60%-24.73%
ALKT
ALKT
Alkami Technology Inc
Information15.66-1.39%1,376 M-23.70-0.6532.509.234.89%-21.93%
ALTA
ALTA
Alterola Biotech Inc
Industrials44.16-1.25%834 M19.002.3645.2239.11
ASRV
ASRV
AmeriServ Financial Inc.
Financial Services3.98-1.24%67 M8.900.454.523.681.53%3.11%
ACU
ACU
Acme United Corporation.
Consumer Defensive28.23-1.16%96 M14.202.2641.9627.22-2.04%-16.23%
APT
APT
Alpha Pro Tech Ltd.
Basic Materials4.47-1.11%58 M17.000.288.643.76-5.89%-25.13%
ATLC
ATLC
Atlanticus Holdings Corporation
Financial Services37.33-1.09%573 M5.3010.3291.9830.58-7.02%-47.66%
AUBN
AUBN
Auburn National Bancorporation Inc.
Financial Services28.00-1.06%94 M12.502.1637.1125.823.32%-13.31%
AEYE
AEYE
AudioEye Inc.
Technology6.73-1.03%72 M-4.70-1.3413.483.106.66%-4.13%
AATC
AATC
Autoscope Technologies Corporation
Manufacturing4.97-1.00%27 M23.600.848.384.84-1.19%-20.99%
AA
AA
Alcoa Corporation
Basic Materials52.76-0.96%9,065 M9.505.2498.0936.618.45%-11.45%
AUMN
AUMN
Golden Minerals Company
Basic Materials0.33-0.94%53 M59.500.010.630.29-1.92%-6.41%
ATXI
ATXI
Avenue Therapeutics Inc.
Healthcare0.29-0.93%6 M-1.00-0.301.850.20-0.34%-68.17%
AEL
AEL
American Equity Investment Life Holding Company
Financial Services42.29-0.82%3,809 M4.907.4644.4927.1216.69%8.66%
ASC
ASC
Ardmore Shipping Corporation
Industrials9.60-0.72%346 M-291.30-0.039.833.079.84%184.02%
ARMP
ARMP
Armata Pharmaceuticals Inc.
Healthcare4.22-0.71%152 M-4.20-1.006.492.82-0.12%-22.99%
ATH
ATH
Athene Holding Ltd. Class A
Financial Services83.33-0.69%16,217 M4.5019.4491.2661.620.00%
ACER
ACER
Acer Therapeutics Inc.
Healthcare1.47-0.67%24 M-1.10-1.393.771.16-4.55%-35.53%
ALIM
ALIM
Alimera Sciences Inc.
Healthcare6.73-0.59%47 M-2.80-2.497.923.94-6.29%31.19%
ARR
ARR
ARMOUR Residential REIT Inc.
Real Estate7.59-0.52%877 M-6.20-1.2511.185.57-1.81%-22.63%
ATHN
ATHN
athenahealth Inc.
Technology9.59-0.52%314 M-41.2010.898.74
ATGE
ATGE
Consumer Defensive37.57-0.45%1,762 M6.006.5240.6019.14-2.42%27.10%
ARKR
ARKR
Ark Restaurants Corp.
Consumer Cyclical21.75-0.41%75 M6.003.6122.2014.392.98%29.27%
APA
APA
Apache Corporation
Energy34.70-0.40%10,671 M3.608.9251.9515.557.73%29.04%
ATIP
ATIP
ATI Physical Therapy Inc
Manufacturing0.95-0.38%217 M-0.20-5.564.630.91-18.66%-71.93%
AFIN
AFIN
American Finance Trust Inc.
Real Estate8.23-0.36%1,003 M-28.009.487.76-9.86%
Healthcare3.38-0.29%6 M-0.50-6.904.503.19-6.11%-12.21%
AMPE
AMPE
Ampio Pharmaceuticals Inc.
Healthcare0.10-0.29%22 M-1.00-0.101.830.09-4.51%-81.81%
ANGO
ANGO
AngioDynamics Inc.
Healthcare24.23-0.29%914 M-34.90-0.6832.0017.562.24%-12.15%
ABSI
ABSI
Absci Corp
Professional, Scientific, and Technical Services4.78-0.21%362 M-3.70-1.4124.512.9323.51%-41.71%
ARVN
ARVN
Arvinas Inc.
Healthcare54.46-0.15%2,969 M-12.50-4.4698.6734.90-2.45%-33.70%
AFBI
AFBI
Affinity Bancshares Inc
Finance and Insurance14.63-0.14%97 M15.200.9918.0013.19-2.47%-5.00%
AR
AR
Antero Resources Corporation
Energy40.26-0.12%11,434 M12.103.0848.8010.9111.77%130.06%
ASTC
ASTC
Astrotech Corporation
Industrials0.48-0.10%24 M-8.10-0.161.210.42-1.07%-29.15%
AAWW
AAWW
Atlas Air Worldwide Holdings
Industrials100.09-0.10%2,845 M6.9016.13101.6258.700.09%6.34%
ACBI
ACBI
Atlantic Capital Bancshares Inc.
Financial Services32.34-0.09%647 M13.402.3833.6822.1412.41%
ALSN
ALSN
Allison Transmission Holdings Inc.
Consumer Cyclical38.77-0.08%3,608 M8.204.6342.0032.552.24%6.66%
AMED
AMED
Amedisys Inc
Healthcare122.36-0.07%3,876 M28.704.30188.88101.61-0.71%-24.41%
AAC
AAC
AAC Holdings Inc.
Healthcare9.880.00%1,235 M91.800.119.909.660.00%1.44%
AAIC
AAIC
Arlington Asset Investment Corp
Finance and Insurance3.390.00%100 M-11.00-0.294.042.882.73%-3.14%
ACC
ACC
American Campus Communities Inc
Real Estate65.420.00%9,125 M130.700.5165.4648.010.08%14.19%
ACIW
ACIW
ACI Worldwide Inc.
Technology26.130.00%2,949 M19.901.3136.0123.630.81%-24.70%
ACRS
ACRS
Aclaris Therapeutics Inc.
Healthcare16.800.00%1,177 M-13.40-1.3419.979.26-6.67%15.54%
AESE
AESE
Allied Esports Entertainment Inc
Arts, Entertainment, and Recreation1.570.00%61 M1.001.562.501.201.30%-8.19%
AFIB
AFIB
Acutus Medical Inc.
Manufacturing1.660.00%43 M-0.30-4.5013.800.487.79%-51.32%
AGM.A
AGM.A
AGM.A
110.370.00%1,155 M9.6011.21124.3787.502.95%-8.02%
AKU
AKU
Akumin Inc
Health Care and Social Assistance0.770.00%60 M-0.80-0.872.870.4617.50%-56.00%
AMTBB
AMTBB
Amerant Bancorp Inc. Class B Common Stock
Financial Services28.720.00%1,090 M19.401.4829.0519.50
AMTI
AMTI
Applied Molecular Transport Inc.
Manufacturing1.960.00%71 M-0.50-3.4933.281.714.26%-85.98%
ANAT
ANAT
American National Insurance Company
Financial Services190.020.00%5,109 M8.0023.74195.89187.100.00%0.62%
ANGN
ANGN
Angion Biomedica Corp
Manufacturing1.030.00%31 M-1.00-1.0113.660.98-1.90%-64.48%
ARDS
ARDS
Aridis Pharmaceuticals Inc.
Healthcare2.310.00%39 M-0.70-3.794.340.880.87%-0.86%
ARNA
ARNA
Arena Pharmaceuticals Inc.
Healthcare99.990.00%6,165 M-9.90-9.69100.0045.507.59%
ASRT
ASRT
Assertio Therapeutics Inc.
Healthcare3.800.00%174 M52.100.064.440.854.11%74.31%
ATRS
ATRS
Antares Pharma Inc.
Healthcare5.590.00%955 M25.300.245.603.110.00%56.58%
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