MTB Insider Trading

Insider Ownership Percentage: 0.82%
Insider Buying (Last 12 Months): $0.00
Insider Selling (Last 12 Months): $44,015,336.22

M&T Bank Insider Trading History Chart

This chart shows the insider buying and selling history at M&T Bank by year and by quarter.

Skip ChartChart Data in Insider Trading History Table

M&T Bank Share Price & Price History

Current Price: $194.68
Price Change: Price Decrease of -2.88 (-1.46%)
As of 10/31/2024 01:00 AM ET

This chart shows the closing price history over time for MTB up to the past year.

Skip Chart and Table DataPrice Data in Insider Trading History Table
Days: 30 | 90 | 365

M&T Bank Insider Trading History

Transaction DateInsider NameTitleBuy/SellNumber of SharesAverage Share PriceTotal TransactionShares Held After TransactionDetails
10/28/2024John R TaylorEVPSell1,436$195.03$280,063.085,618View SEC Filing Icon  
10/28/2024Rene F JonesCEOSell23,071$193.88$4,473,005.4877,226View SEC Filing Icon  
10/22/2024John P. BarnesDirectorSell20,000$193.97$3,879,400.0049,960View SEC Filing Icon  
9/3/2024Denis J. SalamoneDirectorSell10,000$172.03$1,720,300.0044,902View SEC Filing Icon  
8/19/2024Kirk W. WaltersDirectorSell2,471$24.60$60,786.6020,414View SEC Filing Icon  
8/15/2024Kirk W. WaltersDirectorSell20$24.60$492.0024,724View SEC Filing Icon  
8/13/2024Kirk W. WaltersDirectorSell350$24.60$8,610.0039,591View SEC Filing Icon  
8/9/2024Kevin J. PearsonVice ChairmanSell6,095$162.28$989,096.6047,944View SEC Filing Icon  
8/9/2024Michael J. TodaroEVPSell4,791$162.57$778,872.873,086View SEC Filing Icon  
7/29/2024Kirk W. WaltersDirectorSell8$24.85$198.8039,941View SEC Filing Icon  
7/26/2024Kirk W. WaltersDirectorSell7,464$173.97$1,298,512.0815,045View SEC Filing Icon  
7/24/2024Gary N. GeiselVice ChairmanSell500$172.50$86,250.0016,429View SEC Filing Icon  
7/23/2024Robert E Sadler JrDirectorSell1,000$172.23$172,230.0031,796View SEC Filing Icon  
5/14/2024John P. BarnesDirectorSell43,426$154.50$6,709,317.0035,480View SEC Filing Icon  
5/10/2024Christopher E. KayEVPSell1,821$153.78$280,033.388,579View SEC Filing Icon  
5/9/2024Kirk W. WaltersDirectorSell7,767$152.39$1,183,613.136,348View SEC Filing Icon  
5/6/2024Kirk W. WaltersDirectorSell16,179$148.01$2,394,653.796,348View SEC Filing Icon  
5/3/2024Doris P. MeisterEVPSell3,362$147.27$495,121.74View SEC Filing Icon  
5/3/2024John P. BarnesDirectorSell13,360$147.00$1,963,920.0035,480View SEC Filing Icon  
4/25/2024John P. BarnesDirectorSell10,000$147.11$1,471,100.0034,545View SEC Filing Icon  
4/17/2024Doris P. MeisterEVPSell1,638$138.21$226,387.983,362View SEC Filing Icon  
3/13/2024Kirk W. WaltersDirectorSell28,845$145.00$4,182,525.006,367View SEC Filing Icon  
3/11/2024Doris P. MeisterEVPSell3,961$143.60$568,799.605,000View SEC Filing Icon  
2/23/2024Doris P. MeisterEVPSell1,675$137.91$230,999.258,961View SEC Filing Icon  
2/1/2024Doris P. MeisterEVPSell1,000$132.30$132,300.007,274View SEC Filing Icon  
12/11/2023John P. BarnesDirectorSell16,378$133.28$2,182,859.8434,545View SEC Filing Icon  
12/7/2023John P. BarnesDirectorSell32,940$132.80$4,374,432.0034,545View SEC Filing Icon  
12/1/2023Kirk W. WaltersDirectorSell29,004$130.00$3,770,520.007,088View SEC Filing Icon  
11/21/2023Robert J. BojdakEVPSell800$126.17$100,936.0016,897View SEC Filing Icon  
10/30/2023Doris P. MeisterEVPSell1,000$110.58$110,580.006,055View SEC Filing Icon  
10/25/2023Daryl N. BibleCFOBuy5,000$111.04$555,200.0032,876View SEC Filing Icon  
8/11/2023Doris P. MeisterEVPSell1,000$136.02$136,020.007,055View SEC Filing Icon  
7/28/2023John P. BarnesDirectorSell53,542$140.00$7,495,880.0034,545View SEC Filing Icon  
7/27/2023Doris P. MeisterEVPSell1,334$140.43$187,333.628,055View SEC Filing Icon  
6/1/2023Daryl N. BibleCFOBuy10,000$120.61$1,206,100.0010,000View SEC Filing Icon  
5/17/2023Rudina SeseriDirectorSell700$118.40$82,880.001,736View SEC Filing Icon  
9/9/2022D. Scott N WarmanEVPSell2,000$188.55$377,100.008,349View SEC Filing Icon  
8/19/2022Gary N. GeiselDirectorSell533$189.34$100,918.2217,740View SEC Filing Icon  
8/19/2022Michael J. TodaroEVPSell1,050$188.83$198,271.503,667View SEC Filing Icon  
8/15/2022Robert J. BojdakEVPSell1,290$188.80$243,552.0017,785View SEC Filing Icon  
8/12/2022Michele D TrolliEVPSell4,667$189.28$883,369.769,197View SEC Filing Icon  
8/9/2022Kirk W. WaltersDirectorSell21,116$180.00$3,800,880.006,134View SEC Filing Icon  
7/25/2022Edna Jennifer WarrenEVPBuy6$171.20$1,027.206View SEC Filing Icon  
6/8/2022Robert J. BojdakEVPSell525$177.82$93,355.5019,075View SEC Filing Icon  
6/3/2022Christopher E. KayEVPSell2,200$178.83$393,426.005,350View SEC Filing Icon  
5/17/2022Kevin J. PearsonVice ChairmanSell5,000$169.71$848,550.0039,008View SEC Filing Icon  
2/3/2022Jeffrey J TengelPresidentSell302,634$19.78$5,986,100.52View SEC Filing Icon  
11/12/2021D. Scott N WarmanEVPSell3,964$159.88$633,764.32View SEC Filing Icon  
See Full Table

SEC Filings (Institutional Ownership Changes) for M&T Bank (NYSE:MTB)

84.68% of M&T Bank stock is owned by institutions. Institutional ownership can be a sign of analyst confidence in the fundamentals of the stock.

Institutional Buying and Selling by Quarter

This chart shows the instiutional buying and selling at MTB by year and by quarter.

Skip Institutional Buying and Selling Chart and Table DataRead Chart Data in Institutional Trading History Table

M&T Bank Institutional Trading History

Reporting DateHedge FundShares HeldMarket Value% of PortfolioQuarterly Change in SharesOwnership in CompanyDetails
10/31/2024Ascent Wealth Partners LLC1,197$0.21M0.0%N/A0.001%Search for SEC Filing on Google Icon
10/31/2024Principal Financial Group Inc.199,111$35.47M0.0%+1.4%0.119%Search for SEC Filing on Google Icon
10/31/2024Cozad Asset Management Inc.9,245$1.65M0.2%-13.9%0.006%Search for SEC Filing on Google Icon
10/31/2024Jackson Square Capital LLC3,483$0.62M0.2%N/A0.002%Search for SEC Filing on Google Icon
10/31/2024Graypoint LLC1,318$0.24M0.0%N/A0.001%Search for SEC Filing on Google Icon
10/31/2024Forte Capital LLC ADV2,435$0.43M0.0%+10.6%0.001%Search for SEC Filing on Google Icon
10/31/2024M&G PLC8,147$1.45M0.0%-88.7%0.005%Search for SEC Filing on Google Icon
10/31/2024LGT Financial Advisors LLC270$48K0.1%-44.4%0.000%Search for SEC Filing on Google Icon
10/30/2024Harvest Portfolios Group Inc.35,254$6.28M0.2%-9.2%0.021%Search for SEC Filing on Google Icon
10/30/2024Radnor Capital Management LLC1,998$0.36M0.1%N/A0.001%Search for SEC Filing on Google Icon
10/30/2024Catalina Capital Group LLC2,768$0.49M0.2%-3.7%0.002%Search for SEC Filing on Google Icon
10/30/2024Crestwood Advisors Group LLC3,103$0.55M0.0%+1.9%0.002%Search for SEC Filing on Google Icon
10/30/2024Amalgamated Bank32,771$5.84M0.0%-22.5%0.020%Search for SEC Filing on Google Icon
10/30/2024Gulf International Bank UK Ltd13,111$2.34M0.1%-4.2%0.008%Search for SEC Filing on Google Icon
10/30/2024Catalyst Capital Advisors LLC374$67K0.0%N/A0.000%Search for SEC Filing on Google Icon
10/30/2024Mn Services Vermogensbeheer B.V.63,600$11.33M0.1%-2.5%0.038%Search for SEC Filing on Google Icon
10/30/2024QRG Capital Management Inc.1,973$0.35M0.0%+12.7%0.001%Search for SEC Filing on Google Icon
10/30/2024Asset Management One Co. Ltd.65,685$11.70M0.0%+1.9%0.039%Search for SEC Filing on Google Icon
10/30/2024National Pension Service268,138$47.76M0.0%+5.2%0.161%Search for SEC Filing on Google Icon
10/29/2024Robeco Institutional Asset Management B.V.11,341$2.02M0.0%-1.0%0.007%Search for SEC Filing on Google Icon
10/29/2024TrueWealth Advisors LLC1,180$0.21M0.1%N/A0.001%Search for SEC Filing on Google Icon
10/29/2024Van ECK Associates Corp1,627$0.32M0.0%-90.7%0.001%Search for SEC Filing on Google Icon
10/29/2024Janney Montgomery Scott LLC77,438$13.79M0.0%+0.5%0.046%Search for SEC Filing on Google Icon
10/29/2024Visionary Horizons LLC3,533$0.63M0.4%+7.2%0.002%Search for SEC Filing on Google Icon
10/29/2024Farther Finance Advisors LLC2,653$0.47M0.0%+23.7%0.002%Search for SEC Filing on Google Icon
10/28/2024Absher Wealth Management LLC240,142$42.77M5.5%-28.5%0.144%Search for SEC Filing on Google Icon
10/28/2024New York State Common Retirement Fund125,900$22.43M0.0%-25.0%0.075%Search for SEC Filing on Google Icon
10/28/2024Stephens Inc. AR1,212$0.22M0.0%-14.2%0.001%Search for SEC Filing on Google Icon
10/28/2024US Bancorp DE6,743$1.20M0.0%+3.0%0.004%Search for SEC Filing on Google Icon
10/28/2024Meitav Investment House Ltd.2,270$0.39M0.0%+3.1%0.001%Search for SEC Filing on Google Icon
10/25/20241620 Investment Advisors Inc.400$71K0.1%-50.0%0.000%Search for SEC Filing on Google Icon
10/25/2024Folger Nolan Fleming Douglas Capital Management Inc.12,200$2.17M0.2%-10.0%0.007%Search for SEC Filing on Google Icon
10/25/2024Cornerstone Wealth Group LLC28,045$5M0.4%+1.0%0.017%Search for SEC Filing on Google Icon
10/25/2024Fiducient Advisors LLC1,970$0.35M0.0%-9.2%0.001%Search for SEC Filing on Google Icon
10/25/2024First Trust Direct Indexing L.P.5,205$0.93M0.0%+28.5%0.003%Search for SEC Filing on Google Icon
10/25/2024New York State Teachers Retirement System155,652$27.73M0.1%-1.7%0.093%Search for SEC Filing on Google Icon
10/25/2024Adams Diversified Equity Fund Inc.79,400$14.14M0.5%N/A0.048%Search for SEC Filing on Google Icon
10/25/2024Hedeker Wealth LLC3,519$0.63M0.2%+1.6%0.002%Search for SEC Filing on Google Icon
10/25/2024abrdn plc65,045$11.54M0.0%-4.6%0.039%Search for SEC Filing on Google Icon
10/25/2024Cantor Fitzgerald Investment Advisors L.P.18,322$3.26M0.2%-69.9%0.011%Search for SEC Filing on Google Icon
10/24/2024Old Port Advisors9,894$1.76M0.5%-3.6%0.006%Search for SEC Filing on Google Icon
10/24/2024Nisa Investment Advisors LLC67,337$11.99M0.1%-4.4%0.040%Search for SEC Filing on Google Icon
10/24/2024Barrett & Company Inc.10,224$1.82M0.8%-1.8%0.006%Search for SEC Filing on Google Icon
10/24/2024Leuthold Group LLC28,660$5.11M0.6%+34.6%0.017%Search for SEC Filing on Google Icon
10/24/2024Canoe Financial LP588,302$103.20M2.5%+29.4%0.353%Search for SEC Filing on Google Icon
10/24/2024State of Alaska Department of Revenue19,399$3.46M0.0%+6.9%0.012%Search for SEC Filing on Google Icon
10/24/2024Frank Rimerman Advisors LLC5,644$1.01M0.1%+1.0%0.003%Search for SEC Filing on Google Icon
10/24/2024DekaBank Deutsche Girozentrale30,240$5.27M0.0%+1.2%0.018%Search for SEC Filing on Google Icon
10/24/2024Boston Trust Walden Corp48,759$8.69M0.1%-16.5%0.029%Search for SEC Filing on Google Icon
10/24/2024Wealth Enhancement Advisory Services LLC16,306$2.90M0.0%-1.6%0.010%Search for SEC Filing on Google Icon
10/24/2024Forsta AP Fonden35,400$6.31M0.0%+11.3%0.021%Search for SEC Filing on Google Icon
10/23/2024Mirae Asset Global Investments Co. Ltd.111,772$19.61M0.1%+13.6%0.067%Search for SEC Filing on Google Icon
10/23/2024Allworth Financial LP1,260$0.22M0.0%+7.3%0.001%Search for SEC Filing on Google Icon
10/23/2024Hudock Inc.10,402$1.85M0.3%+3.5%0.006%Search for SEC Filing on Google Icon
10/23/2024Court Place Advisors LLC2,854$0.51M0.1%-2.1%0.002%Search for SEC Filing on Google Icon
10/23/2024Financial Management Network Inc.4,117$0.74M0.2%-3.2%0.002%Search for SEC Filing on Google Icon
10/23/2024Ballentine Partners LLC1,732$0.31M0.0%+6.4%0.001%Search for SEC Filing on Google Icon
10/23/2024Assenagon Asset Management S.A.35,549$6.33M0.0%+8.3%0.021%Search for SEC Filing on Google Icon
10/23/2024IFM Investors Pty Ltd31,578$5.63M0.1%-2.5%0.019%Search for SEC Filing on Google Icon
10/23/2024Hennion & Walsh Asset Management Inc.5,817$1.04M0.0%+59.5%0.003%Search for SEC Filing on Google Icon
10/22/2024International Assets Investment Management LLC110,166$19.62M0.0%+17,784.1%0.066%Search for SEC Filing on Google Icon
10/22/2024Monte Financial Group LLC30,557$5.44M2.3%-0.5%0.018%Search for SEC Filing on Google Icon
10/22/2024Courier Capital LLC31,421$5.60M0.4%-0.9%0.019%Search for SEC Filing on Google Icon
10/22/2024Sterling Investment Counsel LLC5,799$1.03M0.4%-22.6%0.003%Search for SEC Filing on Google Icon
10/22/2024Hartford Investment Management Co.10,573$1.88M0.1%-1.2%0.006%Search for SEC Filing on Google Icon
10/22/2024Private Advisor Group LLC27,255$4.86M0.0%+1.6%0.016%Search for SEC Filing on Google Icon
10/22/2024Waldron Private Wealth LLC8,306$1.48M0.1%-2.8%0.005%Search for SEC Filing on Google Icon
10/22/2024Eastern Bank2,139$0.38M0.0%N/A0.001%Search for SEC Filing on Google Icon
10/22/2024Signaturefd LLC1,895$0.34M0.0%+7.5%0.001%Search for SEC Filing on Google Icon
10/22/2024Sequoia Financial Advisors LLC4,897$0.87M0.0%+44.7%0.003%Search for SEC Filing on Google Icon
10/21/2024Sky Investment Group LLC31,603$5.63M1.0%-3.2%0.019%Search for SEC Filing on Google Icon
10/21/2024Traphagen Investment Advisors LLC1,357$0.24M0.0%-15.9%0.001%Search for SEC Filing on Google Icon
10/21/2024Foundations Investment Advisors LLC2,167$0.39M0.0%+14.8%0.001%Search for SEC Filing on Google Icon
10/21/2024Whittier Trust Co. of Nevada Inc.2,178$0.39M0.0%-11.4%0.001%Search for SEC Filing on Google Icon
10/21/2024Robinson Value Management Ltd.26,448$4.71M3.1%+1.4%0.016%Search for SEC Filing on Google Icon
10/19/2024Columbus Macro LLC7,940$1.43M0.5%-4.9%0.005%Search for SEC Filing on Google Icon
10/19/2024Allspring Global Investments Holdings LLC10,803$1.92M0.0%-20.0%0.006%Search for SEC Filing on Google Icon
10/19/2024Vest Financial LLC150,454$26.80M0.5%+1.3%0.090%Search for SEC Filing on Google Icon
10/19/2024OLD National Bancorp IN1,240$0.22M0.0%-33.4%0.001%Search for SEC Filing on Google Icon
10/19/2024Means Investment CO. Inc.4,122$0.73M0.1%-1.5%0.002%Search for SEC Filing on Google Icon
10/18/2024Resonant Capital Advisors LLC2,110$0.38M0.0%+28.6%0.001%Search for SEC Filing on Google Icon
10/18/2024Wealth Alliance Advisory Group LLC1,554$0.28M0.1%N/A0.001%Search for SEC Filing on Google Icon
10/18/2024Ferguson Wellman Capital Management Inc.1,157$0.21M0.0%-24.4%0.001%Search for SEC Filing on Google Icon
10/18/2024Raymond James & Associates66,209$11.79M0.0%+11.0%0.040%Search for SEC Filing on Google Icon
10/18/2024ST Germain D J Co. Inc.14,195$2.53M0.1%-5.8%0.009%Search for SEC Filing on Google Icon
10/18/2024Blue Trust Inc.2,491$0.44M0.0%+79.1%0.001%Search for SEC Filing on Google Icon
10/17/2024Sumitomo Mitsui DS Asset Management Company Ltd17,694$3.15M0.0%+13.6%0.011%Search for SEC Filing on Google Icon
10/16/2024Trust Co. of Vermont16,160$2.88M0.1%-0.8%0.010%Search for SEC Filing on Google Icon
10/16/2024Smallwood Wealth Investment Management LLC1,523$0.27M0.2%-82.7%0.001%Search for SEC Filing on Google Icon
10/16/2024Bleakley Financial Group LLC3,401$0.61M0.0%+9.9%0.002%Search for SEC Filing on Google Icon
10/16/2024nVerses Capital LLC300$53K0.0%N/A0.000%Search for SEC Filing on Google Icon
10/16/2024Culbertson A N & Co. Inc.13,268$2.36M0.4%-0.5%0.008%Search for SEC Filing on Google Icon
10/16/2024Annapolis Financial Services LLC376$67K0.0%+150.7%0.000%Search for SEC Filing on Google Icon
10/16/2024Alliance Wealth Advisors LLC1,281$0.23M0.1%N/A0.001%Search for SEC Filing on Google Icon
10/16/2024Regent Peak Wealth Advisors LLC1,241$0.22M0.0%N/A0.001%Search for SEC Filing on Google Icon
10/16/2024Vontobel Holding Ltd.4,576$0.82M0.0%+1.9%0.003%Search for SEC Filing on Google Icon
10/16/2024Clearview Wealth Advisors LLC1,600$0.29M0.2%-3.3%0.001%Search for SEC Filing on Google Icon
10/16/2024Applied Capital LLC FL1,200$0.21M0.2%N/A0.001%Search for SEC Filing on Google Icon
10/15/2024First United Bank & Trust8,757$1.56M0.6%-2.0%0.005%Search for SEC Filing on Google Icon
10/15/2024Norway Savings Bank5,482$0.98M0.5%-12.0%0.003%Search for SEC Filing on Google Icon
Data available starting January 2016

See Full Table
M&T Bank logo
M&T Bank Corporation operates as a bank holding company for Manufacturers and Traders Trust Company and Wilmington Trust, National Association that engages in the provision of retail and commercial banking products and services in the United States. The company operates through three segments: Commercial Bank, Retail Bank, and Institutional Services and Wealth Management. It offers a range of credit products and banking services, such as commercial lending and leasing, letters of credits, commercial real estate loans, and credit facilities secured by various commercial real estate to middle-market and large commercial customers. The company also provides customers deposit products, including demand, savings and time accounts, and other services; automobile and recreational finance loans, home equity loans and lines of credit, credit cards, and other loan products, as well as residential mortgage and real estate loans; business loans, cash management, payroll, and direct deposit services to consumers and small businesses through branch network, telephone banking, internet banking, and automated teller machines. In addition, it offers trustee, agency, investment management, security brokerage, and administrative services; personal trust, planning, fiduciary, asset management, family office, and other services; and investment products, including mutual funds and annuities, and other services for corporations and institutions, investment bankers, corporate tax, finance and legal executives, and other institutional clients. The company was founded in 1856 and is headquartered in Buffalo, New York.
Read More on M&T Bank

Today's Range

Now: $194.68
Low: $194.14
High: $197.89

50 Day Range

MA: $178.22
Low: $164.65
High: $198.83

52 Week Range

Now: $194.68
Low: $111.08
High: $200.94

Volume

1,070,214 shs

Average Volume

1,039,718 shs

Market Capitalization

$32.48 billion

P/E Ratio

14.41

Dividend Yield

2.80%

Beta

0.75

Who are the company insiders with the largest holdings of M&T Bank?

M&T Bank's top insider shareholders include:
  1. Rene F Jones (CEO)
  2. John P Barnes (Director)
  3. Kevin J Pearson (Vice Chairman)
  4. Denis J Salamone (Director)
  5. Kirk W Walters (Director)
  6. Daryl N Bible (CFO)
  7. Robert E Sadler Jr (Director)
  8. Robert J Bojdak (EVP)
  9. Gary N Geisel (Vice Chairman)
  10. Doris P Meister (EVP)
  11. Christopher E Kay (EVP)
  12. John R Taylor (EVP)
  13. Michael J Todaro (EVP)
  14. Rudina Seseri (Director)
  15. Doris P Meister (EVP)
Learn More about top insider investors at M&T Bank.

Who are the major institutional investors of M&T Bank?

M&T Bank's top institutional investors include:
  1. Canoe Financial LP — 0.35%
  2. National Pension Service — 0.16%
  3. MEAG MUNICH ERGO Kapitalanlagegesellschaft mbH — 0.15%
  4. Absher Wealth Management LLC — 0.14%
  5. Principal Financial Group Inc. — 0.12%
  6. New York State Teachers Retirement System — 0.09%
Learn More about top institutional investors of M&T Bank stock.

Which institutional investors are selling M&T Bank stock?

During the previous quarter, MTB stock was sold by these institutional investors:
  1. Absher Wealth Management LLC
  2. M&G PLC
  3. MEAG MUNICH ERGO Kapitalanlagegesellschaft mbH
  4. Cantor Fitzgerald Investment Advisors L.P.
  5. New York State Common Retirement Fund
  6. Van ECK Associates Corp
  7. Bard Financial Services Inc.
  8. Boston Trust Walden Corp
Within the last year, company insiders that have sold M&T Bank company stock include:
  1. Rene F Jones (CEO)
  2. John P Barnes (Director)
  3. Kevin J Pearson (Vice Chairman)
  4. Denis J Salamone (Director)
  5. Kirk W Walters (Director)
  6. Daryl N Bible (CFO)
  7. Robert E Sadler Jr (Director)
  8. Robert J Bojdak (EVP)
  9. Gary N Geisel (Vice Chairman)
  10. Doris P Meister (EVP)
  11. Christopher E Kay (EVP)
  12. John R Taylor (EVP)
  13. Michael J Todaro (EVP)
Learn More investors selling M&T Bank stock.

Which institutional investors are buying M&T Bank stock?

Within the last quarter, MTB stock was acquired by institutional investors including:
  1. Canoe Financial LP
  2. International Assets Investment Management LLC
  3. SG Americas Securities LLC
  4. Adams Diversified Equity Fund Inc.
  5. Mirae Asset Global Investments Co. Ltd.
  6. National Pension Service
  7. Leuthold Group LLC
  8. USA Financial Formulas