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Performance Management
Oct. 31, 2025
BNY Mellon Bond Market Index Fund  
Prospectus [Line Items]  
Bar Chart and Performance Table [Heading] Performance
Performance Narrative [Text Block]

The following bar chart and table provide some indication of the risks of investing in the fund. The bar chart shows changes in the performance of the fund's Class I shares from year to year. The table compares the average annual total returns of the fund's shares to those of the Bloomberg U.S. Aggregate Bond Index, a broad measure of market performance. The fund's past performance (before and after taxes) is not necessarily an indication of how the fund will perform in the future. Performance for each share class will vary due to differences in expenses. More recent performance information may be available at www.bny.com/investments.

Performance Past Does Not Indicate Future [Text] The fund's past performance (before and after taxes) is not necessarily an indication of how the fund will perform in the future.
Performance Information Illustrates Variability of Returns [Text] The following bar chart and table provide some indication of the risks of investing in the fund.
Performance Additional Market Index [Text] The table compares the average annual total returns of the fund's shares to those of the Bloomberg U.S. Aggregate Bond Index, a broad measure of market performance.
Bar Chart [Heading] Year-by-Year Total Returns as of 12/31 each year (%)
Bar Chart Closing [Text Block]

During the periods shown in the chart:
Best Quarter
2023, Q4: 6.67
Worst Quarter
2022, Q1: (5.98)

Performance Table Narrative

After-tax performance is shown only for Class I shares. After-tax performance of the fund's other share class will vary. After-tax returns are calculated using the historical highest individual federal marginal income tax rates, and do not reflect the impact of state and local taxes. Actual after-tax returns depend on the investor's tax situation and may differ from those shown, and the after-tax returns shown are not relevant to investors who hold their shares through U.S. tax-deferred arrangements such as 401(k) plans or individual retirement accounts. Returns after taxes on distributions and

sale of fund shares may be higher than returns before taxes or returns after taxes on distributions due to an assumed tax benefit from losses on a sale of the fund's shares at the end of the period.

Performance Table Uses Highest Federal Rate After-tax returns are calculated using the historical highest individual federal marginal income tax rates, and do not reflect the impact of state and local taxes.
Performance Table Not Relevant to Tax Deferred Actual after-tax returns depend on the investor's tax situation and may differ from those shown, and the after-tax returns shown are not relevant to investors who hold their shares through U.S. tax-deferred arrangements such as 401(k) plans or individual retirement accounts.
Performance Table Explanation after Tax Higher Returns after taxes on distributions and sale of fund shares may be higher than returns before taxes or returns after taxes on distributions due to an assumed tax benefit from losses on a sale of the fund's shares at the end of the period.
Performance [Table]
Average Annual Total Returns - BNY Mellon Bond Market Index Fund
12 Months Ended 60 Months Ended 120 Months Ended
Oct. 31, 2025
Dec. 31, 2025
Dec. 31, 2025
Dec. 31, 2025
Bloomberg U.S. Aggregate Bond Index reflects no deductions for fees, expenses or taxes | Average Annual Return, Label [Optional Text] Bloomberg U.S. Aggregate Bond Index      
Bloomberg U.S. Aggregate Bond Index reflects no deductions for fees, expenses or taxes | Average Annual Return, Percent   7.30% (0.36%) 2.01%
Class I Shares | Average Annual Return, Label [Optional Text] returns before taxes      
Class I Shares | Average Annual Return, Percent   7.05% (0.57%) 1.82%
Class I Shares | After Taxes on Distributions | Average Annual Return, Label [Optional Text] returns after taxes on distributions      
Class I Shares | After Taxes on Distributions | Average Annual Return, Percent   5.40% (1.85%) 0.59%
Class I Shares | After Taxes on Distributions and Sales | Average Annual Return, Label [Optional Text] returns after taxes on distributions and sale of fund shares      
Class I Shares | After Taxes on Distributions and Sales | Average Annual Return, Percent   4.14% (0.96%) 0.87%
Investor | Average Annual Return, Label [Optional Text] returns before taxes      
Investor | Average Annual Return, Percent   6.66% (0.82%) 1.56%
Average Annual Return, Caption [Optional Text] Average Annual Total Returns (as of 12/31/25)
Index No Deduction for Fees, Expenses, or Taxes [Text] reflects no deductions for fees, expenses or taxes
Performance Availability Website Address [Text] www.bny.com/investments
BNY Mellon Bond Market Index Fund | Class I Shares  
Prospectus [Line Items]  
Highest Quarterly Return, Label [Optional Text] Best Quarter
Highest Quarterly Return 6.67%
Highest Quarterly Return, Date Dec. 31, 2023
Lowest Quarterly Return, Label [Optional Text] Worst Quarter
Lowest Quarterly Return (5.98%)
Lowest Quarterly Return, Date Mar. 31, 2022
BNY Mellon Institutional S&P 500 Stock Index Fund  
Prospectus [Line Items]  
Bar Chart and Performance Table [Heading] Performance
Performance Narrative [Text Block]

The following bar chart and table provide some indication of the risks of investing in the fund. The bar chart shows changes in the performance of the fund's Class I shares from year to year. The table compares the average annual total returns of the fund's Class I shares to those of the S&P 500® Index, a broad measure of market performance. The fund's past performance (before and after taxes) is not necessarily an indication of how the fund will perform in the future. More recent performance information may be available at www.bny.com/investments. Prior to August 31, 2016, the fund's Class I shares were undesignated.

Performance Past Does Not Indicate Future [Text] The fund's past performance (before and after taxes) is not necessarily an indication of how the fund will perform in the future.
Performance Information Illustrates Variability of Returns [Text] The following bar chart and table provide some indication of the risks of investing in the fund.
Performance Additional Market Index [Text] The table compares the average annual total returns of the fund's Class I shares to those of the S&P 500® Index, a broad measure of market performance.
Bar Chart [Heading] Year-by-Year Total Returns as of 12/31 each year (%)
Bar Chart Closing [Text Block]

During the periods shown in the chart:
Best Quarter
2020, Q2: 20.48
Worst Quarter
2020, Q1: (19.63)

Performance Table Narrative

After-tax returns are calculated using the historical highest individual federal marginal income tax rates, and do not reflect the impact of state and local taxes. Actual after-tax returns depend on the investor's tax situation and may differ from those shown, and the after-tax returns shown are not relevant to investors who hold their shares through U.S. tax-deferred arrangements such as 401(k) plans or individual retirement accounts. Returns after taxes on distributions and sale of fund shares may be higher than returns before taxes or returns after taxes on distributions due to an assumed tax benefit from losses on a sale of the fund's shares at the end of the period.

Performance Table Uses Highest Federal Rate After-tax returns are calculated using the historical highest individual federal marginal income tax rates, and do not reflect the impact of state and local taxes.
Performance Table Not Relevant to Tax Deferred Actual after-tax returns depend on the investor's tax situation and may differ from those shown, and the after-tax returns shown are not relevant to investors who hold their shares through U.S. tax-deferred arrangements such as 401(k) plans or individual retirement accounts.
Performance Table Explanation after Tax Higher Returns after taxes on distributions and sale of fund shares may be higher than returns before taxes or returns after taxes on distributions due to an assumed tax benefit from losses on a sale of the fund's shares at the end of the period.
Performance [Table]
Average Annual Total Returns - BNY Mellon Institutional S&P 500 Stock Index Fund
12 Months Ended 60 Months Ended 120 Months Ended
Oct. 31, 2025
Dec. 31, 2025
Dec. 31, 2025
Dec. 31, 2025
S&P 500® Index reflects no deductions for fees, expenses or taxes | Average Annual Return, Label [Optional Text] S&P 500® Index      
S&P 500® Index reflects no deductions for fees, expenses or taxes | Average Annual Return, Percent   17.87% 14.42% 14.81%
Class I | Average Annual Return, Label [Optional Text] returns before taxes      
Class I | Average Annual Return, Percent   17.63% 14.19% 14.59%
Class I | After Taxes on Distributions | Average Annual Return, Label [Optional Text] returns after taxes on distributions      
Class I | After Taxes on Distributions | Average Annual Return, Percent   10.54% 8.93% 11.35%
Class I | After Taxes on Distributions and Sales | Average Annual Return, Label [Optional Text] returns after taxes on distributions and sale of fund shares      
Class I | After Taxes on Distributions and Sales | Average Annual Return, Percent   15.56% 10.48% 11.55%
Average Annual Return, Caption [Optional Text] Average Annual Total Returns (as of 12/31/25)
Index No Deduction for Fees, Expenses, or Taxes [Text] reflects no deductions for fees, expenses or taxes
Performance Availability Website Address [Text] www.bny.com/investments
BNY Mellon Institutional S&P 500 Stock Index Fund | Class I  
Prospectus [Line Items]  
Highest Quarterly Return, Label [Optional Text] Best Quarter
Highest Quarterly Return 20.48%
Highest Quarterly Return, Date Jun. 30, 2020
Lowest Quarterly Return, Label [Optional Text] Worst Quarter
Lowest Quarterly Return (19.63%)
Lowest Quarterly Return, Date Mar. 31, 2020