Disclosures and Methodology
Hypothetical portfolios
The portfolios on this page are hypothetical. They are illustrations of how one model portfolio could be built at different account sizes, and do not reflect actual trading or any actual client account. Risk figures are model forecasts, not predictions of performance. Past performance, actual or hypothetical, does not guarantee future results. Quorus does not provide tax advice.
The net capital loss and percentile figures on this page are hypothetical projections. They do not reflect actual trading, actual client experience, or actual investment performance. They are the output of a model applying stated assumptions to historical market data. Hypothetical results have inherent limitations, including that they are prepared with the benefit of hindsight, do not reflect the impact financial risk may have had on actual decision-making, and may not account for all transaction costs, fees, or market conditions an actual account would experience. No representation is made that any account will or is likely to achieve results similar to those shown.
Methodology
Data. The model and every figure on this page come from one portfolio construction workbook. It builds the 60/40 model portfolio with bitcoin (12 funds at fixed target weights) at $100K, $250K, $1M, $5M and $10M, each funded entirely in cash, and reports the optimizer’s summary statistics for each.
How the model is held. US Equity, AI Tech, Tech and Real Estate (41% of the model) are held as separately managed accounts of the individual stocks inside them; the other 8 funds are bought as ETFs. The optimizer chooses the stocks and weights in each account to follow the model as closely as it can, subject to the account’s size.
Risk figures. Total risk, factor and specific risk, beta, tracking error, active share and the coefficient of determination are estimated using the Axioma Worldwide 4 Equity Risk Model (medium horizon), prices as of October 13, 2026, with the model portfolio as the benchmark. They are forecasts from that model at a single point in time, not realized results, and an account’s actual experience will differ.
Tax-loss harvesting projections. Source: Liberman, Krasner, Sosner, and Freitas (2023), “Beyond Direct Indexing: Dynamic Direct Long-Short Investing,” The Journal of Beta Investment Strategies, 14(3): 10–41. The projections apply that published methodology to the amount each account invests in individual stocks: the account size × 41%, the model’s weight in the funds held as individual stocks. The funds bought as ETFs are not harvested. Loss rates are the Tax Savings Model’s for a long only account funded with cash, over a 5 years horizon; assumption set 2026-09, source figures as of September 2023. They do not reproduce the study’s own historical results, and outcomes for any account will differ from those reported in the source research. Losses are shown gross of fees and before any tax rate is applied; they do not account for wash-sale rules, annual capital-loss deduction limits, loss-carryforward timing, or changes in an investor’s tax situation or tax law.
Costs. No transaction costs, fees or taxes are reflected. Because each account is bought from cash, nothing is sold and no gains or losses are realized in building it.
Important Quorus disclosures
Quorus (“Quorus,” “we,” or “our”) is an investment adviser registered with the Securities and Exchange Commission (“SEC”). Registration does not imply a certain level of skill or training.
This material is provided for informational purposes only and does not constitute (i) investment, legal, or tax advice, (ii) an offer to sell or the solicitation of an offer to buy any security, or (iii) a recommendation regarding any investment strategy. Investors should consult their professional advisers before acting on any information herein.
Past performance is not indicative of future results. All investments involve risk, including the possible loss of principal. Certain statements contained herein constitute “forward-looking” or other subjective views and are based on current expectations, estimates, and assumptions that are subject to change without notice. No assurance can be given that any forecast or goal will be achieved.
Any discussion of “tax-alpha,” “after-tax gains,” or similar terms is for illustrative purposes only. Tax outcomes depend on individual circumstances and may change with future tax-law revisions; results are not guaranteed. Clients remain responsible for all decisions related to their personal tax situation, and Quorus does not provide individualized tax advice.
Services described may be offered through third-party service providers or custodians. Quorus does not custody client assets. References to third-party trademarks and logos are for identification only and do not imply endorsement, sponsorship, or affiliation.
“Quorus” is the trademark of Quorus. All other trademarks are the property of their respective owners.
A copy of Quorus’s current Form ADV Parts 2A & 2B which contain important information about our advisory services, fees, and disciplinary history is available upon request.
Definitions
Account size. The amount invested, in cash, on the day the portfolio is built.
Securities. The number of securities held long, not counting cash.
Total risk. The predicted standard deviation of the portfolio’s performance over a year, from the risk model: √(wᵀQw). Factor and specific variance add, so total² = factor² + specific².
Predicted beta. Each security’s beta is predicted by the risk model, with the benchmark, here the model portfolio, defining the market. Portfolio predicted beta = Σ(holding value × predicted beta) ÷ reference value.
Tracking error. The predicted standard deviation of the active holdings (portfolio minus model), also called tracking error: √((w−b)ᵀQ(w−b)). It is a forecast, not a realized figure.
Active share. The share of the portfolio that differs from the model, compared security by security: ½ × Σ|w − b|.
Coefficient of determination (R²). The square of the correlation, under the risk model, between the portfolio and the model portfolio: (wᵀQb)² ÷ [(wᵀQw)(bᵀQb)].
Net capital loss. Realized capital losses minus realized capital gains from harvesting, before any tax rate is applied.
10th percentile, mean, 90th percentile. The low, middle and high loss outcomes reported in the source research for a long-only account. They describe the spread of the research’s results, not the probability of any result for an account.
One model, five account sizes
The 60/40 model portfolio with bitcoin, built at $100K, $250K, $1M, $5M and $10M
How many securities each account holds, how much risk it carries, and how closely it follows the model, side by side.
How this is calculated
Account size. The amount invested, in cash, on the day the portfolio is built. The workbook builds the same model at $100K, $250K, $1M, $5M and $10M.
Ex-ante tracking error. The risk model’s forecast of how far the account’s return could stray from the model’s in a year, as a standard deviation (active risk). It is a forecast, not a realized figure.
The model. The 60/40 model portfolio with bitcoin: 12 funds at fixed target weights. 4 of them (US Equity, AI Tech, Tech and Real Estate, 41% of the model) are held as the individual stocks inside them; the other 8 are bought as ETFs.
The funds, and how each is held
Every account on this page is built from the same model portfolio. Each fund in it is either held as the individual stocks inside it or bought as an ETF, and that split is the same at every account size.
How this is calculated
Target weights and the ETF / SMA marking come from the workbook’s model tab. A fund marked SMA is held as a separately managed account: the optimizer buys the stocks inside it rather than the fund. Weights sum to 100%.
Risk at each account size
Predicted tracking error is the risk model’s forecast of how far an account’s return could stray from the model’s over a year, as a standard deviation. This section shows it at each account size. Drag the slider, sweep the sizes, or click a point.
How this is calculated
Tracking error. The predicted standard deviation of the active holdings (portfolio minus model), also called tracking error: √((w−b)ᵀQ(w−b)).
R². The square of the correlation, under the risk model, between the portfolio and the model portfolio: (wᵀQb)² ÷ [(wᵀQw)(bᵀQb)].
Each risk figure is estimated using the Axioma Worldwide 4 Equity Risk Model, prices as of October 13, 2026.
How many securities each account holds
The number of securities each account holds. The count covers every stock and ETF held. Click a bar to select an account size.
How this is calculated
Long count: the number of securities held long, stocks and ETFs alike, not counting cash. The account sizes are spaced evenly on the axis, not to scale.
Loss harvesting on the individual stocks
The part of the model held as individual stocks gives each account a cost basis, stock by stock, that can be loss harvested in the future; the funds bought as ETFs are not harvested. Losses are hypothetical and depend on strategy and market environment.
Disclaimer: This scenario is hypothetical and for illustrative purposes only. Actual results may vary and are not guaranteed. Please review the important disclosures, assumptions, and limitations provided at the bottom of this page.
How this is calculated
The cumulative line in the chart below at the selected year, for each outcome: the amount invested in individual stocks × the sum of that outcome’s loss rates through that year.
Disclaimer: This scenario is hypothetical and for illustrative purposes only. Actual results may vary and are not guaranteed. Please review the important disclosures, assumptions, and limitations provided at the bottom of this page.
How this is calculated
Amount invested in individual stocks. The account size × 41%, the model’s weight in US Equity, AI Tech, Tech and Real Estate, the funds held as individual stocks.
Each year’s loss. The amount invested in individual stocks × that year’s loss rate. The rate is a share of the amount invested at the start, not of the account’s value that year, and it differs by year because the source research reports a separate rate for each year an investment has been held. Rates are for a long-only account funded with cash.
Cumulative loss. The sum of every year’s loss so far. Each point on the chart is the running total at the end of that year.
Methodology. Source: Liberman, Krasner, Sosner, and Freitas (2023), “Beyond Direct Indexing: Dynamic Direct Long-Short Investing,” The Journal of Beta Investment Strategies, 14(3): 10–41. This page applies that published methodology to the amount each account invests in individual stocks; it does not reproduce the study’s own historical results, and outcomes for any account will differ from those reported in the source research. Assumption set 2026-09, source figures as of September 2023.
Country Exposures
Geography exposure is estimated using the Axioma Worldwide 4 Equity Risk Model, prices as of October 13, 2026.
How this is calculated
Exposure. The risk model gives every security an exposure to each factor. A portfolio’s exposure is the holdings-weighted sum, Σ wᵢ × Bᵢ. For country and industry factors it is a share of the account; for style factors it is in standard deviations from the market average. Country and industry exposures cover the holdings the equity risk model classifies, so they do not add up to 100%.
How the model’s figures are read. The workbook reports each account’s active exposure (account minus model) before and after it is built. Before, the account holds only cash, so its active exposure is the model’s exposure with the sign reversed. The model’s exposure is that figure reversed; the account’s is the model’s plus its active exposure after it is built.
Shown: the 10 of the risk model’s 93 geography factors with the largest exposure, for the model or any account size, so the rows are the same for every size. They are in order of the model’s exposure. Definitions follow the Axioma Portfolio Optimizer 2025.1 Users Guide (risk decomposition table) and the APO Analytics Glossary.
Sector Exposures
Sector exposure is estimated using the Axioma Worldwide 4 Equity Risk Model, prices as of October 13, 2026.
How this is calculated
Exposure. The risk model gives every security an exposure to each factor. A portfolio’s exposure is the holdings-weighted sum, Σ wᵢ × Bᵢ. For country and industry factors it is a share of the account; for style factors it is in standard deviations from the market average. Country and industry exposures cover the holdings the equity risk model classifies, so they do not add up to 100%.
How the model’s figures are read. The workbook reports each account’s active exposure (account minus model) before and after it is built. Before, the account holds only cash, so its active exposure is the model’s exposure with the sign reversed. The model’s exposure is that figure reversed; the account’s is the model’s plus its active exposure after it is built.
Shown: the 12 of the risk model’s 68 sector factors with the largest exposure, for the model or any account size, so the rows are the same for every size. They are in order of the model’s exposure. Definitions follow the Axioma Portfolio Optimizer 2025.1 Users Guide (risk decomposition table) and the APO Analytics Glossary.
Factor Exposures
Style factor exposure is estimated using the Axioma Worldwide 4 Equity Risk Model, prices as of October 13, 2026.
How this is calculated
Exposure. The risk model gives every security an exposure to each factor. A portfolio’s exposure is the holdings-weighted sum, Σ wᵢ × Bᵢ. For country and industry factors it is a share of the account; for style factors it is in standard deviations from the market average. Country and industry exposures cover the holdings the equity risk model classifies, so they do not add up to 100%.
How the model’s figures are read. The workbook reports each account’s active exposure (account minus model) before and after it is built. Before, the account holds only cash, so its active exposure is the model’s exposure with the sign reversed. The model’s exposure is that figure reversed; the account’s is the model’s plus its active exposure after it is built.
Shown: the 12 of the risk model’s 12 risk factors factors with the largest exposure, for the model or any account size, so the rows are the same for every size. They are in order of the model’s exposure. Definitions follow the Axioma Portfolio Optimizer 2025.1 Users Guide (risk decomposition table) and the APO Analytics Glossary.
How this is calculated
Predicted beta. Each security’s beta is predicted by the risk model, with the benchmark, here the model portfolio, defining the market. Portfolio predicted beta = Σ(holding value × predicted beta) ÷ reference value.
Every statistic, side by side
For reference: the optimizer’s summary for each account size, against the model portfolio as benchmark. Risk figures are model forecasts, not realized figures. Click a column heading to select an account size.
| Statistic | $100K | $250K | $1M | $5M | $10M |
|---|---|---|---|---|---|
| Risk | |||||
| Total Risk | 7.53% | 7.56% | 7.65% | 7.64% | 7.65% |
| Total Factor Risk | 7.27% | 7.32% | 7.41% | 7.41% | 7.42% |
| Total Specific Risk | 1.94% | 1.89% | 1.88% | 1.87% | 1.87% |
| Historical Beta (from risk model) | 0.62 | 0.62 | 0.63 | 0.63 | 0.63 |
| Predicted Beta (from model/benchmark) | 1.02 | 1.02 | 1.03 | 1.03 | 1.03 |
| Total Value at Risk ($) (5.0%) | $12,381 | $31,107 | $125,809 | $628,647 | $1,258,489 |
| Coefficient of Determination | 0.9945 | 0.9966 | 0.9980 | 0.9981 | 0.9981 |
| Benchmark Risk | 7.39% | 7.39% | 7.39% | 7.39% | 7.39% |
| Active Risk | 0.57% | 0.47% | 0.43% | 0.41% | 0.42% |
| Active Factor Risk | 0.27% | 0.29% | 0.33% | 0.32% | 0.33% |
| Active Specific Risk | 0.50% | 0.37% | 0.27% | 0.25% | 0.25% |
| Active Predicted Beta | 0.02 | 0.02 | 0.03 | 0.03 | 0.03 |
| Active Value at Risk ($) (5.0%) | $941 | $1,928 | $6,996 | $33,798 | $68,586 |
| Active Coefficient of Determination | 0.0404 | 0.1175 | 0.3446 | 0.3568 | 0.3671 |
| Active Share | 55.73% | 51.13% | 47.56% | 46.74% | 46.69% |
| Portfolio | |||||
| Long Count | 127 | 266 | 450 | 480 | 482 |
| Long Value ($) | $99,050 | $248,858 | $997,394 | $4,987,339 | $9,974,896 |
| Long Value (%) | 99.05% | 99.54% | 99.74% | 99.75% | 99.75% |
| Cash Value ($) | $950 | $1,142 | $2,606 | $12,661 | $25,104 |
| Cash Value (%) | 0.95% | 0.46% | 0.26% | 0.25% | 0.25% |
| Net Value | $100,000 | $250,000 | $1,000,000 | $5,000,000 | $10,000,000 |
| Reference Value | $100,000 | $250,000 | $1,000,000 | $5,000,000 | $10,000,000 |
| Trades | |||||
| Buy Turnover ($) | $100,000 | $250,000 | $1,000,000 | $5,000,000 | $10,000,000 |
| Buy Turnover (%) | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% |
| Sell Turnover ($) | $0 | $0 | $0 | $0 | $0 |
| Sell Turnover (%) | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% |
| Turnover ($) | $100,000 | $250,000 | $1,000,000 | $5,000,000 | $10,000,000 |
| Turnover (%) | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% |
| Transaction Cost | $0 | $0 | $0 | $0 | $0 |
| Trade Count | 128 | 267 | 451 | 481 | 483 |
Each risk statistic is estimated using the Axioma Worldwide 4 Equity Risk Model, prices as of October 13, 2026.
How this is calculated
Definitions follow the Axioma Portfolio Optimizer 2025.1 Users Guide (Table 5.1, Summary table field definitions) and the APO Analytics Glossary. The benchmark in every account is the model portfolio itself.
Risk
Total Risk. The predicted standard deviation of the portfolio’s performance over a year, from the risk model: √(wᵀQw). Factor and specific variance add, so total² = factor² + specific².
Total Factor Risk. The part of total risk explained by the risk model’s common factors (market, industries, countries, styles): √(wᵀBΩBᵀw).
Total Specific Risk. The part of total risk not explained by the common factors, unique to each security: √(wᵀΔ²w).
Historical Beta (from risk model). The portfolio’s weighted average of the risk model’s Historical Beta attribute for each security.
Predicted Beta (from model/benchmark). Each security’s beta is predicted by the risk model, with the benchmark, here the model portfolio, defining the market. Portfolio predicted beta = Σ(holding value × predicted beta) ÷ reference value.
Total Value at Risk ($) (5.0%). The one-year loss exceeded with 5% probability, assuming normally distributed (Gaussian) results: 1.645 × total risk × reference value.
Coefficient of Determination. The square of the correlation, under the risk model, between the portfolio and the model portfolio: (wᵀQb)² ÷ [(wᵀQw)(bᵀQb)].
Benchmark Risk. The total risk of the benchmark, here the model portfolio itself, as a standard deviation.
Active Risk. The predicted standard deviation of the active holdings (portfolio minus model), also called tracking error: √((w−b)ᵀQ(w−b)).
Active Factor Risk. Active risk computed using only the common factors of the risk model: √((w−b)ᵀBΩBᵀ(w−b)).
Active Specific Risk. The specific risk of the active holdings: √((w−b)ᵀΔ²(w−b)). Active factor and active specific variance add to active variance.
Active Predicted Beta. Σ(active holding value × predicted beta) ÷ reference value. Because the model’s own beta is 1, it equals predicted beta − 1.
Active Value at Risk ($) (5.0%). The one-year shortfall against the model exceeded with 5% probability, assuming normally distributed results: 1.645 × active risk × reference value.
Active Coefficient of Determination. The square of the correlation, under the risk model, between the active holdings and the model portfolio.
Active Share. The share of the portfolio that differs from the model, compared security by security: ½ × Σ|w − b|.
Portfolio
Long Count. The number of securities held long, not counting cash.
Long Value ($). The total value of all long holdings except cash.
Long Value (%). Long value as a percentage of the reference value.
Cash Value ($). The cash held in the portfolio’s cash asset.
Cash Value (%). Cash as a percentage of the reference value.
Net Value. The market value of every holding at the workbook’s prices: long value + cash.
Reference Value. The base for every percentage figure in the account. It defaults to the portfolio’s net value.
Trades
Buy Turnover ($). The total value of all buy trades: Σ(w − h)⁺, where h is the holdings before the trade.
Buy Turnover (%). Buy turnover as a percentage of the reference value.
Sell Turnover ($). The total value of all sell trades: Σ(w − h)⁻.
Sell Turnover (%). Sell turnover as a percentage of the reference value.
Turnover ($). The total value of all trades, buys plus sells: Σ|w − h|.
Turnover (%). Total turnover as a percentage of the reference value.
Transaction Cost. The sum of each traded security’s estimated cost under the workspace’s transaction cost model.
Trade Count. The number of recommended buys and sells (names).
Each account is bought from cash, so nothing is sold and no gains or losses are realized. The workbook’s tax rows are all zero and are not shown, nor are its return-at-risk rows.
Disclosures and Methodology
Hypothetical portfolios
The portfolios on this page are hypothetical. They are illustrations of how one model portfolio could be built at different account sizes, and do not reflect actual trading or any actual client account. Risk figures are model forecasts, not predictions of performance. Past performance, actual or hypothetical, does not guarantee future results. Quorus does not provide tax advice.
The net capital loss and percentile figures on this page are hypothetical projections. They do not reflect actual trading, actual client experience, or actual investment performance. They are the output of a model applying stated assumptions to historical market data. Hypothetical results have inherent limitations, including that they are prepared with the benefit of hindsight, do not reflect the impact financial risk may have had on actual decision-making, and may not account for all transaction costs, fees, or market conditions an actual account would experience. No representation is made that any account will or is likely to achieve results similar to those shown.
Methodology
Data. The model and every figure on this page come from one portfolio construction workbook. It builds the 60/40 model portfolio with bitcoin (12 funds at fixed target weights) at $100K, $250K, $1M, $5M and $10M, each funded entirely in cash, and reports the optimizer’s summary statistics for each.
How the model is held. US Equity, AI Tech, Tech and Real Estate (41% of the model) are held as separately managed accounts of the individual stocks inside them; the other 8 funds are bought as ETFs. The optimizer chooses the stocks and weights in each account to follow the model as closely as it can, subject to the account’s size.
Risk figures. Total risk, factor and specific risk, beta, tracking error, active share and the coefficient of determination are estimated using the Axioma Worldwide 4 Equity Risk Model (medium horizon), prices as of October 13, 2026, with the model portfolio as the benchmark. They are forecasts from that model at a single point in time, not realized results, and an account’s actual experience will differ.
Tax-loss harvesting projections. Source: Liberman, Krasner, Sosner, and Freitas (2023), “Beyond Direct Indexing: Dynamic Direct Long-Short Investing,” The Journal of Beta Investment Strategies, 14(3): 10–41. The projections apply that published methodology to the amount each account invests in individual stocks: the account size × 41%, the model’s weight in the funds held as individual stocks. The funds bought as ETFs are not harvested. Loss rates are the Tax Savings Model’s for a long only account funded with cash, over a 5 years horizon; assumption set 2026-09, source figures as of September 2023. They do not reproduce the study’s own historical results, and outcomes for any account will differ from those reported in the source research. Losses are shown gross of fees and before any tax rate is applied; they do not account for wash-sale rules, annual capital-loss deduction limits, loss-carryforward timing, or changes in an investor’s tax situation or tax law.
Costs. No transaction costs, fees or taxes are reflected. Because each account is bought from cash, nothing is sold and no gains or losses are realized in building it.
Important Quorus disclosures
Quorus (“Quorus,” “we,” or “our”) is an investment adviser registered with the Securities and Exchange Commission (“SEC”). Registration does not imply a certain level of skill or training.
This material is provided for informational purposes only and does not constitute (i) investment, legal, or tax advice, (ii) an offer to sell or the solicitation of an offer to buy any security, or (iii) a recommendation regarding any investment strategy. Investors should consult their professional advisers before acting on any information herein.
Past performance is not indicative of future results. All investments involve risk, including the possible loss of principal. Certain statements contained herein constitute “forward-looking” or other subjective views and are based on current expectations, estimates, and assumptions that are subject to change without notice. No assurance can be given that any forecast or goal will be achieved.
Any discussion of “tax-alpha,” “after-tax gains,” or similar terms is for illustrative purposes only. Tax outcomes depend on individual circumstances and may change with future tax-law revisions; results are not guaranteed. Clients remain responsible for all decisions related to their personal tax situation, and Quorus does not provide individualized tax advice.
Services described may be offered through third-party service providers or custodians. Quorus does not custody client assets. References to third-party trademarks and logos are for identification only and do not imply endorsement, sponsorship, or affiliation.
“Quorus” is the trademark of Quorus. All other trademarks are the property of their respective owners.
A copy of Quorus’s current Form ADV Parts 2A & 2B which contain important information about our advisory services, fees, and disciplinary history is available upon request.
Definitions
Account size. The amount invested, in cash, on the day the portfolio is built.
Securities. The number of securities held long, not counting cash.
Total risk. The predicted standard deviation of the portfolio’s performance over a year, from the risk model: √(wᵀQw). Factor and specific variance add, so total² = factor² + specific².
Predicted beta. Each security’s beta is predicted by the risk model, with the benchmark, here the model portfolio, defining the market. Portfolio predicted beta = Σ(holding value × predicted beta) ÷ reference value.
Tracking error. The predicted standard deviation of the active holdings (portfolio minus model), also called tracking error: √((w−b)ᵀQ(w−b)). It is a forecast, not a realized figure.
Active share. The share of the portfolio that differs from the model, compared security by security: ½ × Σ|w − b|.
Coefficient of determination (R²). The square of the correlation, under the risk model, between the portfolio and the model portfolio: (wᵀQb)² ÷ [(wᵀQw)(bᵀQb)].
Net capital loss. Realized capital losses minus realized capital gains from harvesting, before any tax rate is applied.
10th percentile, mean, 90th percentile. The low, middle and high loss outcomes reported in the source research for a long-only account. They describe the spread of the research’s results, not the probability of any result for an account.