A long-only portfolio holds positive or zero positions in the assets covered by its mandate, with no short positions in those assets. A manager can express a negative view by owning less of a security, or none of it. The manager cannot turn that view into a negative holding without relaxing the constraint.
Long-only describes the direction of positions. Financing, concentration and market exposure still need their own limits.
Put cash inside the budget
For ordinary cash securities, write for each holding's market value divided by positive portfolio equity. A common unlevered long-only specification is
Zero is allowed: the portfolio need not own every security in its investment universe. With cash inside the allocation, “fully invested” means that all equity has been accounted for; it does not mean all equity is in stocks. These conditions make each individual weight at most 100%. They also make the sum of absolute weights equal to one. The CVX Group's portfolio allocation example uses nonnegative weights alongside a unit budget constraint.
Check what the mandate covers. Nonnegative risky-asset weights alone do not prohibit borrowing. An account with USD 100 of equity can own USD 140 of stock and owe USD 40. Its stock weight is 1.4 and its financing weight is −0.4: the weights still sum to one. The stock position is long, but the account is leveraged, and it fails the all-assets-nonnegative specification above. Derivative positions also require separate exposure rules; the sign of a contract holding alone need not describe its underlying market exposure.
A falling stock still reduces wealth
Consider a synthetic one-period portfolio with USD 100 of starting equity: USD 80 in one stock and USD 20 in cash. Hold the positions without trading. Assume no borrowing, external flows, costs, taxes or dividends; cash earns zero. The stock falls 25%.
| Holding | Starting value | Period return | Ending value |
|---|---|---|---|
| Stock | USD 80 | −25% | USD 60 |
| Cash | USD 20 | 0% | USD 20 |
| Portfolio | USD 100 | −20% | USD 80 |
The stock loses USD 20. Cash cushions the percentage loss but does not reverse it. Using period-start weights,
The loss is 20% of initial equity. There was no short position and no borrowing; neither is required to lose money.
Original synthetic one-period buy-and-hold ledger in USD. Cash earns zero; no borrowing, costs, taxes, dividends or external flows. Both bars use the same wealth scale.
The ending stock weight is , while cash is . The portfolio is still long-only, but its weights have drifted. Rebalancing would require a trade; the starting 80/20 allocation does not maintain itself.
For comparison, the USD 140 stock position financed with USD 40 of debt would leave equity of under the same stock fall, assuming no interest or forced liquidation. That is a 35% equity loss. Borrowing changes the loss even though the risky position remains long. Actual funding also brings interest and collateral requirements; the SEC's margin-account bulletin explains these risks for US brokerage accounts.
An underweight is a negative view without a short
A long-only manager can deviate from a benchmark. Let be a security's benchmark weight and its active weight. Then
Suppose a stock is 8% of the benchmark and 3% of the portfolio. The manager is underweight by 5 percentage points, yet still owns the stock. Selling the holding completely would produce an active weight of −8 percentage points. Going further would require a negative actual holding.
This floor makes negative views asymmetric: the strongest underweight in a small benchmark constituent is limited by that constituent's benchmark weight. There is no corresponding requirement to hold a security merely because it appears in the benchmark. SelfMadeQuant's Portfolio Constraints lesson develops this active-weight bound and its role in portfolio construction; the outline is public, and the full lesson requires membership.
A long-only mandate can describe an index fund or an actively selected portfolio. It guarantees neither diversification nor benchmark-like risk: putting everything into one stock satisfies nonnegative weights and a unit budget. Position caps, sector limits, cash limits and risk budgets determine how much concentration or market exposure is acceptable within that feasible set.
Sources
- CVX Group, Portfolio optimization: portfolio allocation vector and asset returns. Formal nonnegative-weight and budget constraints, and one-period weighted returns.
- Qian, Hua and Sorensen, Quantitative Equity Portfolio Management: Modern Techniques and Applications, Chapman & Hall/CRC, 2007, §11.3, pp. 374–375. Long-only constraints as lower bounds on benchmark-relative positions and their role in constrained construction.
- SEC Office of Investor Education and Advocacy, Understanding Margin Accounts. US brokerage borrowing, equity accounting and margin risks; specific lending terms depend on the account.