Can an Auction Set the Issue Price for Fractional-Investment Securities?

When fractional-investment products are explained, the price often appears as a number that has already been decided.

Divide an asset worth KRW 330 million into 10,000 rights, and each piece costs KRW 33,000. The arithmetic is simple. But that calculation only divides the price; it does not discover why the asset should be worth KRW 330 million.

The valuation of the underlying asset and disclosure of the basis for that valuation are important criteria for reviewing an issue price. The required approach to valuation and disclosure, however, varies with the type of security and the issuance structure. Even so, one question remains.

Instead of having the issuer set the price first and investors decide only whether to buy, could investors submit both a valuation and an investment amount so that the issue price and allocations are determined together?

When we built a prototype of Polsto(Polymophic Security Token Offering), a tokenized-securities issuance platform, in 2023, we called this question a fractional auction. The previous article described how we separated the recurring blockchain-integration concerns identified in Polsto into a shared middleware layer called BXB. This article revisits one market-specific business rule that remained within Polsto.

The document organized the value it called the public offering floor price, subscribers' bid valuations and subscription amounts, a uniform issue price, partial allocation to the marginal group, and refunds into five stages. The central idea remains clear. To turn that diagram into an actual rule, however, we must first define more rigorously what valuation, price, amount, and quantity each mean.

This article does not present that design as a current product specification. Nor is it a feature whose implementation, simulation, or operational results have been verified. It examines only a technical price-discovery model that collects bids during a new issuance and calculates the issue price and allocations. It does not determine the fair value of a specific product or prescribe an actual public-offering procedure, and it is neither investment solicitation nor an assessment of legal compliance.

Dividing a Price Is Not the Same as Discovering It

In the simplified model used here, assume that one token represents one unit of a security. If the issuer first sets the total value of the underlying asset, the token price is easy to calculate.

Issue price per token = value of the underlying asset / total number of tokens

The appraised value of the underlying asset and the price investors are actually willing to accept may not be the same. Set the price too high, and the subscription may be undersubscribed. Set it too low, and the issuer may raise less capital while giving up the same ownership interest. In another model with a fixed funding target, the issuer might have to give up a larger interest. A screen that displays only a fixed issue price also makes it difficult to tell whether weak demand comes from the price, the product structure, or insufficient information.

The fractional auction was intended to change this point. Instead of merely indicating subscribe, an investor submits both the asset valuation they are willing to accept and the amount they are prepared to invest. The issuer aggregates those orders to calculate a single clearing valuation, a uniform issue price per token, and the allocation results.

The auction used for Google's 2004 IPO was one reference for the design at the time. But Google's approach did not mean that an auction itself guaranteed market value. According to the prospectus, the clearing price was calculated as the highest price at which all offered shares could be sold, but Google and the underwriters retained discretion to set a lower final IPO price or reject bids they considered manipulative. The prospectus also described the winner's curse and a possible post-listing price decline as separate risks. Google's 2004 SEC prospectus shows both that an auction can be a tool for price discovery and that it cannot turn a price into truth.

The Five Stages in the Original Fractional-Auction Design

Translated into execution order, the document's flow looks like this.

Underlying-asset owner sets a floor valuation
        |
        v
Investors submit bid valuations and reserve subscription funds
        |
        v
After closing, calculate valid demand from the highest valuation downward
        |
        v
Determine the clearing valuation, uniform issue price, and marginal bids
        |
        v
Allocate tokens, finalize payments, and refund unallocated funds

First, the owner of the underlying asset states a floor: the minimum asset valuation the owner will accept.

Second, each subscriber submits two values.

• vᵢ: the maximum total value of the underlying asset that this investor will accept
• mᵢ: the maximum subscription amount the investor will commit if that condition is met

Third, when the auction closes, the bids are aggregated from the highest vᵢ downward to calculate how much capital remains valid at each asset valuation.

Fourth, the system finds the clearing valuation V* by determining the asset valuation at which valid cumulative subscription funds reach the value of the interest being issued. Bids above V* receive priority, and if there is an actual marginal group, it is allocated pro rata only to the extent needed.

Fifth, every successful bidder pays the same issue price per token, p*, calculated at V*, rather than a different price based on the bidder's own vᵢ. Unallocated funds from the marginal group and all subscription funds from unsuccessful bids are refunded.

This differs from a conventional auction with a single highest bidder. Because multiple investors share one asset, there are multiple winners, and both the price and the allocated quantity must be determined. The use of the same per-token price for every successful bidder resembles a single-price auction. U.S. Treasury auctions likewise apply the same price to successful bidders and allocate marginal bids pro rata, but that does not make their rules identical to the fractional auction. The single-price auction for U.S. Treasury securities, in which competitive bidders state desired amounts and corresponding rates or yields against a fixed offering amount, and this model, which seeks to discover the total value of an underlying asset, use different inputs and clearing conditions.

Translating the Square Intuition into a Clearing Condition

The original diagram placed subscription funds on the horizontal axis and bid valuation on the vertical axis, using a square to show the intended equality between them. If both axes use the same currency unit and scale, that equality can be drawn as a square: the two sides from the origin to a point where x = y have equal lengths. In an oversubscribed auction, however, x must be the post-allocation accepted amount, not raw cumulative demand D(V*). The important idea is not the area of the square but the equality between the monetary amounts represented by its two sides.

The image below crops the right-hand diagrams from slides 5 through 9 of the 2023 design deck and rearranges them into one table. It preserves the original sequence: establish the offering floor and square, accumulate subscriptions, partially allocate the marginal group, allow upward rebidding, and finalize allocations and refunds.

Diagrams cropped and rearranged from slides 5–9 of the original 2023 Polsto fractional-auction design deck, which was written in Korean.

If the vertical axis is instead interpreted as a per-token price, however, the two axes have different units and their lengths cannot be compared directly. Likewise, if the horizontal axis is proceeds from a partial issuance while the vertical axis is total asset value, the result is a rectangle when α < 1. To preserve the square, the vertical axis must also represent the value of the interest issued, αV. The clearing condition should define which amounts are equal before the diagram gives that equality a shape.

Suppose that a total of T tokens represents the entire underlying asset and that the existing owner issues a fraction α of it. In this simplified model, α = 1 means issuing the entire asset and α = 0.3 means issuing 30%.

Valid cumulative subscription funds at asset valuation V are:

D(V) = Σ mᵢ  (including only bids where vᵢ >= V)

For the auction to clear, the amount investors are prepared to commit at that valuation must be at least the value of the interest being issued.

D(V) >= αV

Let the clearing valuation V* be the highest value at or above the floor that satisfies this condition. If no value satisfies it, the auction does not clear. Under this definition, the result can take one of two forms.

First, V* may lie between two submitted bid valuations. Valid cumulative subscription funds remain constant within that interval, so D(V*) = αV*, and every valid bid can be accepted in full without a marginal group.

Second, cumulative demand may jump within the group that submitted a bid valuation equal to V*. If H is the total subscription amount from bids with higher valuations and B is the total subscription amount from the marginal group, the following relationships hold.

H = Σ mⱼ  (vⱼ > V*)
B = Σ mⱼ  (vⱼ = V*)
H <= αV* <= H + B

Marginal-group allocation rate β = (αV* - H) / B
Actual payment by bidder i in the marginal group aᵢ = βmᵢ

A real system must also fix the price increment, monetary unit, rounding method when V* lies between submitted bid values, and the rule for distributing any residual allocation within the marginal group.

If the uniform issue price per token is p*, then p* = V* / T. After each bidder's actual payment aᵢ is set, the token allocation can be calculated as follows.

p* = V* / T
qᵢ = aᵢ / p* = aᵢ / V* × T

For higher bids, aᵢ = mᵢ; if there is a marginal group, its bids have aᵢ = βmᵢ; and lower bids have aᵢ = 0.

If amounts and tokens are treated as continuous quantities before rounding, the minimum invariants for this model are clear.

0 <= aᵢ <= mᵢ
Σ aᵢ = αV*
Σ qᵢ = αT
Refund rᵢ = mᵢ - aᵢ
Finalized payment for each bid + refund = reserved funds

An implementation using integer token units and won-denominated amounts must record rounding remainders separately and define the order and rule by which the final units are allocated or refunded.

For α = 1, the square in the original document visualized finalized proceeds = total asset value. Its horizontal side is not raw cumulative demand D(V*), which may include an oversubscribed marginal group, but the post-allocation amount Σaᵢ = αV*. The same intuition works for α < 1 if the vertical axis shows the value of the interest issued, αV*, rather than total asset value V*. In both the article and an implementation, stating that equality directly is more precise than relying on the area of the diagram.

Working Through One Numerical Example

Assume that 9,000 tokens represent the entire underlying asset and that all of them are issued. The owner's minimum acceptable asset valuation is KRW 80 million. The bids from six valuation groups are as follows.

Group	Maximum acceptable asset valuation vᵢ	Maximum subscription amount mᵢ	Cumulative demand at or above that valuation
A	KRW 130 million	KRW 25 million	KRW 25 million
B	KRW 120 million	KRW 20 million	KRW 45 million
C	KRW 110 million	KRW 20 million	KRW 65 million
D	KRW 100 million	KRW 15 million	KRW 80 million
E	KRW 90 million	KRW 20 million	KRW 100 million
F	KRW 80 million	KRW 30 million	KRW 130 million

The following graph does not invalidate the original square; it restates the same intuition. Both axes use the same scale in KRW millions, and the square's sides are explicitly defined as the value of the interest issued and the finalized payment amount. Demand left outside the square is separated as the unallocated and refunded portion of the marginal group.

On equal scales, (finalized payment amount of KRW 90 million, value of the interest issued of KRW 90 million) is the square's upper-right corner. Because H = KRW 80 million < αV* = KRW 90 million < D(V*) = KRW 100 million, only the green KRW 10 million from group E is allocated; the gray KRW 10 million outside the square is refunded.

At an asset valuation of KRW 100 million, valid demand from groups A through D totals KRW 80 million, which is not enough to cover the value of the interest being issued. At KRW 90 million, valid demand through group E reaches KRW 100 million and satisfies the condition. The clearing valuation in this example is therefore KRW 90 million.

The subscription amounts from groups A through D total KRW 80 million. Only another KRW 10 million is needed from group E, so E's allocation rate is 50%. Group F submitted an asset valuation below the clearing valuation and receives no allocation.

V* = KRW 90,000,000
p* = V* / T = KRW 10,000

A: KRW 25,000,000 / KRW 10,000 = 2,500 tokens
B: KRW 20,000,000 / KRW 10,000 = 2,000 tokens
C: KRW 20,000,000 / KRW 10,000 = 2,000 tokens
D: KRW 15,000,000 / KRW 10,000 = 1,500 tokens
E: KRW 10,000,000 / KRW 10,000 = 1,000 tokens
F: 0 tokens

Total allocation = 9,000 tokens
Refund to E = KRW 10,000,000
Refund to F = KRW 30,000,000
Total reserved funds of KRW 130,000,000
  = finalized payment of KRW 90,000,000 + refunds of KRW 40,000,000

This calculation puts numbers to the structure in the document: higher groups win in full, the marginal group wins in part, and lower groups are excluded from allocation. It also reveals the meaning of the bidding contract. Here, mᵢ is not an exact quantity of tokens the investor wants to buy. It is the investor's maximum budget if the conditions are met. If the clearing valuation is below the maximum acceptable asset valuation the investor submitted, the investor receives more tokens for the same amount of money.

If an investor wants a quantity cap, the inputs must change. A conventional single-price, multi-unit auction that issues a fixed number of tokens and accepts a maximum price per token and desired quantity is more natural. The two models may produce similar diagrams, but they are not the same contract. Mixing the bid valuation and subscription amount model with the unit price and quantity model breaks the allocation formula.

What a Uniform Price Does—and Does Not—Provide

The uniform issue price per token, p*, has several benefits that are easy to explain.

• It does not apply a different price to each successful bidder.
• The marginal bid valuation and partial-allocation rule can be disclosed in advance.
• The finalized payment, token allocation, and refund can be verified as one result.
• Compared with discriminatory pricing based on each bidder's submitted valuation, it can reduce the pressure to guess the exact clearing valuation.

But a uniform price does not by itself produce fair value or truthful bidding.

A large bidder seeking multiple units may use a demand reduction strategy, submitting less demand because the bidder considers the effect of its own order on the clearing valuation. Conversely, if the bid valuation determines allocation priority while actual payment occurs at a lower uniform issue price corresponding to the clearing valuation, a bidder who believes it is unlikely to set the clearing valuation may submit an excessively high vᵢ simply to secure priority. The possibility of demand reduction and efficiency losses in single-price, multi-unit auctions is analyzed in research by Ausubel and Cramton. That does not mean the findings apply unchanged to the valuation and budget model in this article, but they expose an attack surface that requires strategic demand submission to be evaluated separately whenever multiple units are allocated at the same price.

The winner's curse also remains when the underlying asset is real estate, art, or copyright—assets for which participants assess the same subject using different information. The investor willing to accept the highest valuation may be the most optimistic, not the most accurate. Bidding does not replace appraisal, cash-flow analysis, review of the rights structure, or risk disclosure. In its 2022 action concerning Musicow, Korea's Securities and Futures Commission also treated the basis for setting the issuance-auction price as material information for investment decisions and pointed out that the related disclosure had been insufficient.

The fractional auction can therefore produce not fair value, but one clearing valuation and one uniform issue price formed under a defined set of bidding rules. How closely those values track the underlying asset's long-term value or the post-issuance secondary-market price is a separate question for validation.

Is Upward Rebidding a Price Signal or a Race for Priority?

The original document allowed bidders to raise their bid valuation during the auction and to increase their subscription amount at the same bid valuation. The idea was that incoming demand could raise the clearing valuation, while an investor who had been only partially allocated or excluded could regain priority.

Combining upward rebidding with real-time demand disclosure makes the process closer to an ascending auction, in which participants raise valuations or amounts in response to visible demand, than to a conventional Dutch auction, in which the price declines over time. If bids remain sealed while only increases are permitted, the information structure changes again. A process that lowers the floor and opens a new issuance auction after a failed auction resembles a Dutch auction only in the direction of lowering the price to find demand.

Open upward rebidding requires additional policies.

• How much of other bidders' bid valuations and subscription amounts should be disclosed in real time?
• Can bids only be increased, or may they also be canceled or reduced before closing?
• When must subscription funds actually be reserved or placed in a payable state?
• Should the closing time be extended when a bid arrives immediately before the deadline?
• How will the system prevent one person from splitting bids across accounts to circumvent marginal-group allocation or participation limits?
• How will bids from related parties or the issuer's side be identified and excluded?
• How will the system reduce follow-on bidding driven by visible orders, as well as transaction front-running and ordering competition in a public mempool?

A sealed-bid or commit-reveal structure that hides bids until closing can reduce some information leakage. On the other hand, a user who misses the commit or reveal stage may see an otherwise valid bid invalidated, and the lifecycle of fund reservation and refunds becomes more complex. Whatever structure is chosen, putting the bids on a blockchain does not by itself eliminate the possibility of manipulation.

A Refund Is Settlement, Not a Side Task

The clearing valuation and uniform issue price attract the most attention on an auction screen, but settlement is the harder part of the actual system.

Payments from higher bids, partial payments from the marginal group, refunds of unallocated funds, and full refunds to lower bids must each be processed exactly once. If the issuance conditions are not met, all subscription funds must be returned. Even if the floor is lowered for another attempt, prior bids must not be carried into a new auction without the investor's consent.

AUCTION_OPEN
  -> FUNDS_RESERVED
  -> AUCTION_CLOSED
  -> PRICE_CALCULATED
  -> ALLOCATION_FIXED
  -> TOKENS_ISSUED
  -> FUNDS_SETTLED / REFUNDED

Retrying any state transition must not create duplicate issuance or duplicate refunds. The system must also prevent a failure between price calculation and the actual transfer of funds from leaving only one side—tokens or payment—in a final state. The policy for assigning the final token and small residual balance caused by rounding must likewise be set in advance.

A ledger can help preserve tamper-resistant records of bid times, rule versions, clearing results, and allocation history. In an institutional system, customers may submit bids through authenticated business accounts instead of handling personal EOAs and signing procedures directly, while an institution-controlled key-management and signing system performs token issuance and transfers. This article uses custodial wallet to describe that technical structure; the term does not determine whether the arrangement legally constitutes a custody business or what license status applies. Even in this model, the auction engine's business state, the reserved-funds ledger, wallet signatures, and blockchain transactions must be connected into one auditable flow.

This boundary overlaps with the middleware discussed in the previous BXB article. The middleware, however, does not decide who receives how much. Auction rules are market-specific business logic; the middleware connects the determined rules so that they are executed consistently across existing systems, wallets, and ledgers.

Issue-Price Auctions and Secondary Markets Must Remain Separate

Fractional investment, tokenized securities, and public offering are not interchangeable terms. Fractional investment broadly describes the division of rights into smaller interests, while a tokenized security is a security recorded using distributed-ledger technology under Korea's capital-markets framework. Whether a right is a security depends on the substance of the contract and business, not its name or whether a token is used.

The Financial Services Commission's Guidelines on Fractional Investment explain that securities regulation, including disclosure obligations, applies to fractional-investment products that constitute securities, and that, depending on the substance of the activities performed, authorization or registration may be required for investment brokerage or other regulated businesses. Tokenized-securities legislation promulgated in 2026 likewise did not create a new asset outside the regulatory perimeter; it accepted distributed ledgers as a new method of recording securities within the existing securities regime. The amended Electronic Securities Act is scheduled to take effect on February 4, 2027.

This article therefore limits the auction to a model for calculating the price and initial allocation at the new-issuance stage. A secondary market, where investors continuously submit and match buy and sell orders after issuance, has a separate market structure and its own licensing and conflict-of-interest questions. The original document noted more trades from bid revisions and increased fee revenue as side effects, but the value of a new-issuance rule cannot be measured by the number of bid revisions. If issuance and secondary trading sit under the same interests, conflicts of interest must be examined before transaction growth.

Price Is a Protocol Too

Tokenization does not set an asset's price automatically. Nor does an auction make investor judgments truthful or guarantee the fair value of the underlying asset.

What mattered in the fractional-auction design was not that a blockchain would calculate the price, but that it tried to treat the rules that create price and allocation as an explicit protocol.

Who submits which values? At what point does a bid become final? Under what conditions does one price emerge? How are tokens divided among investors at the same marginal bid valuation? How are funds returned after a failure or partial allocation? Who can verify the result?

If tokens are issued without answering these questions, price determination remains an internal process of the issuer and platform. Publishing the rules does not automatically create a good market either. Only after small numerical examples, strategic-bidding simulations, boundary values, and failure scenarios have been worked through does it make sense to discuss implementation.

The 2023 fractional-auction document was less a finished answer than a design note that started that review. Rewriting the square from the original diagram as cumulative demand and a clearing condition made the conclusion simpler.

An issue price is not just a number displayed on a screen. It is a business protocol that binds bidding, allocation, payment, and refunds together.

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This article is a technical exploration of a past prototype design, not legal, accounting, or appraisal advice or an investment solicitation. Any real implementation requires separate review of the type of security involved, the distinction between public and private offerings, issuance and brokerage entities, valuation, disclosure, subscription and allocation procedures, and the laws and guidelines in force at the time.