Opinion by Judge MCKEOWN. Dissent by Judge MILAN D. SMITH, Jr.
[481]*481OPINION
McKEOWN, Circuit Judge:
This appeal requires us to “return to the very basics of tax law” and consider whether taxpayers had a cost basis in assets that they later sold, but for which they paid nothing. Washington Mut. Inc. v. United States, 636 F.3d 1207, 1217 (9th Cir.2011). The specific question we address is whether a life insurance policyholder has any basis in a mutual life insurance company’s membership rights. This issue, one of first impression in our circuit, arises out of a trend in the late 1990s and early 2000s towards the “demutualization” of mutual life insurance companies. As many mutual insurance companies transformed into stock companies, the surplus resulting from the sale of shares in the company was divided among current policy holders, often in the form of stock.
Bennett and Jacquelyn Dorrance received and then sold stock derived from the demutualization of five mutual life insurance companies from which they had purchased policies. The Dorranees initially asserted a zero cost basis in the stock and paid tax on the gain. They later claimed a full refund on the taxes they paid upon on the sale of the stock, either because the stock represented a return of previously paid policy premiums or because their mutual rights were not capable of valuation and, therefore, the entire cost of their insurance premiums should have been counted toward their basis in the stock. The government takes the position that the Dorranees are not entitled to any refund; since they paid nothing for their membership rights, their basis was zero. The district court held that the Dorranees had a calculable basis in the stock, albeit not at the level the taxpayers claimed, and thus they were entitled to a partial refund from the Internal Revenue Service (“IRS”). We disagree. Taxpayers who sold stock obtained through demutualization cannot claim a basis in that stock for tax purposes because they had a zero basis in the mutual rights that were extinguished during the demutualization.
Background
A. Mutual Insurance Companies
The first life insurance company in America was a mutual company called the Presbyterian Minister’s Fund, organized in 1759 in Philadelphia.1 For centuries, mutual insurance companies have provided a structure for collecting policyholder premiums and spreading risk and surplus among policyholders, while maintaining policyholder ownership of the company. Mutual insurance companies are distinct from stock companies in that they are owned by the policyholders, not by stockholders. See Edward X. Clinton, The Rights of Policyholders in an Insurance Demutualization, 41 Drake L.Rev. 657, 659 (1992). To ensure that they can pay all of the contractual benefits, these mutual insurance companies generally charge slightly higher rates than other life insurance providers. Surplus is returned to the policyholders in dividends. For decades (and even more than a century for some mutual companies) policyholders joined, became members, and terminated their policies without getting anything back for membership rights.
Starting in the middle of the twentieth century and increasing through the 1980s, [482]*482the mutual model became less economically advantageous when compared to stock companies. Id. See also Paul Galindo, Revisiting the ‘Open Transaction’ Doctrine: Exploring Gain Potential and the Importance of Categorizing Amounts Realized, 63 Tax L. 221, 226 (2009). The economic advantage of stock companies comes, in large part, from the fact that they can raise capital by selling shares, whereas mutual companies are able to raise capital only by increasing the number of policies sold or by reducing costs. Additionally, stock companies have a greater capacity to diversify, which provides an additional layer of financial stability. See Clinton, supra, at 667.
In response to the challenges faced by mutual insurance companies, in the mid-to-late 1990s many states changed their insurance laws to permit “demutualization” of mutual insurance companies. Demutu-alization entails the legal transformation of a mutual company into a stock company. See Jeffrey A. Koeppel, The State of Demutualization, at v (2d ed.1996). As a consequence, by the late 1990s and early 2000s, many mutual insurance companies had transformed into stock companies.
The rapid shift toward demutualization was made possible only by this widespread change in state insurance law. Clinton, supra, at 674. Although state laws vary, including in the scope of regulatory oversight, the demutualization process occurred under operation of law and was monitored by external insurance regulators. Id. at 665. Because policyholders exert only weak influence over the mutual company’s governance (each policyholder has only one vote, out of possible thousands, regardless of the size of-the policy), external regulators focused on ensuring a fair and equitable legal transformation of the insurance companies. Id. at 678.
B. The Dorrances’ Mutual Life Insurance Policies
Bennett Dorrance is the grandson of the founder of the Campbell Soup Company. At the time the Dorrances purchased life insurance policies from five mutual insurance companies2 in 19963, their net worth was approximately $1.5 billion. They bought the policies to cover estate tax for their heirs. Over time, the Dorrances paid premiums totaling $15,265,608. While that sum is definitely substantial, the face value of the policies totaled just under $88 million, such that they would have received a huge contractual payout upon death.
The Dorrances’ contractual rights under the policies entitled them to (1) a death benefit; (2) the right to surrender the policy for “cash value”; and (3) annual policyholder dividends representing the policyholder’s portion of the company’s “divisible surplus.” As policyholders, they also had certain membership rights. Specifically, they were entitled to a portion of any surplus in the event of a solvent liquidation and to certain voting rights. The Dorrances’ membership rights in the mu[483]*483tual insurance companies were not transferable or separable from the insurance policy. If the policies terminated, so too would the membership rights, without any rebate or additional compensation. Voting and other membership rights were governed by state law and company charter.
In 2000 and 2001, each of the insurance companies from which the Dorrances bought policies demutualized. Post-demu-tualization, the Dorrances no longer held any mutual membership rights, but they retained their contractual interests under the insurance policies and continued to pay the same premiums.
Government regulators (both in the United States and Canada) required the insurance companies to produce a “fair and equitable” allocation of the company’s surplus at the time of demutualization. Mutual insurance companies complied with this requirement in a variety of ways, but the companies in question here opted to issue stock to their policyholders.
When determining how many shares of stock to distribute to each policyholder, the insurance companies calculated (1) a fixed component for the loss of voting rights, as every policyholder was entitled to a single vote regardless of policy size, and (2) a variable component for the loss of other membership rights, which was calculated based on the policyholder’s past and projected future contributions to the company’s surplus. As the government’s expert report explained, each company used a different allocation calculation to arrive at a distribution that was “fair and equitable” to policyholders. MetLife, for example, “aimed for around 20%” for the fixed portion, but stated this was a “general target.” Sun Life did not consider policyholders’ contribution to surplus in its allocation calculation, but rather looked at the cash value and annual premiums of eligible policies.
Prior to demutualization, the insurance companies each obtained a ruling from the IRS that the stock ownership company resulting from the demutualization qualified as a tax-free organization under Internal Revenue Code, I.R.C. § 368.
Upon demutualization, the Dorrances received 58,455 shares in Prudential, 3,209 shares in Sun Life, 1,601 shares in Phoenix, 5,039 shares in Principal, and 2,721 shares in MetLife. At the time of receipt, the market value of the stock derived from these policies totaled $1,794,771. As the government’s expert report explained: “Some may think that the cash paid out in demutualization comes from the distribution of positive surplus of the mutual company; however, such is not the case. The cash actually comes from new stockholders which subscribe to the IPO [initial public offering].... ”
In 2003, the Dorrances sold all of the stock for $2,248,806. On their 2003 tax return, in compliance with IRS policy, the Dorrances listed their basis in the stock as zero,reported the $2,248,806 as capital gain, and paid the tax due on that gain. See Rev. Rui. 71-233, 1971-1 C.B. 113; Rev. Rul. 74-277, 1974-1 C.B. 88.
C. Prior Proceedings
By 2007, the Dorrances had a change of heart. They filed a tax refund claim with the IRS, in which they argued that they owed no taxes on the stock sale because it represented a return on previously-paid insurance policy premiums. The IRS did not issue a final determination on the 2007 claim, so the Dorrances filed a complaint in district court. The IRS argued that the Dorrances had a zero basis in their stock because the life insurance premiums that they paid were not in exchange for membership rights in the life insurance policies. The district court denied the cross-motions [484]*484for summary judgment, ruling that there was a calculable basis in the stock, and set the ease for trial to determine how the basis should be calculated.
The district court held a two-day bench trial, which featured expert testimony from both sides regarding the basis calculation. The court rejected the Dorrances’ argument that the “open transaction” doctrine, espoused by the Court of Federal Claims, applied to their refund request.4 It also rejected the government’s zero basis argument. Instead, the district court ruled that the Dorrances had “paid something for the [membership] rights because they paid premiums for policies that included both policy rights and mutual rights” and that their basis was calculable.
The district court calculated the Dor-rances’ basis in the stock using the following formula: (1) the initial public offering (“IPO”) vaiue 0f the fixed shares allocated to the Dorrances in 2003, plus (2) 60% of the IPO value of the variable shares. Applying this formula, the court found that the Dorrances were required to pay taxes on $1,170,678, rather than on the full $2,248,806 value of the stock. Because in 2003 the Dorrances had paid taxes based on a zero basis calculation in the stock, the district court found that they were entitled to a refund.
Both parties appeal the adverse portions of the judgment.
Analysis
The crux of this ease is how to calculate the basis of stock received through demutualization. The question of basis in the stock is a mixed question of law and' fact that “require[s] consideration of legal concepts and involve[s] the' exercise about the values underlying legal principles [and is] reviewable de novo.” Smith v. Comm’r, 300 F.3d 1023, 1028 (9th Cir.2002) (citing Mayors v. Comm’r, 785 F.2d 757, 759 (9th Cir.1986)). The parties do not dispute the district court’s factual findings. Instead, their divergence of views stems from the legal conclusions that follow.
As the taxpayers, the Dorrances bear the burden of establishing basis, and “[t]he fact that basis may be difficult to establish does not relieve [them] from [t]his burden.” Coloman v. Comm’r, 540 F.2d 427, 430 (9th Cir.1976). Because they failed to establish that they had a basis in the membership rights, we afford the basis utilized by the IRS a presumption of correctness — even where, as here, that figure is zero. Id. The Supreme Court explained long ago in a similar context that “[t]he impossibility of proving a material fact upon which the right to relief depends simply leaves the claimant upon whom the burden rests with an unenforceable claim, a misfortune to be borne by him, as it must be borne in other cases, as the result of a failure of proof.” Burnet v. Houston, 283 U.S. 223, 228, 51 S.Ct. 413, 75 L.Ed. 991 (1931).
A. The Structure of Mutual Insurance Policies
In analyzing the insurance policies, it pays to bear in mind that, “[a]s an overarching principle, absent specific provisions, the tax consequences of any particular transaction must reflect the economic [485]*485reality.” Washington Mut. Inc., 636 F.3d at 1217 (citing Kraft, Inc. v. United States, 30 Fed.Cl. 739, 766 (Fed.Cl.1994); United States v. Winstar Corp., 518 U.S. 839, 863, 116 S.Ct. 2432, 135 L.Ed.2d 964 (1996)). The reality here is that the Dorrances acquired the membership rights at no cost, but rather as an incident of the structure of mutual insurance policies.
The logic of this conclusion is simple— when the Dorrances purchased their mutual insurance policies in 1996, the premiums they paid related to their rights under the insurance contracts, not to collateral membership benefits such as voting. Under the insurance contract, policyholders paid premiums for the following “contract rights”: (1) a death benefit; (2) the right to surrender the policy for a “cash value”; and (3) annual policyholder dividends representing the policyholder’s portion of the company’s “divisible surplus.”
Separate from the contract rights, through operation of law and the company charter, each policyholder had a right to vote on certain matters, such as the election of the board of directors. That vote was restricted to one vote per policyholder, regardless of the size or face value of the policy. In addition, in the very unlikely event of a liquidation, the policyholder was entitled to any surplus from that liquidation.5 At trial, the government expert stated that he did not know of a single mutual insurance company that had ever had a solvent liquidation, a point echoed by the MetLife representative. This bundle of rights — derived from operation of law— is referred to as “mutual rights” or “membership rights.”6 These rights are not transferable and upon termination of a policy, the policyholder receives nothing for any membership rights.
The difference between contract rights and membership rights is critical to resolution of this case. The premiums paid covered the rights under the insurance contract, not any membership rights. Notably, the policies themselves generally make no reference to any such membership rights. In other words, premium payments go toward the actual cost of the life insurance benefits provided. The mutual companies did not count membership rights as having a cost (apart from minimal administrative costs, if there is a policyholder vote), so they did not charge policyholders for such rights.
The government’s expert, American Academy of Actuaries member Ralph Sayre, testified that mutual companies calculate premiums based solely on the expected cost of providing contractual insurance benefits. This calculation process is “very precise in actuarial circles” and “there just is no portion of the premium or charge for membership rights.” He linked this analysis to the obvious: “[Ujsually you don’t pay [for] something if ... you aren’t charged for it.” This explanation is consistent with the Supreme Court’s description of what the premium pays for: “It is of the essence of mutual insurance that the excess in the premium over the actual cost as later ascertained shall be returned to the policy holder.” Penn Mut. Life Ins. Co. v. Lederer, 252 U.S. 523, 525, 40 S.Ct. 397, 64 L.Ed. 698 (1920).
In referencing “ownership rights,” by which he meant membership rights, the [486]*486description by the Dorrances’ expert was essentially in line with Sayre’s conclusion: “The ownership rights were not separate from the policy rights and could not be sold. The cost associated with acquiring ownership rights cannot be established exclusively through premium payments.”
Consistent with the general practice for mutual insurances companies, the companies involved in this case did not charge the Dorrances for their membership rights. This point was underscored by Mr. Dorrance’s testimony that, at the time he bought the policies, he actually understood that he would pay less for a policy from a mutual insurance company than he would for one from a stock company. See S. Bancorporation, Inc. v. United States, 732 F.2d 374, 377 (4th Cir.1984) (rejecting refund claim where the taxpayer “introduced no evidence to prove that it intended to pay an enhanced value fpr the [asset] at the time of sale ”) (emphasis in original). It was no surprise then, that in 2003, when the Dorrances filed their tax returns following the sale of the stock derived from demutualization, they listed their basis as zero.
B. The Effect of Demutualization
The membership rights were assigned a monetary value at the time of the exchange only as a consequence of the de-mutualization process. The error of the Dorrances and the district court was to assume that the value received upon demu-tualization was linked with some premium value paid by the policyholders in the past. But the stock the Dorrances received in exchange for the membership rights cannot be understood as a partial return on .their past premium payments and it is well understood that policyholders do not contribute capital to the companies.
By the time of the demutualization, the lion’s share of the surplus that fed valuation of the newly issued stock could not be traced to payments made by current policyholders. Nearly all of the surplus held by the companies at that time was attributable to former policyho’ldérs, not current policyholders like the Dorrances. For example, at the time of demutualization, less than 10% of the Sun Life surplus was attributable to current policyholders; premiums . paid by former policyholders accounted for over 90% of the surplus. Thus, the value at demutualization was not derived from something paid for by the Dorrances.
Sayre explained the situation as follows: The demutualization is not a result of [ ] current policyholders having done something different from the other previous millions of policyholders, but is a result of outside influences, such as tax policy, economic conditions or competitive pressures. The current policyholders are fortunate to be policyholders at the time of- demutualization but their value received is a result-of the new stockholders who are willing to pay them in order to receive their membership benefits for the purpose of what they can do with them in the Tuture.
This anomaly prompted one insurance company official involved in this case to refer to the receipt of stock as a “windfall” for current policyholders. This characterization was echoed by the Sixth Circuit, which referred to demutualization proceeds as “a pot of money that no one expected or even envisioned.” Bank of New York v. Janowick, 470 F.3d 264, 266 (6th Cir.2006); see also Douglas P. Faucette & Timothy S. Farber, National Insurance Act of 2007 & Demutualization of Insurers: The Devil is in the Details, 58 Fed’n Def. & Corp. Couns. Q. 109, 127 (2007) (noting that policyholders “receive payouts that they had not expected, consciously bargained for, or purchased. Sim[487]*487ply put, distribution of the surplus amounts to ‘a windfall resulting from the increase in the value of that policy arising from its unforseen restructuring.’ ” (citation omitted)).
Following the transfer of stock, it was business as usual in terms of the contract rights. After demutualization, the Dor-rances’ insurance premiums remained level — reinforcing the fact that they had not been paying a “premium” for any membership rights in the first place. For example, the premium history for Principal Financial Group shows that the Dorrances’ premium was $124,450 both before and after the 1999 demutualization. This transition occurred under the oversight of regulators who were charged with ensuring that policyholders were treated fairly during the demutualization process and who did not require a reduction in the premiums to sync with the loss of the now-claimed rights. The Dorrances continued to pay the same premiums and receive the same coverage. The stock exchange, for which they paid nothing, was the only aspect of the transaction related to membership rights.
The demutualizations themselves were structured as tax-free, meaning that the initial transaction by which the Dorrances received the stock did not trigger any taxable gain for the policyholders. As an exchange under I.R.C. § 3547, the deal would not have been tax free if there was a gain upon the exchange. I.R.C. § 358(a)(1) (providing that the basis of property received under a § 354 exchange “shall be the same as that of the property exchanged”). In other words, the stock was a direct exchange for the lost membership rights.
Put another way, the basis in the new stock was the same as the basis in what was being exchanged — the membership rights. Hence, the companies told policyholders that the tax basis on the stock was “zero.” For example, with regard to the receipt of stock, Phoenix explained in its Q & A document:
If you receive common stock, you will not be taxed when you receive it. However, if you sell or otherwise dispose of your common stock, you will be taxed on the full amount of the proceeds you receive for the common stock. (Your tax basis in the common stock will be zero.)
The other companies alerted policyholders to the same thing: Sun Life advised that the “cost basis of these shares for tax purposes will be zero” and, after saying that the tax cost would be “zero,” Principal Mutual stated that “if you later sell or otherwise dispose of your Common Stock, you will generally be taxed on the full amount of the proceeds of that sale or other disposition.”
The insurance companies’ advice to their policyholders comports with IRS rulings dating back to the 1970s. Those rulings stated that the policyholder's basis in mutual rights is zero. See Rev. Rul. 71-233, 1971-1 C.B. 113; Rev. Rul. 74-277, 1974-1 C.B. 88. Revenue Ruling 71-233 addresses the tax consequences to policyholders when they exchange their proprietary interests for preferred stock. Consistent with our explanation above — distinguishing between contract rights and membership rights (which are also referred to as proprietary rights), the IRS advised:
Payment by each policyholder of the premiums called for by the insurance [488]*488contracts issued by X represents payment for the cost of insurance and an investment in his contract but not an investment in the assets of X. His proprietary interest in the assets of X arises solely by virtue of the fact that he is a policyholder of X. Therefore, the basis of each policyholder’s proprietary interest in X is zero.
Id.
Within the tax code, the transaction exchanging mutual rights for stock does not operate in a vacuum. Treating the premiums as payment for membership rights would be inconsistent with the Code’s provisions related to insurance premiums. For example, gross premiums paid to purchase a policy are allocated as income to the insurance company; no portion is carved out as a capital contribution. See I.R.C. §§ 803(a)(1), 118. On the flip side, the policyholder is allowed to deduct the “aggregate amount of premiums” paid upon receipt of a dividend or cash-surrender value. I.R.C. § 72(e). No amount is carved out as an investmeñt in membership rights. The taxpayer can’t have it both ways — a tax-free exchange with zero basis and then an increased basis upon sale of the stock.
The district court skipped a critical step by examining the value of the mutual 'rights without evidence of whether the Dorrances paid anything to first acquire them. The basis inquiry is concerned with the latter question. The district court also erred when it estimated basis by using the stock price at the time of demutualization rather than calculating basis at the time the policies were acquired. The stock value post-demutualization is not the same as the cost at purchase.
We have previously explained that basis 8 “refers to a taxpayer’s capital stake in an asset for tax purposes.” Washington Mut. Inc., 636 F.3d at 1217 (citing In re Lilly, 76 F.3d 568, 572 (4th Cir.1996)). “The taxpayer must prove what, if anything, he actually was required to pay ... not what he would have been willing to pay or even what the market value ... was.” Better Beverages, Inc. v. United States, 619 F.2d 424, 428 (5th Cir.1980). Here the Dorrances failed to do so.
Conclusion
This analysis brings us back to the Dor-rances’ burden and the economic realities of this case. Because the Dorrances offer nothing to show payment for their stake in the membership rights, as opposed to premium payments for the underlying insurance coverage, the IRS properly rejected their refund claim. The district court erred when it found after the bench trial that the Dorrances had shown they paid something for the membership rights. It should have found their basis to be zero.
REVERSED.