Beating Broker Margin
A survey of leverage available to the retail investor

Even if you're not familiar with interest rates right now, the published margin rates of those brokers I linked above should obviously jump out as very high. In the case of Fidelity and Schwab, at the time of writing, their \(>13.5\%\) rates exceed essentially every other type of variable-rate secured credit by a wide margin, including prime adjustable-rate home mortgages, HELOCs, and variable-rate auto loans on new cars (loans on used cars seem roughly the same right now). Interactive brokers, who have by far the most competitive margin rate I'm aware of, is much better at 6.83%, but even this can be misleading, as it compounds daily (to be clear, so do Fidelity and Schwab, but the other secured credit types above are generally compounded monthly). That means you'd actually be paying \((1 + 0.0683/365)^{365} - 1 = 7.07 \%\) per year in compounding interest – very sneaky! To be fair, overnight rates like SOFR (I will explain what this is later, but for now just think of it as the canonical risk-free rate) are also usually published with respect to daily compounding, so 5.34% SOFR at the time of writing translates to \((1 + 0.0534/365)^{365} - 1 = 5.48 \%\) when annualized.

Putting aside nitpicks about compounding, this 159bp (basis points, meaning additive hundredths of a percent) gap between SOFR and the best broker margin rate for retail-sized accounts is still notably high – it generally exceeds historical credit spreads of most investment-grade bonds – especially considering the debt is secured by very liquid assets pre-approved by the lender (the broker) and can be called back, including via automated margin calls, at any time. Why do brokers charge such high rates for lending involving so little credit risk? It's clear that they're capable of more competitive rates – Interactive Brokers advertises rates just 52bp over SOFR on balances over $200 million. The only reasonable explanation seems to be that the market for margin at retail account sizes is uncompetitive, with brokers collecting a tidy spread from traders too small to negotiate.

Luckily, retail brokers aren't the only market players offering collateralized leverage on investments – clearing houses provide an analogous service every day, on the same terms to institutions as retail traders, by guaranteeing futures contracts.

A futures contract is a contract in which a buyer (the long position) agrees to pay a seller (the short position) a specified amount of money (the "delivery price") to buy a specified amount² of an underlying security on a specified date (the "delivery date"), regardless of what the actual price (the "spot price") is at that date. Or at least, that was how they used to work³ – now much of the financial industry trades in cash-settled ("regulated") futures, in which money is automatically transferred between the accounts of buyers and sellers by the clearing house according to whose position is profitable, without ever needing to trade in the underlying security. Generally, this is not only done at the delivery date of the contract, but happens in over the lifetime of the contract as the price of the underlying asset rises and falls ("marking-to-market"), such that the clearing house will have already assessed any gains or losses by the time a cash-settled contract expires. The clearing house can automatically (force brokers to) liquidate traders' positions to cover these obligations, and traders are required to have a specified amount of collateral (which is allowed to be in stocks, bonds, etc) for this purpose. Since futures contracts don't require any up-front cost from the buyer, only enough collateral to secure the position, the buyer of a futures contract seems to be receiving a similar product as margin from a broker. Yet clearing houses generally charge the same fees to institutional investors as they do to retail – that means whatever leverage we get from these contracts must be competitive, otherwise no institutional investors would trade them!

This intuition can easily be formalized by a no-arbitrage argument. Here, we'll refer to the price the contract appears to trade at on an exchange, which is not the up-front cost to enter a position, but the number the clearing house uses to credit/debit accounts, as the "delivery price", with the "price" being the ($0) up-front cost to enter a position. When a futures contract expires, the clearing house ensures that its delivery price is the same as the price of the underlying asset by transferring balance between accounts according to position sizes, so a replicating strategy for a futures contract is to simply purchase one unit of the underlying using money borrowed at the risk-free rate, which we will assume for the moment is constant, plus any cost (e.g. we would add storage costs for commodities and subtract dividends for indices) from holding the underlying, which we will assume for the moment are zero. This implies there is a unique arbitrage-free price – we already knew this, it's $0 – but more importantly, it tells us the current delivery price of a futures contract must equal the current price of the underlying plus the interest it costs to borrow this much. If the delivery price were any lower, institutions with access to the risk-free rate would buy the stock, lend the proceeds, and short the future, or vice versa if it were priced higher. In other words, buying a long futures contract and holding it until expiration is essentially the same as borrowing one unit of the underlying at the risk-free rate – that's exactly what we wanted to achieve with margin!

Unfortunately, the two assumptions that this argument rests upon don't reflect reality, and without them, pricing futures becomes much messier. First, we mentioned above that futures contracts are marked to market, meaning cash is transferred on a daily basis as one's position goes up and down. This means that the party with the winning position on a particular day can lend this extra cash at the risk-free rate, while the losing party loses out on this same amount of interest. If the overnight risk-free rate is constant, this doesn't matter for measures which are risk-neutral with respect to all times because the price of the underlying will, in expectation⁴, neither overperform nor underperform an investment at the risk-free rate at all times, so neither side of the contract is likelier to pay additional interest in expectation with respect to such measures, and such measures are what are used to price derivatives due to no-arbitrage constraints (this uses a more complicated version of what was proven in the companion article). However, if we consider the risk-free rate to be a random time series and assume that it is negatively correlated (with respect to a risk-neutral measure) with stock index returns, which has been accurate historically, we get that the long side of the future is likely to receive more money via marking to market when interest rates are lower, and vice versa, meaning the long side does not receive as much when investing this additional money and thus would prefer to buy the underlying with borrowed money as opposed to holding the future. Similarly, the short side is likelier to receive additional money via marking-to-market when interest rates are higher, so should prefer the futures contract to selling the underlying and lending the proceeds. The future should thus trade at a lower delivery price than that found by the calculation above.

Second, when companies issue dividends, their stock falls by the dividend amount on the ex-dividend date because this money is distributed to shareholders, so both capital and appreciation and dividends must be accounted for when constructing the risk-neutral measure with respect to stock returns. But futures holders aren't entitled to a dividend, so the delivery price must be discounted to reflect that futures holders aren't paid a dividend.

Fortunately, if all we care about is getting an implied interest rate closest to SOFR, the no-arbitrage arguments above still ensure that we're getting a pretty good one, just on a slightly different "asset". In particular, the first caveat implies the returns for a long future will depend on when the index rises and falls, being higher if it rises quickly at first and later flatlines than if it had grown uniformly. The second implies that our position is only exposed to capital appreciation of index constituents, not their dividends, though a dividend reduction is implicitly better for us but indifferent for holders of index constituents. Most of us are probably indifferent to the first caveat considering it makes a very small difference and doesn't imply any less diversification. For the second, one could argue that having dividend exposure is better-diversified because dividends aren't perfectly correlated with asset returns, but there's nothing mathematically canonical about a one to one ratio of dividend exposure to capital appreciation exposure, and those conducting this strategy in practice will likely end up with a mix of futures and ETFs anyway given that ETFs can be used as margin for futures. I'll probably do a CAPM analysis on this at some point because this has made me curious, but it could turn out that whatever ratio such investors end up with is actually better than one to one. Conversely, dividends, even qualified ones, are actually quite bad from a tax perspective⁵, though we'll see below that this doesn't matter much because futures in general are probably worse for long-term investors.

But let's say we're not satisfied with futures giving us slightly different exposure, or we really want to compare the implied rate of futures to that of other instruments (which we will attempt in the programming section below). The first issue is more or less impossible to hedge out. Institutions do it by trading "forward contracts" (which are over-the-counter futures contracts settled "the old way", all at once at expiration, rather than by marking to market), but retail investors can't access these, and as far as I'm aware there isn't even any public data on them. In principle, we could go to extreme lengths and e.g. calibrate some stochastic model to find the covariance between stocks and rates, which turns out to more or less encode the entire adjustment we'd need to make, but this would be empirical, not market-based. Luckily, the differences tend to be pretty small for short-dated contracts (which are usually all we should care about due to tax implications we'll explain below), so we can probably ignore this when computing rates at the cost of some precision.

On the other hand, dividend yields can be quite high, typically 1-2% on the S&P 500, so we really need some way to account for these. Fortunately, CME offers quarterly and annual dividend futures for a few indices, which pay out the sum of dividends in that quarter or year at the end of that quarter or year. Their quarterly futures are offered about a year out, and their annual ones to about 5 years out. The problem is, the sum of dividends over the period we hold the future isn't even the quantity we want to hedge: if we instead held all the SPX constituents, we would get not only the dividends, but the interest they generate between when they are paid and when we liquidate the position. That means the difference between the dividend futures and what we want to hedge is a quantity depending on both the future risk-free rate and the temporal distribution of when the dividends are actually paid. Luckily, this difference is also a pretty small quantity, and it can be reasonably approximated (for purposes of computing implied rates) by assuming the dividend is paid at the end of each quarter and invested at market-implied forward rates until the position is liquidated. But we'll unfortunately never be able to perfectly hedge the difference with market-traded instruments here, either.

Still, one can't deny the no-arbitrage arguments showing that futures offer close to risk-free rates, and in this sense, they blow broker margin out of the water. And it's true exchanges only offer them on a few indices and commodities rather than individual stocks, and that their exposure is to weird approximations of the investments we want rather than on the real thing, but many retail investors chiefly partake in set-it-and-forget-it index investing. For these investors, the variety is likely satisfactory, and they probably don't care that their investment won't perfectly track the index as long as it's close enough. Tragically, though, the other caveat is that they're taxed at Section 1256 rates, which means that capital gains on them are assessed at 60% of the taxpayer's long-term capital gains rate plus 40% of the short-term rate. This makes them great for speculative investors who are generally subject to the short-term rate, but unattractive to long-term retirement investors who usually pay the lower long-term rate, and this may even outweigh the margin savings for the latter group. If one's investment goals somehow escape this catch-22 (for example, if one holds all futures in a tax-advantaged retirement account), futures are indeed likely to be a good strategy, but retail investors with holdings in taxable accounts will probably need to look elsewhere.

If you've ever read stories of retail investors using massive amounts of leverage and losing their entire investment, odds are these included options contracts, and you might be wondering if we can use them to lever up our positions at competitive rates. While they are indeed excellent sources of leverage, some nuances affect whether they can recreate the exact return profile of a loan as well as whether they use the same Section 1256 capital gains rates as futures. This section will explain the basics of options, then look at how we might use them to replicate the returns of futures contracts, as well as give motivation for the more generally-applicable strategy of box spreads discussed in the next section.

Despite synthetic futures turning out not to be useful in most cases, I promise there's a point to the last section other than a rant about outdated SEC policies. In particular, think about what would happen if we made a synthetic future – that's buying a call and selling a put – at one strike, say $20, and took the opposite position – selling a call and buying a put – at a different strike, say $10. The results would just cancel out and we'd be left with zero profit, right? Indeed, a quick graph confirms our suspicions:

Explicitly, the value of the position at expiration, if net premiums are invested/borrowed at the risk-free rate and in the notation of the last section, is \[S_1 - 20 + (C^{(\$20)}_p - C^{(\$20)}_c)(1 + r) - S_1 + 10 + (C_c^{(\$10)} - C_p^{(\$10)})(1 + r).\] As we saw before, \[(C^{(\$20)}_p - C^{(\$20)}_c)(1 + r) - 20 = S_0r = (C_c^{(\$10)} - C_p^{(\$10)})(1 + r) + 10\] (our calculation for the synthetic futures didn't depend on the strike), so the positions cancel out and the time-adjusted return is $0 regardless of what happens to the underlying – there's no free lunch, after all. But if we look at when the various payments happen, the premiums, \(C^{(\$20)}_p - C^{(\$20)}_c - C_c^{(\$10)} + C_p^{(\$10)}\), are credited to our account up front, and only at expiration is the differences between our strikes \(S_0(1 + r) - 20 - (S_0(1 + r) - 10) = -\$10\) debited⁷. It may not be immediately clear from the symbolic notation we used for the premiums, but rearranging the equation above, \[S_0(1 + r) - S_0(1 + r) = 0 = (C^{(\$20)}_p - C^{(\$20)}_c - C_c^{(\$10)} + C_p^{(\$10)})(1 + r) + \$10 - \$20,\] and thus we have used this spread to effectively borrow \(\$ 10(1 + r)^{-1}\) and repay \(\$ 10\) – that's the same as a loan!

Thus, we can use this strategy of a "box spread" – "buying" and "shorting" synthetic futures at different strikes – to effectively borrow (and lend) money using the options market, with our margin requirement enforced by the clearing house as our collateral and the clearing house serving as a guarantor to whomever takes the position as the lender. Better yet, we don't even have to make the box spread on the same security we want exposure to – any asset that the clearing house sees as satisfactory collateral is on the table, usually including equities, bonds, and other conventional instruments, meaning we're not restricted to just products with actively-traded options chains. In practice, this means most box spreads are traded on S&P 500 index options, which generally have the most volume and thus the smallest bid-ask spreads. Some options exchanges even allow "bundling" of the four "legs" of the box spread, where investors can offer bids and asks on the entire group of contracts, which must be bought all at once by another market party (who effectively uses them as an alternative to other secured lending markets, see the section below), often further reducing the impact of the bid-ask spread.

Do box spreads suffer from the same Section 1256 tax drawbacks for long-term investors? The answer is complicated: while all feasible options products that could be used to construct box spreads are cash-settled and thus subject to Section 1256, "interest" paid on box spreads is assessed as a capital loss in the tax code, which can be used (in the same year) to offset any kind of gains, whether short-term or long-term, provided gains in the same categories (in this case, 40% of the box spread losses are counted as short-term and 60% long term) have already been offset by losses in the same categories. For long-term investors, this is likely acceptable – not only can box spread "losses" offset their long-term gains, they can even offset some short-term gains. Compared to margin, when itemizing, the interest deductions can offset all net investment income, whether short-term or long term, effectively on a prorated basis, which might be better in some cases, but this isn't clear-cut and depends on the situation. There are also considerations that section 1256 losses can be carried to different tax years while interest deductions can't. The nuances of this can be complicated, but generally the tax implications of box spreads do not invalidate them for wide swaths of investors like the other two strategies do, and often they're actually better than margin with respect to taxes.

It seems box spreads will be satisfactory for a large majority of retail investors, but all these roundabout strategies beg the question: why can't we just do whatever big institutions do to get secured credit? Actually, many of them just use margin; recalling that Interactive Brokers was willing to offer just a 52bp spread over SOFR on balances over $200,000,000 (chump change to many hedge funds, asset managers, etc), it's clear that big enough account sizes have much more negotiating power than retail, and thus can demand better rates. However, and in spite of the fact that margin lenders seem to have exceedingly favorable loan terms, a margin loan secured by a firm's assets is still not completely risk free, and thus will never be given at quite the "risk-free rate". Why? If a firm that has borrowed on margin declares bankruptcy, the lender cannot immediately seize its collateral to cover the loan; instead, these assets are frozen and the lender must go through lengthy bankruptcy proceedings just like any other creditor, and may not even recover the full amount.

To work around this possibility, lenders had to get creative. What if, instead of lending cash secured by collateral, lenders instead "bought" the collateral one day with the obligation to "sell" it back the next for a slightly higher price? Then if the firm they "bought" it from declared bankruptcy, the collateral would legally be the lender's whether or not the borrower were able to repurchase it. These repurchase agreements, or "repos" (presumably "repu" didn't sound cool enough) are the primary way that the largest banks and broker-dealers effectively "borrow" money. In practice, the collateral is almost always treasury bonds (but can be e.g. stocks or other liquid assets⁸) and there is usually a third party bank (almost always BNY Mellon) holding the collateral, to, among other reasons, protect the borrower in case the lender defaults on their obligation to buy (these are "tri-party repos"). We can now finally define SOFR: it is a rate published by the Federal Reserve each night to reflect the "average" overnight rate attached to these repurchase agreements. In fact, the Federal Reserve is often a party to this market to help implement its monetary policy, borrowing or lending to move rates up or down respectively.

Why can't retail investors access this market? Actually, they effectively can if they only want to lend; commercial banks with money market accounts are some of the largest lenders in the repo market, are FDIC insured, and in many cases return rates at or even above SOFR⁹. But to be on the receiving end, prospective borrowers must generally cultivate relationships with individual lending institutions as trading is over-the-counter, and the only institutional borrowers which tend to do so are the largest of the large; according to BNY Mellon data, it only had 118 total accounts belonging to borrowers for purposes of repurchase agreements (though it's possible that broker-dealers participate on behalf of, or to provide margin to, their customers). So it looks like retail will have to make do with futures and box spreads.

Clearly, retail investors can do much better than broker margin when accessing leverage, and the conclusion we can draw from the theory section is that generally speaking, box spreads are the best way to do this. In practice, a retail trader could likely get away with reading the few sentences describing the implementation of a short box spread and simply construct one without any knowledge of the rest of this article, but I hope that this article has provided both a theoretical motivation for how one would discover this type of leverage and satisfactory theoretical arguments showing that rates must be good.