Crypto hedge basis risk is the chance that a hedge and the exposure it is meant to offset move differently. A BTC short used against other crypto assets can reduce one shared price exposure while leaving token-specific losses. To diagnose the result, separate the hedge size chosen at entry from the portfolio’s unexpected relative move, then account for any contract-to-spot gap and holding costs.
Name the exposure that the proxy should offset
A proxy hedge uses a related instrument in place of an exact match for the holding. For example, a short BTC contract might be used to offset some broad crypto exposure in a basket of other tokens. That relationship needs evidence; the label “crypto” does not establish a hedge ratio.
The Federal Reserve Bank of Chicago distinguishes basis risk, arising when the exposure and derivative move differently, from quantity risk, arising from the amount hedged. Its discussion also identifies cross hedging through a related asset as a source of basis risk. That distinction supplies the framework here; it is general derivatives methodology, not a study establishing which tokens BTC can hedge. Chicago Fed: hedging and basis risk.
There are two relationships to inspect. First, does the held portfolio track the chosen BTC benchmark? Second, does the traded BTC contract track that benchmark? A token basket can underperform BTC even when the BTC derivative follows spot exactly. Conversely, a contract gap can change the hedge result even if the portfolio follows its assumed BTC sensitivity.
Write the objective narrowly: reducing a stated price exposure over a stated interval. A proxy does not automatically offset a token exploit, withdrawal restriction or a change in the assets actually held.
Fix the hedge rule before reviewing the result
For a simple linear model, beta describes the portfolio’s sensitivity to the chosen benchmark. An assumed beta of 1.25 maps a 1% benchmark move to a modeled 1.25% portfolio move, before the unexplained part. Correlation alone does not give that size: two return series can move closely together while their percentage swings differ.
ICE’s equity-index hedge example sizes contracts from portfolio value, contract value and beta relative to the index. It also cautions that historical beta depends on the period used and can change. We adapt that sizing structure for the invented crypto example below; the ICE article does not validate its assumed beta. ICE: beta hedge calculation.
If you estimate beta, preserve the return interval, lookback dates, benchmark, quote currency and portfolio weights. Use observations available before entry. A relationship measured using daily closes answers a different question from an intraday hedge measured over minutes. Neither a convenient lookback nor a close historical fit proves that the next adverse move will follow it.
Record any intended partial hedge as well. A smaller position may reflect a deliberate policy. Calling every difference from a full model target an execution error would misdiagnose that choice.
Work through a hypothetical $80,000 portfolio
All values in this example are invented. A fixed basket of non-BTC crypto assets begins at $80,000. Its stipulated entry beta against BTC is 1.25. BTC starts at $50,000, so the illustrative full target is $100,000 of proxy exposure: $80,000 multiplied by 1.25. At that price, the target corresponds to a 2 BTC linear short.
Suppose the trader actually holds 90% of that target: a 1.8 BTC short with $90,000 entry notional. The quantity is the contract’s BTC-equivalent exposure after its multiplier, not the cash posted as margin.
At the synchronized endpoint, BTC and the hedge contract both stand at $46,000, down 8%. The portfolio stands at $68,000, down 15%. Assume unchanged holdings and hedge quantity, a fixed one-to-one quote conversion into USD, and no fees, funding, financing or transfers. This is a price valuation exercise, not a liquidation calculation or an executable quote.
For a linear short, price P&L is quantity multiplied by entry price minus endpoint price. Bybit documents that payoff for its USDT contracts and separately identifies trading and funding fees excluded from unrealized price P&L. Its settlement unit is USDT; our worksheet uses a common USD reporting unit under the stated fixed-conversion assumption. Bybit: linear-contract P&L.
| Price ledger | Calculation | Result, USD |
|---|---|---|
| Portfolio change | 68,000 − 80,000 | −12,000 |
| Actual short result | 1.8 × (50,000 − 46,000) | +7,200 |
| Combined price result | −12,000 + 7,200 | −4,800 |
| Full-target short result | 2 × (50,000 − 46,000) | +8,000 |
| Combined result at full target | −12,000 + 8,000 | −4,000 |
The short offsets part of the decline. It does not preserve the starting portfolio value, and increasing it from 1.8 to the planned 2 BTC would not have eliminated the loss.
Separate the $800 size contribution from the $4,000 residual
An 8% BTC decline maps to a 10% portfolio decline under the entry beta: 1.25 multiplied by −8%. Applied to $80,000, that is a modeled loss of $8,000. The actual portfolio loss is $12,000, leaving $4,000 unexplained by that benchmark relationship.
Two contributions reconcile the combined result:
- Sizing contribution: (target proxy notional − actual proxy notional) × benchmark return.
- Relative-move contribution: starting portfolio value × (portfolio return − entry beta × benchmark return).
The sizing contribution is ($100,000 − $90,000) multiplied by −8%, or −$800. The relative-move contribution is $80,000 multiplied by (−15% − −10%), or −$4,000. Together, they equal the directly calculated −$4,800.
These are accounting attributions against the recorded model. The $4,000 residual does not prove a particular token event caused the loss. It could reflect changed relationships, portfolio-specific news, an inadequate sensitivity estimate or measurement errors. Investigate those possibilities before telling a causal story.
Likewise, the $800 contribution identifies exposure left relative to the illustrative full target. Whether that was undesirable depends on the plan. If 90% coverage was intentional, the arithmetic explains its effect without redefining the decision after the fact.
The useful comparison is the full-target row: even the complete 2 BTC short leaves a $4,000 loss. Enlarging a BTC position cannot guarantee protection against every move in other tokens. Choosing a new beta solely to erase this one observed residual would conceal the issue rather than test the original assumption.
Add a contract gap as a separate row
Now change one hypothetical input. BTC spot still finishes at $46,000, but the hedge contract finishes at $46,800. Keep its entry at $50,000, equal to the starting benchmark. For this example, define contract basis as contract price minus benchmark price: the gap increases from zero to $800 per BTC.
The 1.8 BTC short now earns 1.8 multiplied by ($50,000 − $46,800), or $5,760. Combined with the portfolio’s $12,000 loss, the price result is −$6,240. The additional −$1,440 equals 1.8 multiplied by the $800 widening gap, with a negative sign for the short.
The reconciliation is now −$800 from benchmark sizing, −$4,000 from portfolio-relative movement and −$1,440 from the contract gap. Do not count the gap again inside a residual already calculated against the traded contract’s return. These rows use BTC spot as the benchmark throughout.
The sign follows the payoff: a higher closing contract price reduces a short’s gain from the same entry. Funding is another ledger item. The perpetual basis versus funding guide explains why a price gap and a periodic payment must be measured separately.
Test failures that the endpoint offset can hide
A proxy can rise while the portfolio falls. In a separate hypothetical stress case, let the basket lose 5% while the BTC contract rises 8%. The portfolio loses $4,000, and the unchanged short, whose notional at entry was $90,000, loses $7,200. Both legs lose; the combined price loss is $11,200 before costs. This is a scenario to test, not an assigned probability.
Operational mismatches also deserve their own checks:
- The basket changes. A sale, deposit or changed token quantity can make an unadjusted value change misleading. Reconcile flows and split the period at changes before applying the fixed-holdings calculation.
- The hedge cannot be funded where it sits. Inspect margin requirements and balances for the actual account. The collateral fragmentation worksheet examines why an offsetting asset elsewhere may not be available to meet that account’s obligation.
- The intended quantity does not fill. Record executed quantity and prices. The order-book slope guide measures displayed capacity within declared price distances, so it can help check whether the intended hedge quantity fits inside a price boundary. That snapshot does not guarantee a fill.
- Collateral adds another exposure. A coin-margined position needs a separate collateral valuation. The coin-margined delta reconciliation shows why position exposure alone can miss account sensitivity.
An acceptable endpoint result also does not establish that margin survived every intermediate price. Preserve the path and account events when investigating a liquidation or forced reduction.
Keep a diagnostic sheet before changing quantity
| Record | Validation question |
|---|---|
| Exposure and objective | Which holdings and price risk should this hedge offset? |
| Benchmark and timestamps | Are both valuations synchronized and in one reporting unit? |
| Entry model | Which beta, observations and planned coverage were recorded before entry? |
| Contract units | Does quantity include the multiplier, and is the payoff linear? |
| Actual execution | What filled, and how does it compare with the intended quantity? |
| Relative-price rows | Can sizing, portfolio residual and contract-gap effects reconcile to direct P&L? |
| Costs and account events | Which funding, fees, flows, collateral changes or forced trades remain outside price P&L? |
Start with unit, timestamp and flow checks. Then calculate the sizing contribution against the original target, followed by the portfolio residual and contract-gap effect. Add actual holding and execution costs separately.
If the residual dominates, review the proxy relationship across further observations and adverse scenarios before treating a larger short as the solution. Save the original model alongside that review. For this example, the essential record is three signed price contributions—−$800, −$4,000 and, in the gap scenario, −$1,440—that add back to the account’s modeled price result.