ETF Premiums and Discounts to Basket Value

The ETF monitor maintains a changing basket valuation and compares each synthetic ETF price with that value. The recording comes from Hypercube’s checked-in Rust example, using 160 constituent stocks and 12 synthetic ETFs.

Basket value and market price

Each ETF has non-negative constituent weights that sum to one. The example updates its constant-weight basket return and value as

\[r^{\mathrm{NAV}}_{j,t}=\sum_i w_{j,i}r_{i,t},\qquad V_{j,t}=V_{j,t-1}(1+r^{\mathrm{NAV}}_{j,t}).\]

The simulated ETF price can depart from basket value:

\[P_{j,t}=V_{j,t}(1+u_{j,t}),\qquad q_{j,t}=10{,}000\frac{P_{j,t}-V_{j,t}}{V_{j,t}}.\]

The premium \(q\) is expressed in basis points. A positive premium makes the ETF rich relative to the simulated basket; a negative premium makes it cheap. The displayed ETF/basket action follows that sign.

Standardizing the premium

The fractional premium follows a stationary AR(1) process with \(\phi=0.88\) and innovation scale \(\sigma=0.00040\):

\[u_{j,t}=\phi u_{j,t-1}+\sigma\eta_{j,t},\qquad z_{j,t}=\frac{u_{j,t}}{\sigma/\sqrt{1-\phi^2}}.\]

Here the denominator comes from the known synthetic process. It is not an estimate fitted to real ETF dislocations. The model z-score measures deviation in stationary-standard-deviation units, while the premium in basis points remains the direct price comparison.

Reading the changing cross-section

Hypercube publishes entity-aligned fair_value, market_price, premium_bps, premium_z and cross_sectional_z nodes. The model z-score and the cross-sectional score answer different questions: one scales a premium by its generating process; the other places an observation relative to the current ETF cross-section.

The recording makes the dependency from constituent observations to basket value and relative-value outputs visible. Those outputs are analytical state. The example does not submit orders.

Run the monitor

cargo run -p hypercube-engine --example etf

For a bounded, ANSI-free run:

cargo run -q -p hypercube-engine --example etf -- \
  --entities 160 --funds 12 --top 5 --ticks 1 --no-color

The example omits creation-unit size, fees, borrow, dividends, tax, latency, inventory and authorized-participant constraints. Its rich/cheap display is therefore a synthetic valuation demonstration, not an executable ETF arbitrage result.

Source and related material

• ETF calculation and recording guide.
• Rust ETF example.
• Hypercube architecture.
• Pairs residuals and rolling scores.