CFA Level II · CFA Level II Exam

Exchange-Traded Funds: Mechanics and Applications: formula sheet

Full chapter guide

Key formulas

Premium or discount to NAV: Premium/discount = (ETF market price − NAV per share) ÷ NAV per share; Positive means premium, negative means discount. Many questions give price and NAV and ask the sign or size.
NAV per share: NAV per share = (Fund assets − Fund liabilities) ÷ Shares outstanding; Use it to compare with the market price.
Premium arbitrage rule: Price > NAV (net of costs): AP buys basket, delivers it, receives ETF shares, sells shares; Creation increases the share supply and pushes price down toward NAV.
Discount arbitrage rule: Price < NAV (net of costs): AP buys ETF shares, redeems for basket, sells securities; Redemption reduces share supply and pushes price up toward NAV.
Arbitrage profit per share: Profit ≈ |Price − NAV| − transaction costs − fees; Arbitrage only occurs if the gap exceeds the AP's costs, so small gaps can persist.
Premium or discount to NAV: Premium/(discount) = (ETF market price − NAV) ÷ NAV; Positive means premium, negative means discount. Use NAV per share at the same time as the price.
NAV per share: NAV per share = (Assets − Liabilities) ÷ Shares outstanding; Usually computed at the end of the day.
Arbitrage when at a premium: Buy basket + create ETF shares + sell ETF shares; Profit is the price minus basket cost, less costs and fees. Selling pressure narrows the premium.
Arbitrage when at a discount: Buy ETF shares + redeem for basket + sell basket; Profit is basket proceeds minus ETF cost, less costs and fees. Buying pressure narrows the discount.
Arbitrage profit per share: |Price − NAV| − transaction costs and fees; Arbitrage only works if the gap exceeds costs.
Tracking difference: Tracking difference = ETF return − Benchmark return; Measured over a stated period, for example a year. Signed value. Usually negative for a fund after fees.
Tracking error: Tracking error = standard deviation of (ETF return − Benchmark return) over the periods; Use the sample standard deviation, dividing by n − 1, of the periodic differences. Annualise by multiplying by √(periods per year) if periodic data is used.
Round-trip spread cost: Round-trip cost ≈ Ask − Bid, or as a % = (Ask − Bid) ÷ Midpoint; Buying at the ask and selling at the bid costs one full spread. Half-spread is the one-way cost against the midpoint.
Total cost of ownership (approx.): Total cost ≈ Spread cost (annualised over holding period) + Expense ratio + Other drag; Divide the round-trip cost by the number of years held to compare with the annual fee.
Expected tracking difference: Tracking difference ≈ − Expense ratio + Securities lending income + Other offsets − Other drags; A rough guide, not a rule. Check each item's sign.
Premium or discount to NAV: (ETF market price − NAV per share) ÷ NAV per share; Positive is a premium, negative is a discount. Large discounts in stress signal failing arbitrage or stale NAV.
Counterparty exposure (synthetic ETF): Net exposure = swap mark-to-market value owed by counterparty − collateral held; Only positive net exposure is unsecured. Overcollateralisation reduces it.
Net securities-lending benefit: Fee income to fund = gross lending revenue − lending agent or manager share; Compare with the remaining risk: borrower default and collateral reinvestment losses.
Premium or discount to NAV: (ETF market price − NAV) ÷ NAV; Positive is a premium, negative a discount. Large gaps signal liquidity or pricing stress.
Tracking difference: Portfolio return − Index return; Measured over a period. Fees are a main cause of a negative gap.
Tracking error: Standard deviation of (portfolio return − index return); Measures the variability of the return gap, not its average.
Cash equitization target: ETF amount = cash to invest, in the ETF tracking the benchmark; Aim to make total exposure equal the benchmark weight. Match the ETF to the benchmark.
Round-trip trading cost: Bid-ask spread + commissions + market impact; A spread cost is incurred on entry and exit, which matters for short-term use.
Tracking difference: Tracking difference = ETF return − Index return; Usually negative over time because of fees. Measures the average shortfall; sign and period matter.
Tracking error: Tracking error = standard deviation of (ETF return − Index return); Measures consistency of tracking, not the level of the shortfall.
Premium or discount: (Market price − NAV) ÷ NAV; Positive means premium. A wide gap signals weak arbitrage or illiquid underlying assets.
Total cost of holding: Expense ratio + trading costs (spread, commission, premium/discount) + tax drag; Spread and commission are one-off and weigh more for short holding periods. The expense ratio is recurring.
After-tax return: After-tax return ≈ pre-tax return − tax on distributions − tax on realised gains; Use the tax rates in the vignette. Do not assume rates.

Quick revision

APs create and redeem ETF shares, usually in kind, in large blocks called creation units.
Premium or discount = (market price − NAV) ÷ NAV.
If price is above NAV, APs buy the basket, create shares and sell them, which pushes the price down.
If price is below NAV, APs buy ETF shares, redeem them for the basket and sell it, which pushes the price up.
Arbitrage limits are set by AP costs, so wide gaps can persist when the underlying market is hard to trade.
Total cost of ETF ownership includes expense ratio, bid-ask spread, commissions and tracking difference.
Tracking difference is the return gap versus the benchmark; tracking error is the standard deviation of that gap.
Synthetic ETFs using swaps add counterparty risk; physical ETFs add securities lending risk.
Liquidity in stress depends on the underlying holdings and AP participation, not just the ETF's own volume.
Use limit orders to control execution price in wide-spread or volatile conditions.
ETFs suit core-satellite, rebalancing, cash equitization and tactical exposure.
Choose an ETF by comparing structure, cost, tracking, liquidity and tax treatment together.

Common mistakes

Thinking ordinary investors create and redeem shares with the fund. Fix: Only APs use the primary market. Investors trade on the exchange in the secondary market.
Reversing the action: redeeming at a premium. Fix: Ask where the AP sells high. At a premium the AP sells ETF shares, so it must create them first.
Reversing the trade, such as redeeming when the ETF is at a premium. Fix: Ask which is cheap and which is expensive. Buy the cheap one, sell the expensive one. At a premium the ETF is expensive.
Treating the iNAV as the official NAV or as a price at which you can trade. Fix: The iNAV is an intraday estimate. The NAV is the official end-of-day value. Neither is a guaranteed execution price.
Treating tracking error and tracking difference as the same thing. Fix: Tracking difference is a signed return gap over a period. Tracking error is the standard deviation of the periodic gaps.
Computing tracking error as the standard deviation of ETF returns. Fix: Subtract the benchmark return from the ETF return first. Then take the standard deviation of that difference series.
Saying physical ETFs have no counterparty risk at all. Fix: Physical ETFs avoid swap risk but still face securities lending borrower risk if they lend.
Assuming collateral removes all synthetic ETF risk. Fix: Collateral may be illiquid, fall in value, or differ from the index; only the unsecured gap is protected incompletely.
Using a broad-market ETF for cash equitization when the benchmark is narrower. Fix: Match the ETF to the portfolio benchmark so equitized cash adds no tracking error.
Treating leveraged or inverse ETFs as good long-term hedges. Fix: Remember daily reset. Compounding makes longer-period returns differ. Use them for short holds only.

Exam tips

Draw the two-market picture quickly: investors on the exchange, APs at the fund.
Always compute price minus NAV first. The sign decides the action.
Watch for costs in the vignette. They often decide whether the AP acts.
Link in-kind transfers to tax efficiency when a question asks why ETFs distribute fewer gains.
Expect the same logic to appear in questions on tracking error and trading costs.
Always read when NAV and price were measured in the vignette; mismatched times often explain a gap.
Questions often ask which AP action fits a premium or discount. Trace buy and sell on both sides.
Expect a link to illiquid or foreign underlying markets to explain wider gaps.