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Nowadays, most cross currency basis spread (against USD) is negative, while AUD, NZD basis spread against USD is positive. Can someone explain why these two are positive, unlike the rest?

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A recent report by the BIS provides a good explanation:

Because they are hedging a net US dollar liability, Australian banks on balance supply US dollars in the cross-currency swap market. That contrasts with banking systems that are funding net US dollar assets and so, on balance, demand US dollars in the swap market. This structural difference means that the AUD/USD crosscurrency basis generally behaves somewhat differently from that of other currencies. First, the AUD/USD basis is positive, implying a small hedging cost to obtain Australian dollars (supply US dollars) in the swap market. For many other currencies, the basis tends to be negative, implying a small hedging cost to obtain US dollars (Graph F2, right-hand panel; see also Annex B). For the Australian dollar, this hedging premium arises because while there are a number of natural counterparties to Australian banks, these do not have sufficient hedging needs to match all of the hedging demands of the Australian banks. Second, the AUD/USD basis has been less prone to volatility and tighter availability of US dollars around quarter-ends in recent years. That is because the suppliers of US dollars in this market, the Australian banks, are not subject to the quarter- or year-end balance sheet constraints that arise for banks in some other jurisdictions.

Source: CGFS Papers No 65 US dollar funding: an international perspective, June 2020

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I just found one possible reason online: markets like Australia and New Zealand where local interest rates are relatively high and there is little interest in offshore investment.

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This NEBR paper argues that the anomaly reflects a mismatch between observable but imperfectly matched market rates (for FX and interest rates) - versus unobservable (and thus untradeable) "risk-free", where arbitrage is not possible and CIP = 0. De facto, this creates a bias for countries with higher interbank rates to exhibit more positive xccy basis than countries with lower interbank and more negative xccy basis.

A No-Arbitrage Perspective on Global Arbitrage Opportunities; Patrick Augustin, Mikhail Chernov, Lukas Schmid, Dongho Song; NBER Working Paper No. 27231; Issued in May 2020, Revised in July 2020; NBER Program(s):Asset Pricing, International Finance and Macroeconomics

We revisit the recent literature on persistent deviations from covered interest parity (CIP) by showing theoretically that CIP violations imply arbitrage opportunities only if uncollateralized interbank lending rates are riskless. In the absence of observable riskless discount rates, we extract them empirically using a simple no-arbitrage framework. They deliver novel quantitative benchmarks for foreign exchange contracts that match observed forward currency premiums and cross-currency basis swap rates well. The no-arbitrage benchmarks account for about two thirds of the alleged CIP deviations, while the residual pricing errors line up with measures of intermediary constraints and the expensiveness of the U.S. dollar.

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