Reconciling interest rate parity and the real world

We all ever once heard contributors at Bloomberg talked about ineffectiveness of the Taylor rule to prompt Fed hiking earlier, or your macroeconomics professor talking on Purchasing Power Parity and Interest Rate Parity. Seems like a knowledge that would allow an undergraduate to make side incomes from tracking the rate differential. But that’s unlike reality cause the knowledge is incomplete.

A recap:

  • Relative PPP claims exchange rate movements should exactly offset any inflation differential between the base (your bet’s exposure) and counter currency countries i.e. ECB raising inflation expectations (new baseline to be priced in by market on announcement) to see “HICP inflation ex energy and food averaging 1.1% in 2017 7 and to rise to 1.5% and 1.8% in 2018 and 2019 respectively” due to pick up in wage growth and gradual fading of crisis related factors and U.S. FOMC March’s 2017 projection of Core PCE inflation to 1.9% from 1.8% 3 months back, meant that by relative PPP, we should expect EURUSD spot to strengthen by 0.8% (1.019/1.011 -1) over the projection horizon. If its counter intuitive, think about the same food you eat in your country being more expensive overseas, you would want your local currency to appreciate against the foreign currency so that in real terms, it costs the same regardless of which country you ate it.
  • IRP says there is no arbitrage condition between the forward exchange rate and spot exchange rate, which provides the relationship between foreign exchange and international money market (foreign currency debt maturing in less than 1 year) i.e. In March 2017, 3m T-bill yields 0.98% and 3m Euribor yields -0.33% from OECD. Assuming EURUSD forward curve remains unchanged in level and steepness of slope over the next 3m, by IRP, 3m EURUSD forward should be 1.0657*(1+0.98%)/(1-0.33%) = 1.0797. This meant that the lower Euribor is, a trader earns more yield by carrying a short EURUSD spot, but he makes greater capital loss on his short as the spot converges to a higher forward in a upwards sloping contango EURUSD forward
  • If the current 3m EURUSD forward is more than 1.0797, we can make an arbitrage to short the overpriced forward at a forward premium and long the relatively underpriced spot at a forward discount. This arbitrage on the forward premium is profitable only if the forward curve stays unchanged so that the initial no-arbitrage price we traded on is unchanged, otherwise, if the realised forward curve becomes flatter in the trade horizon (aka forward increase less than spot as spot rise, or fall more than spot if spot falls), his realised spot will converge to a lower than expected forward, and results in earning a forward premium smaller than the loss he made with a negative yield carry by shorting EURUSD spot. Note that his forward price is fixed on the date of entering the contract, so its a one leg fixed, one leg floating relative to a forward benchmark. Of course, the best case scenario is that the contango steepen in the 3m trade horizon such that his capital gains on spot convergence to forward is greater than the negative yield carry. In all these scenarios, we assumed an unchanged 3m Euribor and 3m T-bill yield. However, we can further extend to 2 floating dimension on the curve slope and rate differential. Best case scenario: 1,2,3 month Euribor is higher, 1,2,3 month T-bill yield is lower (cheaper financing the carry portfolio) and the XCRV forward curve is less flat than what IRP dictates the curve should flatten to wrt changes to the financing cost.

If you are confused and is tempted to think about deviating from the formula, you are mistaken. Parity formulas does not necessitate convergence, as non-zero basis spreads do occur into settlement date of forward. But it does dictates the no arbitrage boundary conditions between the international money market and exchange rate. To simplify the general scenario, if the funding currency financing is cheaper, the forward curve will be a steeper contango so that a larger currency depreciation eliminates the larger gains on the wider interest rate differential.

In practice, however, investors in international financial markets do seem able to make profits through such carry strategies. So, why can carry trades be profitable?

The irony that the IRP theory is unprofitable in theory, but profitable in practice is known as the “the forward premium puzzle“.

Summaries of the puzzle are:

  1. After considering transaction cost and other technicalities contributing to a small liquidity premium, carry trade need to be rolled over a longer time to earn a larger net profit
  2. Rising popularity of carry trade does diminish its own alpha. Shorting the funding currency and buying the target currency does tilt their supply and demand such that funding currency that ought to appreciate  in contango conditions is actually depreciating. So diversifying the demand supply disruption across a basket of funding-target currencies does mitigate that vicious cycle!
  3. Statistics on the actual size of carry trade is not indicative of the actual size as these strategies are generally conducted through transactions, such as currency swaps, that are reported as off-balance-sheet items. But argue that the remarkable increase in foreign exchange market turnover between 2001 and 2004 was likely due to a rise in carry trade activities.

This leads us to the “plug in” that would reconcile theory CIP and the real world. It is called Cross-Currency Basis Swap / CCBS / Xccy basis swap.

Fwd / Spot = (1 + domestic rate + basis) / (1 + foreign rate)

Domestic currency is always quoted in USD and hence a basis << 0 implies strong demand for USD as the fx forward curve is less steep i.e. u earn more from rolling down the curve than financing the carry.

In practice, the relationship between F and S is read off market transactions in FX instruments, notably FX swaps and CCBS. If the party lending a currency via FX swaps makes a higher or lower return than implied by the interest rate differential in the two currencies, then CIP fails to hold. (Since swap = differential + basis) Typically, the USD has tended to command a premium in FX swaps. However, strong demand for USD in 2nd half of 2008 post-GFC was a surprise and reasons were summarised below:

  1. Flight to safe haven – TED spread widen when bond portfolio managers sold foreign bonds, US corporate bonds and ABS, and bought T-bills to keep their exposure to US. Safe haven flows strengthened the dollar. This was driven when the Reserve Prmary Fund broke the buck and lose its reputation of being risk free and its ability to secure NAV floor of its original value. US MMF is a huge fund source for US government, banks and corporates. Investors, already risk adverse, flock out of prime funds – able to invest a wider variety of low risk assets and earn a higher yield – into government funds limited to securities backed by the government.
  2. Unwinding of carry trades – When financial markets become very volatile, modest day-by-day yield differentials captured by carry trades pale in comparison to possible daily losses. PM reduce exposures that reduce their sharpe ratios.  As a result, the target currencies that had offered the most lucrative yields would suffer the greatest depreciation, and the funding currencies would appreciate. The expectation based on the pattern of previous volatility spikes and on money market yields (in ascending order: yen, dollar, euro) was that the dollar would lose ground against the yen, but gain ground against the euro.
  3. USD shortage – foreign banks were heavily invested in USD assets but funded this levered exposure beyond the USD deposits they have with unsecured interbank and wholesale markets and with secured funding markets such as repos and cross currency financing using FX swaps. USD became special on the repo desk and their xccy basis widen to factor in the USD premium. Non-US banks and international companies financing US assets, or inventories or international trade in USD e.g. WTI Crude oil, writedown these assets denominated in USD ended up with an imbalance USD A-L (overhedging) with an excess of USD debt. The most cost attractive way of squaring this gap risk was not to roll over the USD debt but instead buy USD outright in spot market to repay debt, otherwise, holding on to USD hedges would cost them (Forward-Spot). This ought to be a lesson for international commerce to move towards multi-currency quotations in trade dealings.
  4. Besides imbalance A-L, real money (not levered) institutional investors and pension funds that did not sold their US equities also had to repay their USD debt earlier as the crash in US equities market reduced their USD exposure and resulted in an overhedged portfolio as well

So, what actually causes the cross-currency basis to exist? A useful way of thinking about the drivers of a given cross-currency basis market is:

  1. What causes the basis to appear in the first place?
  2. What are barriers in place that stop the market from arbitraging the basis away?


What causes the basis to open up in the first place?

Hedging of FX positions is the main driver of the demand for CCBC, and these hedging demands are insensitive to the size of the basis i.e. no mean reversion to zero by natural course.

  1. Bank’s ALM closing mismatched A-L in given currency with CCBC, after satisfying foreign currency funding requirement with borrowing from unsecured interbank (lower rates) or secured repo agreements. Financial institutions play the dual role of putting pressure on the basis and arbitraging another basis. They arbitrage when they lend out USD (Asset), which US banks have a surplus of domestic currency deposits relative to loans, but they do hedge (Liability) their USD lending with CCBS. Overall, banks hedge more against JPY,EUR than they loan out USD as they have net USD assets shown below, resulting in a negative basis for JPY and EUR CCBS. Exceptions are Australia and Sweden where their net USD liabilities allowed them to lend out USD (Asset) to balance their A-L, resulting in a positive AUD CCBS. ccbs and AL.jpg
  2. Any factors that drives PM to increase their exposure to assets in the given currency despite their already large exposure to the currency will prompt FX hedging necessary as indicated by a steep marginal VAR. Hedging demand is insensitive to size of basis, but sensitive only to their portfolio total risk.
  3. Non-financial US firms seeking to borrow opportunistically in markets where credit spreads are narrower. This is relevant only when credit spreads differ systematically for some time. For example, from the below graph, corp credit spreads in the Euro bond market have fallen relative to those in the US dollar bond market, largely driven by ECB bond purchase programmes. US firms have found it more cost-effective to issue in euros (reverse yankee bond) and then swap the proceeds into US dollars. The hedging of currency risk back to their domestic currency by US firms issuing in the euro increases demand for CCBS. Hence, the widening of corporate asset swap spread differentials and the surge in euro issuance since 2014 have coincided with a marked widening of the currency basis. So a wider, negative basis implies a lower cost of placing bonds in that currency relative to USDbox bOn the other side in Europe, top-rated European supranationals and agencies have relied on their funding cost advantage to arbitrage the basis by issuing bonds in US dollars and swapping the proceeds back into euros, thus collecting the currency basis. This activity is reflected in the rising share of US dollar bond liabilities of major euro area supranational agencies compared with their home currency (EUR) bond liabilities. This was a smart move from ECB as they were less invested in US assets and had less FX hedging needs compared to countries like Japan, where life insurers were largely reliant on USD funding to earn higher than domestic yields, and had to pay the USD basis premium to euro banks. Eventually, JPY CCBS basis widen more than EUR CCBS basis did. eur issuance arb.pngHowever, such “issuance arbitrage” slowed when the interest rate swap rate fell below the US Treasury yield in Q3 2015. Since such supranationals have to issue at rates above US Treasury yields, this inversion of US dollar interest rate swap spreads sharply increased their costs of placing a 7- to 10-year bond in USD and swapping it into EUR.
  4. Divergence of monetary policies boost hedging demand through price and quantity effects. By shifting the yield curve downwards and, in particular, by compressing the term premium and credit spreads, monetary easing encourages investors seeking capital gains and lower duration from a bull steepener to buy foreign currency bonds. Likewise, easing encourages foreign issuers to sell bonds in the corresponding currency to obtain cheaper funding, and swap back to home currency later to hedge currency risk. Large-scale asset purchases from central banks strengthen these effects by withdrawing securities from the market, making them more scare and valuable on collateral desk that they demand a lower repo rate. The most dovish case was the adoption of negative interest rates, which remove the intuitive bottom line mindset for repo desk (and goes against GMRA implicit assumption) for very rare collaterals which can demand a negative repo rate. Swap dealers that provide currency hedges expect the outflows from the funding currency to increase when the central bank eases policy. This adds on to the flows for currency risk hedging, which push up the demand for CCBS  causing the basis to widen.

What are barriers in place that stop the market from arbitraging the basis away?

Pre GFC, credit and counterparty risks have not been priced into instruments adequately and mis-transfer of risks led to arbitrageurs with highly levered large balance sheets and likewise, highly levered repo loans from dealer banks. Changes in regulation have reinforced market pressures for a tighter management of balance sheet risks. Changes to CVA incentivise dealers to price the counterparty risk in their derivatives portfolio more accurately. Both Basel III and US leverage ratios require market participants to hold capital in proportion to their derivatives and other exposures. As a result of tighter balance sheet constraints, arbitrage now incurs a cost per dollar of balance sheet. This cost is passed on to the pricing of FX swaps, introducing a premium (or discount, depending on the currency) in response to imbalances in the swap market. One result is that the currency spot-forward relationship goes out of line with CIP.

This cost per dollar of balance sheet is the financing cost of a leveraged (‘renting’ ) balance sheet. As the GFC raised awareness of counterparty risk, many market participants switched from unsecured to secured funding sources, notably repo markets. Reliance on the repo market constrains the arbitrageurs’ flexibility, since the borrower cannot obtain funds without having the underlying security to pledge as collateral. Hence, renting became more expensive and financing leveraged balance sheet for arbitrageurs is ever harder given tighten balance sheet regulations.

The USDJPY case

A proxy for BS renting cost would be repo rate (the difference in the notional loan amount on collateralisation and the higher repurchase price of collateral in the future standardised to the loan amount). And the case study on USDJPY basis is more relevant as it has been the most extreme and persistent non-zero basis among the major currencies, with banks and institutional investors both bidding for hedges.

Japanese banks have been the largest foreign bank issuers of unsecured paper in US money markets, approximately two thirds of their $600 billion of liabilities in US is unsecured funding. Due to the lower availability of wholesale USD funding, because of US MMFs’ disinvestment from foreign banks’ certificates of deposit and time deposits because of Oct 2016 MMF reform, non-US banks and Japanese banks seeked other sources of USD funding and relied more on CCBS for USD funding so much so that the Japanese banks were unable to be counterparties to non-bank hedgers seeking to buy the same CCBS. (An exception was French banks since EUR funding was as cheap as JPY) In particular, Japanese life insurers’ search for yield overseas has led them to increase FX-hedged investments in US dollar denominated bonds (with average hedge ratios of 60–70% vs low hedge ratios for Japan’s pension funds which is unlikely to affect the basis). This was a reason why BOJ started yield curve control so that life insurers would be able to cover their defined contribution plans with domestic bonds. Issuance of Samurai bonds has not played a significant role, owing to the thin corporate bond market in Japan.

repo and cost renting.png
The greater importance attached to quarter-end reporting and regulatory ratios following regulatory reforms led to the basis exhibiting quarter-end spikes, along with repo rates, indicating that arbitrage has become harder.


Given heightened risk aversion post GFC and the massive Federal Reserve balance sheet, it is less likely to find highly rated supranational and quasi-government agencies, which can do issuance arbitrage on the long-term basis thanks to their top credit rating by issuing bonds in US dollars at attractive rates and then swapping them out into foreign currencies. Fed plans for a balance sheet unwinding in the next half of 2017 would increase the funding gap (on-balance sheet) in the USD, which is a proxy for hedging demand via CCSB (off -balance sheet position). While lessons learned the hard way from buying CCBS, and might eventually lead to domestic investors diversifying their assets across countries to neutralise their risk exposure to a particular currency, it would take a long time for countries like Japan to reduce their debt before being able to command higher yields. Meanwhile, international opportunistic borrowing and issuance arbitrage would be here to stay given that divergence of credit conditions will be there for long.

A useful formula to takeaway is:

basis ∝ risk premium * FX hedging demand


  • rp = cost to hedge or arbitrage (currently with spot or in the future with forward) ‘renting’ cost of balance sheet, given net position of CIP arbitrageur (able to finance at low cost like euro banks or has negative net USD asset like AUD) = net position of currency hedger (Japan with large net USD assets)
  • FX hedging demand is higher when ‘real money’ institutional investors have concentrated exposures to asset denominated in USD and marginal VAR implies a need for FX hedging, or banks in the ALM business which have met the capital requirement and have no shortfall in foreign currency, but have gaps between assets and liability in a given currency that would be closed with CCBS.

In other form,

basis ∝

repo spread differential (cost of renting BS) * net USD liability (funding gap) * hedge ratio (beta of foreign asset to exchange rate)

– net issuance arbitrage * ratio of yankee issuance to reverse yankee issuance (ratio of CCBS payers to buyers)

Note: Smaller trade economies or where central banks banned exchange rate forwards, have OTC forwards called NDF (offshore), which mostly cover EM and Asian currencies. Like CFD, both currency stays in domicile with no exchange of principals, so large bet on direction is possible without volatile spots. Only the difference in final spot and fixed forward price is settled. Here’s a good article that explains why Asian NDF have higher volatility than spot, correlation among Asian currencies and which G10 currency they take their lead from, which Asian onshore spot is accessible and how the size and sign of onshore-offshore NDF spread signals on the domestic market pressure on onshore currency and effectiveness of capital controls on controlling flows in or out of onshore currency.

the sign of the onshore/offshore yield spread can signal underlying market pressure on the currency. An onshore interest rate above its offshore NDF-implied counterpart would indicate underlying appreciation pressure on the home currency but effective capital controls limiting capital inflows into the home currency. An onshore rate below its offshore counterpart would indicate depreciation pressure but effective stemming of capital outflows.

Finally, the volatility of the spread may also contain information about the depth of the spot, NDF and onshore money markets, and the ease of transacting across them.

…  Ideally, the comparison should be between a liquid onshore bank interest rate and a similarly liquid offshore implied rate. But the fact that the domestic money market is most liquid at short maturities, while NDF markets tend to be more liquid at medium to long maturities, makes it hard to find good liquidity at matching maturities.

… Since NDFs involve global banks with a higher credit rating than onshore banks or even sovereigns, and in any case start out with only potential credit risk, onshore yields could exceed offshore implied yields even with full capital mobility. This implies that evolving credit and country risk premia may complicate the interpretation of variations in the onshore/offshore interest spreads.

If you are interested more about this:

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