The risk-adjusted covered interest parity

The conventional covered interest rate parity has failed in modern FX markets. A new HKIMR paper suggests that this is not a failure of markets or principles, but a failure to adjust the parity correctly for relative counterparty and liquidity risk across currency areas. Specifically, FX swap rates deviate from relative money market rates due to counterparty risk and from relative risk free (OIS) rates due to liquidity risk. Correct adjustment helps to detect true FX market dislocations.

Wong, Alfred, David Leung and Calvin Ng (2016), “Risk-adjusted Covered Interest Parity: Theory and Evidence”, Hong Kong Institute for Monetary Research, Working Paper No.16/2016.

The post ties in with the subject of price distortions (view summary here), in particular those that are related to liquidity risk premia.

The below are excerpts from the paper. Headings and some other cursive text has been added for context and convenience of reading.

The covered interest parity and its breakdown

“The theory of interest rate parity essentially says that movement of the exchange rate between two currencies is governed by the interest differential between the two countries concerned…The [FX] forward market allows the domestic (foreign) investor to take a forward cover when buying the foreign (domestic) currency asset in a bid to take advantage of possibly a higher interest rate abroad (at home). He can do so by taking an FX swap, i.e., conducting a spot and forward FX transaction simultaneously…The…covered interest parity …is a no-arbitrage condition because there is no profit to arbitrage:

F / S = (1 + r) / (1 + q)

where S is the spot exchange rate, defined as the foreign currency value of one US dollar, F is the…forward…exchange rate, and r the foreign interest rate and q the domestic interest rate [both usually measured by Libor].”

“The CIP [covered interest parity] departure for practically all currencies vis-à-vis the US dollar during the global financial crisis (GFC) in 2007 and 2008 caught many by surprise…The explanations offered…are [mostly] linked to some unusual market circumstances that occurred during the GFC…However, considerable CIP deviations…have persisted…[Also] counterparty credit risk and liquidity funding risk in the interbank money market, as reflected in the spread between the London interbank offered rates (Libor) and its respective overnight index swap (OIS), have remained elevated.”

“The key lies in the difference between the risks involved in money market transactions and those in FX swap transactions: transactions in the money market are uncollateralized and hence unsecured, while those in the FX swap market are effectively collateralized…Obviously the parity condition cannot be expected to hold when counterparty risk is perceived to be significant by market participants…The emergence of CIP deviations merely reflects that the traditional version of CIP wrongly assumes that counterparty risks are the same or absent in money market and FX swap transactions. As long as counterparty risks remain, there will be CIP deviations.”

A risk-adjusted covered interest parity

“We modify the theory of CIP by incorporating into the parity condition the relevant risk premiums that are embedded in the prices of the foreign and domestic financial instruments. In this…risk-adjusted version of the theory asymmetric reappraisal of the risks involved in interbank lending between two countries is what causes the CIP deviations under the traditional version.”

“To understand why CIP does not seem to hold any longer, it is important to note that while exchange rate risk is covered…counterparty and liquidity risks are not. Since money market transactions entail counterparty and liquidity risks, we rewrite [the equation above] as

F / S = (1 + rf + (r – rf)) / (1 + qf + (q – qf))

where rf and qf denote the foreign and domestic risk-free interest rate respectively such that (r − rf) and (q − qf) represent the sums of counterparty risk and liquidity risk premiums in the foreign and domestic money markets respectively.”

“Two risk premiums [are] embedded in the Libor-OIS spread…counterparty and liquidity…Given that the notional principal is not exchanged and only the difference between the interest payments is settled at maturity, the OIS rate is considered as the best proxy for the risk-free rate. At the riskier end of the funding market, the Libor is the average interbank interest rate at which banks lend to each other on an unsecured or uncollateralized basis in London. The nature of the transactions means that the Libor is necessarily risk-embedded.”

“The FX swap market acts almost like a risk screening device that can strip off the counterparty risk premium from the money market [Libor] rate…allows us to estimate econometrically the shares of the two risk premiums…The reason is that FX swap transactions entail practically no other risk except a relative liquidity risk.”

“We postulate that the FX swap dealer behaves as if he tries to filter out in the transaction both the foreign and domestic counterparty risk premiums embedded in the respective money market rates. He takes into consideration only the difference between the foreign and domestic liquidity premiums in setting the interest differential that ultimately enters his forward rate calculation… Hence, this is equivalent to adding the foreign and domestic liquidity risk premiums to their respective risk-free rates:

F / S = (1 + rf + (1 – v) * (r – rf)) / (1 + qf + (1 – w) * (q – qf))

where v and w, both of which lie between 0 and 1, denote the share of the counterparty risk premium in the total risk premium in the foreign and domestic money market respectively such that (1 − v) and (1 − w) are the shares of the respective liquidity risk premium.”

“This theory, put simply, says that the difference between the spot and forward exchange rates is determined by the counterparty-risk-free interest differential between two countries or the risk-free interest differential between two countries adjusted for their relative liquidity premium.”

“Removing counterparty risk premium from the money market rate or adding liquidity risk premium to the risk-free rate is the same as taking a weighted average of the risk-free interest rate and the risk-embedded money market rate, with the weights being the shares of the counterparty and liquidity risk premiums respectively.”

Empirical evidence

“We study a…longer period starting from the beginning of 2002 to the end of 2015…[for] three European currency pairs vis-à-vis the US dollar, namely, the euro, the British pound and the Swiss franc.”

“The empirical evidence found in this study, which encompasses long periods of tranquil and turbulent periods, shows that the so-called CIP departure is not a phenomenon pertaining only to economic or financial crisis, but also one that reflects that financial markets are always vigilant about counterparty and liquidity risks involved in borrowing or lending. Due to the ways in which transactions are conducted, the money market is concerned with both counterparty risk and liquidity risk while the FX swap market only the latter. Therefore, as counterparty risk gets elevated in turbulent times, CIP deviation becomes noticeable.”

“Based on the results of the panel regression, for the tranquil period the share of counterparty risk premium for the foreign currency is estimated at 26% and that of the liquidity risk premium 67%. The share of counterparty risk premium for the US dollar is estimated at 28% and that of the liquidity risk premium at 63%. For the turbulent period, the share of counterparty risk premium for the foreign currency rises to 86% while the share of the liquidity risk premium falls to 20%. On the contrary, the share of counterparty risk premium for the US dollar falls to 25%, while the share of the liquidity risk premium rises to 87%. These sums tend to be larger for the turbulent period, which may be attributable to the limited accessibility of the Libor funding to all market players and also underreporting of Libor.”

Disagreements with conventional views

“According to the risk-adjusted version, the CIP deviation essentially reflects the difference between the counterparty risks in the foreign and domestic money markets. When counterparty risk is greater in the foreign money market than in the domestic money market, the FX swap implied domestic interest rate will be higher than the domestic money market rate…In other words, a higher FX swap-implied interest rate for a currency than the respective money market rate implies that, in the FX swap, the party borrowing the currency is the one that is perceived to have a lower counterparty risk than the other party lending the currency…This…runs counter to the story told by earlier researchers in the literature. In their story, European institutions, which are the dollar borrowers, are generally perceived to have high counterparty risk. Shut off by the cash market, they have no alternative but to resort to borrowing from US institutions in the FX swap market, paying a premium, hence resulting in an FX swap-implied dollar interest rate that is higher than the dollar money market rate… according to the theory of risk-adjusted CIP, a higher FX swap-implied dollar interest rate suggests exactly the other way round, i.e., the party that borrows dollars is the one which is perceived to have a lower counterparty risk.

“Past studies…argue that the surge…in counterparty risk during the GFC…screens certain financial institutions out of the money market, creating a dollar shortage at the benchmark interest rate…excess demand forces these market participants to resort to the FX swap market for obtaining dollar funding, causing the market to charge a premium over what is implied by the interest differential between two money markets to compensate for the additional risk…We believe that the money market is always cleared, i.e., there is no shortage of, or excess demand for, funding…Financial institutions can always choose between the money market and the FX swap market to borrow from…The decision depends on how the borrower weighs between borrowing at a higher interest rate in the money market, and a lower rate in the FX swap market but incurring an opportunity cost, that of having the same amount of fund in another currency.”