Monday, March 20, 2017

Covered Interest Parity

Here's how covered interest parity works. Think of two ways to invest money, risklessly, for a year. Option 1: buy a one-year CD (conceptually. If you are a bank, or large corporation you do this by a repurchase agreement). Option 2: Buy euros, buy a one-year European CD, and enter a forward contract by which you get dollars back for your euros one year from now, at a predetermined rate. Both are entirely risk free. They should therefore give exactly the same rate of return, by arbitrage. If european interest rates are higher than US interest rates, then the forward price of the euro should be lower, enough to exactly offset the apparent higher return.  If not, then banks can (say), borrow in the US, go through the european option, pay back the US loan and receive an absolutely sure profit.

Of course there are transactions costs, and the borrowing rate is different from the lending rate. But there are also lots of smart long-only investors who will chase a few tenths of a percent of completely riskless yield. So, traditionally, covered interest parity held very well.

An update, thanks to "Deviations from Covered Interest Rate Parity" by Wenxin Du, Alexander Tepper, and Adrien Verdelhan. (Wenxin presented the paper at Stanford GSB recently, hence this blog post.)

The covered interest rate parity relationship fell apart in the financial crisis. And that's understandable. To take advantage of it, you first have to ... borrow dollars. Good luck with that in fall 2008. Long-only investors had more important things on their minds than some cockamaime scheme to invest abroad and use forward markets to gain a half percent per year or so on their abundant (ha!) cash balances.

The amazing thing is, the arbitrage spread has not really closed down since the crisis. See the first graph. [graph follows]

Source: Du, Tepper, and Verhdelhan

What is going on?

 Du, Tepper and Verdelhan do a great job of understanding the markets, the institutional details, and tracking down the usual suspects. Their conclusion: it's real. Banks are constrained by capital and liquidity requirements. The trade may be risk free, but you need regulatory capital to do it.

A great indication of this institutional friction is in the next graph [graph follows]:

Figure 7: Illustration of Quarter-End Dynamics for the Term Structure of CIP Deviations: In both figures, the blue shaded area denotes the dates for which the settlement and maturity of a one-week contract spans two quarters. The grey shaded area denotes the dates for which the settlement and maturity dates of a one-month contract spans two quarters, and excludes the dates in the blue shaded area. The top figure plots one-week, one-month and three-month CIP Libor CIP deviations for the yen in red, green and orange, respectively. The bottom figure plots the difference between 3-month and 1-month Libor CIP deviation for the yen in green and between 1-month and 1-week Libor CIP deviation for the yen in red.
It turns out that European banks only need capital against quarter-end trading positions. US banks need capital against the average of the entire quarter. Thus, one week before the end of the quarter, european banks will not enter into any one-week bets. And one week before the end of the quarter (red line, top graph), the spread on one week covered interest parity zooms. One month before the end of the quarter, the spread on one month covered interest parity zooms. (This is called "window dressing" in finance, making your balance sheet look good for a one-day snapshot at the end of the quarter.) If this gives you great confidence in the technocratic competence of bank regulators, you're reading the wrong blog.

So far, so good, but reflect really: this makes no sense at all. Banks are leaving pure arbitrage opportunities on the table, for years at a time. OK, maybe the Modigliani-Miller theorem isn't exactly true, there is some agency cost, and the cost of additional equity is a little higher than it should be. But this is arbitrage! It's an infinite Sharpe ratio! You would need an infinite cost of equity not to want to eventually issue some stock, retain some earnings rather than pay out as dividends, to boost capital and do some more covered interest arbitrage.

At the seminar a pleasant discussion followed, centering on "debt overhang." If a bank issues equity and does something profitable, this can end up only benefitting bond holders. I'm still a bit dubious that this is what is going on, but it is a potential and very interesting story.

But that's still not enough. Where are the hedge funds? Where are the new banks? If an arbitrage opportunity is really sitting on the table, start a new fund or bank, 100% equity financed (no debt overhang) and get in to the business. Especially at quarter end. Really, is there nobody with spare "balance sheet capacity" to grab these quarter end window dressing opportunities? Apparently, low-cost access to these market is limited to the big TBTF banks, which is why hedge funds have not leapt in to the business? (Question mark -- is that really true? ) Still, why not start a money market fund to give greater returns by going the long end of the arbitrage? Alas there are regulatory barriers here too, as even a riskless arbitrage fund can no longer promise a riskless return.

These are the remaining questions. The episode in the end paints, to me, not so much the standard picture of limits to arbitrage. It paints a picture of an industry cartelized by regulation, keeping out new entrants.

But they are great graphs to ponder in any case -- and a good paper.

Update: A hedge fund manager writes:
Right now:
  US T-bill:  +0.98%
  Japan T-bill:  -0.34%
  Difference between spot USDJPY, and 1yr forward USDJPY:  1.91%

So if you start with dollars, you can make 0.98% if you just buy a 1yr T-bill, and 1.57% if you change your dollars to yen, buy a 1yr Japanese t-bill with the money, and enter a 12mo currency forward to change your money back into dollars at the end of it all.  So the arb, which you can lock in for 1yr which is a pretty long time, is 59 bps right now.

[JC: Notice the trade is to buy yen, not dollars. This is a point made in the paper which I didn't cover well enough. There is a big flow of money the other way, borrowing yen, buying dollars and not hedging, since statistically currency depreciation does not soak up the interest differential.]

But a hedge fund can’t lever that trade up.  Hedge funds to a first approximation can’t borrow uncollateralized. They can but unsecured lending to a hedge fund would be at least risk-free plus 200bps and so would destroy the arbitrage.   And while getting leverage on T-bills (for example) is securitized and so the cash is borrowed at a rate that allows the arbitrage, you can’t net generate cash by buying a t-bill (you can borrow the cash to pay for the t-bill and pledge the t-bill as collateral, but you aren’t left with cash you can do whatever you want with after that transaction).  So the hedge fund can’t generate more USD cash in order to turn it into yen, buy Japanese T-bills, etc.

It only works for banks because they have access to unsecured borrowing (deposits) at a rate that allows the arb.  Which hedge funds don’t have access to. [JC: my emphasis]

This pops up in other markets too btw, the ability to get an extra 50 bps or so by using USD cash, if you are willing to do a little gymnastics.  For example, you can go long the S&P 500 with either futures (a synthetic instrument; just a bet) or via an ETF (a cash instrument that requires you to pay for it).  The rolls on S&P futures are priced such that your return from rolling a long S&P 500 futures position is about 50 bps (annually) lower than your return from just buying an S&P ETF.  But the levels at which dealers which provide leverage for long-only equities positions take that 50 bps back again, so you can’t lever up the arbitrage.

My model of this fwiw is:
     -dealers have the cash to do this and had the job of keeping this in line until 2008
     -after 2008 various regulatory constraints and reg cap requirements made this not attractive for big banks unless the spread approachs 100 bps, so they are not really players any more
     -there are some players that will do this.  The biggest are reserve managers.  The second biggest are probably  hedge funds using excess cash balances (not sure how big corporates with cash balances are in this space).  But that’s not enough to make markets efficient. [JC: Sovereign wealth funds, endowments, family offices...?]
     -in general there is a huge universe of people trying to enhance yields on cash.  It seems like those folks should be able to close the gap here.  But most of them (for example money market funds) have constraints that won’t let them do these sorts of trades. [JC: I think currently even though investing FX covered forward is risk free, you would have to offer a floating value fund for that investment.]
     -I assume eventually the market will do what you think it should, and the people seeking to enhance their cash returns will find these trades and structure themselves in a way they can take advantage of them.  But it has taken a lot longer than I thought. [JC Me too. From which I learn that competition, entry, and innovation in banking is a lot less than I thought.] 

Separately, a bit more on debt overhang. At the seminar one colleague opined that we are now at just about the worst set of capital requirements. With historically low capital requirements, banks were willing to do a lot of arbitrage and intermediation. With very high capital requirements, debt overhang is no longer a problem. Our current capital requirements bind, but mean debt overhang is so severe that equity does not want to issue more equity in order to take a pure arbitrage.

My two comments on this: one, it makes a great case for much larger capital requirements! Second, if capital won't flow in to current banks to take an arbitrage opportunity, the other answer is new banks. Back to regulatory barriers to entry.

Update 2: Gordon Liao has a nice working paper, Credit Migration and Covered Interest Rate Parity. He notices that the covered interest arbitrage spread moves closely with corporate bond spreads, over longer horizons. (Not, I think, the gorgeous quarter end effect above).

Source: Gordon Liao

Du, Tepper and Verdelhan make a similar point,

Liao also points to an interesting channel. Corporations can issue debt at the corporate bond rate to invest in arbitrages. Capital will flow, in interesting ways. He also points out that hedge funds integrate the term structure of CIP, smoothing out the deviation across different maturities.

To Gordon this is about limits to arbitrage and segmentation. But once several asset classes get segmented together, they stop being so segmented. When multiple spreads are all moving together one also sees a generic risk premium start to emerge.


  1. John,

    "Think of two ways to invest money, risklessly, for a year. Option 1: buy a one-year CD. Option 2: Buy euros, buy a one-year European CD, and enter a forward contract by which you get dollars back for your euros one year from now, at a predetermined rate."

    An investor's "risk free" rate of return in your scenario is limited by deposit insurance.

    France: $100,000 Euros
    Germany: $100,000 Euros
    Italy: $100,000 Euros

    Also, certificates of deposit holders get their interest payments from loans held by a bank. And if those loans happen to be sovereign debt of ill repute (i.e. Greek), how "safe" is that investment?

    Finally, what are the tax implications of interest earned on European CDs as well as capital gains / losses realized from converting Euros back to Dollars.

    Covered interest parity should work as long as tax structures are similar between two countries - what if they are not?

    1. 1) Tax issues are irrelevant to pass through vehicles like mutual funds and hedge funds. 2) very few countries have withholding taxes on interest for foreigners. There are none, to my recollection, in Europe.

    2. Unknown,

      1. Do hedge funds rely on the carried interest loophole in the U. S. tax code? Would the uncertainty regarding the continuation of that particular tax policy preclude hedge funds from engaging in this practice? One of Trump's campaign promises was to eliminate the carried interest tax exemption.

      2. Is that loophole typical of tax policy in other countries? Does a hedge fund manager pay straight income taxes on interest from Euro CD's (rather than capital gains taxes).

      This is particularly relevant if the securities backing the CD's are dodgy. With the carried interest exemption, hedge fund managers can deduct capital losses on CD's gone bad from taxable income. They have no such recourse if they are paying straight income tax on the interest income from those CD's - losses after the maximum guaranteed by deposit insurance could not be used to reduce taxable income.

  2. Perhaps if there was less regulation, someone could enter and pick up these arbitrage profits. But how much would that improve aggregate welfare? I haven't thought it through very carefully but it seems like this trade is a zero-sum game. On the other hand, if governments could agree on a way to smooth out the noise in exchange rate movements, that would be a clear win.

  3. "Option 1: buy a one-year CD. Option 2: Buy euros, buy a one-year European CD, and enter a forward contract by which you get dollars back for your euros one year from now, at a predetermined rate. Both are entirely risk free."

    Huh? The only risk free leg is a US CD of less than $250,000. The rest of those a risky.

  4. Might it be in a country's best interest to block access if the arbitrage would damage their economy? From Canada's perspective, for example, might it be valuable to have an artificially depreciated currency relative to other developed countries in order to encourage domestic production? Just spit-balling, but the general idea is that inefficient markets might but in the interest of some countries, and those countries could therefore introduce risk or barriers to entry through regulation.

  5. alessandro molinariMarch 21, 2017 at 11:16 AM

    on margins tight to may act only central banks or the countries with negative interest rates, such as Germany and Switzerland. if germany predesse borrowed 100 billion Euros for 2 years at a -0.8% rate could earn in a year more than a billion Euros

  6. Let me make sure I understand this. Are you suggesting that a hedge fund should go to investors and say "Give me your money for a year, and I'll put it in a low-risk investment that will get you 2.3% (L+50) - and you can pay me a (relatively low) fee for managing (relatively low) credit risk and trading costs, and intervening margin calls, etc."? Or are you suggesting that a hedge fund should take capital and try to earn an equity-like return by using it to lever into a position of borrowing in USD and lending in {EUR,JPY,CHF} (or better yet borrow in AUD or NZD to lend in those currencies)? If the former, it's insufficient return for most investors. If the latter, it raises the questions of who is going to lend that hedge fund the USD (or AUD or NZD) unsecured - and at what rate - and who is going to take that hedge fund's deposits - and at what rate? In general, hedge funds cannot borrow unsecured, nor do balance-sheet constrained banks want to take hedge fund deposits over quarter-end.

    To do this trade, you either need to be a regulated bank (in which case you will only do it if the levered ROE > 10% or so that the capital market requires of banks,) or you need to have a pool of capital for low-risk, low-return non-cash investment. That describes Apple, Google, big pharma, and other offshore unrepatriated earnings - and most of those entities are either doing or considering the trade.

  7. Hi John,

    Good post and super interesting facts!
    Manuel Amador, Javier Bianchi, Luigi Bocola and I have some work showing that the zero lower bound on nominal rates together with the pursuit of exchange rate policies by Central Banks (i.e. Switzerland, Denmark) helps understand the post 2008 CIP deviations highlighted by Du, Tepper, Verdelhaan.

    Suppose Switzerland wants to keep, in the short run, the CHF relatively weak vis-à-vis the Euro (because they don't want to lose competitiveness) but in the long run they want to keep it strong (because of inflationary fears). By doing so they are basically promising an appreciation of the CHF, making CHF denominated assets attractive.

    In a world with positive interest rates that would put downward pressure on Swiss rates to restore parity. But what if interest rates are zero? Interest rate can't fall (actually they fall but just a little bit) and CIP deviations ensue.

    Who gains? International investors who holds CHF assets, and receive a positive interest (the CHF appreciation).

    Who loses? Swiss Central Bank which accumulates Euro reserves only receiving a zero nominal interest.

    Why are they doing this? It is the price they pay to pursue their exchange rate policy at the ZLB.

    For those who are interested in more details here is the link to the full paper

    and here is a graph showing that CIP deviations are more likely in country/periods with nominal interest rates close to zero and that they are associated to central banks reserve accumulation

  8. Really interesting. It seems one would have to initiate the trades simultaneously as there is risk in legging into the position.

    1. No, you buy a foreign currency instrument and you finance it by doing a FX swap. In a FX swap you simultaneously buy the currency for the settlement date of the interest bearing security and sell,the currency for a future date. You never have currency exposure for the vast bulk of your position. There is some exposure on your interest income, but it's marginal.

  9. Here's a non-regulatory explanation: Japanese/European banks and insurers borrowing dollars at short-rate (via currency forwards) and "lending long" in USD markets (long duration bonds and equities), driving the cross-currency basis negative. Central banks and the zero lower bound are setting the ceiling and floor, respectively, on short-term rates. No arbitrageur in the world can beat those forces.

    Japanese T-Bill rate falls further negative -> then there is an arb to borrow @ TIBOR and hold as cash

    US T-Bill rate rises -> borrow at overnight rate (pegged close to Fed Funds by Fed's reverse repo facility) and lend "long", i.e. roll-down steep 3-month T-bill curve

    USDJPY cross-currency basis normalizes -> Japanese insurers buy up all US corporate bond issuance

  10. Cross currency basis trader here:

    I think the us vs European regulations is a red herring here. On a technicality the binding requirement (leverage ratio) applies to average of month end dates for EBA regulated banks - not quarter ends - you see the turn in Fedfunds effective rates for this reason - yet it is much less severe in FX swap rates. Also, compliance based on average balance sheet would incentivise US banks to actually be in this arb in quarter end, because they only need to deploy sheet for 1 day in 90 to capture most of the total return, and this cost would be spread out over an average balance sheet over the quarter.
    I think its true source is the ratings agency models - which require banks to maintain a return on balance sheet level, which is of course measured only at quarter end. This is why banks step back on that date - they need a credit rating to stay in business (borrow unsecured) and the cost of that is complying with the ratings agency model profitability metrics - which look at quarter end assets.
    The necessity of maintaining a credit rating in order to gain unsecured dollars is both the barrier to non-traditional business models (Hedge funds etc) and the source of the quarter end effects. A form of regulation perhaps - but not one from government agencies.

  11. My not-so humble take on this. I hope, dear Prof. Cochrane, you don't find the tone insulting. If so, I will change the text according to whatever suggestions you have:

  12. JC, Merrill Lynch published a very nice paper about "Cross Currency Basis" which is what we professionals call this absence of efficient hedging markets. It is more complicated than the cartelization of markets and banking and onerous regulation; they are partly responsible, but not all problems are caused by deviations from pure objectivism ;)

  13. JC, akin to @Nowakowski but also wanted to make sure you and your interested readers caught this very thorough overview on excess reserves by CS's Zoltan Pozsar: It speaks to a number of your more recent articles, in particular on the shift if interest rate parity arbitrage and why banks are encumbered by regulations ( and don't seem to care unless they need a 10% ROE regardless of the risk...silly but true).


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