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 cockamamie 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 into the business. Apparently, low-cost access to these market is limited to the big TBTF banks, which is why hedge funds have not leapt into 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.