FX-hedged yields, misunderstood term premia and $1 tn of negative carry investments

This stand-alone post is the long form discussion of a topic briefly touched on here. It can be read on its own, however a fuller perspective is possible when read as part of a series which starts here.

FX-hedged bond investments from overseas investors have, as shown in the main post, become an integral part of inflows into U.S. debt markets since 2008, accounting for around $1 tn worth of purchases from Asian liquidity-rich countries (most notably Japan, Taiwan and Korea) and European countries, intermediated through mutual funds.

The phenomenon is not constrained to USD-denominated debt only, although it constitutes by far the largest single currency in such currency-hedged structures, with EUR a distant second.

Estimates of worldwide FX-hedged bond investments (independent of target currency) are hard to come by, but usually exceed $2 tn. The rationale for such investments is usually seen in the search for higher-yielding, but still relatively safe assets.

In relation to the size of these flows, the analytical presentation on which such transactions are based and according to which their profitability is assessed, oftentimes appears superficial. Superficial in the sense that considerations are frequently reduced to easily illustrated rule of thumb shortcuts which at best portray parts of currency-hedged investments accurately and at worst vastly overestimate their return potential.

Most such, usually graphically presented, shortcuts are based on a combination of:

  • An assumption that risk-free interest rate differentials alone are reasons enough to invest in FX-hedged “high-yielders.
  • A belief that the shape of the yield curve in the target country at trade initiation – where steep is considered positive – is predictive of return potential.
  • A notion that once these trades are put on, the prospective return (when held to maturity) is locked in.

As none of these assumptions is fully accurate (at least without a large set of constraints), this post attempts to take a comprehensive look at the mechanics and accounting involved in establishing and evaluating a currency-hedged bond portfolio.

The point of this discussion may at a swift glance not be readily apparent; a brief preview of the consequences should provide some degree of tangibility:

Analyzed in a holistic framework, the rational for existing and possible future currency-hedged bond investments is seriously questioned which

  • at the macro level potentially renders one of the largest post-crisis cross-border capital flows as much less profitable, if not outright negatively carrying. The latter option substantially increases the possibility of (at least partial) liquidation of such investments, with considerable upward pressure on bond yields until a new equilibrium is found.
  • at the micro level challenges the portfolio composition of the institutional investors allocating clients’ money. Should such investments indeed prove negatively carrying, the clients will absorb losses. These would arguably not be of significant notional scale, but are of significance in that they represent unnecessary opportunity costs which could have been avoided by a different asset allocation.

One final point to settle before commencing with the main body is the level of abstraction at which this problem should be addressed. As with many aspects of financial markets, the underlying concepts involved are quite straightforward if approached incrementally; a nonlinear narrative paired with overdoses of jargon can, however, have the opposite effect. For this reason, the largest portion of the post will be quite detailed; it will put the issue of FX hedging in a broader context and dissect the variables affecting currency-hedged investments individually. This requires some time, so in addition there is also a technical summary for the jargon-savvy reader at the beginning, concisely outlining the main points in ~200 words.


  • Why hedge and who hedges
  • Hedging instruments: three views (physical vs. FX forwards/swaps vs. cross-    currency swaps)
  • Dissecting return variables of currency-hedged bond portfolios (in a stylized setting)
    • cross-currency basis
    • term premia
    • libor/swap spread differentials
    • credit risk premia
  • the real world: the Japanese case

Technical summary:

A bond portfolio currency-hedged with short-term FX forwards/swaps is structurally similar to a repo-funded bond portfolio; the only difference is that instead of a repo rate, the funding rate is based on a Libor benchmark, which is nudged up (or down) by the respective cross-currency basis. As with any trade funded at a short-term floating rate and exposed to a fixed-rate instrument on the asset side, the key PnL driver (when held to maturity) is not the differential between the two rates at initiation, but the realized term premium at trade conclusion. Term premia are notoriously hard to forecast; most model estimates for the U.S. during the last number of years however produce negative values, implying losses on currency-hedged investments in the sovereign space. Negative cross-currency bases and disadvantageous Libor–OIS (or rather Libor – T-bill) differentials do their part to further diminish potential returns. Most players are willing to accept some degree of credit risk (usually in the corporate space down to ~A-rated issuers), which acts as a counterbalance, improving potential returns. Still, with credit markets offering limited amounts of spread pickup and issuers already quite levered at this time in the cycle, it appears hard to generate substantial – if any – alpha by this type of investment.


I.  Why hedge and Who hedges

From a very fundamental perspective, the reason a need for currency hedging arises is that whenever foreign investors acquire an asset denominated in another currency, they create an FX mismatch relative to their local “base” currency. This occurs because foreign institutions, in an initial step, exchange local currency in the spot market for the relevant target currency, before then proceeding to purchase the selected asset. Since most companies keep their books in their base currency, the profitability of an asset denominated in a different currency is then driven by both the performance of the asset itself as well as changes in foreign exchange rates.

Sometimes, the buyer may only want to take a view on the asset itself and can then attempt to hedge currency risk. If everything is structured properly, the overall return will subsequently only dependent on the purchased asset and not on FX movements.

At the risk of overgeneralizing, there are two broad reasons to hedge foreign exchange risk:

  • a view that foreign currencies will weaken relative to the local currency and
  • being forced to hedge due to institutional constraints & regulations.

The first reason is self-evident. If (1) one’s prediction about future market movements are mostly accurate and (2) point to movements detrimental to one’s PnL, one should try to avoid these losses by eliminating FX risk.

Despite the apparent simplicity of the first reason, the second one is the more common explanation for fixed income managers and may be colloquially summarized as “let’s get the asset right and don’t speculate on FX”. There are two reasons advancing this view: asset volatility and funding structure.

FX-unhedged investments’ PnL depends on the return of the asset and changes in FX spot rates, both of which can vary to an ex-ante unforeseeable degree. Still, there are assets for which the asset volatility is likely to outweigh FX volatility: highly volatile assets like investments in single volatile stocks, venture capital investments or, most extreme, low-delta out-of-the money options. For all these, the asset volatility outweighs FX volatility to such a degree that FX risk is downgraded to secondary importance and is usually not done at all. The same thinking usually also applies to “real” cross border investment, be it Greenfield FDI or M&A and until some years ago to broad financial equity (indexers or quasi-indexers) investments as well.

On the opposite side of the volatility spectrum, the calculations on fixed income securities look very different. Unless ultra-long dated bonds or issues of very low quality are purchased, FX volatility has a very fair chance to be the more important driver of overall volatility. This usually leads fixed income managers to hedge the FX part and only focus on the bond side – their actual expertise.

Even if an institutions has a good track record in forecasting FX, funding structures present another reason these will still likely hedge a large portion of their exposure. Returning to the earlier examples, highly volatile investments in which FX risk only plays a minor role, are funded predominantly by equity which provides a cushion for potential losses. Fixed income buyers, at least those relevant this cycle, are mostly funded by debt or debt-like liabilities. These are foreign banks funded by local-currency, runnable deposits as well as insurance companies with debt-like liabilities. Pension funds are more of a hybrid between debt and equity, with the nature of payouts dependent on the specific demographic profile.

What all share is a limited ability to sustain deeper, permanent capital losses regardless of their origin from losses on the asset side or from unfortunate FX changes. Their balance sheets are rather oriented towards a combination of duration and some amount of credit risk.


II.  Hedging instruments – three views

While the objective of FX hedging is clear, there exist a variety of instruments to reach this destination and with it different perspectives on how to approach the hedging process.

Physical hedging

Once upon a time, before the advent of liquid derivatives markets, investors already (undoubtedly at a much smaller scale) faced the need to neutralize FX risk. For those required to hedge, the only way to do so was to add a new physical leg to an existing positon, to counter the previously created FX imbalance in order to leave the overall structure FX neutral.

More concretely, a foreign institution starting out with a local currency deposit converts this in the FX spot market into a foreign currency bank deposit and then purchases a bond denominated in that foreign currency, thus incurring FX risk.

To counter this, the institution then borrows, in the same currency the bond is denominated in, an amount equal to what was invested on the initial leg and converts these funds into its local currency, keeping it there on deposit with a safe depository institution. By doing so, the initial leg is long foreign currency, while the second leg is short an equal amount.

Structuring difficulties aside, a look at the cash flows of these two legs

  • on the initial leg, the institution foregoes local interest rates but receives foreign interest rates on the bond;
  • on the second leg, the institution pays foreign interest rates to the bank it borrowed funds from and receives local interest rates after funds were converted to its base currency;

shows that the issue of currency hedging is much better approached from a fixed income perspective, than say the hedging done in the equity space.

With the emergence of derivatives markets, physical hedging for end-users has been replaced by the instruments discussed in the next sections. This derivatization holds for most players, with one major exception: banks themselves. Banks with global deposit franchises do preferably match their regional assets and liabilities on balance sheet without resorting to derivative structures. With the financial infrastructure already in place, this is usually more cost-efficient.

Compared to the pre-crisis heyday however, when banks expansion across the Atlantic was funded by short-dated deposits, shifts in global wholesale money markets have pushed some banks away from the physical hedging model. The progression of Basel regulations, (inter-bank) funding turning away from unsecured to secured channels and most recently money-market reform in the U.S. has driven some foreign banks, which once were physical hedgers, into derivative markets.

FX forwards I

Forward FX markets developed as a natural add-on to the spot market. Instead of exchanging currencies now, participants agree today to exchange a fixed amount at a designated FX rate on a future date. This setup makes forwards the prime vehicle for expressing outright FX views as well as for hedging short-term cash flows, which is a lot simpler than dealing in the underlying loan and deposit markets.

For hedging foreign assets, the use of FX forwards comes closest to how hedging is approached in equity markets. Neglecting for a moment the precise factors according to which forward exchange rates are set, forwards, especially of short maturities, correlate closely with spot FX rates (which is obviously unsurprising given the most important input required to calculate FX forwards are spot rates).

Seen this way, shorting foreign currencies in the forward market then neutralizes the previously incidental, but undesired long FX position. Such a view is similar to how hedging is approached in the equity space, where market or sector risks can be neutralized by shorting index futures or sector ETFs.

Cross-currency basis swaps (CCBS)

Cross-currency basis swaps are the modern incarnation of the physical hedging previously analyzed and are best approached as collateralized lending with foreign currency collateral. In repo terminology, CCBS is very similar to cross-/ multi-currency repos, the only difference is that CCBS is cash- whereas repo is security-based.

As an example, consider a floating-for-floating CCBS entered by say a Japanese investor wishing to acquire a USD-denominated bond. The institution starts out with a yen deposit, but instead of exchanging it for dollars in the spot market, it now seeks a lender willing to provide dollars by posting its yen deposits as collateral.

When a counterparty is found, the two exchange the agreed upon amount at the start of the contract, after which the Japanese investor is able to purchase the desired USD-denominated bond. The dollar lender (which if it did not lend to the Japanese institution would receive short-term U.S. interest rates on its funds) will charge the Japanese investor the same rate it forgoes. In a floating-for-floating CCBS this means USD Libor. Since the USD lender is collateralized with yen deposits (or whatever it decides to invest in after receiving the funds), the necessity to charge a spread reflecting the creditworthiness of the Japanese counterparty is greatly reduced. Since the yen deposits the USD lender receives may also earn interest during the trade, it will have to pass these on by paying JPY Libor to the Japanese institution.

At the end of the contract, the initial amounts of principal are re-exchanged (i.e. the collateral is handed back). During the contract both parties enjoyed access to a different currency while at same time they have both received the interest rate prevalent in their home country.

Whereas the “FX-forward-angle” viewed the hedging process as an additional step to neutralize previously taken FX risk, the “CCBS-view” looks at the whole process in unified way in which dollars are received through symmetric cross-currency collateralized lending.

In brief,

  • the USD providing counterparty lends USD and acquires yen deposits, receives USD Libor and pays yen Libor;
  • the Japanese institution lends yen and acquires USD, pays USD Libor and receives yen Libor.

Fx forwards II: FX swaps

Instead of approaching hedging with FX forward contracts from the equity perspective, it can also be viewed through the collateralized lending lens. To do so, spot and forward transactions are paired and conducted with a single counterparty. In such a case, the transaction is referred to as an FX swap.

As with CCBS in the previous example, the Japanese investor at initiation swaps yen for USD. However, and in contrast to CCBS, no interest payments are exchanged during the contract. Instead, the forward FX rate at which the transaction will be closed out at the end of term is adjusted to reflect interest rate differentials. This way, a lender of a higher yielding currency (for instance USD relative to JPY) will receive lower yen interest payments during the term but will be compensated by a higher, and at trade initiation predetermined, yen in the forward market.

As an example, consider U.S. 1y interest rates at 5% and the Japanese equivalent at 1%. For simplicity further set USD/JPY to 100 at the beginning of the contract. Based on Covered-Interest Rate Parity (which results in the lower yielding currency trading higher in the forward market than in spot), the one year forward FX rate is ~96 due to a four percent interest rate differential. A U.S. investor lending USD and receiving only 1% interest in Japan will enjoy a predetermined ~4% FX gain, resulting in a total return of 5%. This is equivalent to what could have been received in the U.S.

CCBS vs. FX swaps

While both are used to hedge FX risk (or, more accurately, to fund foreign currency activities by providing local currency collateral), there are differences in how they are used.

FX forwards/swaps are used at shorter tenors, mostly in the 3m region and selectively up to ~2y. Longer versions exist but liquidity is focused on the short-term space and is used by foreign investors hedging FX risk, banks’ treasury departments arbitraging cheaper funding sources, exporters & importers hedging future foreign currency receipts/payments, central banks managing their reserve portfolios and speculative investors either taking outright FX positions or arbitraging across the basis curve.

The product is relatively balance sheet friendly for dealers in that transactions on a matched-book basis do not inflate dealer balance sheets.

CCBS in contrast is used for longer term transactions (2y+), which is attributable to its original use as a liability-driven instrument, primarily employed by corporations and banks to hedge foreign currency bond issuance.

Both instruments are traded over-the-counter, enabling a certain flexibility in terms of contract design. FX swaps and CCBS are fully collateralized at the exchange rate prevailing at trade initiation. Changes in spot rates can however lead to over-/under-collateralization, which in the interbank-market is solved by trading resettable mark-to-market swaps to avoid the buildup of unsecured claims. End users, particularly corporates hedging long-term foreign currency bond issuance, are often hesitant to agree to a process of frequent collateral exchange so that, for an extra cost, versions without variation margin are traded. These dominate the Dealer-to-Customer market.


III.  Dissecting return variables of currency-hedged bond portfolios

This is the core of the essay and instead of immediately importing the prevailing market pricing (a task that will be postponed to the fourth section), it will consist of a set of progressive examples which isolate the single PnL drivers an institution acquiring FX-hedged bonds encounters. This is done in a somewhat idealized environment so as to (hopefully) maximize intuitive understanding while simplifying calculations.

As has been done in the prior case, the examples will be based on a hypothetical Japanese institution with a yen-funded balance sheet which now seeks to diversify its portfolio by purchasing currency-hedged USD-denominated bonds. The swap counterparty (SC) to any of the hedging transaction entered by the Japanese institution is a hypothetical FX (swap) desk at any of the major dealer banks.

Before proceeding, it is again worth considering for a minute the major differences between CCBS and FX swaps. Both can be used to fund activities in other currencies on an FX-hedged basis. Consequently, the following examples could be presented either as CCBS, FX swaps or both, side by side. The last option offers some redundancy, the FX swap representation is somewhat unaesthetic due to a constant back and forth between FX forward points and bond yield levels, which leaves CCBS as the most suitable form of representation.

This preference for a CCBS representation may appear strange, as (1) most foreign institutions hedge through FX forwards/ swaps and (2) they do so at short tenors, a space where CCBS is usually not traded. Such considerations are true, what is equally true though is that by shortening tenors, CCBS and FX swaps become “more similar” (thus de-emphasizing the lack of actual CCBS transactions at short tenors; it is only the “yield-based” representation which is of interest). This is the case because FX swaps are more of a term instrument which is priced of the swap curve in both countries, whereas CCBS is a floating rate product based on Libor rates. Once maturities converge to the reference tenor of CCBS at 3m, the products are functionally equivalent.

0 – Initial situation

For a conservative Japanese fixed-income investor, which is assumed to be benchmarked to short-term JGB bills, the opportunity set within Japan is small.

On offer are:

  • JGB bills, which always provide the benchmark’s yield, but also earn a negative return;
  • bank deposits, earning a bit higher yield but still in negative territory;
  • longer-term JGBs which, while still slightly positive at longer tenors, have compressed significantly due to (1) the BoJ’s Quantitative Easing program and (2) yield curve control operations. Further, this choice may expose the investor to potentially rather asymmetric duration risk;
  • local corporate bonds, of which the amount outstanding is small and spreads are low as (1) the size of the corporate universe is small, with bank loans constituting the preferred financing vehicle (2) corporate fundamentals have improved over the last decades leaving many corporations with excess cash (3) limited financing needs due to excess cash and a limited growth trajectory in Japan, which impedes a supply response to low spreads.

Given this limited and unappealing opportunity set, many institutions look outward.

I – CCBS, 3m, bank deposit

Reversing the actual asset allocation process, let’s first consider how the Japanese investor can access USD funding without incurring FX risk and then later incorporate how decisions on the asset side affect PnL calculations.

As outlined, the institution will enter into a floating-for-floating CCBS, in this first example with a maturity of three months.

At the start of the contract the Japanese institution exchanges (assume USD/JPY at 1 for simplicity) ¥100 deposits for $100 deposits with a Swap Counterparty (SC). After three months the trade is unwound; the initial principal exchange is reversed (the investor hands back $100 and receives ¥100 from the SC) and interest payments for the three months are made. The interest payment flows are presented in Figure 1.

I - CCBS, 3m, bank deposit.png
Figure 1

Short-term interest rates, for now deliberately vaguely defined, at a 3m tenor are hypothetical and assumed to be 6% in the U.S. and 0.4% in Japan. After three months, along with the return of principal, the Japanese institution will have to pay interest for one quarter which amounts to 150 bps (i.e. $1.5) to the SC and in return will receive 10 bps (or ¥0.1) interest on its yen funds.

From where does the investor obtain the necessary funds to pay the short-term USD interest rate to the SC? During the three months of the trade, the investor did not (in this first example) buy another asset with the USD funds received through the CCBS but left these in a deposit account with a U.S. bank where they earn the same short-term USD rate the investor is obligated to pay to the SC.

Said differently, there is a principal exchange at the beginning and the exact same amount is then reexchanged at the end of the trade. During the trade, the investor receives a U.S. short-term rate and at the same time will have to pay the same interest rate to its SC. From the SC, the investor will receive interest based on a short-term yen rate. As the USD interest payments cancel out, the institution will be left receiving the short-term yen interest rate.

This shows two things:

  • The whole trade (so far) is PnL neutral for the Japanese investor. The investor receives the same return that could have been achieved by staying in yen deposits.
  • The trade is unaffected by the general level of interest rates in the U.S. as the investor has both a long and a short exposure to USD short-term rates, resulting in an overall neutral stance.

Lastly, maintaining the same 3m interest rates as described, it is simple to show the equivalence of the same trade done through an FX swap.

Set USD/JPY to 1 at initiation. 3m interest rate differential put the 3m forward at [(1+0.004/4) / (1+0.06/4)] = ~0.9862.

At initiation the institution exchanges ¥100 for $100 and enters into a 3m forward contract with a notional of ¥100 at 0.9862. In the U.S. it will receive $1.5 in interest, ending with a balance of $101.5 before closing the forward contract. Exchanging $101.5 at the forward rate [101.5 * 0.9862] into JPY leaves the investor with ¥100.1, a return of 0.1% and equivalent to the yen interest rate to be received per quarter.

II – CCBS, 1y, bank deposit

Let’s now extend the maturity to a one year time frame. Nothing changes with regard to the principal exchanges at the start and end of the contract but instead of one interest exchange cycle there will be four. Importantly, since these are based on floating short-term rates the exact path is unknown. The first interest payment (the one covered in I – CCBS, 3m, bank deposit) can be inferred from markets, the latter three are dependent on the level of future interest rates. This is the case for both USD and JPY rates.

To illustrate payment flows let’s assume a future rate path. In the U.S., let’s assume during the first two quarters the short-term interest rate is 6% and during the following two it is 8%. In Japan, things will be kept simple as the main focus of the examples will lie on the USD window, so let’s assume rates will stay at 40 bps throughout.

This assumed path leads the investor to pay its swap counterparty 150 bps at the end of the first and second quarter and 200 bps at the end of the third and fourth quarter. On the flipside, the rate on its bank deposit will equally move up after two quarters ensuring that interest earned on deposits still exactly matches payments to the SC. In Japan, the investor will earn [4 * 10] bps for a total of 40 bps.

II - CCBS, 1y, bank deposit.png
Figure 2

The investment is still PnL neutral as there is no difference in executing the above or leaving funds on deposit in Japan. Importantly, although the path of future short-term interest rates is uncertain, the investor is both long (in form of a floating-rate deposit) and short (in form of a floating-rate payment to SC) USD interest rates and thus holds a hedged position which remains unaffected by changes in interest rates.

Searching for the closest equivalent to a 1y CCBS transaction in the FX swap market may be a bit counterintuitive. It is not a hedge done through a 1y forwards, but four successive 3m hedges. This is the case because 1y forwards are priced of 1y interest rate differentials which, given imperfect foresight by market participants, can differ from realized short-term rates. Consecutive 3m hedges on the other hand adapt to interest rate changes every rollover, which at a 3m tenor equals that of a CCBS.

III – CCBS, 1y, bank deposits, non-zero basis

What the above examples so far implicitly assumed is a zero cross-currency basis, which is another way of saying that both institutions, the investor and the SC, accept to enter the trade earning no extra return over the respective short-term interest rates of their base currencies.

Sometimes however, due order imbalances, the basis can diverge from zero. Over the last years such imbalances have developed in many crosses as foreign investors have shown an appetite for FX-hedged U.S. debt which far exceeds that of U.S. institutions for hedged foreign paper. In such cases, SCs act not only as neutral matching engines between end investors, but will become lenders of USD to provide clients the requested funds. Due to post-crisis regulations, balance sheet costs for global dealer banks have increased, leading banks to approach arbitrage opportunities more cautiously as the regulatory costs such trades entail have to be factored in. This results in SCs not immediately arbitraging small non-zero bases, but requiring more incentives to nonetheless facilitate one-sided demand.

Returning to the micro view, let’s say the Japanese investor still wants to enter into a II – CCBS, 1y, bank deposit type trade. However due to overwhelming demand for such trades, the SC will not take the other side of such a transaction at a zero cross-currency basis. In order to make the trade work, the Japanese investor will have to offer the SC a monetary incentive to again facilitate the trade.

This incentive is organized as a payment along with interest rate payments and can be structured in two conceivable ways:

  • Either the Japanese investor will pay a spread in addition to the U.S. short-term interest rate or
  • the SC will have to pay a negative spread to the investor relative to the interest rate it earns in Japan (i.e. it can keep parts of the interest received in Japan)

The second case, paying USD interest flat and receiving less interest on the non-USD leg is the common quoting convention used in markets today. Consequently, a negative basis means the non-USD investor has to provide incentives to the SC to enter the trade.

For the continuation of the above examples however, the first option is much more expedient because all calculations can be handled in the USD window on the left, leaving the JPY window untouched. This switch away from the quoting convention will not materially affect the trade’s PnL in all but the most volatile markets1.

Adding an annual negative cross-currency basis of 50 bps to the example examined in the previous section results in a quarterly 12.5 bps additional payment to the SC.

III - CCBS, 1y, bank deposit, non-zero basis.png
Figure 3

The trade, while still interest rate neutral, has been turned into a negatively carrying trade due to the additional interest payment. The investor now, instead of earning short-term yen interest rates, earns short-term yen interest rates -50 bps. Since the interest income in USD is insufficient to pay the SC, the investor will have to convert additional JPY into USD to effect the negative cross-currency basis payment.

Said differently, in the yen window the institution still earns JPY short rates, the same rate it would receive on regular bank deposits in Japan. In the left window, the blue bars representing short-term USD rates still cancel out but the negative cross-currency basis puts the USD window return at -50 bps.

In total, the investor now earns JPY short-term rates -50 bps, exactly 50 bps less than not entering the trade and staying in bank deposits in Japan.

IV – CCBS, 5y, bank deposit

This is an intermediate step which adds nothing new but lengthens the tenor to five years and slightly adjusts the presentation.

Instead of four interest exchanges as in Figure 2, in a 5y CCBS there are 20. Rather than showing each payment as before, all payments are now squashed into one bar whose height represents the average expected interest rate during the 5y term. In the below representation this means during the next 5 years short-term USD rates are expected to average 6%.

A floating-rate tag is added as a reminder that the rate changes in line with short-term rates and can accordingly take on values very different from the currently prevailing rate and also the expected average value.

Since the investor retains both a long and a short exposure to USD short-term rates, the direction of future short rates does not influence the PnL in this example. With the introduction of duration risk in the next section, this changes and the new sizing of the bars will simplify the illustration in these cases.

IV - CCBS, 5y, bank deposit.png
Figure 4

Yen short rates are also floating rate but, as previously mentioned, are assumed to stay at 40 bps throughout. Assuming they would vary, this would not affect the decision of whether to enter into a CCBS and venture abroad or stay in bank deposits in Japan as both ultimately earn yen short-rates in the yen window. In the CCBS case, the investor additionally earns a positive or negative level of alpha depending on the excess returns generated in the USD window, which is however independent and unaffected by the path of short-term yen rates.

As this step only lengthened tenors and adjusted the presentation, the trade remains PnL neutral and carries no interest rate risk. The investor is still long a floating rate deposit and is mandated to pay the same rate of interest to the SC.

V – CCBS, 5y, Treasury bond

With this step, the gap between the hypothetical world presented so far and the real world is considerably reduced.

Instead of staying in bank deposits throughout the CCBS contract (as was done in all prior cases), the investor now, immediately after receiving USD, acquires a 5y U.S. Treasury bond.

A 5y Treasury is a fixed-rate bond with a static coupon throughout its life. Consequently the investor for the first time takes on duration risk.

This is the case as the investor is now exposed to a fixed-rate product (carrying duration risk) on the asset side while the payments to the SC remain based on short-term floating rates.

Duration exposure introduces two ways to approach the investment’s PnL.

  • An end of trade perspective, where the PnL is assessed only after the bond matures and the CCBS is closed after five years.
  • A continuous mark-to-market (MTM) approach, beginning from the moment the bond is acquired, which takes into account the PnL of the bond investment resulting from changes in the yield curve. Extrapolated a bit, this approach further assumes the sale of the bond ahead of maturity and the closeout of the CCBS ahead of the 5y mark.

Both approaches serve a purpose, however for different audiences.

The first approach is more geared to the hold-to-maturity investor who, before purchasing an asset, will consider all required variables and if their composition is deemed appealing will enter the trade with the intention to hold the investment to maturity. An investor of this type allocates funds based on the absolute level of the involved variables (yield levels in this case) whenever they are deemed attractive.

The MTM approach is a view taken by traders striving to profit from shorter-term market movements. Whether a trade when held-to-maturity is attractive is only of secondary importance; only the short-term changes in market pricing are of immediate concern. This type of view requires constant market access as trades are always closed out prior to the maturity of the underlying instrument. Compared to investors, traders are not attracted by absolute yield levels but by prospective changes in yield levels.

The question is which of the two approaches better describes the perspective of the hypothetical Japanese institution serving as an example in this post. As this institution serves only as representation of the demand in the real world (in this case mostly depository institutions and insurance companies), views of these actors have to be examined. Such institutions, with AuMs in the tens to hundreds of billion U.S. dollars, are “investors” in the most literal sense. The size of their balance sheets disincentives large portfolio reconfigurations at a quick pace, as the potential market impact costs of their actions usually exceeds expected PnL gains. These institutions are (yield-) level players which consider the return of investments on a hold-to-maturity basis. Of course, attention is still paid to current market pricing which may lead to early closeouts of positions deemed no longer PnL accretive; the view taken is however still one based on the absolute attractiveness of an investment and not prospective near term changes in market pricing.

In consequence, a hold-to-maturity perspective will be adopted throughout the remainder of this post. This decision is beneficial in several ways:

  • It requires an assessment only at the start and the close of the trade rather than at any possible moment in between.
  • It avoids situations in which, assuming perfect foresight, a profitable hold-to-maturity investment can turn into a loss on an interim PnL basis. Equally, again assuming perfect foresight, loss making hold-to-maturity investment can be profitable on a MTM basis during the trade.

Back to concrete examples, it is quite easy to illustrate the duration exposure assumed by the investor by simulating various future short-term interest rates trajectories.

For instance, assume the institution purchases a newly issued 5y Treasury bond offering an 8% yield. Over the life of the bond the investor will earn 5 * 8%, so approximately 40%2. Through the CCBS, the investor is still required to pay short-term USD rates to the SC.

As a most simple example, again assuming perfect foresight, let’s say short-rates stay at 2% throughout the five year term (alternatively presented as a list in which each entry presents the average short-term rate during a year, here [2,2,2,2,2]). In this case the investor will have to pay the SC 5 * 2% = 10% during the 5y period. The excess returns in the USD window is calculated by subtracting these 10% from the 40% received as interest on the fixed-rate Treasury bond for a cumulative alpha of ~30% or ~6% per year.

Graphically, this situation will be presented by an 800 bps bar representing the income received on the fixed-rate 5y Treasury bond. The payments to the SC are again squashed into one bar representing the average short-term rate, which in this example coincides with the starting short rate of 2%. Further, the 8% yield on the bond can now be separated into a portion representing the average short rate of 2% during the trade and an annual excess return part of 6%. This excess return of a fixed-rate risk free asset over risk-free average short rates is also referred to as term premium.

V (1) - CCBS, 5y, Treasury bond.png
Figure 5

The term premium is directly tied to the future path of short-term USD interest rates during the term of the investment. Let’s for example maintain the yield on the bond but alter the path of short rates to represent a scenario more characteristic of the last number of years, in which future short rates are expected to be higher than at the moment. More concretely, let’s assume a short-term interest rate path of [2,4,5,5,9]. Now the investor still earns ~40% on the bond but is required to pay the SC a total of 25%, reducing the excess return to 15%, or seen from an annual term premium perspective, 3%.

V (2) - CCBS, 5y, Treasury bond.png
Figure 6

What this second example shows is twofold:

  • Higher short-term USD interest rates during the trade will directly affect the trade’s PnL. This is unsurprising; it is just what duration risk is.
  • The starting short-term interest rate is of no help in assessing the profitability of a potential investment, only the average short rate (or in an ex-ante sense, accurate predictions thereof) over the whole term is. Said differently, the shape of the yield curve (also referred to as “steepness” or “flatness” of the curve) at trade initiation is not in any way directly predictive of future excess returns.

To stress these points let’s push the future short rate path to a more extreme level of [2,7,8,12,16]. The investor now has to pay the SC an average short rate of 9% for a total of 45%. This is less than the 40% received on the bond resulting in a negative excess return of 5%, or a negative annual term premium of 1%.

Graphically presenting negative term premia is trickier. The 8% yield received is insufficient to cover the average payment to the SC. So on top of the 800 bps received, an additional grey bar is added to represent the payment to the SC not covered by the interest received on the Treasury bond. As a counterbalance, an equally sized box in the negative area is added, reflecting the funding need for the extra payment (i.e. the negative term premium).

V (3) - CCBS, 5y, Treasury bond.png
Figure 7

A different way of showing the irrelevance of the yield curve at trade initiation is to consider a setting reminiscent of 2006 or early 2007 in which a downward sloping yield curve still offers a positive (ex-post) term premium to the investor. Set the bond yield again to 8% and set the future short rate path to [10,8,6,6,5]. In this case, the average short rate is 7% implying a 1% term premium in spite of an inverted yield curve at trade initiation.

Two more observations in this section, first on possible early closeouts of trades and then on ex-ante and ex-post term premia.

The examples so far have been conducted on a hold-to-maturity basis. Alternatively, the institution may exit a trade ahead of maturity, which in some cases (from a superficial view) may increase returns. For instance consider the third example in this section with the 5y bond at 8% and a future short rate path of [2,7,8,12,16] yielding an annual negative excess return of -1%. Apparently this trade, at a cash level at least, is PnL accretive during the first two years earning 6% and 1% in excess cash returns respectively. A closeout after two years seems sensible. This however misses the MTM dimension of the investment which in the previous examples, due to their hold-to-maturity nature, could be neglected. After two years, the level of yields and expected future yields will have risen substantially, resulting in MTM losses on the bond investment which more than offset the gains from interest rate differentials during the first two years.

Very very crudely, after two years the initial 5y bond is then a 3y bond with 8% coupon resulting in a duration of slightly below 3. The yield with which to discount these cash flows depends on the future short rates and term premia. Future short rates are then [8,12,16] for an average of 12% and the term premia curve is assumed to be flat resulting again in a negative term premium of -1%. Put together this yields a 3y yield of 11%. An estimate of the price of the initial 5y bond after two years can then be calculated by multiplying the “current_yield – coupon” difference times the duration. This yields (11% – 8%) * 3 = 9%, which represents the cumulative discount factor, or presented on a par basis, a current price of ~91. Overall, this 9% MTM market loss of principal more than compensates for the cash surplus generated during the first two years.

Finally, examples in this section were mostly based on perfect foresight of future short-term interest rates. This benefit is obviously not available to market participants in the real world. So while ex-post versions of term premia can be calculated as above, ex-ante versions are driven by each participant’s interest rate outlook and are by definition not homogenous, allowing for a spectrum of different views.

What is important to retain nonetheless is that

  • The PnL of fixed-rate instruments funded at a floating-rate are primarily determined by term premia, which in turn depend on the future path of short-term interest rates.
  • Given sufficient rate increases, practically all such packages of fixed-rate instruments funded at floating-rates can be turned into unprofitable investments.
  • Even though term premia are hard to forecast on an ex-ante basis, econometric models along with judgments about what potential term premia estimates imply for the future levels of short-term interest rates, can assist in reaching decisions defined by a fairly coherent process.

VI – CCBS, 3m, T-bill

The previous discussion on how to account for duration exposure in CCBS-funded trades is arguably the most important section of this post, as the considerations around term premium are oftentimes discussed unintelligibly or not taken into account at all.

Of somewhat lower importance (and also less controversial), the next two sections add a few more details

  • first on the until now vaguely defined short-term interest rates involved and
  • secondly on credit risk,

to fully close the gap between the hypothetical world this section started with and the real world.

In order to consider the effect short-term interest rates can have on CCBS-funded trades, it is useful to revisit the very first example I – CCBS, 3m, bank deposit, which considers only one interest exchange. Back then, the only specification given was that in the USD window short-term USD interest rates are received and paid while in the JPY window short-term JPY interest rates are received. In a standard CCBS, these interest rates are 3m USD and 3m JPY Libor respectively.

Of course, this designation alone has so no PnL effects. What does however is when institutions are purchasing assets which are evaluated not against Libor rates but other, usually government benchmark, curves. In these instances, differences in the spread between Libor and government curves can have quite notable PnL effects on CCBS-funded investments.

Building on I – CCBS, 3m, bank deposit, let’s relax the assumption that the institution lends funds on an unsecured basis to banks. In order to avoid unnecessary counterparty risks such lending would entail, most institutions either seek to lend on a secured basis or even more preferred, purchase risk-free instruments. In both the U.S. and Japan, these would be 3m T-bills.

For the Japanese institution this means that either it will stay within Japan and buy a 3m JGB bill or it will enter into a 3m CCBS, receive USD, purchase a 3m U.S. Treasury bill before closing the trade after three months when the T-bill matures.

As long as Libor—T-bill spreads in Japan and the U.S. are the same, the trade’s PnL is unaffected.

For instance assume the details as given in I – CCBS, 3m, bank deposit (3m USD Libor at 6% and 0.4% in Japan). Further assume a 30 bps spread between Libor and government bills in both countries. This puts U.S. 3m T-bills at 5.7% and 3m JGB bills at 0.1%. In such a setting, during the 3m duration of the investment, the institution will receive [5.7% / 4] = 142.5 bps interest on the T-bill but will have to pay 150 bps to the SC. The 7.5 bps shortfall is, similar to the negative term premium case, reflected by two boxes added on top (reflecting the extra funds required to pay the SC) and bottom (reflecting the corresponding funding need) of the dark blue bar. Observed in isolation, the USD window now contributes a negative 7.5 bps to the institution’s PnL.

VI (1) - CCBS, 3m, T-bill
Figure 8

In the yen window, the investor receives a 3m JPY Libor payment of 10 bps which can be decomposed into a JGB bill contribution of 2.5 bps and a Libor spread of 7.5 bps. Since the investor is benchmarked to the return of government securities, the 7.5 bps are excess returns in the yen window. Combined with the loss of equal size in the USD window, this shows that the trade is PnL neutral. Either the investor stays in Japan and earns 2.5 bps on JGB bills or it enters the CCBS trade ultimately earning the same return.

Graphically, this equivalence is easily noticeable by the purple boxes of equivalent size in the USD and yen window. In this simple example, they represent the only PnL driver in each window.

In cases where Libor spreads across countries are of non-uniform size, PnL effects arise. While these can be positive or negative, the emphasis will be on the latter as this reflects the real world situation encountered by most foreign institutions.

The PnL negative effect is simple to illustrate by increasing the 3m USD Libor rate in the previous example from 6% to 7% for a Libor – T-bill spread of 130 bps. The PnL of the USD window in this case is -32.5 bps as reflected by the much larger purple box. The gains in the yen window remain 7.5 bps for an overall negative PnL of 25 bps.

VI (2) - CCBS, 3m, T-bill
Figure 9

As a final point, it is worth noting that such PnL effects are independent of the length of the trade or the asset bought, as long as the asset is evaluated against a government benchmark. For instance, extending the above trade to a 5y term and substituting the T-bill with a 5y Treasury bond with a zero term premium, is still a loss-making investment. The bond, at a zero term premium, will over its life yield the same amount of interest as a series of T-bills, which is less than the required Libor payments to the SC and will not be compensated by the small gain in the yen window.

VII – CCBS, 5y, corporate bond

The final step in this decomposition is to step from the risk-free world into the non-government market where corporate issuers have to offer an excess spread to investors as compensation for contingent default and liquidity risk. This discussion should be rather straightforward since the PnL considerations involving credit risk are the same for foreign and domestic U.S. investors alike.

Viewed through the hold-to-maturity lens, non-government bonds offering a positive credit spread, held to maturity without a default, will directly benefit the investor’s PnL. The size of such gains depends on the size of the credit spread when the bond was initially bought. In the event of defaults, the relative size of defaults in the portfolio and recovery rates along with the starting credit spread determine the overall PnL contribution.

For instance, building up on V (2) – CCBS, 5y, Treasury, (5y Treasury at 8%, [2,4,5,5,9]), let’s assume the institution purchases a 5y corporate bond offering a 100 bps spread above the government curve. Assuming no default occurs, this excess spread (also referred to as credit risk premium) can be added to the 300 bps gains due to a positive term premium for an overall Pnl of +400 bps per annum.

VII (1) - CCBS, 5y, corporate bond.png
Figure 10

A bond default on the other hand could seriously affect the USD window’s PnL. A binary view focused on a single bond (which either defaults or does not) is however not a good illustration of how larger institutions approach credit risk. A better idea is attained by zooming out to the portfolio level.

In order to contain negative effects of the binary default situation, institutions tend to

  • hold diversified portfolios with bonds from many issuers and
  • require certain rating qualifiers to be fulfilled before a bond can be acquired.

Putting these two approaches together, along with historical default scenarios provided by rating agencies, allows for an improved understanding of how much of the excess spread received may be lost due to negative credit events under various conditions.

In fact, institutions have two broad options in how they approach the management of their bond holdings, which are briefly described.

Viewed through the by now accustomed perspective of the Japanese institution, an initial decision is made to purchase a broad array of 5y USD-denominated corporate bonds. The investor is relatively risk averse and largely debt-funded, implying a moderate propensity to assume credit risk. This is reflected in a rating constraint which, let’s say, allows only purchases of bonds with a single-A credit rating.

Given these specifications, the investor then rushes out to acquire bonds which fulfill the requirements.

From there, the institution has two options as to how it can proceed during the 5y term.

The first option is a “buy-and-hold” strategy, which in any event maintains the original portfolio composition. Although all bonds are A-rated at the time of purchase, with the passage of time, ratings drift will change the makeup of the portfolio. Most bonds will retain an A-rating, some will be downgraded to BBB or BB or even lower and some (usually a smaller portion) will be upgraded. All these transitions will be tolerated by an investor subscribing to the buy-and-hold mentality. The justification for such a view may look as follows: Despite ratings drift, the sufficiently high initial rating will in almost all cases ensure a highly (if somewhat lower) rated portfolio during the investment period, which still largely fulfills the rating qualifications as set out. Further, rating migrations may have mark-to-market effects on the portfolio, but as long as bonds do not default, such fluctuations do not affect the ultimate PnL. The only losses an investor following this line of thought faces are defaults by the initial bonds. Calculations of a base case require cumulative average default rates and average recovery rates, both of which are available from ratings agencies for the last half-century.

The second option is a “static-rating portfolio”. In this case, the investor again starts with a portfolio composed of A-rated bonds. From time to time, the investor then reviews the portfolio (here at an annual periodicity to allow for simple calculations from ratings agencies’ transition matrices) and corrects for ratings drift by selling any bond with a rating other than A. Assuming an unchanged level of corporate spreads overall and flat credit curves, the investor will realize a capital gain on bonds which have been upgraded and losses on downgraded issues. Further to be taken into account are default losses, which compared to the first strategy are small and result from A-rated bonds directly jumping to default within 1 year.

Quantified, the baseline scenarios for these approaches look as follows:

annual credit costs by rating letter
Figure 11

Under the buy-and-hold approach, annual average credit costs during the 5y investment are 9.7 bps, which are the result of a 5y cumulative default rate of 0.73% for the A-rated cohort paired with an average volume-weighted recovery rate of 33%.

The static-ratings approach is more costly at 20.1 bps of which 14 bps is attributable to net rating migration losses and 6 bps to “jump-to-default” losses.

Statistics for AA & BBB rated initial pools (which loosely represent the outer bounds of foreign demand) are also provided and confirm the single-A-rated case. The static-ratings approach is in the baseline case about twice as costly as the buy-and-hold strategy. The direction of this difference is hardly surprising as the static-ratings approach continually strives to maintain the high initial credit quality of the portfolio. Ratings drift in the buy-and-hold scenario in contrast is not countered.

What these baseline scenarios allow is simple evaluations of credit markets under normal conditions. For instance, in a situation in which A-rated bonds are offered with a spread of 70 bps, an investor following a static-ratings approach can expect excess profits of around 50 bps on average. Such a situation can be graphically presented by adding two boxes: one on top representing the additional spread received and one on the bottom representing the average expected credit losses.

VII (2) - CCBS, 5y, corporate bond
Figure 12

Importantly, it is also possible to scale these credit loss rates according to a discretionary outlook which deviates from the historical averages. In this respect, it seems sensible to briefly focus on the shape of credit losses around the baseline scenario.

Both of the distributions roughly follow a power law, where most of the times credit losses are barely noticeable. Then, during a default cycle, losses spike to levels several times that indicated by the baseline scenario. The height of such spikes, judged from the worst 5y cohorts (starting in 1985, 1998 and 2006 respectively), seem to be up to about 3x the baseline level. The two strategies react differently to default cycles. The buy-and-hold strategy suffers the full effect of increased levels of defaults whereas the static-ratings approach is less affected since even in recessions, straight jumps to defaults are rather rare. It instead suffers manageable losses due to increased downgrade ratings migration and wider spread differentials between ratings. Taken together, these are however smaller than what the buy-and-hold investor faces in a default cycle. In brief, the buy-and-hold approach is on average less costly, comes however with potentially longer tails (i.e. higher losses) in a default cycle.

Lastly, and hopefully apparent by now, the considerations above are based on hold-to-maturity scenarios. In cases in which bonds are sold ahead of maturity, the PnL depends, aside from default rates, on the difference between current and initial purchase spreads. This is relevant insofar as foreigners’ activity has historically been procyclical: purchases during the middle and latter part of the credit cycle when spreads are low and unwinds during recessions and early recovery at much wider spreads. In such instances, supposedly (i.e. when held to maturity) PnL accretive investments can be turned into losses when bonds are liquidated at lower mark-to-market levels ahead of maturity.

Summary: I-VII 

This third section was entirely dedicated to the study of PnL drivers affecting currency-hedged bond portfolios. For the sake of clarity, each driver was mapped out individually. All factors are now integrated in a concluding example, in which the Japanese institution acquires a currency-hedged portfolio of 5y single-A-rated USD-denominated corporate bonds.

The variables assumed are presented below. These are still hypothetical, but not too distant from reality (unlike some of the previous examples which clearly were).

Summary All-in-one scenario

Visually this looks as follows:

Summary (1)- CCBS, 5y, corporate bond
Figure 13

The investor earns 390 bps p.a. in the USD window, of which 300 bps is attributable to the 5y Treasury yield and 90 bps to single-A credit spreads. Annual credit costs amount to -10 bps, which is the baseline scenario for A-rated issues under the buy-and-hold approach. The Treasury yield can be broken down into the average T-bill rates during the 5y term (270 bps in this case) and a 30 bps term premium. To the SC, the investor has to pay Libor plus the cross-currency basis of -40 bps. Averaged for the 5y term, this payment amounts to 335 bps annually (average 3m T-bill + Libor spread + cross-currency basis).

In Japan, the institution receives 25 bps in 3m JPY Libor payments from the SC per year, which can be decomposed into 10 bps from 3m JGB bill rates and a Libor spread of 15 bps. As in previous examples, the JGB bill rate is the investor’s benchmark and is assumed to be constant for reasons of simplicity.

The final PnL can be calculated in two different ways.

The first method – summing up PnLs by currency and then adding these values – has been used in previous cases already and is simple to do. On average, the investor realizes an excess return of [380 – 335] = 45 bps in the USD window per year. In Japan, the return above the benchmark rate is 15 bps. Combined, this results in an overall PnL of 60 bps per year.

Alternatively, the individual drivers can be rearranged in order to create a reduced form solution. This process is shown in the artistic masterpiece below.

Summary (2)- CCBS, 5y, corporate bond
Figure 14

Each factor contributing to the final PnL is pulled into a new window at the right side and stacked in a single row.

Also important is which boxes from the initial windows play no role in the final PnL. In the USD window these are the dark and light blue boxes representing the average 3m T-bill rates and in the JPY window the orange box representing 3m JGB bill rates. All of these represent the general level of interest rates throughout the investment’s life. What this shows is that the excess return of the investment is independent of differences in overall yield levels. In the USD window, the blue boxes cancel each other out and only the term premium enters the final PnL. Risk-free short rates in Japan are the investor’s benchmark and only deviations from it enter the excess return calculation.

The single bar in the new window can then be netted to return the expected 60 bps excess return.

The six boxes can be further reduced (by netting boxes of the same color) to four return drivers:

  • term premium
  • Libor – T-bill spread differential
  • credit risk premium
  • cross-currency basis

This reduced form solution enables PnL calculations directly from the input values, without having to resort to diagram representations.

Summary All-in-one scenario - reduced form PnL calculation

The reduced form is evidently the fastest and cleanest presentation and is therefore used to evaluate real market scenarios in the next section.


IV.  the real world: the Japanese case

After the lengthy preparatory work, it is now possible to plug in real data into the established framework and assess the profitability of investments. As done throughout the post, the examples will focus on a Japanese institution purchasing various kinds of USD-denominated securities.

The below data table (as of September 2017) provides the input values required for the calculations. The upper portion of the matrix contains among other things government-, swap-, cross-currency basis- and term premia curves, which form the foundation of any overseas bond investment on a currency-hedged basis. Various types of USD credit instruments are presented in the lower part, with values indicating the excess spread offered above maturity-matched risk-free interest rates.

japan usd dashboard
Figure 15

As a first set of examples, consider the Japanese institution acquiring a 5y Treasury bond which is held to maturity. Maturity-wise, the mid-point of the curve represents the area where demand from shorter-term focused institutions (banks and depository firms) and maturity-matchers (life insurance companies) overlaps and consequently well approximates the actual tenor composition of securities held by Japanese institutions.

5y Treasury bond live

Case (1):

In this first example, the institutions enters a 5y CCBS and acquires a 5y UST.

The term premium estimate, which for the moment is assumed to be “correct”, is taken from the ACM model provided by the NY Federal Reserve.

The cross-currency basis at the 5y tenor is -58 bps.

The Libor–T-bill spread differential at initiation is -13 bps. This spread accounts only for the first three months of the 5y horizon and could move to different levels during the remaining 4.75y period. Simple extrapolations from FRA-OIS markets indicate however that this level is about in line with expected differentials in the future (and thus is assumed at as constant throughout the 5y term). If anything, indications from forward markets point to higher spreads on the USD side in the future, which would push the cross-country differential even lower than the -13 bps assumed here.

Summed up, these three factors imply an annual loss of 117 bps. With a 5y CCBS, the cross-currency basis is fixed as seems the Libor–T-bill spread differential, leaving the term premium as the only somewhat free variable. As mentioned, in this first case the term premium is assumed to be “correct”, meaning its predictions of average future short rates are accurate. With the 5y UST at 164 bps, a negative TP of -46 bps implies an average short rate of 210 bps during the 5y period from 2017-2022. This path of future interest rates lies squarely within the band of reasonable estimates by market participants, highlighting that the Japanese institution’s investment is negatively carrying under normal market conditions already.

Case (2):

This case builds up on (1) but will play through a different term premium scenario. In contrast to (1), the TP estimate of -46 bps taken from the ACM model is considered as an estimate subject to uncertainty (with deviations up and down both possible) rather than an expression of certainty. The focus here will lie more on playing devil’s advocate with regard to what is necessary to turn the investment PnL positive rather than to consider even lower term premium scenarios (which are equally, if not more likely, would however not alter the conclusion: the investment should be unwound).

Along these lines, one possibility for instance is to set the TP so as to create a neutral PnL scenario and consider the implications for short-term interest rates. With the TP the only free variable, this means the TP has to compensate for the entire -117 bps loss in (1), which results in a TP of 71 bps to create a zero PnL. Retranslating this TP into average short rates form 2017-2022 results in a value of [164-71] = 93 bps. In other words, to turn the investment PnL neutral, average USD short rates during the next 5y must be lower than the current 3m T-bill yield – a scenario very different from the steady rise in yields expected by policy makers and most market participants.

Case (3):

This again is based on (1) but considers a different hedging strategy. Instead of hedging the whole 5y term at the outset, the investor can also create rolling hedges at shorter maturities should such a strategy be deemed cheaper. In the real world, this is usually done through rolling 3m FX forward hedges. Due to the equivalency of CCBS and FX swaps at the 3m tenor, this can be easily presented in the developed framework.

The reason for preferring such a hedging strategy is the shape of the cross-currency basis curve which at -27 bps at the 3m tenor is much less negative than at the longer tenors.

This shape implies that during the first three months, the investor would be much better off by hedging through shorter maturity CCBS. Looking at the entire 5y term, the decision is less straight forward since, as with most curves in fixed income analysis, the shape of the curve represents both expectations of future basis values and a term premium component.

So, observing the cross-currency basis curve through a “rational expectations & limitless arbitrage” lens (i.e. a cross-currency basis curve with a zero TP), the shape implies a drift lower for shorter tenors with the passage of time to around -55 bps. At the other end of the spectrum of possible views there is a “limits-to-arbitrage” perspective which holds that banks’ swap desks face different capital/risk limits at different tenors and can facilitate one directional demand more easily at shorter tenors, thus resulting in the downward sloping curve.

The reality probably lies in the middle, with the rolling hedges indeed cheaper than the term hedge but not as cheap as indicated by the current 3m value. For illustrative purposes, -35 bps as average 3m basis during the next 5y is chosen to reflect this middle way.

Even plugging in this less negative basis value (while leaving the other inputs unchanged) still results in a deeply negatively carrying trade.

5y A-rated corporate bond live

Case (4):

Instead of a 5y UST, the investor now purchases a 5y A-rated corporate bond. The first three values remain the same as in (1), only the credit component is added. As of September 2017, the spread offered by 5y A-rated corporate bonds is 69 bps, the annual credit cost is assumed to be 10 bp, which is the baseline scenario of the “buy-and-hold” approach. While the credit risk premium contributes positively, the overall PnL is still negative at -58 bps per year.

Case (5):

This is similar to (2) in that the term premium variable is adjusted so as to create a neutral PnL.

Case (6):

Based on (4), but scales credit losses by a factor of three to mimic a recessionary environment. Higher credit costs than those indicated by the baseline estimate, even if not necessarily at recessionary levels, are somewhat likely during the next years, with corporate structures, especially in the IG space, already quite leveraged. Unless such higher leverage is countered by lower volatility in cash flow & profit related variables, higher default rates and lower recovery rates should be the expected.

Case (7):

This is a “devil’s advocate upward scenario” which asks what would be necessary for the investment to yield a somewhat decent PnL of 100 bps annually; a value about in line with return expectation generated by the simplistic models presented in the prior post. The investor is granted the cheaper rolling hedges and the baseline credit loss rate. In this configuration, the term premium would have to be 89 bps, translating into average short-term U.S. interest rates of 75 bps from 2017-2022.


the big picture

There are two properties uniting all of the above scenarios:

  • Under most future interest rate trajectories, the considered investments are negatively carrying.
  • In order to create positive carry situations, U.S. interest rates would have to stay unexpectedly low in the future – in some cases to the point where interest would have to fall from current levels. In other words, currency-hedged bond investments by foreign investors in highly-rated USD securities are super leveraged to a persistently low yield environment.

Unless such a view is taken deliberately, most of the positions established during the last half decade will likely face significant unwinding pressures at some point, when the negatively-carrying nature of such investments is more broadly acknowledged.

While this post has focused on a representative Japanese investor, the situation faced by FX-hedged bond investors in broader Northeast Asia and Europe is similar. These countries all exhibit negative cross-currency bases (in TWD & KRW much more negative than in Japan even) and, like the Japanese institutions, struggle with the low risk premia offered by U.S. bond markets.

Together these countries have established currency-hedged positions in USD-denominated securities worth ~$1 tn over the last decade with the overall position size likely around ~$1.5 tn.

Given the size of these positions, the last few paragraphs of this post will be used to reflect on what an unwind of these investments may look like.

Apparently, most investors are and remain content with their positions at the end of 2016 and also so far in 2017 (as indicated by additional purchases), in spite of the likely negative-carry nature as indicated by the calculations above. In all likelihood, an upward move in short-term USD rates is required to change the broader market perception (even though, as shown, the negative carrying nature is currently already visible).

Such a move causes two direct PnL effects:

  • It will lower the net interest income, since payments to the SC increase (in the FX forward market this materializes as more negative forward points for USD/X crosses, which in turn increases hedging costs), eventually turning net interest income negative.
  • At the same time, bond portfolios will suffer mark-to-market losses as the whole curve shifts up.

Under these conditions, if foreign institutions begin to liquidate portions of their accumulated currency-hedged bond portfolios, the question turns to what size would have to be unwound to create a new sustainable equilibrium and also what the effects of such sales would be on markets.

Without crystal-ball-type-foresight, these questions are not really answerable without a big basket of if-conditionals. Even without hard numbers, it is easy to see the size of the unwind to be in the $100s bn, with large effects on the risk premia embedded in USD fixed income markets.

In theory, the extent of an unwind should be of a size significant enough to create a new equilibrium, in which the excess return offered aligns with return expectations by foreign institutions. This point, while it may require quite sizeable liquidations may then however be reached faster than expected due to the peculiar two-sided effects currency-hedged bond portfolios have on markets.

Whenever an investor purchases an asset, marginal upward pressure is put on the price of the asset in question. When many investors put on similar trades, such upward pressure can become structural, as has been the case with foreign inflows into U.S. debt, which have compressed term and credit risk premia. At the same time, the investors establish hedges which, in a banking system no longer defined by excess financial elasticity, put pressure on cross-currency basis curves to move lower.

Together, this means that whenever a wave of FX-hedged demand enters the U.S., the appeal of such investments is lowered from two sides at the same time: (1) yield levels are pushed lower and (2) hedging costs increase.

Seen from this perspective, the currently unappealing nature of currency-hedged bond investments can be partially blamed on foreign institutions themselves, as they have pushed term & credit risk premia curves lower and basis curves wider into negative territory.

In an unwinding scenario, the two-sided effect structure persists and would then work inversely to increasing the appeal of investments by pushing risk premia higher and the cross-currency basis towards more neutral levels.

(Back to previous post >>)

1 In extremely volatile FX markets, PnL differences can arise. For instance, whereas the Japanese investor faces no further FX risk under the conventional arrangement (in which the USD lender earns a profit in Japan), it will have to pay for the spread on top of USD Libor by converting JPY into USD, the amount of which will depend on the then prevailing exchange rate.

In other words, under the regular convention, the USD lender faces FX risk on its “negative-basis profits”, whereas in the approach used here, the USD borrower faces FX risk to effect the “negative-basis payment” to the SC. >>

2 This calculation (and the ones following) are crude approximates of the more correct decimal values attained by factoring in compound interest as well as matching cash income and cash payments every time period instead, as done here, only at the end of the investment. Since the focus here lies more on the intuition of the PnL building blocks of FX-hedged bond investments than absolute mathematical precision, the small deviations from actual values will be accepted. >>

FX-hedged yields, misunderstood term premia and $1 tn of negative carry investments

2 thoughts on “FX-hedged yields, misunderstood term premia and $1 tn of negative carry investments

  1. RD says:

    OK, first AMAZING work. here is my question, and it goes deep right away. Will the recent spike in term premium on the Treasury curve cause a flight back into duration or steep curve trades by asian buyers at the expense of floating rate ABS paper–specifically CLOs that presumably offered better adjusted returns thanks to LIBOR on both sides (just exposure to the basis?). The importance of the Japanese bid for CLO AAAs at L+110 cannot be overstated–they are the only buyers and the rest of the arbitrage has lost so much quality the market cannot sustain a repricing of Japanese demand for the top of the stack, for whatever reason (Higher rolling FX basis or a re-balalncing away from floating rate debt). Once again, FANTASTIC work here.


    1. Thank you for the kind words. Indeed a deep issue; longish answer follows.

      Basically concur with your view on CLOs for the overseas investor base; due to LIBOR on both sides there is a) no term premia, b) LIBOR spread differential drag so the x-ccy basis is the only issue.

      Also agree regarding the importance of the Japanese bid for structured assets. Don’t think I have a fully comprehensive view of the current demand structure – historically Norinchukin is the standout player, city banks (MUFG primarily) involved to a somewhat lesser degree.

      If ACM term premia estimates are believed, the recent backup of the curve is explained by term premia changes somewhere between 50-66%, depending on the specific tenor. At the margin, this could lead to your suggested rotation into duration, possibly to the detriment of CLO allocations.
      I would add a couple more thoughts though:

      In most models, the embedded term premia (despite the recent up move) is still negative. Following the reasoning in the post, this should still rather lead to liquidations of current fx-hedged bond portfolios, at least for duration unconstrained actors. Such sales would relieve pressure from the FX basis and potentially enable others to acquire CLO AAAs at lower spreads for the same total return. Lower spreads at the top of the stack would then provide the sought support for the equity arb.

      Even though term premia models can be quite interesting in their setup, the information content they provide is low in my view. The ACM model for instance is at its core more or less a regression of the five first principal components of the curve on historical term premia. It seems preposterous to expect high-quality results from such a crude process. Consequently, I would be rather hesitant to infer potential changes in asset allocations from such measures alone. This obviously does not mean these models are pointless (e.g. I think their portrayal of a negative term premia world is correct), but they should be approached with some caution.

      Ultimately I think your suggested scenario depends a lot on how Norinchukin will react. As far as I can tell, they are quite confident holding securitized assets (dating back to pre-08), so would be surprised to see any sizeable & rapid changes there.

      Given current pricing, I would (for what it’s worth) much rather hold the top of the U.S. CLO stack than the upper IG bond spectrum, both currency-hedged.

      In case of full flexibility (not realistic for most though), would attempt to source the complete credit risk synthetically (snr & snrmez slices of CDX HY preferably), eliminating most of the x-ccy basis exposure while still long the correlation risk CLOs provide.

      Liked by 1 person

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