Why is the 30-year forward yen at about 50 to the dollar?

Nick Rowe likes to teach PPP with a thought experiment, asking students to imagine how they might guess an exchange rate between the dollar and a foreign currency.  Thus if you went to Japan and noticed that most prices seem to be about 100 times higher than in the US, you might guess that 100 yen equals one dollar.  Of course PPP often does not hold true, but it’s still probably the best first guess for the exchange rate, if you had absolutely nothing else to go on.

In that case, it is more useful to think of the exchange rate being caused by the Japanese price level being 100 times higher than in the US?  Or should we think about the price level difference being caused by the exchange rate?  Is this even a meaningful question?

I like to think about the two price levels as being in some sense more fundamental, as I could imagine a case with no contract between the two countries.  Then once contact is made by Commodore Perry, the exchange rate conforms to the pre-existing price levels.  But you can also imagine a new country being settled by England, and choosing to use the dollar rather than the pound.  In that case the two price levels would be determined by the choice of the exchange rate.  The adoption of the euro is an obvious recent example, which caused Italian prices to plummet dramatically.

In a recent comment section I’ve discussed the fact that the 30-year forward dollar trades at roughly 50 yen (actually 49.332).  Is that exchange rate caused by the interest rate differential, or is the interest rate differential caused by the forward exchange rate?  People in the financial markets may focus on interest rate differentials as the primary factor, as the 30-year forward exchange rate is not very liquid and seems to be roughly 50Y/$ merely to prevent easy arbitrage opportunities, given the interest rate differential.

[I tried to see if interest parity held, but I don’t know the interest rate on 30-year zero coupon bonds.  So I took the yields on actual 30-year bonds as a proxy.  The US 30-year bond yields 3.17% and the Japanese bond yields 0.747%.  The differential is 2.423%.  Then I took 1.02423, and raised it to the 30th power, which equals 2.0508.  Then I took the actual exchange rate of 106.17, and divided by 2.0508, and got 51.77 as the implied 30-year forward yen. Is that right?]

In my view, it makes more sense to think of the expected 30-year forward exchange rate of 50 as the fundamental factor, and the interest rate differential as contingent on that expected future exchange rate.  Conversely, consider what would happen if we were to start with the interest rate differential as fundamental.  Then thinking in terms of interest rates, what would the BOJ have to do to prevent the yen from getting so strong in 30 years?  Obviously they need to make monetary policy more expansionary.  That’s how you weaken a currency.  But how do you do that in terms of the interest rate differential?  Obviously you need to get rid of the interest rate differential if you want the yen to be worth roughly 106 out in the year 2048.  But how do you get rid of the interest rate differential, while making monetary policy much more expansionary?

Let’s assume the BOJ cannot do anything about the level of interest rates in the US.  If they want the yen to be worth 106Y/$ in the year 2048, they need to get Japanese interest rates up to 3.17% on 30-year Japanese government bonds.  Even more daunting, they must do so with a highly expansionary monetary policy.  (Cochrane and Williamson are smiling at this point.)

So how do you do that?  Normally, a decision to raise interest rates is treated by the financial markets as a tight money policy, which causes the currency to appreciate.  So the BOJ needs to get interest rates up to 3.17% on 30-year bonds, and keep the exchange rate close to 106Y/$.  So how do they do that?  The simplest solution is to go back to Bretton Woods, and peg the yen to the dollar at 106.  If credible, that will cause Japanese 30-year bond yields to rise to 3.17%, and after 30 years the exchange rate will still be 106.  Because of PPP, Japan’s inflation rate over the next 30 years probably won’t be much different from the US inflation rate.  More importantly, the current expected inflation rate will rise to roughly 2%, just as in the US.

The fact that investors now expect the yen to be trading at about 50Y/$ in 2048 tells you just how far away from success the BOJ remains.  This is why I say that any talk of exiting from monetary stimulus is crazy.  Monetary policy in Japan remains extremely tight, expected to produce very low inflation over the next 30 years.  They need more than tinkering; they need a dramatic regime change.  I don’t advocate a fixed exchange rate system, but that’s one example of a radical regime change that would “work”.  A better option might be level targeting, combined with a “do whatever it takes” approach to monetary policy implementation.  I.e. buy as many assets as needed to get prices or NGDP rising along the desired level targeting path.

We don’t have that regime today, which makes the 30-year forward yen a useful proxy for policy credibility.  Only when the 30-year forward yen rises far above the current level of 50 can the BOJ start relaxing.  The BOJ has had some success in boosting prices and NGDP, but very little success in convincing the markets that this policy will continue in the very long run.  It seems like markets believe that once Abe is gone the BOJ will revert to its old habits.

PS.  If the regime change is credible they won’t have to buy very many assets.



41 Responses to “Why is the 30-year forward yen at about 50 to the dollar?”

  1. Gravatar of Tildeon Tildeon
    5. March 2018 at 15:27

    Interest parity doesn’t hold – 30Y XCCY is currently priced at -50bps, (details in your previous post). This isn’t even a function of the long time horizon, even for “short dates” (say sub 1y or 3m) a similar differential appears between the forward exchange rates implied by interest rates and the actual forward exchange rate.

    I’m not 100% clear on why the forward exchange rate is so important here though. If the BoJ’s target is 2% inflation, then the market instrument they should be targeting should be JGBI breakevens rather than an instrument tied to the US economy and monetary policy.

  2. Gravatar of BC BC
    5. March 2018 at 17:03

    “Is that exchange rate caused by the interest rate differential, or is the interest rate differential caused by the forward exchange rate?”

    The reason financial types tend to think the interest rate differential determines the forward exchange rate is probably because derivatives pricing textbooks usually treat the prices of primary instruments (underlying spot prices, interest rates/bond prices) as given and calculate prices of derivatives (forwards, futures, options) from those primary prices.
    Stocks/commodities/currencies and bonds are considered to exist first and derivatives are merely contracts that are written on those underlyings.

    Also, in finance courses/texts, it’s drummed into students that derivatives prices don’t contain any information about expectations of future spot prices (except maybe with respect to the so-called risk-neutral distribution). Derivatives prices merely reflect no-arbitrage conditions given spot prices, interest rates, and carrying costs (dividends for stock, foreign interest rates for FX, storage costs for commodities). For example, S&P futures prices aren’t where the market expects the S&P price to be in the future. If they were, then that would mean that the market expected stocks to return the same as T-bills since F = S*exp((r-d)*T), where r is risk-free rate. (One could say, however, that S&P futures prices are where the market would have expected the S&P price to have been in the future in a risk-neutral world given current spot prices.)

    Given the choice between saying “the market trades forward contracts at prices that reflect interest rate differentials” and “the market adjusts interest rate differentials to reflect what its expectations for the future exchange rate would have been in a risk neutral world”, the former seems easier.

  3. Gravatar of Garrett Garrett
    5. March 2018 at 17:18

    Another reason “finance types” think of things in terms of rates of return is that that’s how to compare different types of investments.

  4. Gravatar of B Cole B Cole
    5. March 2018 at 17:21

    Excellent blogging.

    Time to ponder money-financed fiscal programs?

  5. Gravatar of B Cole B Cole
    5. March 2018 at 17:23

    I discuss money neutrality here.


  6. Gravatar of Sean Rushton Sean Rushton
    5. March 2018 at 18:04

    Expectation of yen appreciation has killed Japan since the Plaza Accord, when the yen was allowed to appreciate three fold versus the dollar. They should have devalued and fixed to the dollar in 1995.

  7. Gravatar of Sean Rushton Sean Rushton
    5. March 2018 at 18:06

    No wonder consumers and businesses prefer to hold cash rather than spend or invest.

  8. Gravatar of John Hall John Hall
    5. March 2018 at 18:12

    Scott you’re right about how to do the calculation at the 30-year.

    I agree with much of BC’s point, but I would emphasize that the relationship between exchange rates and interest rate differentials is governed by an arbitrage. It’s not exchange rates on one hand and interest rate differentials on another. If there is a deviation from covered interest parity that someone can profit risk-free from, then they will engage in transactions necessary to do so until it is no longer profitable. To take advantage of it, you may need to engage in a foreign currency transaction AND invest that money. Making these trades will move markets if you do them in enough size.

  9. Gravatar of HL HL
    5. March 2018 at 18:15

    Another brilliant post!

  10. Gravatar of Arilando Arilando
    5. March 2018 at 18:59

    How exactly did the Euro cause Italian prices to plummet dramatically?

  11. Gravatar of ssumner ssumner
    5. March 2018 at 21:39

    Arilando, The exchange rate between euros and lira was more than 1000 to 1.

  12. Gravatar of phil_20686 phil_20686
    6. March 2018 at 01:02

    I believe that Japan yields are usually quoted as simple yields, not compound yields, so the compound yield is actually (1 + 0.747%*30)^(1/30) and then you end up with 50.7 as the forward price of the yen.

  13. Gravatar of H_WASSHOI H_WASSHOI
    6. March 2018 at 05:33

    I begin to learn programming

  14. Gravatar of ssumner ssumner
    6. March 2018 at 07:48

    Sean, There are also downsides to fixing to the dollar, as its value is also highly unstable.

  15. Gravatar of ssumner ssumner
    6. March 2018 at 07:51

    BC, You said:

    Also, in finance courses/texts, it’s drummed into students that derivatives prices don’t contain any information about expectations of future spot prices”

    Why do people believe that? It’s a rather bizarre claim. If the Venezuelan currency trades at a 99.9% discount, does that really tell us nothing about where people expect it to go?

  16. Gravatar of Patrick R. Sullivan Patrick R. Sullivan
    6. March 2018 at 08:13

    ‘How exactly did the Euro cause Italian prices to plummet dramatically?’

    Nominal, not ‘real’ prices. If the Euro = 1,000 Lira at the switchover, then, say, a loaf of Italian bread that had sold for 1,000 Lira, would magically go for one Euro.

  17. Gravatar of LK Beland LK Beland
    6. March 2018 at 08:16

    Another way of seeing it:

    USA: 10-year and 30-year break-even inflation rates: ~2.1%.

    Japan: 10-year break-even inflation rate: ~0.5%. (For sake of argument, let’s suppose that the 30-year break-even in Japan is also 0.5%.)

    2048 Price level predictions (as a % of 2018 price level):
    USA: 186%
    Japan: 116%

    From a PPP standpoint: 116 / 186 * 106 Yen/USD = 66 Yen/USD. Pretty consistent with that 50 Yen/USD figure.

    Basically, interest rate differentials embed inflation expectation differentials and add a credit market component.

  18. Gravatar of Patrick R. Sullivan Patrick R. Sullivan
    6. March 2018 at 08:20

    Somewhat off topic, but for those who think the Neel Kashkari & Co. are on the right track to raise bank capital requirements to 25%;


    Amazon.com Inc. AMZN +0.84% is in talks with big banks including JPMorgan Chase & Co. about building a checking-account-like product the online retailer could offer its customers, according to people familiar with the matter.

    The effort is still in its early stages and may not come to fruition, the people said. The talks with financial firms are focused on creating a product that would appeal to younger customers and those without bank accounts. Whatever its final form, the initiative wouldn’t involve Amazon becoming a bank, the people said.

    About that last line; Hardy, har har! (Which is why Milton Friedman abandoned his idea of 100% reserve banking, too).

  19. Gravatar of Doug M Doug M
    6. March 2018 at 09:44

    US 11/47 STRIP currently trades at 3.19/3.16
    the JGBP 3/48 is currently at 0.771.

    Both are pretty close to the coupon bonds, and does not change the math.

    There is an arbitrage between the spot rate, the two interest rate curves and the forward rate. Our Professor suggests that the Forward rate should be the driving factor. But, conventional wisdom is that the forward rate is the tail of the dog, and goes where the other variables take them.

    There is no liquid long-dated forward contract. While there is liquidity in both bonds and spot rates. Any quote you might find will be the arbitrage free rate. That would suggest that the forward rate is the tail of the dog.

    Just because these rates are connected by an arbitrage does not mean that forward rates are in a particularly good perdictor of future moves in the currency rates. The history of currency trading shows that there is very little correlation between the FX forwards and the actual currency moves.

    And a lot can happen in 30 years. 30 years ago, the Japanese economy was the envy of the world. Japan was the China of the 80’s. The Nikkei was at 30,000, soon to top out at 35,000 and then drop to 10,000. (currently 21,417).

    Regarding stimulative policy and the forward curve, if the central bank is eases, pursues an easy policy, that should make the spot rate for the currency fall. It shouldn’t have much effect at all on the forward rate or the relationship between the spot rate and the forward rate.

    But the 50 forward Yen does suggest that the market has little confidence that the BoJ will succeed in “reflating” the Japaneses economy, or that the rate of inflation will be less than the US rate of inflation.

  20. Gravatar of Max Max
    6. March 2018 at 11:13

    “I.e. buy as many assets as needed to get prices or NGDP rising along the desired level targeting path.”

    It matters what they buy, though. Your post explains why the 30-year Japanese bond would be a terrible asset for the BOJ to buy…effectively it would commit the bank to validating current low-inflation expectations (if they don’t want to lose money).

    Or in other words, central banks should bet on their success, if anything, and not against themselves.

  21. Gravatar of John Hall John Hall
    6. March 2018 at 11:49

    In response to BC you said, “Why do people believe that? It’s a rather bizarre claim. If the Venezuelan currency trades at a 99.9% discount, does that really tell us nothing about where people expect it to go?”

    He’s getting into the argument about whether covered vs. uncovered interest rate parity holds. Covered interest rate parity tends to hold in deep and liquid capital markets. However, the evidence for uncovered interest rate parity is more mixed. That is, the question is whether the forward currency rate can reliably predict the spot currency rate.

  22. Gravatar of ssumner ssumner
    6. March 2018 at 21:19

    Max, But if the BOJ actually were to decide to create higher inflation, the bond yields would reflect that immediately, even before the BOJ bought the bonds.

    Everyone, I understand that actual exchange rates are volatile, and hard to predict. I see the forward rate as a forecast, albeit one that often turns out to be inaccurate. The same is true of any other forecast of a variable that is hard to predict.

    As far as whether the forward exchange rate is the dog or the tail, keep in mind that the liquidity of the forward market has no bearing on that question.

  23. Gravatar of Benjamin Cole Benjamin Cole
    7. March 2018 at 03:05


    The Grattan Institute has blamed high immigration for runaway house prices
    Think tank said people who worked hard needed parents to help them buy home
    Feared Australia would be a ‘less equal society’ if high immigration continued

    Read more: http://www.dailymail.co.uk/news/article-5461261/Australia-tap-brakes-immigration-slow-house-prices.html#ixzz593lLyGTD
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    I do not endorse xenophobia. (In fact, I live overseas now).

    But if Australia’s propertied-financial class refuses to allow housing to be built, but wants cheap labor and immigrants….

    And also to run large current-account trade deficits, so that heavy capital flows into property markets….

    How should Aussie voters respond?

    Of course, they should respond by eliminating property zoning.

    If that cannot be done, then immigration and trade must be handled, no?

    Otherwise, the Aussies get “free trade” and immigration….and lower living standards.

  24. Gravatar of H_WASSHOI H_WASSHOI
    7. March 2018 at 06:26


  25. Gravatar of Mikio Mikio
    7. March 2018 at 09:37

    Excellent post. The new vice governor of the BOJ Wakatabe has proposed NGDPLT. He will have a chance to promote his ideas within the institution, which will resist and move slowly. But at least there is some hope. Otherwise, yes: markets are saying once Abe is gone, the old regime will re-emerge.

  26. Gravatar of mpowell mpowell
    7. March 2018 at 12:55

    You already explained how the futures market is based on the interest rate differential. This means it is explicitly not a forward prediction of the $/yen future exchange rate, right?

  27. Gravatar of ssumner ssumner
    7. March 2018 at 13:57

    Thanks Mikio.

    Mpowell, No, I’m saying the interest rate differential is based on the future expected exchange rate.

  28. Gravatar of B Cole B Cole
    7. March 2018 at 17:02


    Maybe you are right, but Kuroda was just appointed to another five-year term. The two new deputy governors appear even more aggressive in their proposals to seek growth.

    All good news, but still we see no inflation.

    Many observers say they do not expect the Bank of Japan to ever sell back the debt it has purchased. Adair Turner for example. I sure wonder when such a sell-back would happen.

    So we have a gigantic expansion of the monetary base, and no inflation and dubious expectations the monetary base would ever be reduced again.

  29. Gravatar of Mikio Mikio
    7. March 2018 at 22:48

    Scott, B Cole:

    FYI, the BOJ explicitly refers to the CPI ex fresh food index. Here is the direct quote for their January report:

    “[The BOJ} will continue expanding the monetary
    base until the year-on-year rate of increase in the observed CPI (all items less fresh food) exceeds 2 percent and stays above the target in a stable manner.”

    That index is now at 0.9% y/y. So in that sense they may be proven broadly right that they hit 2% by late 2019 or so in a best case scenario.

    The question is what do they define as “stable manner” – if by that they mean the CPI ex fresh food and energy to hit 2% as well (vs. 0.4% now) – forget that.

    As for the monetary base, the problem is that many people now already actually believe the BOJ is de facto tapering already, due to Yield Curve Control policy.

    It’s also what some ex-central bankers are communicating. See here for example: https://www.bloomberg.com/news/articles/2018-02-20/boj-likely-to-stay-on-virtual-normalization-path-kiuchi-says

    It is this sort of perception that Kuroda & Co. need to refute. I suspect a lot of resistance from the “Germans” within the BOJ, like the ECB was facing a lot of pushback from BuBa…

    Wakatabe has an uphill battle to do, even as Vice Chair. Amayiya is more of a technocrat, not really a reflationist.

  30. Gravatar of Sales Sales
    8. March 2018 at 01:06

    Is the 30y $yen rate a prediction? If so who is doing the predicting? What about the one week forward $yen rate, is that a prediction too or is it a function of the spot $yen rate and interest rates? The prediction argument seems like a dead end, predictions are like opinions, they are cheap and everyone has one. If one wanted to test predictions then there is always the forward FX market. The 30y forward $yen rate is produced by the current spot rate and long term interest rates for the $ and yen which themselves are a function of current monetary policy in Japan and the US. Of course expectations of future policy matters but those are already in the price.

  31. Gravatar of HL HL
    8. March 2018 at 03:54

    In fact, Amamiya is already going around and stressing financial stability aspect of the mandate. That more or less offsets whatever Wakatabe is trying to achieve in the BOJ MPM discussion. My expectation is that Amamiya’s political “heft” within the BOJ is too large to be challenged effectively by Wakatabe…

  32. Gravatar of Benjamin Cole Benjamin Cole
    8. March 2018 at 04:54


    Okay, good comments, no arguments.

    But the point remains: There has been a huge increase in the Japanese monetary base, and no hint about buying it back. But no inflation, and this situation has persisted for years—indeed the BoJ keeps buying JGBs (and some ETFs-stock).

    What fraction of the market (or population) thinks the BoJ will sell back bonds in bulk any time soon or ever? I am a minute part of the market, but I am very dubious the BoJ will ever sell its hoard of bonds.

    I guess that would make an interesting survey question. Ask people what they think their central bank will do.

    In the US, I would guess about 1% of the population could tell you who is Jerome Powell. Maybe 0.5% (or less) could discuss the QE-thing. So there is a market expectation about the Fed?

    And that “market expectation” influences how barbers, and farmers, and mechanics and landlords and the global oil market set prices? Really?

    I gotta say, the “market expects a central bank to buy back bonds and so there is no inflation” seems a little thin.

  33. Gravatar of Benjamin Cole Benjamin Cole
    8. March 2018 at 05:32

    Fun side note:

    “Milton Friedman’s celebrated “monetary and fiscal framework” article (Friedman (1948)) is, as far as I know, the earliest reference where a case for money-financed budget deficits is made. In Friedman’s view, the ideal policy framework would require that governments maintain a balanced budget in structural terms (i.e. under full employment), but that they let automatic stabilizers operate in the usual way, with the deficits generated during recessions being financed by money creation (and, symmetrically, with surpluses in boom times used to reduce the money stock). Such
    a “rule” would be a most selective countercyclical tool for, in the words of Friedman, “…in a period of unemployment [issuing interest-earning securities] is less deflationary than to levy taxes. This is true. But it is still less deflationary to issue money.”


    I always liked Milton Friedman.

  34. Gravatar of Michael Rulle Michael Rulle
    8. March 2018 at 06:08

    Since the forward exchange rate and the value of the interest rate differentials are identities, starting from thought zero, it would seem like a classic chicken and egg problem. You believe the relative liquidity of the forward currency market, which I assume is pretty low, compared to the bond markets does not change your belief that the primary driver is the exchange rate. I agree with commenters who describe how we were taught the calculation, which I agree still should have no bearing on your view. But it is still difficult to except but I can give no supporting argument.

    Would this same logic hold for the S&P 500? It would seem not. But it is still a yield differential which determines the forward price. Of course, the expected return of currencies should on average be zero, which your arbitrage calculation, at least for dollar/yen, supports.

    That is not the case in the S&P, however. That is, I do not think the expected return on the S&P is zero—-although expected returns are generally determined by subjective views based on historical averages, which is not theoretically satisfying.What is the difference?

  35. Gravatar of Michael Rulle Michael Rulle
    8. March 2018 at 06:12

    I know if one just plays the arbitrage game in the S&P one can only earn excess basis points over the risk free rate. But I am addressing the point of the implied forward price in S&P versus the implied forward price of the yen

  36. Gravatar of Mikio Mikio
    8. March 2018 at 06:36

    HL – yes, Amamiya is the BOJ equivalent of a “German Bundesbanker”… However, the battle is not yet lost. If you compare the new board with the previous, if slightly shifted in favor of reflationists. And Amamiya himself told parliament that untilanyeky he will follow Kuroda’s decisions.

    Benjamin – they are discussing exit. That’s about reducing base money. As for the lack of inflation, I blame (1) lack of long term policy credibity because everyone knows institutional covservatism is strong and (2) they keep paying interest on excess reserves. The -0.1% applies only on a very small proportion of the ER. It’s symbolic. In reality, they are neutralizing much of the base money expansion. The Fed did something similar – which is why it took so long to reach 2%.

  37. Gravatar of ssumner ssumner
    8. March 2018 at 09:54

    Mikio, Thanks for that information—very helpful. I didn’t know they were still paying positive interest on ERs. Why is that?

    I think it’s mistake for BOJ officials to suggest they are on track for 2% inflation, which is clearly not true. It reduces BOJ credibility. Honesty is always the best policy, when it comes to monetary policy.

    HL, Interesting.

    Michael, I’m more focused on the expected future value of the yen, rather than the forward rate specifically. I’ll do another post.

  38. Gravatar of ssumner ssumner
    8. March 2018 at 11:36

    Sales, It’s an estimate of a prediction.

  39. Gravatar of Mikio Mikio
    8. March 2018 at 20:49

    Scott – agree on credibility problem. The problem is that there is an ideological divide.

    The IOR is paid because the BOJ applies the -0.1% only on a very small part of the reserves, called “policy balance” (usually about 6-7% of the reserves).

    It applies 0% on three-fifths of the reserves (“basic balance”) and pays +0.1% on the rest, called “add-on-macro balance”.

    That means it currently pays about 0.055% on total reserves of about 349 trillion yen. The system is designed to never go negative. Assumes reserves continue to growth at current pace, the IRO will fall to 0.01% by 2030 – but it will never go negative.

    I think this was a mistake – a wrong signal.

  40. Gravatar of Benjamin Cole Benjamin Cole
    9. March 2018 at 19:48


    Well all good, except the “market expectations” stance is a bit of a tautology.

    That is, if we see 3% inflation in Japan in 2020, then you can say, “Now the market believes the BoJ is serious.” If we see 1% inflation in 2020, you can say, “Market expectations are the BoJ lacks resolve to hit the 2% target.”

    BTW David Glasner has an interesting take on “market expectations” in his latest post.

  41. Gravatar of ssumner ssumner
    12. March 2018 at 15:59

    Mikio, Thanks, that really does seem like a mistake.

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