Implications of adjustment to riskier dollar assets in a portfolio balance framework, illustrated in three steps

Consider a hypothetical world economy with assets denominated in dollars and euros.

Define the exchange risk premium on dollar denominated assets as:

rp = iUS – i* – E(ds)

where E(.) is the expectations operator, and ds is the change in the log exchange rate in the next period. (Note that this is not the default risk premium; it is the premium, in common currency terms, required to induce portfolio holders to hold the stock of dollar denominated assets outstanding).

Let the share of dollar assets in the total world portfolio be called x and x is a positive function of the exchange risk premium.

x = alpha + beta [rp]

Inverting this expression, one finds that then the risk premium is an increasing function of x. Thus:


Figure 0: Portfolio balance model, with dollar and euro assets.

where x0 is the initial share of dollar assets. Note that in a simple one period mean-variance optimization framework, the slope depends on the coefficient of risk aversion. The higher the degree of risk aversion, the greater the slope of this rp(x) line.

Step 1. Risk aversion rises. The risk premium rises from rp0 to rp1

Figure 1: Risk aversion rises.

Step 2: SWFs reduce desired holdings of dollar assets [1], [2], [3] as desirability of dollar denominated assets drop (perhaps because default characteristics change); central banks follow. The risk premium rises from rp1 to rp2

Figure 2: Desired zero-risk-premium portfolio holdings of dollar assets drops.
Step 3: Government debt outstanding increases (as budget deficits increase due to either revenue shortfall, or financing contingent liabilities [4]). The risk premium rises from rp2 to rp3.

Figure 3: Stock of dollar denominated assets relative to world assets exogenously increases, x0 rises to x1.
One could consider cases where the initial risk premium is less than zero; the analysis is the same. The required rate of return on dollar denominated assets must rise relative to where it started. For that to occur, returns on dollar denominated assets must rise, or the dollar must be expected to appreciate at a greater rate than before. This can occur if the dollar drops discretely.

For other analyses along these lines, see this post, and references contained therein. This set of notes also lays out the logic.

Turning to the real world, where might the exogenous increase in dollar denominated assets come from (the increase in risk aversion we’ve already seen)? From Peter Hooper, Thomas Mayer, Torsten Slok, “Fannie, Freddie, Sheila and
Hank,” Global Economic Perspectives (Deutsche Bank, July 21, 2008), not online:

In our view the true costs of the US housing market downturn and financial crisis for the public purse is likely to be recognised only gradually. Hence, the final costs could far exceed the numbers presently being discussed in the political domain. Our bottom-up calculation suggests that the total costs related to GSE losses, capital injections to keep the housing market growing (even at recently subdued rates), and FDIC insurance funding by banks could come to as much as USD70bn over the year ahead (losses of USD30bn at the GSEs and the FDIC each covered by existing reserves plus some USD10bn new capital to accommodate a desired expansion of the mortgage market).

However, the risks to these estimates seem on the upside. Past experience in the US and other countries suggests that the total cost for the taxpayer over a number of years could accumulate to something on the order of USD600bn (in 2007 prices). Nevertheless, if our estimates are in the right ballpark, the eventual increase in the US government’s gross debt ratio by 4.5% of GDP would be quite small when compared to the fall-out of the really big financial disasters of the last two decades. …

This is why I have continually stressed that the Bush Administration’s (previous) emphasis on the small size of the budget deficit to GDP ratio was misguided. Contingent liabilities abounded (especially after Medicare Part D was implemented, courtesy of the muzzling the Medicare actuary [5]), and in any case, the full employment budget balance has always been in the red since the 2001 and 2003 Bush tax cuts [6].

By the way, it’s not clear that even if it were possible to commit to not saving the financial system, it would prevent the the increase in the rp. The shift in the rp(x) schedule is a function of how dollar denominated assets are perceived by global investors. Should the government fail to back up at least the mortgage backed bonds, the the leftward shift would be even more pronounced, even if the stock of government debt failed to increase (x0 shift right in Figure 3) as much.

Is this all surprising? Here are some prescient remarks from September 2005:

Do more benign outcomes support the rationale for continued inaction? Suppose we consider a more likely outcome in which investors merely slow their acquisition of U.S. Treasuries, or state actors such as the People’s Bank of China choose to diversify their reserve currency holdings, away from dollars and toward other currencies. That is, they do not actually “dump” the dollar holdings, but acquire them at a slower pace.

In this scenario, the premium necessary to induce investors to hold U.S. Treasuries will rise gradually but inexorably, slowing the economy. Because of the large and increasing budget deficits set in place, expansionary fiscal policy will be off the table. The role of monetary policy will also be circumscribed. Lowering interest rates further would alarm holders of U.S. Treasuries, an alarm that would be well founded given the tremendous incentives the Fed would have to inflate away the government’s debt held by foreign residents. So America will be trapped in slow growth, with no viable policy options. In such a state, policymakers may be even more tempted than they are now to impose tariffs and sanctions, increasing further the possibility of trade wars.

The entire analysis can be found in this Council on Foreign Relations Special Report No. 10, “Getting Serious about the Twin Deficits.

21 thoughts on “Implications of adjustment to riskier dollar assets in a portfolio balance framework, illustrated in three steps

  1. Charlie Stromeyer Jr

    According to Brad Setser, the Chinese hold about 10% of all the GSE agency debt so I doubt that the U.S. government would fail to back up the agency debt. (By the way, my friend works for the Chinese government and he says that they are mostly incompetent, so at least we have this much in common with the Chinese people.)
    According to both Bill Gross of PIMCO and the Nobel prize winning economist Joseph Stiglitz, our federal deficit is about to explode much higher.
    Disclosure: I am still short 10 year U.S. Treasuries, and I am patiently waiting to go long gold and gold equities.

  2. DickF

    Since we are dreaming monetary dreams consider a situation where China and Russia get tired of allowing the US to wage monetary war and decide to tie their currencies to gold breaking their loose and stormy tie to the dollar.
    There would be an immediate and huge increase in demand for rubles and renimibi with an equally huge decrease in demand for the US$. There would be a sudden and increasing repatriation of dollars and a consequent rapid run up in US inflation. Unless the FED very quickly responded by drawing down the excess dollars chronic inflation would quickly turn to hyper inflation.
    The oil producing countries would quickly begin to move toward use of the more stable currencies to price their oil leaving the depreciating dollar to flounder for itself. Quickly other countries including the euro block would follow choosing stable trade with China and Russia and the oil producing states unstable trade with the US.
    Ultimately the US would have to join the move to return to gold;otherwise, the instability of the dollar compared to the stability of the currencies of the rest of the world would cause great instability in the US economy.
    It is interesting to consider that China is moving in the direction of a gold anchor. Right now the Chinese economy is neither large enough nor strong enough to confront the US$ but an alliance with Russia could create a trading block large enough to compete with the US. This would especially be the case if the major oil producers joined them.
    The game of analyzing unstable floating currencies would become a thing of the past and businesses could shift resources from lawyers and accountants to production.

  3. Charlie Stromeyer Jr

    DickF or anyone else, what would happen if the major oil producers pegged their currencies to a basket that includes the price of oil (perhaps once oil prices have bottomed)? Thanks.
    Disclosure: Long both Asian and Middle Eastern currencies and Middle Eastern equities.

  4. GWG

    Just read the entire report and wanted to compliment you on an excellent piece of work. I especially liked your comparisons to the demise of Britain and wish our policy makers on both sides of the isle could see this danger. Unfortunately it seems as if the collective discount rate for the American public has risen, thereby making the odds of taking action to avert this outcome all the more remote.

  5. DickF

    Help me understand your question. Do you mean pegged to a basket of goods including oil, or do you mean to a basket of currencies, or something else.
    Just a quick thought. The oil producers do not have economies big enough to counter economic attacks by the US and so under floating regimes they are generally better pegging to a currency of a larger economy with which they trade such as the euro or the dollar. The oil producers are signigicantly one income economies and that doesn’t help.
    The contrast between modern Venezuela and Colombia is a good example. Each country is basically the same in climate and raw materials, but the Colombian economy is much more diverse and is much stronger. Of course there is also the difference between how free the markets are in Colombia versus Venezuela. Free markets create a diverse, growing economy while centrally planned economies are generally weak or weakening.

  6. samson

    Thanks once again for a thought-provoking post. I have a question about the framework you used. You’re post (and the notes) illustrate a demand curve for dollar-denominated assets. What do you suppose are the determinants of the supply of dollar-denominated assets in this model? Is it perfectly inelastic? Furthermore, what fundamental parameters shift this supply? Could shifts in the supply mitigate the risk-premium increase illustrated above?

  7. don

    Risk of dollar-denominated assets is relative when measuring the effect on exchange rates and your analysis looks at just one side of the issue. What about the other side? For example, consider the following. Germany exports more than the United States, with much of its exports consisting of capital equipment. Given the highly unionized economies in the euro zone, its monetary policy is more constrained by inflation concerns than is the U.S. Fed. The euro area is not an optimal currency area, as labor is not that mobile among the member countries.
    Now, suppose the U.S. slowdown catches abroad, German exports suffer more than apace, and (given a less flexible monetary policy) the euro area suffers a more painful contraction than the U.S. The pain from the slowdown will not be evenly spread among the euro countries, with the result that there may be serious pressure for some of them to exit the single currency. How would this affect currency risks?
    If the dollar were to drop precipitously versus the yuan, China’s economy could end up in very serious trouble, with a painful domestic contraction and perhaps serious political unrest, with the result that an equally precipitous drop in the yuan would occur.
    My question is, how useful is a partial analysis that examines just the effects of a particular U.S. circumstance? As I hope the above arguments show, risks for foreign currencies are not independent of what happens to the dollar. For similar reasons, I don’t see how the one-sided analysis is very useful for determining the value of the dollar against other things, like commodities.

  8. Charlie Stromeyer Jr

    don, if Germany contracts wouldn’t it help bring down inflationary pressures in the Eurozone thus making ECB monetary policy more flexible? Either way, both Jim Rogers and I think that the Euro is a flawed currency which is why I am not long the Euro (but not long the U.S. dollar either).
    Also, since there is much greater labor flexibility in the U.S. won’t it mean that in a serious U.S. contraction that U.S. firms will begin aggressive layoffs in an attempt to preserve margins (while simultaneously forgetting that consumers drive about 70% of U.S. GDP)?

  9. MarkS

    I had a great time reading Fred, Charlie, and Don’s comments. They were very entertaining. At the end of the day, I’m with Menzie… No matter how the dominoes fall, its inevitable that the US currency will decline in foreign exchange markets, and US inflation will remain above the world mean, if the TWIN DEFICITS are not replaced with positive numbers. These financial declines will result in the decay of American political, cultural, and technological influence. Fools focus on past achievements, the hoi polloi focus on present diversions, and the wise focus on future accomplishments.

    I firmly believe that the erosion of the petroleum dollar recycle system, (accelerated by the US invasion and misadministration of Iraq, and MCB derivative enabled money expansion), has placed an inflation (currency depreciation) discount on American securities. Consequently, the yields on the securities have to increase in order to tread water. Obviously, the yields have not increased, so investors sell US securities, and the US financial markets go into a dive.

  10. Menzie Chinn

    GWG: Thanks for the compliment.

    samson: Please see Engel and Frankel, “Do Asset Demand Functions Optimize over the Mean and Variance of Real Returns? A Six-Currency Test,” Journal of International Economics 17, November 1984. for a technical explication of the model being used. For better or worse, the exchange risk premium, in this framework, is a function of the covariance of relative returns in real terms on government debt. I have expanded the interpretation of the assets to include other assets.

    The stocks of assets are exogenous in this interpretation. What is true is that if the US government endogenously responded to borrowing costs by reducing the rate of expansion of government debt, then the increase in the exchange risk premium would be mitigated (i.e., the movement right of x in Step 3 would be less pronounced, or could even be a move leftward).

  11. wimpie

    Menzie, nice job!
    Besides the insolvency of the US financial system, has anything surprised you since your 2005 analysis?

  12. DickF

    Frankel’s suggestion is probably a better solution that what we are seeing today since a basket of currencies would spread the risk, but this still does not remove the fact that since Nixon took the world off of gold we have seen massive worldwide inflation. A basket of currencies would not stop this. You may feel that worldwide inflation would not be a problem since all countries would experience it but consider an isolated country where the king debased the currency. Would this cause problems for his people? Even in a closed system inflation creates problems.
    Another question is would the dollar be included in the basket and if so would oil be valued in dollars – a dollar double hit if you will? Perhaps oil could be valued in gold. Then again maybe the whole basket could be valued in gold for an anchor as good as gold.

  13. don

    Greater labor market flexibility means that wages can decline instead of people getting laid off.
    A reduction in German demand would reduce inflationary pressures in the euro zone, but my view is that for any level of inflationary pressures or demand deficiency, the ECB is less able to respond by cutting rates than is the Fed.
    I guess my point is one of timing and dynamics. Clearly, an exogenous factor that causes the dollar to fall relative to the euro will have adverse effects on euro area economies. Whether they could be serious enough to more than reverse the initial dollar decline is a matter for conjecture. (In my example, the euro ends up dashed on the rocks.) In any event, it seems inappropriate to ignore possible reactions when forecasting exchange rates.
    Another thing to note is that the U.S. is beginning this episode with more than enough aggregate demand to maintain its own employment, if only the current account leakage could be reduced. The euro area has no such excess demand. A move towards protectionism seems more likely to hurt them than us, even if it is directed only against Asian economies.

  14. Charlie Stromeyer Jr

    DickF, I personally don’t have any problem with moving to a gold standard, but I truly doubt that the rest of the world would be willing to adopt such a standard (so this means I agree with you that Frankel’s suggestion would be better than the status quo).
    don, both the most recent NABE survey and the unemployment claims data seem to indicate more layoffs, but I agree with you that the ECB has less monetary policy flexibility than the Fed (also partly because the ECB is only supposed to be fighting inflation and thus cannot also consider unemployment).
    I’m also not sure the U.S. has excess demand given the weakness in housing, airlines, autos and finance.
    As for the U.S. current account deficit (CAD) do you think that this would help: Suppose growth in Chinese exports to the U.S. slows down because of a possible U.S. contraction then perhaps the Chinese will be forced to start spending some of their massive forex reserves?

  15. don

    Charlie –
    U.S. domestic spending exceeds U.S. income, ergo CA deficit and ‘excess’ aggregate demand.
    It would surely help global demand if China started spending some of its reserves.

  16. Charlie Stromeyer Jr

    don, by U.S. domestic spending do you mean consumption (C) plus government spending (G) as in the aggregate demand curve?

  17. Charlie Stromeyer Jr

    don or anyone else, shouldn’t the U.S. current account deficit boost aggregate demand outside the U.S.? I must admit that neither I nor anyone else really seems to understand all the potential factors involved in current account deficits and surpluses (which is evidently why economists are still studying this topic).

  18. don

    Charlie- domestic spending = C + I + G. Yes, the U.S. deficit is helping sustain global demand.
    In my opinion, Asian currencies are undervalued (yen and yuan) and help sustain the U.S deficit. As for Menzie’s analysis, I think it matters why the U.S. dollar share of world assets rises. Suppose it is because of Asian currency interventions (including implicit intervention, which may be behind the undervalued yen, as yen borrowers are convinced Japanese authorities will step in to prevent yen appreciation beyond a certain point). Then, there may be automatic reaction to a drop in the dollar, as those who stay pegged to the dollar intervene to keep their currencies from also rising. The one-dimensional analysis Menzie presents just seems too simple. For example, it has the obvious fault that it treats the dollar exchange rate as a single value. The dollar is rather wildly undervalued against European currencies, but is substantially overvalued against the major Asian currencies.

  19. Charlie Stromeyer Jr

    Thanks for the explanation, don. I agree with what you say, and by the estimates that I have seen the Euro is thought to be about 20-30% overvalued relative to the U.S. dollar.

  20. Menzie Chinn

    don: I agree a general equilibrium model would be preferable in principle. But this is hard to do in a way that captures the nuances you wish to, and most DSGEs do not have portfolio balance motivations of the sort I have exploited.

    While the model is overly simple, the main point of it is heuristic, rather than predictive. If the substitutability of dollar assets declines vis a vis assets denominated in other currencies, there is an exogenous decline in the zero-risk-premium share of dollar assets, and the stock of dollar assets rises, then ceteris paribus, the exchange risk premium on dollar assets must rise. How it rises depends, and is not explained in this model.

    Allowing for other currencies does not change the basic message, as long as international investors do not want to hold large stocks of assets denominated in yuan and other inconvertible currencies.

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