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 , ,  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 ). 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.
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 ), and in any case, the full employment budget balance has always been in the red since the 2001 and 2003 Bush tax cuts .
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.