Journal Issue

People’s Republic of China: 2011 Spillover Report—Selected Issues

International Monetary Fund
Published Date:
July 2011
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This chapter derives the global bond market implications of shifts in China’s reserve allocation using a simple static mean-variance framework. It provides an example where a reallocation of China’s holdings of U.S. reserve assets to emerging market (EM) assets by, say, US$100 billion could increase U.S. yields by 12 bps and reduce EM yields by about 48 bps. Yields on other advanced market (AM) debt, which are close substitutes of U.S. debt, would also increase. In this framework, the quantitative results are linear and can be scaled. Given the many uncertainties involved in this estimation, the results need to be interpreted with caution. In practice, the effect of such a reallocation would also depend on the speed of its reallocation, an effect that is not possible to assess in the simple model employed here.

1. China’s reserves. At over $3 trillion and rising, China’s international reserves are by far the largest in the world. The portfolio composition of these reserves is not known, but is widely believed to be mainly in U.S. dollar assets, given the size and depth of U.S. financial markets. Senior Chinese policy makers have publicly ruled out a rapid change in the composition of China’s reserves. However, concerns expressed by them on the value of the dollar and the strength of U.S. policies, measures taken to promote the use of the renminbi in cross-border trade settlements, and calls for a more diverse international reserve currency system have fueled speculation that gradual diversification may occur.

2. Methodology. This chapter analyzes the potential impact on global yields of a shift in China’s reserve portfolio away from U.S. assets and into EM assets under a variety of scenarios and assumptions. In a baseline experiment, it is assumed that China reduces its holdings of U.S. reserves by $100 billon and increases its holdings of EM assets by the same amount. This reshuffling increases the stock of U.S. debt available in the market while reducing the stock of available EM debt. In equilibrium, these changes need to be absorbed by a representative global bond investor through changes in bond yields. This investor requires to be compensated for the required portfolio shift, as this affects the mean-variance characteristics of his portfolio (see Appendix I).

3. Results. Simulation results for a reallocation of China’s reserves from U.S. government bonds to EM government bonds by $100 billion are as follows (Figure).

  • First, increasing the market supply of U.S. debt increases yields by about 12 basis points. This effect is similar to the estimates of Warnock and Warnock (2009), who found that foreign purchases of U.S. Treasuries of 1 percent of GDP were associated with a 19 bps reduction in long rates. At 2009 GDP, this would correspond to an impact of 13 bps for a purchase of US$100 billion. On the other hand, the effect is larger than available estimates of the effect of U.S. quantitative easing. For instance, Gagnon, Raskin, Remache, and Sack (2010) estimated that Federal Reserve purchases between December 2008 and March 2010 of US$1.7 trillion of longer-term agency debt and mortgage-backed securities lowered longer term yields by 30–100 bps.

  • It also increases the yields on U.K., Euro Area and Japan debt by between around 20 and 35 basis points, while it reduces EM yields significantly (by some 200 points).

Experiment: China reduces holdings of US assets by $100 bn and increases holdings of EM assets by $100 bn

(change in basis

4. Robustness. To check the robustness of the results, a number of sensitivity analyses are undertaken, including: changes in risk aversion parameters; inclusion of U.S. agency debt in the pool of debt affected by the reallocation; consideration of alternative re-allocation scenarios; and estimation of yield means and variances over alternative sample periods.

Sensitivity Analysis

(change in basis)
  • Risk aversion. As would be expected, the magnitudes change slightly.

  • U.S. reserve assets. In the baseline, only U.S. government debt was considered as part of U.S. reserve assets. U.S. agency debt has long been considered a close substitute for U.S. government debt, given the implicit (and, more recently, explicit) government guarantee. If agency debt (around US$8 trillion at end 2009) is included in the global pool of public debt, then a US$100 billion shift by China out of U.S. debt represents a smaller portion of the global debt market, and as such it generates a smaller impact on yields (the impact is some 20 percent smaller).

  • Broader re-allocation. If, instead of investing entirely in EM debt, China were to spread its purchases equally across the U.K., Japan, the Euro Area, other AMs, and EMs (by US$20 billion each), then the impact of shifting out of China is smaller on both the U.S. and EM debt. (The impact on U.S. yields is lower because the market supply of debt that is closely substitutable for U.S. debt is reduced, causing demand for the latter to increase in the ensuing portfolio reallocation.) Yields on non-U.S., non-EM debt also fall in this experiment, given their reduced supply.

  • Shorter sample period. If expected returns and covariances are calculated with a shorter sample (post 2002 only), then the impact of the baseline portfolio shift is larger on U.S. and Japan yields and smaller on EM yields (and basically unchanged for others). This is because the 1990s were a turbulent period for many EMs, while the latter part of the sample has been relatively more turbulent for AMs (in relation to the longer sample). Thus, EM debt is perceived as less risky in a shorter sample, with the opposite being the case for AM debt.

  • Market debt. As discussed above, one of the assumptions underlying this exercise is that all the public debt that is not held as official reserves is considered as “being in the market” and priced according to the mean-variance framework. This may not be the case to the extent that a portion of the outstanding debt is held by financial institutions that follow passive investment strategies and hold their debt to maturity. Moreover, a portion of outstanding debt may not available to global investors (e.g., because of limited liquidity or other constraints). In this framework, the share of the debt that is not truly available in the market could be subtracted from the world stock of marketable securities, implying that a given nominal shift in China’s holdings would require a bigger re-shuffling in terms of portfolio shares (given the smaller base), and in turn proportionally higher yield adjustments.

5. Caveats. These results are subject to a number of caveats, including: the model’s focus, which is limited to mean-variance trade-offs; the sensitivity of the results to the estimation period; limited data availability; the model’s high-level approach, which abstracts from finer asset differences; and the static nature of the exercise, which does not allow for assessing the effect of more gradual shifts over time:

  • The mean-variance framework requires exogenous factors to account for the level of current global bond holdings. Under the reasonable assumption that these factors are stable, this framework can be used to assess the implications of changes in the stock of different debt securities. The model is less able to account for the level of yields themselves.

  • The results are sensitive to the estimation of expected value of returns and their covariance matrix. The sample includes in particular the last global crisis, a period of large and volatile changes in yields. Going forward, it is not clear in principle whether the sample means and variances over this period will be a benchmark for pricing.

  • Because of data constraints, EM bond market behavior is modeled on the EMBI segment. By construction, this is the most liquid segment of EM external debt. This may lead to underestimation of the impact of global shocks on EM bond markets, given the trend in recent years of increased foreign participation in domestic local currency debt markets, where liquidity may be lower and unevenly distributed across different segments.

  • There are also a number of issues involved in the calculation of the relevant stocks of outstanding bonds, for instance, whether private securities (such as corporate bonds) could be considered as close substitute of government securities.

  • In practice, the effect of such a reallocation of reserves would depend on more factors than simply the outstanding stock of securities. These factors, which are not included in the simple model considered here, include the speed of implementation, how this is communicated (or not) to the market, and how other official holders of U.S. dollar securities would react.

Appendix I. Methodology

1. Mean-variance framework. In a mean-variance framework, portfolio shares are chosen to maximize a quadratic utility function (see Neely, 2010):

where μ and V are the vector of expected (excess) returns and covariance matrix of returns, respectively; γ is a parameter of risk aversion; and w is the vector of portfolio allocations (as a share of total wealth). These shares are not constrained to sum to one because the portfolio constraint is met by investment/disinvestment in a risk-free asset.

2. Portfolio maximization yields the following relation between expected returns, their covariance matrix, and the optimal portfolio weights:

In equilibrium, this solution links expected returns to risk preferences (as summarized by γ), risk (as captured by V), and the supply of the risky assets included in the market portfolio (summarize by their shares, w). This relation is the basis for the simulations conducted this note in which the relative supplies of different bonds are affected by China’s decisions to reshuffle its holdings of reserve assets among different bonds.

3. Risk aversion. It is useful to relate the parameter γ to the standard Arrow-Pratt measure of relative risk-aversion, R(W). Simple algebra yields

where W is the wealth level at which risk aversion is evaluated, normalized to one in what follows. With this normalization, equation (3) determines a relationship between γ and R that allows for a calibration of γ for a range of values of relative risk aversion R, for which there is available empirical evidence. Results are presented for relative risk aversion ranging between 1 and 7, with 4 regarded as the “central” scenario.

4. Application to bond yields. In the simulations considered in this note, it is assumed that China reallocates its reserve assets by reducing its holdings of U.S. assets and purchasing EM assets. For a given bond k, equation (1) then implies that the change in real monthly return can be written as follows:

where vj,k denotes the covariance in monthly real returns between country j and k; Δμk is the change in equilibrium return for bond k; and Δwj is the change in the supply of asset j available in the market as a percentage of total wealth in the market.

For illustrative purposes, the term corresponding to U.S. bonds has been separated from the other countries. For example, equation (4) implies that an increase in the supply of U.S. bonds available in the market (Δwus > 0) will raise (reduce) the returns on those bonds whose returns are positively (negatively) correlated with U.S. returns, vk, us > 0 (vk, us < 0). The total impact is proportional to the change in the supply of U.S. bonds, the strength of the comovement between bond returns, and the parameter of risk aversion. Finally, changes in monthly real returns are translated into changes in annual yields by assuming that these changes are permanent.

5. Data and estimation. μ and V, the vector of expected (excess) returns and covariance matrix of returns, are calculated from total bond return indices for the countries or regions included in the exercise. For indices in U.S. dollars (the U.S. long-term bond and EM indices, for which the JPMorgan EMBI indices are used), a monthly real return is calculated by subtracting the U.S. monthly CPI inflation rate. For the indices in local currency (Germany for the Euro Area, Japan, United Kingdom, and Canada for other AMs), monthly nominal returns are first converted into U.S. returns using the monthly change in bilateral exchange rates. Finally, excess real returns are calculated by subtracting the U.S. short term rate. For the baseline calculations, the sample starts in 1991 for AM returns and 1995 for the EM index; the Middle East begins in 1998.

In principle, the equilibrium summarized in equation (2) applies to the stocks of financial assets that are outstanding in the market at a given point in time, expressed as a percentage of the world’s financial wealth that is allocated to different assets according to the mean-variance framework. Two assumptions were made to operationalize this approach. First, there is a representative world bond investor that decides global government bond allocations according to mean variance preferences defined over bond returns only. Second, reserve assets held by central banks are excluded from the pool of bonds whose returns are allocated according to the mean variance framework. The rationale for the latter is that reserve accumulation decisions by central banks are not made primarily according to the risk-return features of their reserve assets.

Data on outstanding stocks for public debt securities as of end 2009 were obtained from the Global Financial Stability Report, October 2010, Statistical Appendix, Table 3. This was combined with COFER data on the currency composition of world reserve assets, and with staff estimates of China’s net portfolio asset holdings (with the additional assumption that the latter reflect mostly holdings of official reserves). This yields the breakdown of public debt securities by issuer and market availability is presented in the chart below.

Public Debt Securities

(end 2009, US$ trillion)

1/ Does not include agency debt.

2/ Staff estimate based on China’s IIP, US TIC, CPIS.

3/ Does not included unallocated reserves.


    GagnonJosephMatthewRaskinJulieRemache and BrianSack2010Large-Scale Asset Purchases by the Federal Reserve: Did They Work?Federal Reserve Bank of New York Staff Report No. 441March.

    WarnockFrancis and VeronicaWarnock2009International capital flows and U.S. interest rates,Journal of International Money and Finance 282009 pp. 903919.

Prepared by Roberto Benelli (SPR).

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