The Instability of the Market for Government Bonds in the EMU

3.1 Benchmark: Monopolistic Safe Asset

Safe assets have a unique position in the financial system based on legal requirements, contractual norms, or benchmarking. To offer different risk classes to different investors, insurance companies and funds often announce a share of safe assets to characterize their portfolios. This directly follows from modern portfolio theory, which shows that mean-variance–efficient portfolios can be formed as a combination of holdings of the risk-free asset and holdings of a portfolio that contains only risky assets. Differences in risk aversion translate to different shares of risk-free assets in the portfolio (Merton 1972; Tobin 1958). Portfolio choice is separated into two stages: the construction of the optimal risky portfolio and the share of the safe asset in investment. The choice of this safe asset in the context of a currency union is especially noteworthy.

This asset needs to be simple, not “information intense.” Within countries, particularly advanced countries, the government bond functions as this asset. This one asset serves as the ultimate storage of value and as a benchmark. Benchmarking is important in this respect since “an asset is [only] safe if others expect it to be safe” (Caballero, Farhi, and Gourinchas 2017: 30): reputation and history matter. This explains the strong effect of inertia as a determinant of safe assets, found by Habib, Stracca, and Venditti (2020). Depending on their risk preference and on the relative price of the safe asset, investors or intermediaries on behalf of them invest in the safe asset. Together with the other reasons to hold safe assets (collateral in the interbank market, a requirement for central banks), the share of risk-free assets in the portfolio held by investors determines the demand for safe assets. The size of the market for government bonds is given by governments in need of financing, which is given at any point in time but has strongly increased over the last three decades.

For all these, I treat the market for government bonds as a differentiated sub-market of the financial market. In secondary markets of government bonds, prices adjust continuously such that demand equals supply. New information affects risk assessments, consumption opportunities (yacht, car), and other investment opportunities (land, real estate) requires the reshuffling of wealth, gifts, and requests to transfer wealth to other people. Insurance contracts end, and new one are agreed on; thus, the demand for safe assets changes continuously. If the demand for safe assets exceeds the supply at a given price, not all potential investors asking for a safe asset can buy one. At a higher price, however, the market clears. The last transaction always gives the market price.

Demand for the safe asset results from investor i, who sees her willingness to pay v _i exceeding price p of the government bond that serves as safe asset.^[4] Moreover, the investment must be preferable to the best alternative investment with net value v _io − p _o , v _i − p > v _io − p _o . Supply results from government bond holder j, who has an alternative usage of his wealth, v _j < v _jo − p _o + p. Demand for the safe asset falls in price p, while supply increases in p. The size of the market changes if the government issues new bonds. New bonds need demand, which might affect prices. Thus, the demand for government bonds reads as

In most of the European countries forming the EMS, domestic investors held the vast majority of the government bonds. Overall, a European market for government bonds did not exist; government bonds were traded on national markets.^[5] With the final fixing of the exchange rate in 1998, the bond market became one European (EMU) market where bonds issued by different governments but all in the same currency are traded at the same time. Concerning their investment in “safe assets”, investors changed from sorting by nationality to sorting by risk aversion.

3.2 The Safe Asset Choice in the EMS

Since there are more government bonds than only the domestic one, there is no reason to invest in domestic government bonds and use them as safe assets and as a benchmark. Instead, a foreign government bond could be used if it provides higher value. To illustrate this, I consider two countries, k and l, issuing bonds in different currencies. Investing in bond k involves additional transaction costs c ^er and additional exchange rate risk r i e r for an investor who lives in country l but not for an investor who lives in k. Thus, decision (1) to buy bond k D _i,k = 1 changes to the following:

For both, in addition, it must hold that the investment in the k-bond is preferable to an investment in the outside option.

According to (2), investments in bonds of the government in k by investors from l are less likely than from investors living in k because of the higher costs c e r + r i e r that l-located investors incur when buying k-bonds. While “market expectations” of a change of the exchange rate are included in the price of the bonds, the individual component of risk-averse investors r i e r remains. Moreover, simplicity–not to bother with a foreign currency and exchange rate expectations–favors investment in the government bond from the home country. Incentives for an investor living in k to sell a k-bond and switch to a l-bond are smaller than in the one-currency world, because the comparison v i k − p k < v i l − p l − c e r − r i e r is tilted towards keeping k. There is a home bias in investments in government bonds; k-bond investors in l must have a particularly large willingness v _jk to pay for the k-bond. With national currencies, the bond in the national currency was the safe asset.

When the exchange rate risk reemerged in the EMU in 2010, investors adjusted their portfolios. After trade, less foreigners from country k held l-bonds. The share of k residents offering k-bonds, in contrast, was smaller than in the single-currency world. Thus, transaction costs and exchange rate risk yield sorting mainly along the home currency. The arguments from above concerning the risk remain, but the investor-bond-specific components must be particularly large to overcome the home bias introduced by the different currencies.

3.3 Bid and Ask Decisions with Two Bond Markets

The investor makes a discrete choice to decide which bond to use for saving. She compares the difference of her willingness to pay and the price of the bond of country k v _ik − p _k , to this difference for country l v _il − p _l taking into account the costs related to the transactions involving two currencies c ^er and risk r ̄ e r .^[6] Moreover, there is an outside option generating net value v _io − p _o . For simplicity, I assume that both bonds have the same face value and maturity and that every investor cares only for one unit.

Demand depends on the prices of both bonds p _k and p _l which are endogenous variables in the market but exogenous from the perspective of the investor. While the demand for the government bond of country k falls in the own price, it is positively affected by the price of the “substitute”, the bond of the government from l. v _ik and v _il vary with changes in the economic conditions and the evaluation and expectations of these conditions in the future.

The probability that investor i located in country k bids for bond k depends on i’s willingness to pay v _ik and v _il , which are investor specific and at least in parts unknown. Let us denote the known part of the willingness, the attractiveness of bond k, by ν ̄ k und the unknown part by ɛ _ik which collects all unknown elements of the willingness to pay and the individual risk component r i k e r , which is zero for a resident of k. The attractiveness of bond k is proxied by political stability, fiscal stability, the size of the bond market, a stable financial system, and external stability and inertia in empirical studies (see Habib, Stracca, and Venditti 2020). While the realization of ɛ _ik is unknown, I assume that the unknown components of all investors are drawn from the same known distribution with a known mean and a positive variance σ ². Let r ̄ k l e r be the difference of the sample means of the unknown investor-bond – specific components of the two bonds and r ̄ k k e r be zero. If the residuals would be i.i.d. and assumed to be double-exponentially distributed, the relative demand of the different bonds at given prices is given by the multinomial logit.^[7]

where μ is a positive constant and c k k e r = c l l e r = 0 . The probability that investor i chooses bond k increases in the attractiveness of bond k ν _k and decreases in its price p _k . The probability to choose bond k, however, is also positively affected by price p _l , the cost of exchanging currencies c k l e r and the average risk aversion r ̄ k l e r , and negatively by the attractiveness of bond l. The probabilities of choosing bond k, bond l, and the outside option o add to one. Thus, the probabilities give market shares.

The probability differs from an investor from country l, as seen above, when discussing the home bias. The probability of an l investor to invest in a k-bond is given by

All else equal, this probability is smaller than probability (3) of a k resident for transaction costs and exchange rate risk.

If no new debts are issued by the government, the supply of bond k depends on the bond offers of k-holders. Holders of k-bonds might decide to invest in bond l given the prices or in the outside alternative, which offers the expected net payoff v _io − p _o . The probability P i k − sale that bond k is offered by a k-bond holder in k is given by a multinomial logit again. It equals the sum of the probabilities that the outside option or the l-bond is preferred.

The supply of k-bonds depends not only on the own characteristics p _k and ν ̄ k but also on the characteristics of the substitute l-bond p _l and ν ̄ l and on costs and obstacles to work with two currencies c k l e r and r ̄ k l e r . Since k and l are substitutes as safe assets, any change in k’s characteristics affects the supply of l.

3.4 Equilibrium Prices

At the secondary market, a transaction of bond k takes place if a supply of bond k finds an investor who wants to buy it at the proposed price p _k . Let N _h be the number of investors in country h. Multiplying the probability to bid for bond k P j h k with the number of investors N _h gives the demand for the k-bond from country h. The supply is given by the product of the probability to sell P h k − sale and M h k , the number of k-bonds held by investors in h. Market equilibrium is given by

The equilibrium (6) determines price p _k jointly with an equilibrium condition for the l-bond. The probabilities P ^h are functions of both prices, p _k and p _l , and of the net value of the outside option.

If transaction costs c ^er are significant and investors are risk averse, there is a home bias in government bond holdings even with fixed exchange rates, as in the EMS. This is not the case in a currency union, where the exchange rate risk disappears and differences in the probabilities between investors from different countries vanish.

4.1 Bid and Ask Decisions in the EMU Bond Market

To see the consequences of the Europeanization of the market, assume there are two countries with two government bonds denoted in the same currency. Savers do not have a systematic nationality preference and want to use the bond to shift consumption opportunities into the future. They choose the instrument with the better risk–return characteristics. The choice between the bonds differs from (2) because no exchange rate risk and no transaction costs bias the decision in favor of the home bond. The probability to invest in the bond from country k does, therefore, not depend on the residency of the investor.

Interdependencies between the government bonds are therefore stronger than with “national currencies” in the fixed exchange rate regime. Adjustments of bond holdings are done mainly in reaction to bond price changes and changes in the expectations about future bond prices that enter the willingness to pay. The supply of bond k depends on investors’ willingness to sell bond k if no new debt is issued.

Here too, nothing differentiates domestic investors’ decisions from those by investors from other countries.

4.2 Self-Selection Based on Risk Sensitivity

Without home bias, investors choose only with respect to return and risk. As investors differing in risk aversion choose a portfolio with systematically different fractions of the safe asset, investors differing in risk aversion also self-select into holding different government bonds. This yields a sorting of the “safe assets”, which may be reflected in their price. The prices of government bonds in the EMU are more affected by other bonds’ prices than in a fixed exchange rate system such as the EMS. Prices have a structure such that the price of a bond that is perceived as “safer” cannot be lower than the price of a “riskier bond”. Investors do not sort according to currencies but according to risk and return.

Recall that the probability that i chooses to bid for a bond of country k in (7) depends on the attractiveness ν ̄ k of bond k, the observable part of investors’ willingnesses to pay. Investor i’s willingness to pay v _ik is investor bond specific, and at least in parts, unknown. A systematic effect in the unknown components of two bonds, k and l, stems from differences in risk and the individual translation of risk differences in the willingness to pay of investor i.

Bidders for bond k in (7) are, at given prices p _k and p _l and a given value v ̄ i o of the outside option, characterized by an investor-specific component ɛ _ik which is particularly large. Since ɛ _ik increases in the investor’s risk sensitivity, the group of bidders for bond k includes investors who are particularly risk sensitive if bond k is perceived as a less risky investment. If, in contrast, bond l is attractive for an investor j, the investor sells bond k if she holds it and bids for bond l instead. At given prices p _k and p _l , this applies to less risk-sensitive investors. The outside option is, by assumption the most risky, accounting for the fact that government bonds are “risk-free assets”.

Two aspects become apparent in this discussion: (i) investors self-select into a particular bond according to their individual risk sensitivity, and (ii) in contrast to the simplifying assumption above, the residuals ɛ _ik and ɛ _il are therefore not independent.^[8] Since the correlation is negative, higher ɛ _ik are more likely to come with lower ɛ _il than under independence, which increases the absolute expected value of the difference ɛ _il − ɛ _ik and increases the probability to choose bond k for investors with a high risk sensitivity. Sorting along risk sensitivity is more pronounced with negatively correlated residuals.

Thus, before trade at a given price difference, the group of investors offering bond k and the group of investors bidding for bond k differ systematically in their realization of the unknown investor-specific part ɛ _i = ɛ _il − ɛ _ik . Risk-sensitive investors bid for bond k, while less risk-sensitive or even risk-neutral investors (large ɛ _i ) offer bond k. There is a potential for gains from trade even at unchanged prices if the numbers of investors on both sides of the market are not too different. After trade, the price might be unchanged, but the distribution of investors holding k and those holding l is not the same as before trade. Trade facilitates a self-selection into groups of investors differing with respect to their risk sensitivity, which is reflected in the differences of the bonds the investors hold.

4.3 Sorting at Unchanged Prices

There is a critical ε ̲ below which all investors, who are characterized by such an investor-specific component ɛ _i , bid for bond k. Investors characterized by ɛ _i values above ε ̲ bid for bond l or the outside option. The group of bond k holders consists of investors with unknown components between ε ̲ and −∞, whereas the group of new bond l holders consists of investors with unknown components above ε ̲ . Investors with the largest ɛ choose the outside option. I denote the ɛ that makes an investor indifferent between the l-bond and the outside option by ε ̂ . Thus, the group of new investors holding l-bonds consists of investors with investor-specific components between ε ̲ and ε ̂ . Investors who hold bond k with a realization ɛ _i smaller than ε ̲ , keep bond k, while those with a realization above offer their bonds. Among l-holders, investors who want to sell bond l and bid for bond k are characterized by a ɛ that is smaller than ε ̲ . Figure 3 visualizes the different cutoff values.

Figure 3:

Self-selection along risk sensitivity after trade at unchanged prices.

There are three groups of investors in government bonds in this model: (1) investors who hold k-bonds, (2) investors who hold l-bonds, and (3) investors who would like to hold either a k- or l-bond but do not hold one yet. The relative size of the group depends on the price difference, on the relative attractiveness of the two bonds, and on the total amount of bonds issued by the governments in countries k and l. The size and composition of the groups, in turn, affect the excess demand or excess supply of the bonds and, therefore, the direction of price change. While the size of the groups is exogenously determined by the supply of bonds, the composition of the holders is endogenous and can change even if there are no changes in prices.

The supply of bond k on the secondary market at price p _k is given as the product of the size M ^k of the group of k-holders and the fraction of those who are willing to sell their bonds P i , E M U k − sale . The supply depends on the composition of k-holders because the composition of the group determines the supply at a given critical value ε ̲ . If all k-holders are characterized by ε i > ε ̲ , all offer their bonds, and the supply equals M ^k . If all k-holders are characterized by ε i < ε ̲ , the supply is zero. Hence, the composition of the group is decisive.

At any given time t, group size, group composition, and price p _k,t are predetermined; price p _k,t is the price of the last transaction. At p _k,t two investors can agree on the transactions at the prevailing price. That leaves the price unaffected but changes the composition of bond holders of each group. If there are P i , E M U k − sale * M k investors willing to sell at p _k,t and P i , E M U k * N bidders (where N denotes the number of investors), there will be trade at p _k,t at the size of the smaller market side.

Suppose there are more bidders than sellers. P i , E M U k − sale * M k k -bonds change the owner. These include all k-holders with ε i > ε ̲ who are after trade not in the group of k-holders anymore. Thus, the group includes more risk-sensitive investors after trade than before trade. The group of investors who have chosen the outside option is less risk sensitive after trade.

4.4 Price Changes

After trade, the distributions of the two groups holding different bonds differ significantly if the perceived risk of the bonds differs. The gains from trade have been realized, and no further transaction can be agreed on at given prices. No k-holder is willing to sell her bond if, as assumed above, there are more buyers than sellers of k-bonds at p _k and p _l . There are potential buyers of bond k at p _k but no seller. These potential buyers could offer a higher price for the k-bond to find a k-holder who agrees to sell at the higher price. The new price offer changes the selling decision. Investors with the smallest individual component ɛ _i might be willing to offer bond k at the new (higher) price. The buyer is necessarily characterized by an investor-specific component that is smaller than ε ̲ . Thus, ε ̲ falls.

The supply of bond k is fixed by government debt in country k, while demand in the secondary market depends on the price of the asset and on the composition of the different groups holding different assets. Price increases of bond k reduce and, in equilibrium, remove excess demand. The price adjustment of bond l removes excess demand for bond l. If no new bonds are issued and the supply of the outside option does not change, the market shares of the assets do not change with the new prices if every investor holds as many assets as before. The distribution of the individual risk-sensitivity component, however, changes in a systematic way.^[9]

4.5 Equilibrium Prices

Demand for each bond equals supply in equilibrium. It holds, that

which determines the prices p _k and p _l at the start of the next period. The probabilities P are functions of both prices p _k and p _l and the value of the outside option as derived above. Relative prices affect the size of the groups that sell or buy one of the government bonds. This interrelationship reflects the fact that in a currency area, the government bonds of the different countries compete with one another while they only interact with the outside option if they have a “monopoly” as a safe asset in a national currency setting.

The interaction with the outside option determines the price of the safe asset and the price of the outside option. Since in equilibrium the demand of the safe asset equals the supply and the supply is given by the amount of government debts, the two prices determine the size market segment for the safe asset. In the EMU, the price of the “most risky safe asset” and the price of the outside option are most affected by the market size of the safe assets. In the example with only two safe assets, market size strongly affects p _l and p _o . If not all government bonds are bought, sellers reduce the price p _l to increase the “attractiveness” of an investment in bond l.

In equilibrium, the prices of the two bonds can therefore be the same, or they can deviate. They are the same if the higher-risk-government bond is demanded enough to meet the supply even without compensation for the higher risk. If the demand for the risky bond is smaller than the supply, the prices must be lower, and the investors must be compensated for the higher risk by higher interest rates. Therefore, the government bond that is perceived as less risky (here k) cannot be cheaper than the riskier bond (here l). Thus, p _k ≥ p _l . This ordering has been observed for the government bonds of the EMU countries since 2007. Before, we had seen the same price for government bonds in the EMU even if the country risk was perceived as different.

5.1 Price Convergence and the Europeanization of Government Bond Holdings

Sorting with respect to currencies vanished with the introduction of the euro and the Europeanization of bond portfolios. Figure 2 illustrates this well. The home bias retreated. The probability that investor i from country k bids for the l-bond was no longer affected by transaction costs c ^er and the exchange rate risk r i e r . However, bonds were less differentiated since they were all issued in the same currency. This homogenization yielded tougher competition in the sense that the government bonds of different countries in the euro area became close substitutes.

Without devaluation risk, high-interest-rate bonds from governments in the southern European countries were attractive for financial institutes in the lower-interest-rate countries in the north of Europe. In aggregate, the demand for high-interest-rate-bearing bonds exceeded the supply such that their interest rates fell (see Figure 1). The share of foreign investors increased. Hence, in the period between 1998 and 2003, the excess demand for high-interest-rate-bearing bonds brought their prices up and interest rates down. This is shown in Section 3.5, where price changes result if bidders offer a higher price in order to (i) outbid competitors and (ii) lure bond holders to sell. The excess demand for formerly high-interest-rate-bearing bonds shrink with trade. A rising price makes the bonds relatively less attractive for investors. There is sorting with respect to risk sensitivity, with less risk-sensitive investors more likely to invest in (formerly) high-interest-rate-bearing bonds.

5.2 The Financial Crisis, the Euro Crisis, and the Reemergence of the Exchange Rate Risk

In the financial crisis, the default risk of sovereign debts became an issue in the EMU. Interest rates differentiated because some governments had to compensate investors for the additional risk. Other governments gained from the investors’ need to find an alternative safe investment. Thus, the interest rates on government bonds reacted differently to the reduction of the policy rate by the ECB after September 2008 (see Figure 1). The large additional demand of financial resources by the governments was met in some countries at higher interest rates, while other countries, in particular Germany and France, gained from their supply of a perceived risk-free asset in the financial crisis (“flight to quality”). Thus, the perceived default risk of the sovereign was priced in when the euro crisis started in the spring of 2010.

In that spring, the sustainability of the Greek debt stock was doubted. Moreover, it was not certain that Greece would remain in the EMU. This increased the default risk and reintroduced the exchange rate risk for Greek government bonds. No resorting could be found at existing prices since the investors had already self-selected in the different groups. The higher risk, must have been compensated by higher nominal interest rates for government bonds. The Greek government experienced this already during the financial crisis (2.9 % points spread in March 2009).^[10]

However, in the spring of 2010, whether Greece could remain in the EMU was questioned. Foreign investors faced the exchange rate risk again, while Greek investors did not. For foreigners, the Greek bond lost attractiveness, and many left the Greek bond market. The Greek bonds sold by foreign investors must have been bought by Greek investors, yet for these Greek investors, foreign bonds did not become less attractive and Greek bonds not more. Thus, they were willing to buy the bonds only at a lower price.^[11]

The marginal investor does not need large price changes to reconsider her choice and choose bond l. However, with three out of four Greek bonds held by foreigners, the marginal bond holder is rather likely to be a foreigner. Nonetheless, all foreigners faced the Grexit risk. Thus, to convince the marginal investor was not enough, if three out of four investors reconsidered their investment yet, to persuade investors with a large risk sensitivity, a larger price reduction was needed. This explains the strong increase in interest rates within a rather short time. Interest rates increased from 6 % at the end of January 2010 rather steadily to 12 % at the end of 2010 and 21 % at the end of 2011.^[12] Also for Spain, the increase in the spread of interest rates on government bonds over German government bond’s interest rates went along with the flight of foreign investors from the Spanish government bond market, as Figure 4, which is taken from Amor and del Val (2019), shows.

Figure 4:

Risk premium and non-residents debt holding.

5.3 Stabilization by the ECB

Exit risk is one-sided. The currency of the exiting country is expected to depreciate heavily. Investors are likely to incur some re-evaluation losses. These are particularly pronounced for foreigners who do not want to consume in the new currency. However, residents from the exiting country could also isolate from devaluation losses by keeping euro-denominated safe assets. Given a positive exit risk, the government bond is not perceived as a safe asset anymore,^[13] yet risky assets pay a risk premium that might render the government debts of the country perceived as exit candidates unsustainable.

Among the euro-denominated government bonds, the Greek bond has been the most risky. Since not enough Greek investors could be found, other EMU members’ governments stepped in, and later, the IMF helped out. However, low prices alone did not help, since they went hand in hand with risk increases. It took an engagement of the ECB and ECB president Draghi’s promise to do “whatever it takes” to stabilize the sovereign bond crisis in Europe. If investors can be sure that the ECB buys the bonds when they want to sell them, the risk is gone. Since 2015, the interest rate spreads of EMU countries over German government bonds have been very modest, and German interest rates have been negative since the beginning of 2019. The ECB, however, holds a large share of the government bonds now, as reported in Table 1. It cannot continue to do this if price stability remains an objective of the ECB. In the summer of 2022, the interventions stopped, and interest rate spreads increased again.

However, the question is this: how much does the market outcome with the ECB’s “abstinence” depend on expectations about future ECB interventions? Private investors’ willingness to invest depends certainly on the expectation about a future fire sale. The TPI addresses this. If the function of a government bond as the risk-free asset is lost, sovereign debt becomes an asset as others. A government bond also loses the characteristic of a risk-free asset if these functions are taken up by bonds from another country (see DeGrauwe (2011), comparing Spain and the UK).

The TPI, however, is not the solution for the institutional difficulties in the EMU. It can buy time because it allows to conduct monetary policy and protect the coherence of the EMU. However, for a sustainable solution, member countries must admit that there is also interdependence in fiscal policy. This would help rearrange stabilization policies in the EMU such that the supra-national level assumes more responsibility. This is necessarily related to intra-EMU transfers and requires a new institutional setup. The ECB’s need for the TPI must call for initiatives on a new institutional framework of stabilization policies in the EMU.^[14]

Central banks are lenders of last resort. They stabilize the banking system and ensure in crisis times that government bonds find demand at a price that keeps government debts sustainable. The Bank of England has just acted like this. Yet, this is ruled out in the EMU. The ECB is not allowed to buy government bonds directly. Purchases at the secondary market had been limited and balanced across countries. Thus, the ECB cannot act as a lender of last resort. The TPI aims at mitigating the problem.