Intertemporal diversification of sub-sovereign debt

The theorem on the value of corporate capital presented in the seminal papers by Modigliani and Miller (1958, 1963) states that in frictionless markets with the absence of taxes and bankruptcy costs the value of assets is unaffected by the capital structure of the firm. By extension, the costs associated with government debt will ultimately be covered by the taxpayers and the structure of government debt becomes irrelevant (Cochrane 2015). Taking the theorem to reality, it is obvious that some assumptions fail though and, conversely, that the structure of debt is relevant. Roll-over risk arises when a debt contract matures and then is renewed, or rolled over. Depending on the contract, roll-over risk can incorporate many types of risks such as uncertainty in the exchange rate or other foreign market frictions. The roll-over risk of a debt contract issued on the domestic market, in the domestic currency, can be decomposed into at least two parts. First, the risk that interest rates will be substantially higher at maturity relative to the initial debt contract, resulting in increased costs when the debt is refinanced. Second and arguably more hazardous, the risk that credit markets are illiquid at maturity, in which case refinancing becomes inaccessible and full repayment of the debt is required. Thus, high reliance on rolling over short-term debt increases the risk that the debt matures in a period when banks and capital markets are facing liquidity difficulties. Brennan and Schwartz (1978) present the first quantitative effort in modeling optimal leverage. They argue that bankruptcy is triggered when the firm’s asset value falls to the debt’s principal value. Leland (1994) argues that this type of bankruptcy is not the primary type observed in the economy and suggests that an additional bankruptcy trigger would be when firms are unable to raise sufficient funds to meet their current debt obligations. To derive a closed-form solution to the analytical model Leland assumes that debt is time independent, which he argues is equivalent to a debt contract being rolled over indefinitely. Modigliani and Miller (1958), Merton (1973) and Black and Cox (1976) all treat debt as having infinite maturity in different frameworks.

Asset-liability management (ALM) is the process of matching the cash flows of assets and liabilities in an effort to reduce risks. It is argued that ALM was developed in the late 1970s and early 1980s as a response to the heavy regulations imposed on US insurance companies (Financial Accounting Standards Board 1985; Ryan 2013). The time to maturity of debt is matched with the horizon of the investment; thus, there is no reliance on the rolling over of debt. This process is usually applied by banks, insurance companies and pension funds where both the asset and liabilities are primarily made up of financial securities. This makes matching more manageable since future cash flows of both are well defined and easily modifiable. For other institutions such as municipalities ALM becomes potentially more difficult. Swedish municipalities are prohibited to collateralize assets to live up to their debt obligations and by their nature public goods and services are illiquid which further complicates matching assets and liabilities. Additionally, Cochrane (2015) argues that although some of government assets are tangible, the bulk of assets are made up of the present value of an infinite stream of future tax revenues that are even more difficult to predict and internalize. For these institutions intertemporal diversification becomes a more suitable, albeit blunter tool for hedging against liquidity risk.

In theory, intertemporal diversification of a debt portfolio is the process of reducing the amount of debt maturing at each given point in time, given a set amount of debt. In practice, this implies taking on a large number of smaller loans and choosing a more disperse maturity structure. In terms of sector-wide liquidity shocks diversification of the maturity structure reduces the risk that a substantial share of the debt matures during each period, such that repayment can be covered without the need of refinancing. Thus, intertemporal diversification is a way to hedge against the systemic risk, i.e., a market-wide liquidity risk. Therefore, measures which describe the distributional characteristics of the debt maturity structure of a portfolio are also useful tools for evaluating the risks of said portfolio.

The strategy of intertemporal diversification is nothing new from an investment perspective. Dollar-cost averaging is an investment strategy that states that many small stock purchases at fixed amounts, with fixed time intervals, are beneficial from a risk mitigation perspective over a lump sum purchase. If stock prices are high, the fixed amount will buy the investor fewer stocks and vice versa. Dollar-cost averaging results in potentially lower returns compared to lump sum purchases but arguably comes at a lower downside risk. The criticism of dollar-cost averaging is based on the fact that stock markets historically have had a long-run upward trend, and therefore, it is optimal to purchase earlier rather than later. In the context of debt management, there is no obvious reason to assume that liquidity has a long-run upward trend. Thus, the criticism of dollar-cost averaging does not carry over to the process of intertemporal diversification of debt.

The optimal choice of debt maturity for corporations is a subject which has been addressed by numerous authors in the field of corporate finance, specifically contract theory. Early work by Myers (1977) suggests that short-term debt is optimal because long-term debt may lead to future underinvestment due to debt-holder claims on future cash flow.³ Unfortunately, this research is proven inapplicable on the subject of government debt maturity. The reason is that the intrinsic conflict of interest between debt and equity holders which gives rise to the debt overhang in the model is not present. This is not to say that there is no debt overhang problem present. One can easily see that high leverage and public spending by the current generation can pose debt overhang on future generations. The difference is that equity holders in the Myers model have the power to affect the amount of leverage that a firm undertakes while future generations have no power over the debt structure and public spending of the current generation. Therefore, we instead turn to empirical studies that focus on the debt maturity structure of sovereign states.

Some authors try to rationalize governments’ choices of debt maturity and their findings will be of use when constructing the models later in this paper. Missale and Blanchard (1994) investigate the evolution of the term structure of government debt of the OECD countries over a 30-year period from 1960 to 1990. They observe that term and amount of outstanding debt generally does not seem to have a strong relationship. However, when focusing on countries with debt-to-GNP ratios close to 100% the term of new debt is inversely related to the amount of outstanding debt. They conclude that in order to maintain the credibility of its anti-inflation stance the government may need to decrease the maturity of the debt as the amount of outstanding debt increases. Arguably, the explanation that is given by Missale and Blanchard is not related to the study of local governments since monetary policy is a central government issue. However, there could be multiple dimensions to this relationship not highlighted by the authors. One can assume that high levels of leverage can constrain the budget of the local government. In an effort to relieve this constraint by reducing the cost of borrowing the local government may choose to borrow and refinance at a shorter maturity.

Another explanation is given by Barro (1995, 1997) who argues that the type of debt that the government issues is of importance if there is uncertainty regarding real interest rates, level of public outlay and the tax base (aggregate consumption and GDP). The government may choose an appropriate maturity structure so as to smooth tax rates over different states of nature. For instance, the maturity structure of the debt can be designed so as to insulate the government’s financing costs from shifts in real interest rates. This implies that local governments with a volatile tax base may choose to diversify its maturity structure or borrow at a longer maturity. A long-term maturity structure gives leeway such that debt can be repaid prior to maturity at high-tax-revenue states of nature while new debt is undertaken in low-tax-revenue states. By this strategy the maturity may retain its long-term structure.

A more recent paper by Cestau (2010) finds empirical evidence for a U-shaped relationship between the share of short-term debt issued by sovereign states and the per capita income level. This suggests that countries with high and low income levels have on average a larger share of short-term debt compared to countries with medium income levels. The author argues that high-income countries, due to their creditworthiness, are less likely to face illiquidity and are therefore less concerned as regards to roll-over risk. Medium-income countries face a higher probability of market illiquidity and attempt to hedge against this risk by a larger share of long-term debt. Finally, low-income countries prefer to avoid the additional costs of long-term debt. Similarly to Barro, Cestau points out that the income of the population and by extension the tax revenues are of importance when the government chooses debt structure. Where they differ is that Cestau implies that the level of income is of primary importance, whereas Barro emphasizes the importance of the level of uncertainty of income.

Intertemporal diversification is a way to hedge against market-wide illiquidity, whereas diversification of creditors and financing channels is used when diversifying against idiosyncratic risks intrinsic to the creditors. Thierfelder (2008) argues that high-quality firms in addition to direct funding by debt securities utilize a backup line of credit in case of market illiquidity. Thus, credit institutions take the role of “lenders of last resort.” This can also be observed in the Swedish municipal sector where large municipalities that have access to direct funding by issuing debt securities also utilize other financing channels. Similarly, Gate and Strahan (2006) show that in times of market illiquidity credit institutions experience funding inflows, thus acting as safe havens. They argue that it is the ability to hedge against market-wide liquidity shocks that allows these institutions to supply credit even under these circumstances. A similar behavior could be observed for the Swedish municipal sector during the 2008–2009 financial crisis when Kommuninvest became the “lender of last resort.”

Finally, the effect of the political election cycle is discussed. The Swedish local governments, like all democratically elected governments, are faced with the political realities of running for office and potentially staying in office over multiple cycles. As shown by Nordhaus (1975), a sufficient level of current social investments is necessary to raise consumption for the next period, i.e., after the up-and-coming election. However, from the electorate’s point of view social investments are costly due to increased taxation and/or inflation. Therefore, social investments will be at a sub-optimal level and in equilibrium the social rate of return on public investments will be higher than for private investments due to the democratic myopia. Nordhaus also observes that there is a predictable pattern in policy over the incumbent’s term in office, starting with relative austerity and ending with the potlatch right before the election. In terms of local governments the conclusions do not perfectly follow. For instance, the individual local government policy effect on inflation is much less substantial than that of the central government. Small municipalities can be viewed as price takers that have no effect on inflation. Thus, increasing local public investments financed through debt does not have any obvious macroeconomic consumption costs from the perspective of the electorate. In the theoretical model the perfect democracy will make decisions that are against the interests of future generations. Social investments can be financed through new debt with no added cost in terms of consumption, and the risk of refinancing can be avoided by pushing repayment onto future generations. Therefore, it is expected that more long-term debt will be undertaken close to the election so as to supply the electorate with a more diversified basket of public goods and improve the public perception of the incumbent. This comes with an added cost in terms of a reduction of expected future consumption. However, although this kind of strategic maneuvering is not specifically prohibited in the legislation, it could be at odds with the overarching aim of the Swedish Local Government Act, specifically the principles of sound financial management and non-speculative action. Thus, this could deter such strategies from being applied. The Swedish Local Government Act is discussed further in next section.

The Swedish political system is divided into three levels of government: local, regional and national. The local government acts on a municipal level and is in closest proximity to the citizens. The municipal assembly is its highest decision-making entity and has final authority regarding questions of a financial nature such as budget, taxes, fees and liabilities. The municipal assembly is elected by the citizens every fourth year at the same time as the parliamentary elections. The areas of responsibility differ between the three tiers of government. Table 1 gives a detailed overview of responsibilities for the local and regional levels; the central government is omitted since Kommuninvest only issues loans to local and regional governments. The governments can choose freely how to supply their services, either by employing private companies or by subsidiaries. A majority of companies owned by local governments operate in capital intensive sectors, such as housing and energy. The time horizon of Swedish municipal investments is on average approximately 20 years (Kommuninvest (2017)).

The Swedish sub-sovereign governments have the constitutional right to self-governance with free right of decision-making in the context of their responsibilities. Swedish sub-nationals are required under the Swedish Local Government Act (Kommunallag 1991: 900) to operate in accordance with sound financial management. The rules laid out by the act are exercised by municipalities, counties and their subsidiaries. It entails setting up operational and financial goals and guidelines for the organization and the economic use of resources in both the short-and long-terms. The use of debt or the collateralization of assets to finance its operations is not considered consistent with sound financial management. Therefore, liabilities are only to be used for the funding of investments. The Local Government Act also states that sub-nationals are prohibited from partaking in activities of a speculative nature. A sub-sovereign government’s main purpose is supplying its residents with public services rather than profit seeking. However, in line with the Local Government Act and the principle of sound financial management a sub-sovereign government must present a budget surplus at the end of each fiscal year.

The freedom enjoyed by Swedish sub-nationals does not imply the freedom to default on debt. In 1992 the municipality of Haninge was unable to cover the unforeseen costs of one of its subsidiaries and came close to bankruptcy. The ordeal was resolved by a government bail-out of the municipality and the acquirement of the subsidiary. This was seen as a loan that the municipality of Haninge had to amortize. The government bail-out possibly sent a signal to creditors and investors that Swedish municipalities cannot go into bankruptcy. In addition, a Swedish district court decision stated that a municipality cannot cease to exist and that only the parliament can decide on the merger of two or more municipalities, in which case the assets and liabilities of one carries over to the others. Sub-sovereign governments are liable for all obligations they enter into, with all their tax power and their total assets. Swedish municipalities are autonomous and thus have the right to levy taxes and to set local fiscal policies. The amount and consistency of tax revenues are important factors that dictate the level of risk acceptance for the individual municipality.

In addition, a system for local governmental fiscal equalization has been implemented to ensure that local governments have equal basic conditions for providing their residents with public services. The system, one for municipalities and one for counties, is comprised of an income equalization and a cost equalization part. Income equalization is state-funded in the form of grants, and its primary purpose is to even out differences in the tax base of the local governments. The cost equalizations primary purpose is to even out differences in structural costs. The local governments with unfavorable cost structure are paid a cost equalization grant, while those with a favorable structure pay a charge. Both tax revenues and state grants are allowed to be used to cover both operational costs and expenditures for investments purposes. Equalization somewhat diminishes the effect of taxes on the risk acceptance of municipalities.

Swedish municipalities rely on issuing debt or taking on credit to finance large investments. Some of the larger actors have the option of issuing debt securities directly on the financial markets. Smaller municipalities usually lack the necessary investment volumes of their larger counterparts but can collectively establish in-house banks that issue debt securities on their behalf with the intent of pooling risks, thus reducing credit spreads and interest costs. The current main source of financing is loans from Kommuninvest of Sweden.

Kommuninvest of Sweden AB is a credit institution owned by Kommuninvest economic association. Its mission is to supply the Swedish municipalities, counties and their subsidiaries with sustainable, reliable and cost-efficient financing. All members face a common, non-negotiable price structure which is set by the 3-month STIBOR spot and swap rates in addition to a Kommuninvest specific margin which is more or less constant over the whole term structure. In addition, Kommuninvest has historically never restricted its lending for any of its products in contrast to commercial banks that may periodically refuse to finance loans of certain maturities. Membership is open but not obligatory to all Swedish municipalities and counties. As of June 2016 there are 274 member municipalities (out of 290 possible) and 11 member counties (out of 21 possible) (Kommuninvest 2017). All commitments entered into by Kommuninvest of Sweden are jointly guaranteed by its members. Each member contributes participation-capital based on a population model and has one vote regardless of size or contribution. Members decide on the overall direction of the organization and bear the ultimate responsibility. Even though the legal status of an economic association under Swedish law does not require the conformation to the Local Government Act, Kommuninvest has self-imposed to follow these regulations. Thus, for all intents and purposes Kommuninvest is viewed as a municipal subsidiary.

The organizational structure and pooling of risks is of importance in terms of the institution’s creditworthiness. Since 2002 Kommuninvest has received the highest credit rating by Moody’s rating house (Aaa) and likewise from Standard and Poor’s since 2006 (AAA). Another important factor is the organization’s funding strategy. According to its stated directive funding must exceed its lending by at least 15 and at most 35%. This excess liquidity is invested non-speculatively under active management with a low-risk profile so as to abide by the Local Government Act which prohibits financial speculation and requires sound financial management. The purpose of the liquidity portfolio is to be able to supply the sector with credit even in times of market illiquidity. Funding is relatively well diversified in terms of product diversity, maturity structure and issuing region. Main issuing regions are Sweden, Europe, USA, Australia and Japan. In addition, Kommuninvest is a member of Sveriges Riksbank’s RIX system for large payments (Sveriges Riksbank 2017a, b). This allows for the intraday lending in case of illiquidity.

The commercial banks have lost a large part of their market share over recent years whereas direct lending and financing through Kommuninvest have increased in relative terms. The evolution of the market share divided between the three financing sources is depicted in Fig. 1.

As of 2012 Kommuninvest is the largest financing channel of municipalities and counties in Sweden. As shown in Fig. 6 in “Appendix” there was a substantial inflow of new Kommuninvest members during the financial crisis, in particular in the year 2009 when 24 municipalities joined the organization. In 2008 14 new members joined. Comparing the 2-year average shows that the number of new members joining the organization was at its peak during the financial crisis.

In order to describe the maturity structure of the debt portfolios five measures are constructed. I propose the following measures which are primarily constructed to capture the different distributional characteristics of the maturity structure.

Weighted Standard Deviation of Time to Maturity⁴ :

Equation 1 is the weighted standard deviation of the time to maturity at the point in time \( t \), for municipality \( i \) where the sum of weights \( \sum\nolimits_{j = 1}^{n} {w_{i,t,j} } \) is equal to 1. \( M_{i,t,j} \) is the time to maturity of an active loan \( j \), \( \bar{M}^{w}_{i,t} \) is the weighted mean time to maturity for all active loans in the portfolio, and \( N_{i,t} \) is the number of active loans. Equation 3 represents the contract-specific weights where \( P_{i,t,j} \) is the loan-specific principal amount. The undiscounted principal amount is used in the dispersion calculations following the work of Choi et al. (2018).

Interquartile Range of Time to Maturity (IQ Range) is:

The dispersion measure as shown by Eq. 4 is the difference between the time to maturity of the 3rd and 1st quartiles, or equivalently the difference between the 75th and 25th percentiles. By construction this measure does not incorporate the 25% highest and lowest observations in the data and therefore does not include outliers.

Weighted Mean Interquartile Range of Time to Maturity (WMIQR (i), (ii)) is:

In order to take into account the size of each loan when calculating the range the above measure is constructed. Equation 5 represents the range between two weighted means. Equations 6 and 7 define two sets: A and B. Both are comprised of M and P pairs for municipal group \( i \), at time \( t \). Set A is conditioned upon that M is greater than or equal to quartile, \( Q_{x} \). Set B is conditioned upon that M is less than or equal to quartile, \( Q_{y} \). Weights are calculated over both sets by the principal values as shown by 8 and 9. Two measures are constructed using this method where \( Q_{x} \) and \( Q_{y} \) differ. First, \( Q_{x} \) represents the 3rd quartile, or the 75th percentile, and \( Q_{y} \) the 1st quartile, or the 25th percentile. Thus, by construction this measure only incorporates the 25% highest and lowest observations in the range calculation. Hereafter, this measure will be denoted the WMIQR (i). Second, \( Q_{x} = Q_{y} = Q_{2} \) where \( Q_{2} \) is the 2nd quartile, or the median. In contrast, this calculation incorporates all loans. This measure will be denoted WMIQR (ii).

In addition to the abovementioned intertemporal dispersion measures one supplementary measure is constructed to capture another distributional characteristics of the maturity structures.

Weighted Mean of Time to Maturity is:

\( \mu \) is the weighted mean of time to maturity of the municipal portfolio \( i \), at time \( t \). The sum of weights \( \sum\nolimits_{j = 1}^{n} {w_{i,t,j} } \) is equal to 1. The weighted mean is interpreted as a frequency variable which shows how often the debt is refinanced.

Table 4 in “Appendix” gives a summary of the time to maturity variable and the abovementioned measures. The average time which a municipal group is represented in the data is shown by \( {\bar{\text{T}}} \) and is approximately 153 months or 13 years. As previously discussed the portfolios of the municipal groups are characterized by a short maturity structure. The average time to maturity is overall 2.201 years and the average weighted mean is 2.210, suggesting that time to maturity and principal amount are positively correlated. This is due to the fact that the latter is weighted by the principal amounts and the former is not. However, when graphing the principal amount against the time to maturity for all loans as of June 1, 2016, the relationship is negative as shown in Fig. 3. Notice that the average values of Table 4 are calculated over the whole time series for all municipal groups while Fig. 3 is depicted at a certain point in time t. The intertemporal diversification as expressed by the standard deviation is 1.779 years. The short maturity structure in addition to a relatively low degree of intertemporal diversification suggests that large debt volumes are rolled over with a high frequency.

Per construction the IQ range is lower than the WMIQR (i); they take on the values, 2.324 and 3.571 years, respectively. The magnitude of the WMIQR (ii) depends on the dispersion of the maturity structure for all loans and their relative size. Since the WMIQR (ii) measure has a lower value compared to the IQ range, 2.253 and 2.324 years, respectively, it suggests that the principal amounts of loans closer to the median are larger in magnitude. However, this difference is relatively small. Moving “down” from the WMIQR (i) to the IQ range the dispersion falls with approximately 1.25 years.

Figures 4 and 5 depict the evolution of the measures over the 19-year period for the total sector debt portfolio, i.e., the measures are only calculated over \( t \) and \( i \) is omitted. These series are not used for the main analysis and should not be directly compared to the regression results. The figures are only intended to give a general overview of the evolution of the measures on a sector level.

All measures have negative trajectories for the initial 5 years after which they stabilize with some minor fluctuations. The period of the 2008–2009 financial crisis is illustrated by the two vertical lines. The weighted mean had a positive trajectory prior to the crisis which continued through the crisis period following a fall for the post-crisis period. The weighted standard deviation had a positive trajectory for the pre-crisis period and then started to fall prior to the crisis and continued its negative trajectory for the subsequent periods.

Figure 5 depicts the evolution of the three range measures over the same time period. The series for the three range measures are very similar. Dispersion started to greatly increase around the start of 2006 and continued its trajectory up to early 2008. During the crisis dispersion started to fall and continued to fall for the post-crisis period to once again stabilize around its 2002–2005 levels at the start of 2011.

In this part of the section robustness testing is conducted for the abovementioned fixed-effects model. First, we will run our regressions using least absolute deviation, thereby controlling for potential outliers. As previously discussed, there have been a large number of municipalities joining Kommuninvest over the years and that new memberships peaked during the financial crisis. In addition, the Kommuninvest market share has steadily been increasing over the years. Second, we will assess whether the inflow of new members or the rebalancing of municipal portfolios is causing the results or whether our findings are indeed driven by changes in municipal financing behavior.