The household debt ratio is an unsuitable risk measure – there are much better ones

New Ekonomistas post (in Swedish). Here is an English translation.

The Riksbank focuses one-sidedly on the debt ratio, household debt relative to disposable income, as a measure of any risks associated with household debt. An example is the Riksbank’s latest Economic Commentary on household debt, which is discussed in this post. But on a closer examination, the debt ratio is an unsuitable risk measure. There are much better ones. And they give a very different picture of the risks associated with household debt.  Why the debt ratio would be a good risk measure is justified by the Riksbank in this way:

As most households pay their borrowing costs using their current incomes rather than their assets, the debt ratio, that is debts in relation to disposable incomes, is often used as an illustrative measure. (Speech by Skingsley, page 2)

Thus, the Riksbank maintains that household debt is an “illustrative measure of risk” and implies that a higher debt ratio implies a higher risk. But this is of course not the case. Any risks associated with household debt depends on such factors as the households’ total balance sheets, including their loan-to-value (LTV) ratio and the ratio of net wealth to total assets, and, in particular, on the households’ repayment capacity and resilience to disturbances, which Finansinspektionen (the Swedish FSA) presents in its regular Mortgage Market Report.

Borrowing-cost measures

The Riksbank’s justification above is furthermore a justification for relating the borrowing cost, rather than debt, to disposable income. One measure of this is what is called the interest ratio, average interest payments relative to disposable income. This is reported, for instance, in the Riksbank’s report Financial Stability.


Source: Financial Stability 2013:2, Sveriges Riksbank.

The Riksbank is making a great fuss about the debt ratio, now at about 170 percent of disposable income, being historically high. But the interest ratio, which is a better measure of the borrowing costs than the debt ratio, is thus not historically high but somewhat lower than the average 1971-2013.

The debt ratio is a problematic measure of risks associated with debt from a more general point of view, because it is a relation between a stock, debt, and a flow, disposable income. It is generally better to relate stocks to stocks and flows to flows. The interest ratio is a relation between two flows, interest payments and disposable income.

The interest ratio, currently about 4 percent, refers to aggregate household debt and aggregate disposable income. One can do alternative calculations of the interest ratio with alternative assumptions for individual households.

Is a debt ratio of 300 percent problematic?

The Riksbank is making a great fuss about the obvious circumstance that the debt ratio among households with debt is higher than the aggregate debt ratio, the average debt ratio for households both with and without debt. The debt ratio for households with debt is according to the Riksbank about 300 percent, compared to about 170 percent for all households.

Is 300 percent a problematic and too high debt ratio? What are the borrowing costs for such a debt ratio? Swedish mortgage rates are today lower than 3 percent. Assume instead a substantially higher mortgage rate of 7 percent. (According to Finansinspektionen’s Mortgage Market Report the banks use an assumed mortgage rate of about 7 percent to assess the borrowers’ repayment capacity.) Then the mortgage rate after a 30 percent tax deduction is 0,7*7 = 4,9 percent, about 5 percent.

This implies a nominal interest payment of about 0,05*300 = 15 percent of disposable income. Is this high or low? What should one compare with? On possible comparison is the 28 percent of disposable income that according to Statistics Sweden was the average housing expenses for rented apartments in Sweden 2012. Then 15 percent is obviously much less, even if fees paid to the housing cooperative (“bostadsrättsförening” in Swedish) are added for owner-occupied apartments. The nominal interest payment is the interest payment that keeps the nominal debt constant. With positive inflation, the real debt then falls over time.

The nominal interest payment may be relevant for borrowing- and liquidity-constrained households. But for households that are not liquidity-constrained, the real interest payment, the interest payment that is required to keep the real debt constant, is more relevant than the nominal. With an inflation rate of 2 percent, the real mortgage rate after tax is 5 – 2 = 3 percent. Then the real interest payment is only 0,03*300 = 9 percent of disposable income. (This assumes that the Riksbank in the future keeps inflation on average at 2 percent, on contrast to what has been the case so far, see here and here.)

But this calculation disregards real growth of disposable income. The real interest payment keeps the real debt constant. If real disposable income grows over time, the debt ratio will fall over time. To assess whether or not a particular debt ratio is sustainable in the long run, one can calculate the debt service that keeps the debt ratio constant. This can be done precisely as one does with the so-called debt equation to assess whether or not a particular country’s public debt is sustainable. According to the debt equation, it is then the difference between the real after-tax mortgage rate and the real growth rate of disposable income that the debt ratio shall be multiplied by. Then the debt service that keeps the debt ratio is constant is only (3-2)*300 = 3 percent of disposable income.

These results on borrowing costs for a debt ratio of 300 percent are summarized in table 1 below. They indicate that a debt ratio of 300 percent need not be problematic and is sustainable in the long run with a margin. table-1-borrowing-costs-for-debt-ratio-300-percent

Balance sheet measures

Other more relevant measures of risk than the debt ratio can be constructed by relating the debt to other stocks in the households’ balance sheets, such as the value of the households’ housing or their total assets, as is also discussed in this post (in Swedish only).

As is well known from the figure below from the Riksbank’s report Financial Stability, the households’ real and financial assets have grown relative to disposable income in parallel and somewhat faster than the household debt (by real assets is meant the households’ owner-occupied houses, owner-occupied apartments, and leisure homes). Household debt relative to income is historically high, but so are the households’ real and financial assets and their net wealth. Swedish households have never been richer than now.

An increase of debt, assets, and net wealth relative to disposable income makes households rather more resilient to disturbances, not more vulnerable, as is discussed in this post.


Source: Financial Stability 2013:2, Sveriges Riksbank.

From the data in the above figure, the households’ aggregate LTV ratio, their debt over their real assets, can be calculated. It is illustrated in the figure below. We see that households’ LTV ratio is far from historically high but instead lower than the average for 1971-2013.


Source: Financial Stability 2013:2, Sveriges Riksbank.

From the same data, one can also calculate the households’ net wealth relative to their total assets (excluding collective pensions). It is not lower than its historical average but higher, at about 70 percent.


Source: Financial Stability 2013:2, Sveriges Riksbank.

When it comes to the distribution of debt and assets across different households, there are no disaggregated data on assets available after 2007. The distribution in 2007 and the disaggregated household balance sheets are discussed in this post (in Swedish only). Those disaggregated data are hardly a cause for concern about household debt.

Debt in relation to human capital instead of disposable income

The debt ratio is, as said above, problematic because it relates a stock (debt), to a flow (disposable income). The natural stock related to the flow of disposable income is what is called human capital, the present value of current and future disposable income. With 3 percent real interest rate after tax and 2 percent real growth of disposable income, the present value of 25 years of future disposable income is about 22 times current disposable income.

Arguably, a better measure than debt relative to disposable income is debt relative to human capital. One can see this as the LTV ratio for the human capital.

A debt ratio of 300 percent of disposable income is then an LTV ratio of 3/22 = 14 percent of human capital. But the household’s assets include not only its human capital but also its real and financial assets. When these are taken into account, the LTV ratio is of course even lower. This is further discussed in this post and this paper.

New borrowers’ LTV ratio, repayment capacity, and resilience to disturbances

Finansinspektionen’s Mortgage Market Report gives a detailed picture of the new borrowers LTV ratios, repayment capacity, and resilience to disturbances in the form of mortgage-rate increases, housing-price falls, and income falls due to unemployment. New borrowers are realistically more vulnerable than old borrowers, who have seen their debt rations and LTV ratios fall because of higher disposable income and higher housing prices.

The new borrowers’ average LTV ratio has the last few years stabilized around 70 percent, as shown in the figure below. An average equity of 30 percent for new borrowers is a substantial buffer.


Source: The Swedish Mortgage Market 2014, Finansinspektionen.

Finansinspektionen analyzes the new borrowers’ LTV ratios, repayment capacities, and resilience to disturbances in considerable detail. It concludes that the new borrowers’ repayment capacity and resilience to disturbances are good. Finansinspektionen’s detailed information about the new borrowers’ repayment capacity and resilience to disturbances is in my mind currently the most reliable and relevant measures of risks associated with household indebtedness.

Altogether, these better risk measures than the debt ratio all give a completely different picture than the debt ratio about the any risks associated with household indebtedness. There are good reasons to tone down – or rather abolish – the debt ratio as a risk measure.