Denmark’s move to a holistic and dynamic risk budget

The primary purpose of the reserves is to ensure the National Bank of Denmark will be able to intervene to support the fixed exchange rate policy. Moreover, reserves must be able to support financial stability and lend to the International Monetary Fund at short notice. To ensure the fulfilment of these objectives, reserve assets are categorised into two tranches: a liquid tranche (tier 1) and a less-liquid tranche (tier 2). The amount that may be invested in the less-liquid tranche is capped.

In addition to the consideration of a sufficiently liquid reserve, the Danish central bank also aims to increase earnings while keeping risk at a target level. To that end, it takes on investment risk. Investment risk can be taken in both the tier 1 and tier 2 tranches, as well as in derivatives-based overlay strategies. A German government bond, say, would belong in the tier 1 tranche, as it is a liquid asset, although its inherent interest rate risk is part of the investment risk. A corporate bond, on the other hand, as a less-liquid asset, would belong to tier 2, and add interest, credit and liquidity risk to the investment risk. The derivatives-based overlay includes bond and equity index futures. The use of an overlay facilitates the separation between liquidity and risk management decisions. Due to individual assets’ differing risk characteristics and the use of derivatives, the breakdown of the portfolio in terms of cash assets (see Figure 2.1, left-hand column) – which is dominated by money-market instruments – is very different from the breakdown in terms of risk (see Figure 2.1, right-hand column). For Figure 2.1, risk contributions reflect the combined contributions from assets and liabilities, and, adjusted for diversification, are computed as marginal risk contributions.

Overall risk is managed using a holistic risk budget, which – on a day-to-day and mark-to-market basis – seeks to capture the risks on all assets and liabilities. Specifically, risk is defined as the average financial result in the worst 5% of cases (ie, expected shortfall), and the budget specifies an acceptable range for the risk. In keeping with the central bank’s accounting principles, gold as well as all financial assets and liabilities are marked-to-market – and revaluations directly affect the profit and loss (P&L) account. Overall risk includes investment risk but also risks related to the central bank’s policy tasks as discussed below. The holistic approach makes apparent the benefits of diversification and thereby also facilitates the introduction of new asset classes.

At the level of governance, the transformation has resulted in major simplifications. In the reserve management area, policymakers can now focus attention on decisions regarding liquidity and the overall risk level, and, in turn, delegate decisions concerning detailed lines and limits to the operational level. In particular, the board of governors now expresses its risk tolerance through the single, overarching risk budget.

Once an all-encompassing risk metric is in place, a decision must be taken on what overall risk level to target. For the typical central bank, the trade-offs and constraints are arguably more diffuse than for tightly regulated institutions such as banks and pension funds. Therefore, what should guide risk appetite?

To answer this, we revisit our mandate. Central banks’ main task is not to take financial risks to generate profits, but rather to ensure monetary and financial stability. However, often the fulfilment of central banks’ policy mandates – whether they involve management of exchange rates, quantitative easing programmes or gold purchases, etc – will entail some significant and unavoidable financial risks. Taking no risk is usually not a viable option. Hence, a natural starting point for deciding on the risk level is to consider a situation where the central bank does not engage in any return-seeking activities, and only holds the assets and liabilities it needs to fulfil its policy functions. This situation is referred to below as the central bank holding its “policy portfolio”. In this case, the central bank does not take on any investment risk, and is only exposed to “unavoidable policy risks”.

The exact meaning of unavoidable policy risks will differ among central banks and monetary policy regimes. For countries with a floating exchange rate, fluctuations in exchange rates vis-à-vis the main reserve currencies will be an unavoidable source of risk. For central banks engaged in quantitative easing, market and credit risk will also be significant policy-driven sources of risk – seen from a fair-value perspective.

In the case of Denmark, there are three major sources of unavoidable policy risks related to the central bank’s policy mandates. First, the central bank must hold a sufficiently large currency reserve. This exposes the National Bank of Denmark to fluctuations in the exchange rate in terms of the euro. The fixed exchange rate policy, however, ensures that these fluctuations are very limited. Also, holding currency reserves necessarily exposes the central bank to fluctuations in the spread between domestic and foreign short-term interest rates. In 2018, this contribution to risk has been limited, as the spread between short-term rates in Denmark and in the euro area has been fairly stable. Second, the central bank must – according to the country’s central bank act – hold a certain quantity of physical gold. Gold is the main source of risk in the portfolio (see Figure 2.1) as the volatility of the gold price is much higher than for any other policy-related asset or liability. Third, the central bank must provide credit against collateral to domestic banks. Due to the terms and collateralised nature of these credit provisions, this risk is comparatively small.

To calculate risk numbers and decompositions of profit and loss for the policy portfolio, the concept of unavoidable policy risks has to be made fully explicit. There are inevitable trade-offs between realism and simplicity, but the guiding principle is that the central bank should be able to hold the policy portfolio if it decides to do so (see Box 2.1).

Given that the risk of the policy portfolio in a sense represents the central bank’s innate risk level, a natural first step to consider is what return-enhancing strategic exposures can be added without increasing overall risk. Or, in other words, what reallocations can be undertaken to move the portfolio vertically in the risk/return space closer to an efficient allocation? As it turns out, returns from bond and equities have historically had low – or even negative – correlations with gold returns (measured in euros). Therefore, adding moderate equity exposures to the policy portfolio can actually increase the expected return without increasing overall portfolio risk.

One way to think about this is that, until a certain level of equity and duration exposure has been reached, a central bank holding a portfolio where risk is dominated by gold has a comparative advantage in taking on equity exposures. Such a central bank faces a highly attractive risk/return trade-off at low levels of equity exposure. As more and more exposure is added, however, the tradeoff converges to that faced by the market as a whole.

In early 2018, the National Bank of Denmark’s investment risk increased the expected return, but it did not increase the total financial risk. In other words, total risk was comparable to the risk of the (specified) policy portfolio. The Board of Governors decided to express the risk budget as a symmetric range around the risk level of the policy portfolio of the form: [risk of policy portfolio – a; risk of policy portfolio + b] where a and b are constants (and, in National Bank of Denmark’s case, a = b). At the time of writing, March 2018, risk is centred around the risk of the policy portfolio, but it could in principle be higher (a < 0, b > 0) or lower (a > 0, b < 0).

It follows that the upper and lower risk limits shift with the risk of the policy portfolio. The risk budget therefore becomes dynamic, as it uses the policy portfolio as reference. One consequence of this is that if the gold price (or its volatility) has increased since the previous rebalancing, the target for equity exposure will typically also increase. This reflects the role of equities in diversifying gold exposure: with higher gold exposure, more equity exposure – which offers additional expected return – can be added without increasing overall risk.

This built-in positive co-movement between gold and equity exposures contrasts sharply with the mechanics of a static, absolute risk budget in the form [a, b]. In that case, were gold exposures to increase, say, if its price increased, it would be necessary to cut back on other exposures, such as equities, in order to continue to meet the absolute risk target. This reaction pattern is particularly unfortunate given that more gold exposure actually improves the marginal risk/return trade-off for equity exposure in the portfolio. Also, selling equities at a time when gold is soaring will usually lead to inappropriate, procyclical behaviour.²²This is not an entirely theoretical concern. Jukka Pihlman and Han van der Hoorn, “Procyclicality in Central Bank Reserve Management: Evidence from the Crisis,” IMF Working Paper No. 10/150, 2010, shows that central bank reserve managers partially withdrew from riskier investments during the financial crisis of 2008–09, and point to a potential conflict between the reserve management and financial stability mandates of central banks. In more extreme, but not unimaginable scenarios, gold exposure could increase so much as to render the absolute risk budget unattainable.

The dynamic risk budget, on the other hand, takes into account the unavoidable nature of the risks stemming from the policy portfolio. By doing so, it ensures that the resulting risk budget is actually attainable by those responsible for day-to-day portfolio management. Seen from this perspective, the dynamic risk budget is a way to facilitate an ongoing, consistent choice of the risk/return trade-off over time and market states. The dynamic risk budget was implemented in June 2017, and since then the risk of the actual portfolio has been brought gradually in line with the risk of the policy portfolio, mainly via limited adjustments to equity and duration exposure (see Figure 2.2).

The distinction between the policy portfolio and the actual portfolio also allows for decomposition of the P&L account into components that reflect the policy mandates and other components, which in turn reflect active investment decisions. Doing this retrospectively for 2017, one can see that the policy portfolio suffered losses on the asset side due to gold and negative money-market rates. However, when one looks at the actual portfolio, due to diversification benefits and generally favourable market developments, the active exposures in equity and credit markets, as well as duration exposure, more than offset the losses of the policy portfolio. This resulted in a modest, positive overall financial result for the actual portfolio for the year (see Figure 2.3). Note that the numbers in Figure 2.3 are preliminary, and include only profit/loss from financial portfolios (not administrative expenses, etc).

How does the investment process centred around the dynamic risk budget work in practice? The overall purpose and governance of the central bank’s financial portfolios is laid out in its principles for portfolio management. A more specific investment mandate, which must be approved at least annually by the board of governors, stipulates the overall risk budget, a cap on less-liquid investments and lists the set of eligible instruments.

Portfolio adjustments – including rebalancing towards the time-varying risk target – are decided at a monthly investment meeting chaired by the head of reserve management. Typical decisions include changes to duration (across currencies and maturities) and/or to equity exposure. The decisions are implemented within the following couple of weeks, unless the adjustments are unusually large or involve illiquid instruments. In the case of abrupt market developments or large changes in placement needs (eg, due to substantial intervention in the foreign currency markets), ad hoc investment meetings can be convened.

As long as the size of the reallocation is within the overall risk budget and exposure limits stated in the investment mandate, the portfolio adjustments can be implemented without a further approval process. This facilitates a very short cycle from analysis to implementation, reducing the likelihood that the reallocation proposals are overtaken by subsequent market developments.

The starting point for the periodical rebalancing decisions is a model-based proposal, which reflects the implicit “baseline view” incorporated in the model’s risk premia assumptions. These assumptions imply some leaning towards investment strategies exhibiting more carry (see Box 2.2). To mitigate the notorious robustness issues in portfolio optimisation, diversification constraints are imposed and the model is only allowed to reoptimise over a limited set of key exposures. The model-based proposal aims to bring the actual portfolio back to the centre of the dynamic risk budget in the most efficient way. At the monthly investment meeting, the proposed reallocations to individual exposures are then evaluated, also factoring in considerations that are not modelled explicitly.

Taking a quantitative portfolio model as the starting point for the investment process can have additional advantages in a central banking environment, where there is little incentive for risk-taking. For instance, the compensation of staff involved in asset allocation decisions is generally not linked directly to financial performance. There are good reasons for this, especially in view of the subordinate role profitability plays among central banks’ objectives. However, this incentive structure may lead to biases towards too little financial risk-taking, which a data-driven approach can help to alleviate to some extent.

The risk-budget approach requires a relatively sophisticated quantitative framework. All balance-sheet items must be mapped to underlying “risk drivers” in a consistent way, and the volatility and correlation of these risk drivers must be carefully modelled. To control, and thoroughly understand, the modelling trade-offs involved, the National Bank of Denmark develops and maintains its own risk model (see Box 2.2).

One of the key modelling choices is how to handle expected returns. To allow for quantification of risk/return trade-offs, it is necessary to set return expectations for all individual investment strategies considered. This is fraught with difficulties, not least because historical returns – especially for bonds – are unlikely to be a good guide for future returns. Driven by a desire for simplicity and consistency across investment strategies, a rather mechanical two-step methodology is used (see Box 2.3). Another more recent challenge is the potentially asymmetric bond returns at the current yield level. This is handled by using a “shadow-rate model” when simulating future yields. Addressing the issue of asymmetries is particularly pertinent at present, as one may otherwise overstate the potential diversification benefits between bonds and equities.

Given the notorious robustness problems of mean-variance style optimisation across a large number of assets, the portfolio model is only allowed to explore the risk/return implications of changes to a rather narrow set of major risk factors, mainly the level of equity exposure and key rate exposures to major government bond curves. Further, although it is the ambition to place the portfolio at an attractive position in the expected shortfall/expected return space, staying on the largely hypothetical efficient frontier at all times is neither realistic nor desirable in practice.

Over the past couple of years, the National Bank of Denmark has transformed its approach to reserve management. Simpler investment governance and the introduction of a holistic risk budget based on a quantitative model encompassing all assets and liabilities have been major milestones. The most recent step – implemented in 2017 – has been to define a “policy portfolio” reflecting the central bank’s unavoidable policy risks, and to use this as a reference when setting the overall risk level. This has made the risk budget dynamic, reflecting that risks related to policy mandates vary over time.

The in-house risk modelling effort has enabled a better understanding of the key trade-offs, a high degree of customisation to fit the central bank’s analytical needs and swift implementation of new instruments and metrics. As a result of this transformation, the investment process has become more data-driven. When we periodically rebalance the portfolio, the starting point is a model-based proposal for bringing the portfolio closer to the risk budget centre in the most efficient manner.

Overall, the central bank’s new approach to reserve management has contributed to significant excess returns relative to a continuation of the previous investment strategy – and without increasing overall risk. At some point, of course, the discretionary investment exposures will lead to significant losses, and it will then be crucial to clearly communicate why having such exposures makes sense and to stay the course in times of distress.