Alasdair Thompson, PhD, discusses one of the important decisions that insurers will have to make: constructing the discount curve to reflect the cash flows and liquidity of their liabilities.

## Introduction

Under IFRS 17, insurers are required to discount the value of their liabilities using a discount curve that reflects the cash flows and liquidity of those liabilities. The standard does not prescribe the method by which this discount curve is calculated, but does offer general principles for constructing a curve by either a "bottom-up" or "top-down" method. In a recent whitepaper (Thompson and Jessop 2018), we offered one method by which this calculation could be performed using Moody's Analytics Expected Default Frequency (EDF™) model of real world defaults to calculate credit adjustments on a portfolio of corporate bonds.

Although this method can be most easily classified as a top-down approach to calculating the discount curve, we believe the implied illiquidity premia that can be derived using our method are also applicable to insurers following a bottom-up approach.^{1 }A follow-up paper (Thompson and Jessop 2019) applied this method to a range of economies across Europe, Asia, and North America and calculated credit risk and illiquidity premia, showing how this could be decomposed across ratings, sectors, and maturities.

For a method to be of practical use by insurers, it must produce sensible and interpretable results over time, and it must understand changes in the decomposition of market spreads between credit and illiquidity risk. Recently, a number of works have also shown that the assumptions made about discount rates and how they are applied can have significant implications for an insurer's balance sheet, future profits, and volatility (Conn 2019, Morrison 2019).

## Stress Sensitivity Analysis

Understanding the sensitivity of the credit and illiquidity premia to changes in the underlying risk drivers allows us to gain confidence in a model ^{2} and to predict how it will behave under different market conditions. We conduct a simple sensitivity analysis of our credit risk model by stressing each of the core risk factors in turn on a univariate basis and examining how the average implied illiquidity premia across a portfolio of corporate bonds moves under each test.

A series of multiplicative stresses are applied to each variable, so that for every bond in a given sample, the same multiplicative stress is applied – for example, every default probability increases by 10%. We find that, if everything else is equal, more than 90% of the change in spreads is passed through to the illiquidity premia, the remainder being accounted as a change in credit risk premia due to changes in the cost-of-capital.

Conversely, changes in the default probability are scaled by the average loss given default, and hence a 10 basis point change in EDF only leads to around a 1.5-2 basis point decrease in illiquidity premium.

It is important to note here that these sensitivities are in terms of the residual illiquidity premia on an asset portfolio. The sensitivity of the final illiquidity premium applied to discount liabilities under a bottom-up approach would be multiplied by an application ratio that reflected the difference in liquidity characteristics between the asset and liability instuments. This could dampen the impact of changes in the underlying risk factors (assuming the application ratio was less than one).

High sensitivity to spreads, where everything else is kept constant, makes intuitive sense for our model: a change to spreads will not affect the expected loss and will change the unexpected loss only through an increase in the cost-of-capital, which in current market conditions is dominated by the equity term.^{3} Hence, most of the impact of a spread stress is passed through to the implied illiquidity premium.

The sensitivity to spread changes will be of particular importance when considering the impact of a change in risk-free basis – for example, between government and swap rates or between inter-bank offered rates and overnight indexed swaps. The high sensitivity to spread changes indicates that the change in IP from a change in risk-free basis will be very close to the average basis spread.

In our analysis we also examine the variation in sensitivity between different economies, and find a range of sensitivities. This reflects the point-in-time nature of these results and shows that each sensitivity depends on the levels of both the variables under consideration (the relationship between the independent and dependent variables is not necessarily linear) and the levels of the other variables. When the loss given default is higher, the sensitivity to EDF will be higher, and vice versa.

## Historic Correlations

The sensitivity analysis in the previous section revealed how the credit and illiquidity premia vary in response to univariate changes in the underlying risk drivers. In reality, however, these risk drivers are far from independent. In practice the EDF will be correlated with spreads and is directly driven by changes in leverage and volatility.

Figure 1 shows a strong correlation between average 1-year EDF and spreads (in particular, the figure shows 5-7 year A rated spreads, though spreads themselves show a high correlation across ratings and maturities), but the correlation is significantly less pronounced for longer-term default probabilities.^{4}

Note that the average EDF term structure actually inverts around the financial crisis in 2009, with 1-year default probabilities higher than 5- or 10-year. The 10-year EDF in particular is, on average, almost completely constant over time.

Changes in EDF are not strongly correlated with changes in spread over short time periods, but generally a stronger correlation is observable when considered over longer time periods. There is a significant correlation between changes in 1-year EDF and spreads, but very little correlation for longer-term EDF.

Notably there is also a lag between changes in spreads and changes in EDF, with annual log changes to mean 1-year EDF correlated most highly with spreads at a lag of 2-4 months. Log changes to 5-year EDF have a less consistent optimal lag and a lower correlation.

## Backtesting the Model

The preceding analysis suggests that illiquidity premia have a strong, but not perfect, correlation with overall market spreads. We also expect that the credit risk component of shorter dated bonds will be more dynamic than for bonds of a longer duration. A static analysis of univariate sensitivities and a view of historic correlations between these factors can tell us only so much, however. To get a clearer picture of the overall stability of the model and the dynamics of the decomposition between credit and liquidity risk, we now turn to a full backtest of the model.

Consider the behavior of the model under recent market conditions, absent of any particular market-wide credit event. Figure 2 shows the evolution over the last four years of the spread decomposition for an AUD (left) and CAD (right) denominated portfolio of investment-grade corporate bonds. In both cases, movements in spread are explained primarily by changes in illiquidity premium. For the CAD portfolio in particular, the credit component of the spread is almost constant.

Under stable market conditions, the model produces stable estimates of credit risk and slowly varying illiquidity premia. Under stressed market conditions, the behavior could be significantly different, and the credit risk premium should be significantly larger. In Figure 3 we compare the decomposition of spreads for five economies at two dates: the end of September 2011 (during the Euro sovereign debt crisis) and the end of December 2018. Overall spreads are noticeably higher in 2011 than in 2018 across all economies and both credit and illiquidity components are higher in 2011.

Comparing 2011 vs. 2018, around 45-70% of the change in spread is attributed to changes in liquidity. Recall that the univariate sensitivity to spread was around 90%, but in this real example the probability of default, the average leverage, and asset volatility will all have changed, offsetting some of the change due to the increase in spreads.

## Term Structure Dynamics

Our analysis of the dynamics of average 1-year, 5-year, and 10-year EDFs revealed that the 1-year EDF exhibited more point-in-time behavior, with a clear correlation to average spreads, while 5-year and 10-year EDFs are more through-the-cycle. We therefore expect that more of the variation in spreads over time will be explained by changes in credit risk for shorter dated bonds, while for longer dated bonds spread changes will be associated with changes in illiquidity premium.

A cross-sectional regression of illiquidity premia versus spreads for a larger sample of dates and economies produced a similar result to our backtesting, with 68% of changes in spread attributable to changes in illiquidity premia.

However, when we consider only short dated bonds, with a duration under three years, the sensitivity falls to 52%, while for bonds with a duration greater than five years, the sensitivity rises to 81%.

Not only does our model allow us to produce a term structure for illiquidity premia, but we can also understand different dynamics in the decomposition of spreads across risk categories for different portfolio durations. This is a key feature of our model, which we believe allows insurers to more accurately tailor liquidity adjustments to their business.

## Conclusion

The sensitivity and stability of credit spread decomposition is a key determinant in selecting an appropriate model to derive illiquidity premia for the purpose of setting discount curves under IFRS 17. We have tried to verify that our model can form an appropriate and usable method for this purpose.

The analysis shows that over short time periods, the majority of movement in spreads will be attributable to changes in liquidity. This is particularly true for long duration bonds, but even for short duration bonds there is a significant sensitivity of illiquidity premia to spread changes. Over longer time periods or under more significant market-wide movements, the credit component will vary such that rather than keeping a constant absolute credit adjustment, there is a consistent ratio of credit adjustment to overall spread.

Compared to previous simple proxies that defined the illiquidity premium as 50% of the market spread minus a constant adjustment, our method explains more short term variation in spreads due to changes in liquidity.

It also offers a more sophisticated breakdown between portfolios of different durations. This is important as different types of business, whether general insurance or life, for example, will likely be backed by different asset portfolios with different average credit quality and duration. In line with the requirement under IFRS 17 that the illiquidity premium should reflect the characteristics of the liabilities under valuation, our method offers a way to take account of these differences.

Many insurers will want to align their approach to IFRS 17 with existing regulatory or economic capital calculations. In Europe this is likely to mean starting with the Solvency II regulations and internalizing and adapting the calculations as required.

For some parts of the calculation, aligning methodology between Solvency II and IFRS 17 may be straightforward – for example, the choice of risk-free rate or the interpolation and extrapolation method and ultimate forward rate. For other parts, such as the credit risk adjustment, alignment may be more difficult.

The European Insurance and Occupational Pensions Authority (EIOPA) specifically adjusts for probability of default and cost of downgrade, but applies a minimum of 35% of the long-term average spread. EIOPA then scales the credit-adjusted spread by a factor of 65% to derive the final volatility adjustment.

An insurer that wants to internalize this method would need to justify the use of the 35% floor and 65% application ratio, and the specific choice of those numbers. Furthermore, the EIOPA volatility adjustment provides only a single reference point and a flat term structure that does not account for the differing credit decomposition dynamics across duration and over time.

- To find out more about Moody's Analytics solutions for IFRS 17, go to: www.moodysanalytics.com/IFRS17

**Footnotes**

^{1 }Since illiquidity premia are not something that can be observed directly on the market, we

believe that most bottom-up calculations will need to use a hybrid method where the cost

of liquidity is derived from a top-down analysis. The volatility adjustment under Solvency II

could be seen as one such hybrid method where the volatility adjustment is derived by EIOPA

by making a credit adjustment to a top-down portfolio, but it is then applied bottom-up by

insurers by adding it to a risk-free curve.

^{2} The model being referred to throughout this paper is the credit risk premium adjustment to

Moody's Analytics EDF model, described in Thompson and Jessop (2018).

^{3} Within our model we use a weighted average cost-of-capital (WACC), which is given by the

leverage weighted sum of the cost-of-debt and cost-of-equity: The cost-of-debt and cost-ofequity

are, respectively, taken to be the average bond spread across the portfolio and the

equity risk premium.

^{4} Moody's Analytics EDF model estimates a term structure for default probability at horizons

from 1 to 10 years. Over the short term, default frequency is driven by both idiosyncratic

and systemic factors, while over the longer term idiosyncratic risk dominates, giving a more

acyclical result and a more stable probability of default. See Nazeran and Dwyer (2015).

* References*

- https://www.moodysanalytics.com/-/media/whitepaper/2019/Implementing-IFRS-17-Discount-Curves-Theoretical-and-Practical-Challenges
- https://www.moodysanalytics.com/-/media/article/2019/profit-emergence-under-ifrs9-ifrs17-theimpact-of-choice-of-liabillity-discount-rate.pdf
- https://www.moodysanalytics.com/-/media/article/2018/a-cost-of-capital-approach-to-estimatingcredit-risk-premium.pdf
- https://www.moodysanalytics.com/-/media/whitepaper/2018/moodysanalyticscreditriskandilliquiditypremiadec2018.pdf
- https://www.moodysanalytics.com/-/media/whitepaper/2015/2012-28-06-public-edf-methodology.pdf
- https://www.moodysanalytics.com/-/media/whitepaper/2019/whitepaper-ifrs-17-credit-andilliquidity-premia-sensitivity-and-backtesting.pdf