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We reexamine the relationship between credit spreads and interest rates from a capital gain perspective of bond portfolio. Capital gain sensitivity between US BBB-rated bonds and Treasury bonds is weak and positive in normal periods, but strong and negative during recessions. In the upward phase of business cycles, changes in interest rates are fully reflected in the bond yields, leaving spreads unchanged, while in the downward phase, rates and spreads move in opposite directions. This alternation between two distinct regimes reconciles a long-standing division in the literature. We then discuss the efficiency of shorting Treasury bonds as a hedging strategy and policy suggestions.

The postcrisis monetary policy, which resulted into uncertainty regarding further moves in risk-free interest rates, poses questions on the resilience, profitability, and stability of the international financial system, especially in what concerns the financial health of banks and corporate firms. The recently observed low borrowing costs have allowed financial institutions to clear their budgets but have also limited profits and raised concerns on whether the restructuring of balance sheets and the increase of capital buffers will be enough when interest rates eventually increase. Such an increase is expected to apply pressure on the valuation of assets, particularly for companies with ongoing legacy burdens. Therefore, the historical relationship between risk-free rates and asset valuation becomes a key indicator, both for companies and investors. In addition, the choice of metrics used for assessing this sensitivity plays a vital role in what effects can be captured.

In this paper, we employ capital gains of bond portfolio containing risk-free government and risky BBB-rated nongovernment US securities to evaluate hedging strategies that consist of holding risky and selling risk-free assets. Our motivation for focusing the study on BBB-rated bond portfolios is based on their importance for institutional investors, such as pension funds and insurance companies, as the investment guidelines of a vast majority of them allow only very limited exposure to high yield debt securities, while the BBB-rated bonds provide more attractive returns than higher quality investment-grade instruments. We opt for studying bond portfolio instead of single securities, as for the institutional investors the large aggregates represent the main focus of their activity, contrary to cherry-picking of fixed-income exposures, which in a first place may interest individuals with a rather restricted funding capacities. This aspect also allows us to reduce the necessary computation capacity and still be able to produce valuable investment insights. By using the capital gains metric to study the sensitivity of relatively risky US BBB-rated bonds to risk-free US Treasuries (UST), we show that the relationship between credit spreads and yields of risk-free assets is not constant, as suggested by earlier research (e.g., [

In the first regime, which takes place during normal periods of economic growth, any changes in the yield of risk-free assets are fully mirrored by changes in the yield of investment-grade BBB-rated bonds, keeping credit spreads stable. In that context, spread-to-rate sensitivity is null. From a capital gains perspective, the sensitivity of capital gains of US BBB-rated bonds to the capital gains of UST bonds is positive and equal to one.

In the second regime, which manifests during a recession and a subsequent sharp recovery, capital gains sensitivity turns to be negative. The spreads of US BBB-rated bonds and the yields of UST move in opposite directions due to flight-to-quality behavior and a fall in interest rates. Thus, spread-to-rate sensitivity becomes negative.

The large differences among previous results, based on spread-to-rate sensitivity analysis and on different choices of models and data, produce inconclusive answers to questions on the actual dynamics between credit spreads, yields, and interest rates. The literature is broadly separated to papers that identify a negative spread-to-rate relationship [

For instance, the Merton [

Finding a common denominator between the two aforementioned streams of research on interest rate sensitivity is challenging. Thus, to reconcile a pile of contradictory results, we opt for a different capital gain approach and demonstrate its capacity to provide clearer results over the long-range observation intervals. It is also worth mentioning that the financial crisis caused a radical change in the real-world fundamentals and regulatory frameworks, so to revisit old problems, new techniques allowing for deeper insights are needed. Towards that direction, capital gains sensitivity is able to capture long-term effects better than spread-to-rate sensitivity, as the former directly focuses on the end-of-period bottom-line portfolio results, while the latter is usually obtained by averaging of the daily sensitivity figures, which are subject to greater computational uncertainty due to smaller amplitudes of examined changes.

A simple metric of the sensitivity of capital gains rather than the sensitivity of credit spread to risk-free interest rates has been proposed to study the interest rate sensitivity of US corporate debt [

The capital gains metric is defined as the change in capital gains of a portfolio containing only US BBB-rated bonds over the corresponding change in capital gains of a portfolio containing only UST. While the connection between risk-free interest rates and risky bond yields unavoidably underlines our work, the main focus, however, lies on the profits or losses of bond portfolio. This approach is not widespread in the main stream of financial analysis and usually is employed when the effects of taxation and tax regulation on the performance of financial assets are discussed because tax legislation usually differentiates between capital gains and interim payments.

It is also worth noting that hedging mid- to long-term exposures, usually classified as hold-to-collect and hold-to-collect-and-sell, may differ from intraday short-term hedge methodologies. Additionally, the differences across the normal and distressed market regimes in the behavior of risk-free and risky bond portfolios suggest that hedging interest rate risk by shorting UST, or equivalently holding an interest rate swap that receives a floating rate for a fixed rate, is rather not a completely efficient strategy.

This paper is further motivated by a series of recent reports from regulatory authorities that show a renewed public interest on the relationship between interest rate risk, asset valuation, and regulatory framework [

The rest of the paper is structured as follows. Section

We use the monthly time series of blended yields and average coupons to model the price dynamics of the US BBB-rated and UST bond portfolios on a period from March 2001 to August 2016. Our data come from yield and coupon indices, which are used to model prices and investigate the dynamics of annual capital gains of both US BBB-rated bonds and UST securities. The reason for limiting the analysis to the US nongovernmental BBB bond portfolio and the UST portfolio is rooted in the importance of BBB-rated fixed-income exposures for institutional investors, in general, and insurance companies and pension funds, in particular, due to their attractive risk-return attributes. On the other hand, UST bonds represent investment targets of choice for many investors as they are largely considered to be safe-haven investments, which are also commonly employed as proxies for risk-free instruments used for designing diverse hedge strategies. In addition, by limiting the number of indices used in our research, we are able to keep under control the necessary computation capacity and produce valuable investment insights.

For US BBB bonds, we use the Citi Broad Investment-Grade US Credit BBB Yield to Maturity Local (Bloomberg ticker: S200YL) and the Citi Broad Investment-Grade US Credit BBB Average Coupon Local (Bloomberg ticker: S200CP). The constituent members of the pair of the S200YL and S200CP indices are the same and represent nongovernmental BBB-rated debt issued in the US, which comprises corporate, financial, and municipal issuers. For UST securities, we employ the Citigroup indices: Treasuries Yield to Maturity Local (Bloomberg ticker: SA14YL) and Treasuries Average Coupon Local (Bloomberg ticker: SA14CP). The constituent members of the SA14YL and SA14CP are identic and represent U.S. Treasury bonds, excluding Treasury Bills. We resort to yield and coupon indices to analyze capital gains because there is no price index available with similar length and characteristics and because the focus is on portfolios rather than individual assets. Since interest is not reinvested, a total return index is not necessary. Although herein only the US BBB bonds and UST portfolio are employed, we consider that our findings will hold also for many other portfolios, such as Corporates, Financials, Muni, Emerging Market (EM) Corporates, EM Financial, and EM Sovereigns, among many others.

Our methodology is based on [

The price _{UST} of a UST portfolio with an investment horizon (residual maturity) _{UST}, face value _{UST}, and yield _{UST} is_{UST} is the blended yield given by the SA14YL index and _{UST} is the average coupon given by the SA14CP index. The nominal face value _{UST} is set to US$ 1,000 million.

Capital gain is defined as the difference between the initial price and the final price of the entire portfolio, excluding interim coupon payments over a given period. In essence, the initial price is the price the investor would have to pay to purchase one fraction of the bond index, while the final price is the price at the end of the given period. As the indices are continuously rebalanced, our asset is continuously changing. Since we do not aim to assess the efficiency of rebalancing, the associated transaction costs and costs of carry are ignored. After the historical price series is constructed, the capital gain can be written as_{UST} stands for the capital gains of the UST portfolio, _{BBB} stands for average annual coupon, _{BBB} stands for face value of a principal payment, and _{BBB} is the blended yield. The yields and coupons are given by the respective indices S200YL and S200CP. The face value is again US$ 1,000 million. Capital gains of US BBB-rated bond portfolio can be written as_{UST} and _{BBB}, which can be used to calculate the sensitivity of the relatively risky US BBB-rated bond portfolio capital gains to the capital gains of the risk-free UST bond portfolio. Following the earlier definition, the sensitivity _{BBB/UST} (_{2}, _{1}, H) is the ratio of the capital gain of the corporate bond portfolio to the capital gain of the UST portfolio over a period (_{1}, _{2}).

The horizon _{2} − _{1}. To make the capital gain-wise sensitivity more representative, we calibrate the rolling window of length

It is important to remark that although the measure practically uses bond face values and yields, it can also provide intuition for the dynamics of interest rates. Interest rates and the yields of UST move towards the same direction, so an increase in the Fed rate pushes the yield curve for UST bonds upwards. Changes in nominal rates (e.g., due to inflation, fiscal, or monetary policy) are matched by changes in the yield curve, with a direct effect on the credit spread between government and corporate bonds. Our method fits well with a strategy that hedges interest rate risk by shorting the UST portfolio and essentially assesses the profitability of a long position in US BBB-rated bonds coupled with a short position in government bonds. This intuition is useful for connecting our findings with the wider literature that explicitly uses interest rates and spreads.

Figure

Yields and average coupons for the US BBB-rated (a) and UST bonds (b), %.

For UST bonds, the average coupon almost always exceeds the corresponding yield rate, with the exception of the two-year-long period preceding the global financial crisis, namely, from the second half of 2005 until the end of the first half of 2007. To a lesser extent, the same holds for corporate bonds apart from the financial crisis period: mid-2008 to mid-2010. Notably, the surge in the yields of corporate bonds during the financial crisis is well above the coupon curve, signifying a period where these assets were traded at a great discount. This change in trend will become apparent later on.

We then proceed to discount the future cash flows for the two portfolios based on the yield and coupon data. The resulting bond prices (see Figure

Present values of portfolios: US BBB-rated bonds vs. UST.

Capital gains for each portfolio can be directly calculated from our earlier definition. While the interpretation for the separate UST and US BBB-rated bond portfolios is straightforward, we also discuss the capital gains of a US BBB-rated portfolio hedged by taking a short position in UST bonds. In this case,

Figure

Yearly capital gains for the US BBB-rated, UST, and hedged portfolios.

The main intuition lies in the interpretation of capital gains sensitivity across the portfolios we consider, namely, the US BBB-rated and UST portfolios and the hedged portfolio. Instead of using average sensitivity over the entire sample, we examine the behavior of sensitivity within much shorter time intervals determined by local extrema. Local minima and maxima are treated as turning points which separate upward and downward tendencies in capital gains dynamics.

The tracking of large movements in UST capital gains reduces the uncertainty in the denominator of equation (

Phase-averaged sensitivity of US BBB-rated bonds, 2002–2016.

The bold line depicts the two different regimes. During normal economic conditions, the average sensitivity is positive, while during the crisis, it is negative and amplified. We clearly observe the time-varying behavior of capital gains sensitivity over each phase, similar to [

As discussed earlier, the definition of our measure can be interpreted as a gauge of hedging success when a long position in the BBB-rated portfolio is balanced by a short position in the UST portfolio. In terms of cash flows, this can be seen as either a permanent position or an interest rate swap that pays a fixed rate to receive a floating rate equal to that of the corporate bond portfolio. It becomes apparent that all the gains from the short position in UST during the precrisis period are wiped away during the crisis downturn and recovery. As such, an all-weather hedge or its equivalent in the form of a swap is inefficient.

Section

Up to this point, our empirical findings point towards a structural break in the time series we use. This underlines a functional discrepancy best represented by the contradiction between the Merton [

From the vast literature on Markov-switching and regime-switching models, we select a set of simple applications in line with the arguments detailed in [_{t} does not depend on _{t−1} but is drawn from a discrete probability distribution. On the other hand, an autoregressive (AR) specification where _{t} follows a Markov process, thus allowing the transition probabilities to follow an AR process, would introduce autocorrelation in states since _{t} would depend on _{t−1}. This is an unwelcome feature for our model for many reasons. Markov-switching AR (MSAR) models are better suited for quarterly or annual data, and the introduction of lagged states multiplies the states. In our case, due to autoregression, there would be four possible regimes instead of two, without providing any additional intuition. Also, an MSAR specification would not allow the probabilities to adjust quickly enough to changes in states. Regardless, preliminary estimations of an AR specification yielded very similar results, so we base our discussion on the DRMS models only.

A general specification of the DRMS model that captures all the subcases we consider is^{2}_{s} = ^{2} (constant across both time and states) and remains as above in the case where both means and variances are state dependent (_{s} and ^{2}_{s} omitting

Table _{t} = _{st} + _{t}, _{t} ∼ Ν(0, ^{2}) for states _{1,2} are both statistically significant, with a negative value of −2.41 and a positive value of 0.70, respectively. The probabilities for each state are 0.838 and 0.968, respectively, which show very high persistence for both regimes.

Markov-switching regression in means only for sensitivity.

Parameter | Estimate | St. error | 95% confidence interval | ||
---|---|---|---|---|---|

_{1} | −2.408 | 0.163 | −14.74 | 0.000 | (−2 |

_{2} | 0.701 | 0.662 | 10.60 | 0.000 | (0 |

0.791 | 0.044 | (0 | |||

p11 | 0.838 | 0.073 | (0 | ||

p21 | 0.033 | 0.015 | (0 |

The Merton case corresponds to state 1; the Kamin and von Kleist case corresponds to state 2.

The transition probabilities from state 1 (2) to state 2 (1) are 0.162 (0.032), which show a very low rate of change (see Table

Transition probabilities between state 1 and state 2 for all models.

Regime switch in means only | |||||
---|---|---|---|---|---|

Sensitivity | BBB hedged by short UST | ||||

State from/to | State 1 | State 2 | State from/to | State 1 | State 2 |

State 1 | 0.838 | 0.162 | State 1 | 0.987 | 0.013 |

State 2 | 0.033 | 0.967 | State 2 | 0.104 | 0.897 |

Regime switch in means and standard deviations | |||||

Sensitivity | BBB hedged by short UST | ||||

State from/to | State 1 | State 2 | State from/to | State 1 | State 2 |

State 1 | 0.837 | 0.163 | State 1 | 0.987 | 0.013 |

State 2 | 0.111 | 0.889 | State 2 | 0.087 | 0.913 |

The Merton case corresponds to state 1; the Kamin and von Kleist case corresponds to state 2.

Figure

Regime change in means only: state plot for the sensitivity time series. Probability with respect to state 1.

Figure

These findings show that sensitivity and credit spreads vary over time, with two distinct regimes appearing, which correspond to two different theoretical approaches on the relationship between credit spreads and interest rates. During crises, credit spreads and interest rates move in opposite directions following the Merton pattern of negative sensitivity. During normal periods, any changes in interest rates (risk-free yields) pass on nearly completely to the yields of corporate bonds, which implies stable credit spreads and the Kamin and von Kleist pattern.

When regime changes are allowed in both the mean and the variance, the parameters and transition probabilities are generally similar (Table

Markov-switching regression in means and standard deviations for sensitivity.

Parameter | Estimate | St. error | Z | 95% confidence interval | |
---|---|---|---|---|---|

_{1} | −1.345 | 0.201 | −6.68 | 0.000 | (−1 |

_{2} | 0.842 | 0.142 | 5.94 | 0.000 | (0 |

_{1} | 0.909 | 0.097 | (0 | ||

_{2} | 0.516 | 0.042 | (0 | ||

p11 | 0.837 | 0.048 | (0 | ||

p21 | 0.111 | 0.032 | (0 |

The Merton case corresponds to state 1; the Kamin and von Kleist case corresponds to state 2.

We can now proceed to the capital gains of the hedged synthetic portfolio where UST bonds are shorted. The capital gains of the hedged portfolio are calculated as follows. First, the present values of the UST and BBB portfolios are calculated using equations (

The CG_{hedged} series is used to estimate different Markov-switching models, whose results are reported in Tables

Markov-switching regression in means only for the US BBB portfolio hedged by shorting UST bonds.

Parameter | Estimate | St. error | 95% confidence interval | ||
---|---|---|---|---|---|

_{1} | −11.397 | 4.038 | −2.82 | 0.005 | (−19 |

_{2} | 134.794 | 14.953 | 9.01 | 0.000 | (105 |

47.034 | 2.556 | (42 | |||

p11 | 0.988 | 0.009 | (0 | ||

p21 | 0.104 | 0.068 | (0 |

State 1 is the Merton case; state 2 is the Kamin and von Kleist case.

Markov switching regression in means and standard deviations for the US BBB portfolio hedged by shorting UST.

Parameter | Estimate | St. error | z | 95% confidence interval | |
---|---|---|---|---|---|

_{1} | −13.258 | 3.812 | −3.47 | 0.001 | (−20 |

_{2} | 119.439 | 18.024 | 6.63 | 0.000 | (84 |

_{1} | 42.970 | 2.556 | (38 | ||

_{2} | 69.012 | 9.987 | (51 | ||

p11 | 0.987 | 0.009 | (0 | ||

p21 | 0.087 | 0.057 | (0 |

Merton case: state 1; Kamin and von Kleist case: state 2.

Regime change in means only: state plot for the capital gains hedged US BBB portfolio, 3/2002–9/2016.

One of the changes, which lasts longer, takes place between 2010 and 2011, which corresponds to the financial crisis. The other change takes place in 2004, is slightly less pronounced, and coincides with a minimum in the time series of UST capital gains. It is worth noting that this minimum of UST capital gains occurs within the one-year-long time interval (June 2003–June 2004), when the federal fund target rate remains at its local minimum value of 1%. The transition probabilities are again very persistent, as shown in Table

In its turn, Table

Figure

Regime change in means and standard deviations: state plot for the capital gains of the UST-hedged US BBB portfolio, 3/2002–9/2016.

It must be stressed that such effects can be identified only if averaging over a very long sample is avoided. The average sensitivity for the entire period is slightly below zero, meaning the strong negative sensitivity in the second period cancels out the low positive sensitivity in the first and third periods. This may lead to flawed or counterintuitive results, particularly if the effect of one regime is very strong or if strong effects in all regimes negate each other. It is even possible to conclude that there is no sensitivity relative to either yields or capital gains. This finding also provides an illustration on why long spread-to-rate sensitivity averages failed to capture the dynamics depicted by our measure.

The estimation results provide sufficient evidence on the time variation in the relationship between credit spreads and yields or interest rates. They suggest a compromise between the pattern identified by Merton [

Capital gains of the hedged US BBB portfolio exhibit two regime changes which coincide with the two highest capital gains of the UST Long portfolio (see Figure

US federal fund effective rate.

The same discussion can be held in terms of default probabilities. In state 1, changes in risk-free interest rates (yields) have a significant opposite effect on US BBB bond yields, while in state 2, a change in risk-free interest rates is reflected by changes in US BBB bond yields of the same size and magnitude. During the precrisis period (state 2), the average capital gains sensitivity of US BBB-rated bonds is close to 1, averaging at 0.84, particularly between 2004 and 2007. Therefore, the response of US BBB bonds to changes in the yields of risk-free assets on a capital gains basis is slightly lower than 1-to-1, and changes in the yield of risk-free assets passing on to the yield of corporate bonds are slightly reduced. According to [

This, in turn, is a signal for the creditworthiness of debt issuers. After 2010, the intuition of Kamin and von Kleist emerges again, with a positive average sensitivity of 0.78.

Although the time span of our analysis ends in August 2016, there is an interesting period ahead with environments with prolonged low interest rates that had fostered risk-taking up to the coronavirus crisis. Such risk-taking scenario has been faced by advanced economies for some time and then, later, on the eve of the pandemic-fueled crisis, by some developing countries. As the impacts of the coronavirus crisis, from the point of view of the interest-rate-based finance, are commensurate with those of the 2007–2008 global financial crisis, we consider the interest rate sensitivity of the BBB-rated nongovernmental US bonds during the coronavirus recession to be negative and amplified. It is so because the US Treasury yields are diminishing towards the all-time low, while the precoronavirus bubble in the BBB-rated debt outstanding makes the yields of the nongovernmental relatively risky BBB-rated bonds climb. Thus, in accordance with our back-on-the-envelope estimates, our conclusions hold in this environment. However, thorough rigorous investigation of the low interest rates’ influence and the impacts of coronavirus on the interest rate sensitivity is desirable and will be addressed in our further research. We also posit that during the initial recovery from the coronavirus crisis lows, the interest rate sensitivity will remain negative, this time because of the increase in UST treasury yields—due to the economic recovery—accompanied by the decrease in BBB-rated yields—due to improving business conjuncture and, hence, diminishing probabilities of default. The sensitivity plot around the coronavirus crisis will be qualitatively similar to that in Figure

The performance across diverse asset categories changes according to the phases of the business cycle [

The first and third period of our sample, where spreads are generally constant, can be related to the mid and late phases of the business cycle, both empirically and theoretically. During those periods of normal to moderate economic growth, default probabilities are low and creditworthiness is only moderately by changes in the risk-free rate. During the second period, however, the inverse relationship can be related to the downside of the business cycle, where a recession (crisis) and the first stage of recovery have taken place. The observed flight-to-quality puts pressure on the prices of UST bonds, which are coupled by a central bank trying to stimulate the economy by reducing interest rates. Either of these factors, or their joint occurrence, pushes the yields of the risk-free assets upwards. Figure

Spread-to-risk-free rate dynamics compared to observed yields. (a) Negative spread-to-rate sensitivity in distress compared to null sensitivity in “normal” times. (b) US BBB-rated (blue) and UST (red) bond yields.

At the same time, the deteriorating economic conditions, low business performance, and increased uncertainty make corporate debt riskier, which pushes US BBB-rated yields upwards. Thus, companies face more difficulties in servicing existing debt and issuing new one at an acceptable rate. Prices of corporate bonds move downwards and prices of government bonds move upwards. The movement from the second to the third period of our sample can be seen as the return to a “normal” state after an increase in interest rates from the central bank. Tighter monetary policy, coupled with an improvement of economic conditions, reduces the premia of corporate bonds since the yields of risk-free assets increase and default risk decreases. Capital losses are observed in UST portfolios while positive capital gains occur in corporate bond portfolios. The capital gains sensitivity of the US BBB-rated bonds during the recovery phase changes from negative to slightly positive.

Our findings for the downward phase of the business cycle agree and expand on [

Under these circumstances, the dilemma of an investor in US BBB-rated bonds is a choice between a short position in UST bonds or, equivalently, an interest rate swap that receives a floating rate for a fixed rate. Our findings suggest that such a hedge is meaningful and profitable in the upward section of the business cycle, where spreads are relatively stable. If this position, however, is maintained during a recession or an early recovery stage, any profits will likely be eliminated swiftly, as suggested by our results [

To study the comparative dynamics of US BBB-rated debt and UST bonds, we propose a comprehensive measure of sensitivity based on capital gains of the representative portfolios. The approach puts direct emphasis on profits or losses incurred by a portfolio due to changes in the underlying yields. While compared to assessing spread-to-rate sensitivity metrics, the capital gains measure reveals itself as a more suitable for the long-run investment perspective as this measure, by construction, is primarily focused on the profits or losses of bond portfolio on a year-on-year basis.

We reconcile two opposing strings of literature that assume a constant relationship between credit spreads of US BBB-rated bonds and the yields of risk-free UST, by showing that the relationship is not permanent but changes over time between two different regimes. The first regime corresponds to periods of high and moderate growth in the business cycle, during which credit spreads have little to no reaction to changes in interest rates and risk-free yields [

Apart from the theoretical contribution, our findings also have practical value for portfolio management and policy regulation. A sensible hedging strategy for bond portfolio would be to hold a long position in government bonds and a short position in risk-free bonds. Note that holding a short position in UST in such a synthetic portfolio is largely equivalent to a fixed-for-floating interest rate swap. However, under time-varying sensitivity, such a position is economically inefficient since losses in an economic downturn may be so severe that they may cancel out the gains obtained in normal times. Therefore, for long-term investments, dynamic positions and a proper reassessment of fundamentals are crucial. A portfolio investor that considers the phase of the economic cycle would not always rely on shorting UST as a hedge strategy, but would alter, or even reverse crossing a crisis, his exposure to risk-free UST instruments along the business cycle.

The implications for policy makers and portfolio investors alike lie in the proper timing of trends. A policy maker, on the other hand, should expect that, other positive effects notwithstanding, a reduction in interest rates during a recession may put additional pressure on corporate yields during a time of low economic performance and perceived high default risk. Our remarks contribute to the ongoing discussion of exposure to credit risk and risk assessment under the Basel III capital accord, namely, Pillar II methodologies.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.

This research was supported by IPL (Instituto Politécnico de Lisboa) and by FCT, I.P., the Portuguese national funding agency for science, research and technology, under the project UIDB/04521/2020.