Fidelity Fixed Income White Paper - Amazon Web ……2 Fidelity Fixed Income White Paper: Generating...

Fidelity Fixed Income White Paper

MARCH 2019

Generating alpha in bottom-up systematic credit portfoliosJoe Hanmer Director of Quantitative Research, Fixed Income

2 Fidelity Fixed Income White Paper: Generating alpha in bottom-up systematic credit portfolios

Factor investing has become wildly popular in recent years both among academics and investment managers. Academic researchers have contributed to an exponentially growing number of discovered factors in what has been described as a ‘factor zoo’ (Cochrane, 2011). However incorporating these factors into fixed income portfolios has proven difficult in practice. Below we describe a way to construct fixed income factor portfolios that can minimise some of the pitfalls while preserving the benefits. But first we provide a brief overview of fixed income factor investing.

Investment practitioners have discovered that factors explain a considerable proportion of what was previously assumed to be active portfolio managers’ alpha (e.g. Ang et al., 2009). Moreover, as the popularity of factor investing has grown, the investment industry has started offering numerous factor-based instruments that allow investors to access factor risk premia.

Figure 1: Schematic of the factor investing universe

Source: Fidelity International, March 2019.

Factor landscape

Value

■ Liquid instruments (stocks, futures, forwards)

■ Low transaction costs

■ Electronic trading

■ Good data availability (decades of public history)

■ Plentiful academic research

■ Simple single instruments

Illiquid, hard to short, many bonds per issuer and under-researched by academia

Fidelity bottom-up

systematic credit strategies

Factor mutual funds

Factor ETFs

CTAs

Hedge funds

Quality MomentumMean

reversionHow to get exposure

Equity

Commodities and FX

Rates

Credit

ContentsFactor landscape 2

Our factor approach in corporate bonds 4

Creating systematic bond portfolios 6

Results for US investment grade portfolios 7

Expanding beyond US investment grade 9

Conclusion 9

References 10

3

Most of the developments in factor investing have focused on equities, which benefit from high liquidity, electronic trading, low execution costs, excellent availability of data, and plentiful academic research. Yet despite those characteristics being less immediately apparent in fixed income, factor-based solutions can also be implemented with bond products. Indeed, there already are a few, backed up by findings from recent academic studies.

Portfolio factor exposure can enhance returns by harvesting the risk premium associated with a factor. In low yield environments this can be a welcome addition to performance. Furthermore, factor-based portfolios can benefit from lower risk and greater diversification due to the low correlation of fixed income factors with equity factors and macroeconomic variables, and between the factors themselves.

Just as in equity factor investing, fixed income factor information can be employed in the investment management process in several ways. One use is ’low-touch’ factor-premia-based investment funds, which provide exposure to a single factor or combination of factors. Another is to consider factors as a means for idea generation. Selecting bonds based on factors in active portfolios can generate independent alpha or improve diversification.

Factor information can also be useful in the performance attribution of active strategies. The source and nature of excess returns can be assessed by looking at intentional and unintentional exposures to fixed income factors (as is now common in equity funds).

However identifying factors and constructing portfolios around them presents some difficulties. The main dangers are re-discovering well-known and already documented return drivers and falling into the trap of data mining – generating false positives by repetitively testing the same historical data.

Agreeing on factor definitions is another point of contention. In recent years we have seen a series of studies on multifactor fixed income portfolios (Houweling and van Zundert, 2017; Brooks et al., 2018; Israel et al., 2018). These papers identified the same factors successfully employed in equities: value, momentum, carry, size and quality/low risk/defensive factors. But the definitions of these factors differed between the studies as well as from those commonly used in equities. For example, the value factor represents the difference between bond prices and intrinsic values. However, evaluating the latter is not obvious. Bond spreads, agency ratings, duration, return volatility and other default risk measures have all been used to represent the value factor (Brooks et al., 2018; Israel et al., 2018), while Houweling and van Zundert use a regression to arrive at a ‘fair’ spread value of a bond that can be compared to the market spread.

It is typical to find a wide range of factor definitions in both bonds and equities, which raises concerns about the danger of overfitting – finding non-causal relationships in historic data by using too many dimensions or testing too many possible solutions. Adjusting the definition of factors while evaluating performance on the same data inevitably leads to false positives with factors that fail to perform in out-of-sample tests despite excellent results in backtests (Harvey at al. 2016, Lopez de Prado and Lewis, 2018).

Another issue that has been difficult to address in fixed income factor research is transaction costs. Evidence of excess returns generated by factors without considering transaction costs has little practical value. Previous studies addressed the problem by relying on fixed transaction costs for all bonds (Israel et al., 2018) or by estimating breakeven costs and comparing them to average values observed in the market (Houweling and van Zundert, 2017). However, relying on average and fixed values does not resemble the actual circumstances that investors face.


We believe that to recreate factor exposure returns we need to investigate additional factors similar to those identified in equities (value, momentum, growth, low vol etc.). However due to the differing drivers and nature of fixed income returns, we do not believe in limiting the bond factor to exact equivalents of factors explaining equity returns. For example, the asymmetry of fixed income returns and the limited upside compared to equities make applying equity factors directly to bonds unlikely to result in positive risk premia.

The empirical study section of this paper describes a novel ’bottom-up’ method of factor construction and assesses the performance of these factors in realistic scenarios. We conduct our approach initially on the US investment grade market and make as few assumptions as possible about how to define factors given it is not obvious how to translate factors to fixed income. We therefore assume that factors provide a consistently positive risk-adjusted return through time and allow our algorithm to decide which data to use.

Figure 2: Explanation of the factor construction approach


■ Steps 1 and 2: The first steps of our method involve collecting and transforming data. At Fidelity we have amassed a substantial database of corporate bond information across asset classes and data types. We also use proprietary systems to map stocks to bonds and CDS (credit default swaps), as well as fit credit spread curves. This allows us to produce time series for each issuer across a variety of inputs, from fundamental accounting data to bond market data to data mapped from equivalent equity issuers where appropriate, and these time series are comparable across all corporate sectors.

■ Step 3: Each variable is then transformed into a signal using common numerical procedures such as cross-sectional z-scoring and differentiating to get momentum. This results in about 200 signal variables available for each issuer, where the signal score is a normalised value capped and floored at +/-2.

■ Step 4: The signal variables for each issuer are assigned to one of three factor groups:

1. Fundamental: variables relating to company fundamental information.

2. Valuation: cross-sectional and historical deviations from the mean for signals based on bond and equity characteristics.

3. Sentiment: momentum and trend signals based on bond and equity characteristics.

Our factor approach in corporate bonds

1 Collection of data

Bond data

Equity data

Accounting fundamentals

Accounting estimates

CDS data

Index data

ESG data

2 Transforming or combining data

Ratio calculations

Equity mappings

Curve generation

3 Multiple scoring methods

Cross-sectional

Time series

Momentum

Mean reversion

4 Grouped into categories

Grouped by data type and scoring method

Each group allocated to fundamental,

sentiment or valuation bucket

~200 time series per issuer

~80 time series per issuer

5

Within each group, several rounds of aggregation are performed by summing weighted underlying signals.1 The weights are chosen to maximise the information ratio (a measure of risk-adjusted return) of a combined factor portfolio after transaction costs. The signal return time series used to determine aggregation weights are adjusted for known risk premia associated with exposure to duration and spread. Finally, the weights are constrained to a range between zero and 50 per cent to avoid a single signal dominating the aggregated variable.

To illustrate the advantages of this approach we can think about the quality factor used in equities and other fixed income factor portfolios. A simple definition of quality in fixed income could be derived from the issuer’s credit rating or a bond’s spread and duration. Instead, we put all the fundamental data into one group, which does not contain backward looking credit ratings, and allow our algorithm to decide which fundamental data and scoring methods best predict returns. This makes our factor construction dynamic; it is responsive to changing market conditions, unbiased by the choice of a single definition (the algorithm can weight multiple definitions of quality) and can consider the volatility of each definition by considering transaction costs.

Using this procedure, we constructed three time series for each factor group. They exhibited small cross-sectional correlation and promising return predictability. These groups were then put through the same algorithm to produce a single factor time series per issuer. This approach allows weights to vary over time if market conditions or regimes change.

To assess the performance of the overall credit factor generated, we can split the universe into quintiles and compare performance. The left-hand chart in Figure 3 shows the consistent out-performance of the top two quintiles and underperformance of the bottom two. The right-hand chart shows that the top quintile outperforms the bottom by 50 percentage points on aggregate over a 10-year backtest.

Figure 3: Performance of the credit factor


However we cannot directly harvest this alpha as these returns are only representative of each company. In equities it would be possible to create a long-short portfolio to capture this. But in fixed income we need to construct a long-only bond portfolio that has significant exposure to our factor.

To construct actual bond portfolios we need a way to differentiate between bonds from the same issuer. We have developed two factors to do this: bond roll down and bond residual to its issuer curve. The roll down factor is the natural return from holding a given bond for one year assuming no change in its yield curve. We use proprietary credit curves, which are fit to every issuer in the universe, to estimate the roll down for each individual bond at its current duration. The residual factor also uses these proprietary curves and calculates the premium over the credit curve for each bond (this is a simple measure of how cheap a bond is relative to its issuer).

1. The returns used for this performance calculation are generic 5-year return time series calculated from our issuer curves. These are not tradeable instruments but proxies for the return gained from having exposure to a given issuer. These returns are at a consistent duration and are market beta adjusted to control for known factors such as spread and duration.

Quintile performance of overall credit factor Top versus bottom quintile performance

1st

2nd

3rd

4th

5th0.75

1.00

1.25

201820162014201220102008

1.0

1.2

1.4

1.6

201820162014201220102008


We have shown that our factor construction methodology is robust and, in theory at least, able to generate significant alpha. The question now is whether we can construct a long-only bond portfolio to harvest this alpha and whether it is resilient to transaction costs.

The portfolio is constructed at each month end, matching the frequency of index rebalancing to minimize excessive turnover. We aim to maximise the function shown in Figure 4 subject to the constraints in Figure 5 by using an in-house optimisation tool. The constraints aim to keep the main sources of risk in the portfolio – credit beta, duration, sector exposure and country exposure – as closely aligned with the index as possible, as well as cap the relative and absolute exposure to any single issuer.

To perform the optimisation, we translate both factor scores (the bond roll down and bond residual to its issuer) and transaction costs into expected return to make them numerically comparable. Returns for our credit factors are calculated by multiplying the level of factor exposure by the return expected from one unit of factor exposure. Transactions costs are estimated by regressing the spread, duration, amount outstanding and years since issue of a bond, allowing the transaction costs reflected in the model to be dynamic through time, adjusting to the market environment by varying with the market spread level. This approach maximises exposure to positive alpha issuers and bonds within each issuers structure, whilst limiting turnover by considering transaction costs.

Figure 4: Explanation of the objective function maximised in portfolio generation


Figure 5: Table of constraints applied during portfolio construction

DTS (duration times spread) is our preferred measure of credit risk

Constraint

Credit Beta Relative DTS +/- 20

Duration Relative spread duration +/- 1 year

Bonds Minimum weight 10bps maximum weight 100bps

Issuers Maximum weight 500bps maximum relative weight 200bps maximum relative DTS 40

Sectors Relative DTS +/- 25

Rating Coarse rating relative weight +/- 50bps

Country Relative DTS +/- 20


Creating systematic bond portfolios

MaximiseCredit factor

Bond rolldown

Bond residual

Transactions costs

The alpha generating credit signal

Penalise for turnover versus current portfolio

The bond specific factors to differentiate within tickers

7

The results shown here use the US investment grade universe (ICE Bank of America Merrill Lynch C0A0 index) and focus on excess return over a key-rate-matched basket of swaps. Initially we conducted the backtest without considering transaction costs to show the return in frictionless markets. This portfolio outperformed the index by 25 basis points (bps) per month before transaction costs (the orange line in Figure 6), indicating the factor construction has considerable alpha potential. However, portfolio turnover was around 50 per cent per month, resulting in a negative return after transaction costs given the less liquid nature of credit markets and high trading costs.

When we introduced controls to limit turnover to around 10 per cent per month, alpha fell to 8bps per month before costs (the blue line in Figure 6). This allowed us to harvest 6bps of alpha after transaction costs.

Figure 6: Excess return of our optimized portfolio versus the index

Index – ICE Bank of America Merrill Lynch C0A0. Source: Fidelity International, March 2019.

The portfolio has systematic positive exposure to all three of our value-adding factors (Figure 7). It has a higher credit factor exposure (around 0.9 on average2), a higher roll down exposure and a higher residual exposure than the index. The portfolio contains around 150 issuers compared to over 1000 in the index and closely matches the index on all other exposures resulting in a historic tracking error of around 1.5 per cent.

2. You may notice that the index has a negative exposure to our credit factor on average. This shows that standard market cap indices, where an issuer’s weight is proportional to the amount of debt they issue, is an inefficient index construction methodology.

Results for US investment grade portfolios

1.0

1.2

1.4

1.6

20182017201620152014201320122011201020092008

Controlled turnover

Factor returns


Figure 7: Factor exposure of the optimized portfolio versus the index

Index – ICE Bank of America Merrill Lynch C0A0. Source: Fidelity International, March 2019.

We performed several tests to validate the implementation of the portfolio. The main consideration was liquidity and how realistic the turnover level was in practice. To test this, we performed the same backtest except we only allowed the optimiser to pick the most liquid bonds from the index by ranking the universe by liquidity and removing the bottom half of the population. Encouragingly this led to only a slight fall in alpha generated from the portfolio (0.1bps per month).

Weighted average exposure Weighted average roll down (bps) Weighted average residual (bps)

Index

Index

Portfoli Po ortfolio

Index

Portfolio

-0.6

0

0.6

1.2

201820162014201220102008-20

-10

0

10

20

201820162014201220102008-10

0

10

20

30

201820162014201220102008

9

Conclusion

Credit markets have developed in recent years – the availability of more reliable historical data and the introduction of more electronic trading has made systematic investing possible in the more liquid markets. As the popularity of fixed income factor-based strategies grows, it is worth keeping in mind that not all approaches are equal. In this paper we have outlined some of the issues that can arise when constructing corporate bond factors and tested their performance. We have demonstrated a post-transaction-cost alpha of around 6bps per month in US investment grade and high yield, and 4.5bps per month in European investment grade.

Our approach is differentiated in four key ways:

■ We avoid the prescription of specific factor definitions influenced by heuristic presumptions about the market by allowing our algorithm to select the value adding factors.

■ The factor creation is dynamic, reacting to changes in market regimes.

■ We have issuer-level and bond-level factors that separate the selection of issuers and bonds in our portfolio construction.

■ We consider turnover at all stages of the process. Rather than adding transaction costs as an afterthought, we build them into both the factor construction process and the portfolio creation.

Factor investing is a new frontier for fixed income investors. Our approach can provide a credible alternative to both traditional management styles, passive or fully actively managed. It has the potential to generate substantial alpha and, due to the systematic nature of the implementation, could be provided at a lower cost than a typical active solution, making it a viable alternative for active investors seeking lower cost products and passive investors seeking higher returns.

We also conducted backtests on the European investment grade and the US high yield markets.

In the European investment grade universe (defined by ICE Bank of America Merrill Lynch ER00), we made a small change to the constraints to account for the differing geography. In Europe, country groupings (such as European periphery) are highly correlated. We therefore added a constraint on the exposure to any country grouping. As expected, the return from our credit factor was lower than the US due to the lower breadth of the investment grade market in Europe. However, our portfolio still generated significant positive alpha.

When we introduced turnover controls into our objective function, the factor portfolio generated alpha of around 6bps per month before transaction costs while turnover fell to around 8 per cent per month. This led to a significant post-transaction-cost alpha of 4.5bps per month.

It is much harder to realise post-transaction-cost systematic alpha in the high yield market due to the lower liquidity on offer. In the high yield version of our multifactor approach we found that including CCC-rated or non-rated names made the proposition unfeasible, so we concentrated on an index containing BB and B-rated names. We also found that the roll down bond factor is unprofitable; we assume this is because issuers with attractive valuations tend to exhibit significantly inverted yield curves making them punitive to hold in our portfolio. We therefore excluded this factor in the high yield construction process.

When we introduced turnover control into our process we generated 12.5bps per month with turnover of around 10 per cent per month. This resulted in significant alpha of 6.1bps per month after transactions costs. In high yield, some of this alpha comes from a liquidity premium. When we tested the approach whilst excluding the least liquid half of the universe, we found that post-transaction-cost alpha fell to around 4bps per month.

Expanding beyond US investment grade


Ang, A., Goetzmann, W. N., and Schaefer, S. (2009). Evaluation of active management of the Norwegian government pension fund–global. report to the Norwegian Ministry of Finance.

Brooks, J., Palhares, D., and Richardson, S. A. (2018). Style Investing in Fixed Income.

Carhart, M. M. (1997). On persistence in mutual fund performance. The Journal of finance, 52(1), 57-82.

Cochrane, J. H. (2011). Presidential address: Discount rates. The Journal of finance, 66(4), 1047-1108.

Fama, E. F., and French, K. R. (1992). The cross‐section of expected stock returns. the Journal of Finance, 47(2), 427-465.

Fama, E. F., and French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of financial economics, 33(1), 3-56.

Harvey, Campbell R., Yan Liu, and Heqing Zhu. “… and the cross-section of expected returns.” The Review of Financial Studies 29.1 (2016): 5-68.

Houweling, P., and Van Zundert, J. (2017). Factor investing in the corporate bond market. Financial Analysts Journal, 73(2), 100-115.

Israel, R., Palhares, D., and Richardson, S. A. (2017). Common factors in corporate bond returns.

Lopez de Prado, M., and Lewis, M. J. (2018). Detection of False Investment Strategies Using Unsupervised Learning Methods

References

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