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Vanguard Research July 2018 Global active bond fund returns: a factor decomposition How much of a global active bond fund’s return can be explained by risk factors, and how much can be attributed to alpha (manager security selection and market timing)? We studied the ten-year average performance of 15 types of global active bond funds sorted by investment mandate and currency to find out. We found that the average fund return variation could largely be explained by common bond factors such as term and credit, as expected. However, currency and high yield exposures also contributed significantly. The majority of the 15 fund types generated statistically significant positive average gross alphas on both equal-weighted and asset- weighted bases. On a net basis, alphas were generally statistically indistinguishable from zero. With all else equal, funds with lower expense ratios will have higher net alpha. Global active bond funds are not all created equal. Due diligence, particularly performance attribution, is critical when evaluating active manager efficacy and the sources of a fund’s results. Daren Roberts; Thomas Paradise; and Chris Tidmore, CFA

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Page 1: Global active bond fund returns: a factor decompositionVanguard Research July 2018 Global active bond fund returns: a factor decomposition How much of a global active bond fund’s

Vanguard Research July 2018

Global active bond fund returns: a factor decomposition

■ How much of a global active bond fund’s return can be explained by risk factors, and how much can be attributed to alpha (manager security selection and market timing)? We studied the ten-year average performance of 15 types of global active bond funds sorted by investment mandate and currency to find out.

■ We found that the average fund return variation could largely be explained by common bond factors such as term and credit, as expected. However, currency and high yield exposures also contributed significantly. The majority of the 15 fund types generated statistically significant positive average gross alphas on both equal-weighted and asset-weighted bases. On a net basis, alphas were generally statistically indistinguishable from zero. With all else equal, funds with lower expense ratios will have higher net alpha.

■ Global active bond funds are not all created equal. Due diligence, particularly performance attribution, is critical when evaluating active manager efficacy and the sources of a fund’s results.

Daren Roberts; Thomas Paradise; and Chris Tidmore, CFA

Page 2: Global active bond fund returns: a factor decompositionVanguard Research July 2018 Global active bond fund returns: a factor decomposition How much of a global active bond fund’s

1 Global active bond funds are the active subset of Morningstar’s global fixed income category. Global fixed income portfolios invest in fixed income securities domiciled in developed countries throughout the world. Some may also include those of emerging markets.

2 The currency in which a fund is offered.2

Notes on risk

All investing is subject to risk, including possible loss of principal. Past performance does not guarantee future results. Bond funds are subject to interest rate risk, which is the chance bond prices overall will decline because of rising interest rates, and credit risk, which is the chance a bond issuer will fail to pay interest and principal in a timely manner or that negative perceptions of the issuer’s ability to make such payments will cause the price of that bond to decline. High-yield bonds generally have medium- and lower-range credit quality ratings and are therefore subject to a higher level of credit risk than bonds with higher credit quality ratings. There is no guarantee that any particular asset allocation or mix of funds will meet your investment objectives or provide you with a given level of income. The performance of an index is not an exact representation of any particular investment, as you cannot invest directly in an index. U.S. government backing of Treasury or agency securities applies only to the underlying securities and does not prevent share-price fluctuations. Unlike stocks and bonds, U.S. Treasury bills are guaranteed as to the timely payment of principal and interest. Although the income from the U.S. Treasury obligations held in a fund is subject to federal income tax, some or all of that income may be exempt from state and local taxes. Investments in securities issued by non-U.S. companies are subject to risks including country/regional risk and currency risk. These risks are especially high in emerging markets. Currency hedging transactions incur extra expenses, may not perfectly offset foreign currency exposures, and may eliminate any chance to benefit from favorable fluctuations in those currencies.

Introduction

What are the sources of an active global bond fund’s return?1 How much is attributable to factors (systemic exposures) and how much to manager security selection and timing? These are a few of the many due diligence questions investors should ask. Knowing how a fund achieves its performance will help them gauge whether it is suitable for meeting their objectives.

Previous Vanguard research (Bosse 2013) examined the performance of U.S. active bond funds from 1998 through 2012. It found that differences were based on long-term, persistent bets on risk factors such as credit risk. Our paper expands the scope of that research to include global active bond funds, acknowledging the roles of foreign currency and available investment mandates. It seeks to explain the variance of average global bond manager returns using factor-based regression.

The global active bond fund landscape

As of December 31, 2016, the Morningstar database contained more than 7,000 global active bond funds. They included all investor share classes in more than 26 base currencies2 and net assets under management (AUM) of $638 billion. As Figure 1 shows, the most common benchmark provider was Bloomberg Barclays. Many funds used flagship indexes such as the Bloomberg Barclays Global Aggregate Bond Index as a starting point for portfolio construction. More than 85% of the funds (based on AUM) offered investment strategies in six base currencies: the U.S. dollar (USD), the European euro (EUR), the British pound (GBP), the Swiss franc (CHF), the Australian dollar (AUD), and the Canadian dollar (CAD).

For the purposes of our analysis, common broad global investment-grade benchmarks have more similarities than differences. As shown in Figure 2, these include market-capitalization-weighted index construction,

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Figure 1. Morningstar database of global active bond funds

Common benchmark providers Funds’ AUM by base currency

35% Bloomberg Barclays17% FTSE17% Not benchmarked13% Other 7% J.P. Morgan 4% Bank of America/Merrill Lynch 4% Absolute return 3% Custom

35% USD25% EUR15% Other11% GBP 6% CHF 5% CAD 3% AUD

Source: Morningstar, Inc., as of December 31, 2016.

Figure 2. Selected benchmark descriptions

Bloomberg Barclays Global Aggregate Bond Index(BbgBarclays Global Agg)

FTSE World Broad Investment-Grade Bond Index (FTSE WBIG USD)

J.P. Morgan Global Aggregate Bond Index (Old GABI)

Inception date January 1, 1990 December 31, 1998 December 2002

Coupon Fixed-rate, callable fixed-to-floating-rate (during fixed- rate term only) bonds with step-up coupons that change only on predetermined schedule

Fixed-rate, no-zero- coupon bonds

Varies for developed and emerging-market debt

Minimum maturity At least one year At least one year Varies by sub-asset class

Minimum amount outstanding

$300 million in USD and equivalent in local currencies

Varies by sub-asset class Varies by market

Minimum quality BBB–/Baa3 or higher (S&P and Moody’s, respectively)

BBB–/Baa3 or higher (S&P and Moody’s, respectively)

BBB–/Baa3 or higher (S&P and Moody’s, respectively)

Weighting Market capitalization Market capitalization Market capitalization

Rebalancing Monthly Monthly Monthly

Currency CAD, CLP, MXN, USDCHF, CZK, DKK, EUR, GBP, HUF, ILS, NOK, PLN, RUB, SEK, ZAR, AUD, HKD, JPY, KRW, MYR, NZD, SGD, THB

AUD, CAD, CHF, DKK, EUR, GBP, JPY, MXN, MYR, NOK, PLN, SEK, SGD, USD, ZAR

Only USD- and EUR-denominated instruments are eligible for the credit asset index.*

* For inclusion criteria for all other asset classes, see JPMorgan Chase & Co. (2017).

Notes: Currencies listed are the Canadian dollar (CAD), Chilean peso (CLP), Mexican peso (MXN), U.S. dollar (USD), Swiss franc (CHF), Czech krona (CZK), Danish krone (DKK), European euro (EUR), British pound (GBP), Hungarian forint (HUF), Israeli shekel (ILS), Norwegian krone (NOK), Polish zloty (PLN), Russian ruble (RUB), Swedish krona (SEK), South African rand (ZAR), Australian dollar (AUD), Hong Kong dollar (HKD), Japanese yen (JPY), Korean won (KRW), Malaysian ringgit (MYR), New Zealand dollar (NZD), Singapore dollar (SGD), and Thai bhat (THB),Sources: Bloomberg, FTSE Russell, and J.P. Morgan.

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J.P. Morgan Old GABI

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Figure 3. Selected index characteristics as of December 31, 2016

Correlations Duration and yield to maturity

Annualized returns Volatility

Sources: Bloomberg, FTSE Russell, and J.P. Morgan.

investment-grade-bond-only profiles, minimum amounts outstanding, and monthly rebalancing. Figure 3 shows that the similar criteria have led to similar risk, return,

duration, and yield characteristics and near-perfect correlations. Therefore, we included all global bond funds at the start of our analysis.

Page 5: Global active bond fund returns: a factor decompositionVanguard Research July 2018 Global active bond fund returns: a factor decomposition How much of a global active bond fund’s

3 The factor analysis is intended to be explanatory in nature only (it does not consider factor replication). Interpretation of and reasons for factor risk are beyond the scope of this paper.

4 We excluded the following broad categories that did not meet this criterion: absolute return, custom benchmarks, regional strategies, equity benchmarks, and funds with no benchmarks.

5 Six base currencies were enough to create a sufficient sample of the average investor experience for the global active bond manager categories as defined. Because of data constraints and fund counts, the Global Credit category did not have six currencies. Only fund categories whose base currency was the same as their benchmark’s were included. 5

A factor-based framework to explain average manager return

One approach to performance analysis is to calculate a fund’s return in excess of its prospectus or style benchmark. However, managers are not necessarily limited to holding securities in their fund’s benchmark. For instance, Thatcher (2009) found that large-capitalization, active fund managers held mid- and small-cap stock positions during periods when those stocks outperformed to increase returns. This mismatch means that a fund’s excess return can provide a misleading view of alpha.

Another strategy is to use a factor-based framework to estimate alpha (Rowley et al., 2017). This approach greatly reduces benchmark mismatch and allows funds to be compared regardless of investment mandate. Removing the emphasis on a benchmark also increases the available sample size.

Our analysis used a factor-based framework to assess the ten-year (2007 through 2016) performance of active global bond funds. We used a four-factor model consisting of term, credit, high yield, and currency. Term and credit factors have been well-researched in academic literature (Fama and French, 1992). We added high yield and currency to the model as they represented additional exposures managers could use to express their investment views.

The role of currency (FX) has been examined by Pojarliev and Levich (2008). They analyzed the performance of FX-only funds using four factors: FX carry, FX trend, FX value, and FX volatility. Since our research sample included funds with the ability to use full or partial hedging and FX strategies, our definition of currency was intentionally less specific. We were not concerned

with the type of currency strategy an active global bond manager might implement; we only analyzed to what extent currency exposure may have affected performance.

Prior academic literature and researchers have identified numerous other factors, but we limited our study to these because they have been extensively tested and widely accepted. We also confined our analysis to funds whose investment strategies could be reasonably explained by factors.3

Data and methodology

We first grouped each global active bond fund into a broad category based on its stated benchmark.4 For example, a fund benchmarked to the Bloomberg Barclays Global Aggregate Bond Index would be assigned to the Global Aggregate category. Our broad categories were:

• Global Aggregate

• Global Government

• Global Credit.

Next, we further grouped funds by base currency, the currency in which they offered investment. Each fund’s broad category and base currency created its global fund category:5

• Global Aggregate USD, EUR, GBP, CHF, AUD, and CAD

• Global Government USD, EUR, GBP, CHF, AUD, and CAD

• Global Credit USD, EUR, and GBP.

For each fund category, we created a time series of monthly cross-sectional average excess return over the risk-free rate on both equal- and asset-weighted bases for the 120 months ended December 2016. In this way, we captured the performance of more than

Page 6: Global active bond fund returns: a factor decompositionVanguard Research July 2018 Global active bond fund returns: a factor decomposition How much of a global active bond fund’s

6 The currency factor for each global fund category is specific to its base currency.6

1,500 funds and mitigated the effects of survivorship bias. The average AUM of the funds in our sample over this period represented approximately 20% of global active bond manager AUM. Figure 4 shows the average equal-weighted monthly return in excess of the risk-free rate on both gross- and net-of-expense-ratio bases by fund category. The average return was positive for all 15 categories. However, the returns as displayed do not explain what accounts for the managers’ performance. In addition, because the returns are not stated in a common base currency, manager comparisons are insufficient.

To allow for a comparison across fund categories, each category’s cross-sectional monthly average return in excess of the risk-free rate was regressed on four independent variables: term, credit, high yield, and currency (see Figure 5).6 We used the following formula:

Ri,t,c = ai,c + β1i,cTermi,t + β2

i,cCrediti,t + β3i,cHighYieldi,t +

β4i,cCurrencyi,t + εi,t,c

where R = monthly excess return, i = currency, t = time, and c = category.

Figure 4. Average monthly excess return

Equal-weighted global fund returns were positive before accounting for factor exposures

Figure 5. Factors used in the regression analysis

Note: Because of insufficient data, gross AUD returns and Global Credit funds denominated in CHF, AUD, and CAD were excluded from the analysis.Source: Vanguard calculations, based on data from Morningstar, Inc., and Bloomberg.

* Corporate credit excess return is the corporate credit total return minus the duration-neutral Treasury total return.Source: Vanguard.

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Risk-free rate (Rf) Ibbotson and Associates 1-month Treasury bill total return

Term Bloomberg Barclays Global Government Bond Index 10+ year total return (base currency-hedged) minus Rf

Credit Bloomberg Barclays Global Aggregate Float Adjusted Bond Index (base currency-hedged) corporate credit excess return*

High yield Bloomberg Barclays Global High Yield Bond Index (base currency-hedged) total return minus Bloomberg Barclays Global Aggregate Bond Index (base currency-hedged) total return

Currency Bloomberg Barclays Global Aggregate Float Adjusted Bond Index currency return excluding base currency

Page 7: Global active bond fund returns: a factor decompositionVanguard Research July 2018 Global active bond fund returns: a factor decomposition How much of a global active bond fund’s

Figure 6. Adding the currency factor materially increased the model’s explanatory power

Source: Vanguard calculations, based on data from Morningstar, Inc., and Bloomberg.

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Regression results

We conducted stepwise regressions to understand the improvement in adjusted R-squared attributable to the four factors. For each fund category, we regressed the equal- and asset-weighted cross-sectional average

returns against term, term + credit, term + credit + high yield, and term + credit + high yield + currency. Adding the currency factor materially increased the model’s explanatory power. Figure 6 displays the adjusted R-squared results for each fund category.

Page 8: Global active bond fund returns: a factor decompositionVanguard Research July 2018 Global active bond fund returns: a factor decomposition How much of a global active bond fund’s

Figures 7a and 7b show the equal- and asset-weighted regression results for each of the four factors. As expected, term and credit provided high degrees of statistical significance in all fund categories. For example, Global Aggregate and Global Credit funds had statistically significant credit coefficients, as did selected Global Government funds (USD, EUR, and CHF).

Conventional wisdom would suggest that government funds should not have credit exposure. However, in this case, the average Global Government USD, EUR, and

CHF funds may have invested in corporate bonds or, within those categories, the average manager return may have had a high correlation to the credit factor.

For the high yield factor, we observed that four of the six Global Aggregate categories and all of the Global Credit categories had coefficients statistically significant to at least 1% on an equal-weighted basis. For Global Aggregate USD funds, the exposure to high yield was generally consistent with AQR Capital Management (2017) findings.

Figure 7a. Term and credit coefficients were generally statistically significant

Source: Vanguard calculations, based on data from Morningstar, Inc., and Bloomberg.

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Page 9: Global active bond fund returns: a factor decompositionVanguard Research July 2018 Global active bond fund returns: a factor decomposition How much of a global active bond fund’s

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Figure 7b. Surprisingly, high yield and currency coefficients were statistically significant

Source: Vanguard calculations, based on data from Morningstar, Inc., and Bloomberg.

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Page 10: Global active bond fund returns: a factor decompositionVanguard Research July 2018 Global active bond fund returns: a factor decomposition How much of a global active bond fund’s

Figure 8. Statistically, gross alphas were significant (and positive); net alphas were not different from zero

Note: Because of insufficient data, gross AUD returns were excluded from the analysis.Source: Vanguard calculations, based on data from Morningstar, Inc., and Bloomberg.

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The two biggest insights from the regression results involved currency and alphas (see Figure 8). The currency coefficient for most of the 15 fund categories was statistically significant to at least 1% (and all were

significant to at least 10%) on an equal-weighted basis. On an asset-weighted basis, it was significant to at least 1% for 13 out of 15 categories.

Page 11: Global active bond fund returns: a factor decompositionVanguard Research July 2018 Global active bond fund returns: a factor decomposition How much of a global active bond fund’s

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Figure 9. Average monthly net excess return factor decomposition (equal-weighted)

Note: Because of insufficient data, Global Credit funds denominated in CHF, AUD, and CAD were excluded from the analysis.Source: Vanguard calculations, based on data from Morningstar, Inc., and Bloomberg.

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AlphaTermCreditHigh yieldCurrency

These results prompt the follow-up due diligence question, “To what degree did the excess return come from currency?” During this time, the average global bond fund investor could have reasonably expected that some portion of excess return would come from currency, although the amount would vary by fund category. However, currency exposure also varied significantly by fund manager. Using the Games-Howell post-hoc method7 (see Appendix A-4), we found that on average, non-Australian Global Aggregate and Global Government fund managers took on more currency exposure than that of the average Australian global fund manager.

Secondly, 10 out of the 15 and 7 out of 15 fund categories had statistically significant positive average gross alphas on an equal-weighted and an asset-weighted basis, respectively. Our findings are generally consistent with Konstantinov (2016), who looked at short- and long-term alpha for EUR base-currency funds. Net alphas were generally statistically indistinguishable from zero; most were positive. This suggests that during this time, after accounting for factor exposure, the average manager generated outperformance because of selection or timing on a gross basis but not on a net basis. Again, these results represent the average fund

in each category. The inverse relationship between expense ratio and excess return is well-documented (see Elton et al., 2002, and Kinnel 2010). All else being equal, funds with lower expense ratios will have higher net alpha. The takeaway for investors is that finding low-cost managers is critical.

Sources of return

Our models help estimate the sources of return for each fund category (see Figure 9). In effect, the source is a function of each factor’s return and each category’s sensitivity to that factor. During the ten-year period studied, the term factor contributed the majority of average monthly return variation. Credit and high yield, while positive, made relatively marginal contributions.

Currency’s contribution (to the degree it was successfully used by the fund manager) varied. For example, its contribution to GBP managers’ return benefited from many possible strategies (such as no hedging or partial hedging). However, its contribution to CHF managers’ return was negative. After accounting for factors, net alphas contributed to varying degrees, most significantly for AUD managers.

7 The Games-Howell post-hoc test is a nonparametric approach used to compare combinations of groups.

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Implications for investors

Regardless of which fund category investors choose for their portfolios, they must clearly understand what type of market exposure a fund offers. Using a factor-based regression analysis, we were able to decompose returns into factor exposures and alpha. However, investors may choose other means (or other factors) to isolate risks. For example, an investor with adequate tools and data could choose a holdings-based approach. Nonetheless, all investors should consider the following due diligence questions (at a minimum) before investing in an active global bond fund:

• Am I comfortable taking on the risks this fund may expose me to?

• Am I comfortable with a possible risk-return overlap with other funds?

• Does the risk-return profile of this fund align with the goals of my broader portfolio?

• Is there a more efficient way to obtain similar exposures?

We highlight these sample questions not to discourage investors from allocating to active global bond managers in whom they have conviction. We simply believe that they should make well-informed choices that will best meet their portfolio objectives.

Conclusion

We analyzed the time series returns of several categories of active bond fund managers. We found that return variation could be explained predominantly by four factors: term, credit, high yield, and currency. Average gross alphas were generally positive; net alphas were statistically no different from zero.

When selecting global active bond funds, investors should be cognizant of the sources of their returns. These findings represent merely a sample of the due diligence needed. Follow-up questions can lead to more informed decisions that can help investors realize their objectives.

References

AQR Capital Management, 2017. Alternative Thinking: The Illusion of Active Fixed Income Diversification, available at: https://www.aqr.com/Insights/Research/Alternative-Thinking/The-Illusion-of-Active-Fixed-Income-Diversification.

Bloomberg Barclays, 2017. Bloomberg Barclays Index Methodology, available at: https://www.bbhub.io/indices/sites/2/2017/03/Index-Methodology-2017-03-17-FINAL-FINAL.pdf.

Bosse, Paul M., Brian R. Wimmer, and Christopher B. Philips, 2013. Active Bond-Fund Excess Returns: Is It Alpha . . . or Beta? Valley Forge, Pa.: The Vanguard Group.

Elton, Edwin J., Martin. J. Gruber, and Jeffrey A. Busse, 2002. Are Investors Rational? Choices Among Index Funds. Journal of Finance 59(1): 261–288.

Fama, Eugene, and Kenneth French, 1993. Common Risk Factors in the Returns on Stocks and Bonds, Journal of Financial Economics 33(1993): 3–56.

FTSE Russell, 2018. FTSE World Broad Investment-Grade Bond Index (WorldBIG) Factsheet, available at: https://yieldbook.com/x/ixFactSheet/factsheet_monthly_wbig.pdf.

JPMorgan Chase & Co., 2017. Index Methodology, available at: https://markets.jpmorgan.com/#homepage.

Kinnel, Russel, 2010. How Expense Ratios and Star Ratings Predict Success, available at http://news.morningstar.com/articlenet/article.aspx?id=347327.

Konstantinov, Gueorgui, 2016. Capturing Short-Term and Long-Term Alpha of Global Bond Portfolios: Evidence From EUR-Investors’ Perspective, Financial Markets and Portfolio Management, 2016 30 (3) 377.

Pojarliev, Momtchil, and Richard M. Levich, 2012. A New Look at Currency Investing. Charlottesville, Va.: CFA Institute.

Rowley, James J., Jr., Garrett L. Harbron, and Matthew C. Tufano, 2017. In Pursuit of Alpha: Evaluating Active and Passive Strategies. Valley Forge, Pa.: The Vanguard Group.

Thatcher, William R., 2009. When Indexing Works and When It Doesn’t in U.S. Equities: The Purity Hypothesis. Journal of Investing 18(3): 8–11.

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Appendix A-1—Equal-weighted cross-sectional monthly average regressions

Global Aggregate funds U.S. dollar (USD) European euro (EUR) British pound (GBP)

Coef. Std. error t-stat. p-value Coef. Std. error t-stat. p-value Coef. Std. error t-stat. p-value

Intercept (net alpha) 0.068 0.049 1.40 0.164 0.017 0.038 0.44 0.658 0.013 0.064 0.20 0.841

Term 0.421 0.026 16.45 0.000 0.364 0.019 18.87 0.000 0.433 0.035 12.44 0.000

Credit 0.249 0.064 3.88 0.000 0.266 0.050 5.37 0.000 0.239 0.084 2.83 0.005

High yield 0.134 0.032 4.23 0.000 0.030 0.024 1.27 0.208 0.104 0.039 2.68 0.008

Currency 0.483 0.022 21.82 0.000 0.313 0.014 22.37 0.000 0.417 0.028 14.70 0.000

Adjusted R-squared 91% 89% 83%

Observations 571 267 46

Swiss franc (CHF) Australian dollar (AUD) Canadian dollar (CAD)

Coef. Std. error t-stat. p-value Coef. Std. error t-stat. p-value Coef. Std. error t-stat. p-value

Intercept (net alpha) 0.047 0.052 0.91 0.366 0.105 0.035 2.98 0.004 −0.080 0.054 −1.47 0.144

Term 0.403 0.028 14.63 0.000 0.351 0.017 20.09 0.000 0.431 0.028 15.44 0.000

Credit 0.308 0.070 4.42 0.000 0.157 0.044 3.58 0.001 0.183 0.071 2.57 0.012xx

High yield −0.024 0.033 −0.73 0.466 0.117 0.022 5.41 0.000 0.133 0.035 3.78 0.000

Currency 0.472 0.020 23.04 0.000 0.059 0.012 4.82 0.000 0.553 0.025 21.90 0.000

Adjusted R-squared 86% 80% 89%

Observations 27 82 24

Global Government funds

U.S. dollar (USD) European euro (EUR) British pound (GBP)

Coef. Std. error t-stat. p-value Coef. Std. error t-stat. p-value Coef. Std. error t-stat. p-value

Intercept (net alpha) 0.027 0.056 0.49 0.624 0.038 0.043 0.89 0.374 −0.035 0.048 −0.73 0.470

Term 0.371 0.029 12.63 0.000 0.289 0.022 13.10 0.000 0.391 0.026 14.88 0.000

Credit 0.189 0.074 2.57 0.011xx 0.291 0.057 5.12 0.000 0.010 0.064 0.15 0.881

High yield 0.089 0.036 2.45 0.016xx 0.008 0.027 0.30 0.766 0.035 0.029 1.19 0.235

Currency 0.343 0.025 13.49 0.000 0.357 0.016 22.26 0.000 0.584 0.021 27.34 0.000

Adjusted R-squared 82% 86% 94%

Observations 73 154 67

Swiss franc (CHF) Australian dollar (AUD) Canadian dollar (CAD)

Coef. Std. error t-stat. p-value Coef. Std. error t-stat. p-value Coef. Std. error t-stat. p-value

Intercept (net alpha) 0.001 0.031 0.02 0.983 0.186 0.048 3.86 0.000 −0.021 0.046 −0.44 0.659

Term 0.447 0.016 27.39 0.000 0.405 0.024 16.90 0.000 0.437 0.024 18.24 0.000

Credit 0.133 0.041 3.21 0.002 0.084 0.060 1.39 0.169 0.081 0.061 1.32 0.189

High yield 0.008 0.020 0.38 0.702 0.023 0.030 0.77 0.442 0.098 0.030 3.23 0.002

Currency 0.476 0.012 39.30 0.000 0.032 0.017 1.89 0.061x 0.634 0.022 29.28 0.000

Adjusted R-squared 95% 72% 94%

Observations 50 19 52

Global Credit funds

U.S. dollar (USD) European euro (EUR) British pound (GBP)

Coef. Std. error t-stat. p-value Coef. Std. error t-stat. p-value Coef. Std. error t-stat. p-value

Intercept (net alpha) −0.100 0.042 −2.35 0.020xx 0.044 0.049 0.90 0.370 0.172 0.098 1.75 0.082x

Term 0.449 0.022 20.09 0.000 0.389 0.025 15.53 0.000 0.450 0.054 8.39 0.000

Credit 0.660 0.056 11.79 0.000 0.637 0.064 9.89 0.000 0.408 0.130 3.14 0.002

High yield 0.228 0.028 8.27 0.000 0.091 0.031 2.93 0.004 0.096 0.060 1.60 0.111

Currency 0.105 0.019 5.41 0.000 0.096 0.018 5.29 0.000 0.382 0.044 8.75 0.000

Adjusted R-squared 94% 84% 67%

Observations 236 81 32

Note: Data in boldface were significant at the 1% level, data followed by xx were significant at the 5% level, and data followed by x were significant at the 10% level.Source: Vanguard.

Page 14: Global active bond fund returns: a factor decompositionVanguard Research July 2018 Global active bond fund returns: a factor decomposition How much of a global active bond fund’s

14Note: Data in boldface were significant at the 1% level, data followed by xx were significant at the 5% level, and data followed by x were significant at the 10% level.Source: Vanguard.

Appendix A-2—Asset-weighted cross-sectional monthly average regressions

Global Aggregate funds U.S. dollar (USD) European euro (EUR) British pound (GBP)

Coef. Std. error t-stat. p-value Coef. Std. error t-stat. p-value Coef. Std. error t-stat. p-value

Intercept (net alpha) 0.058 0.042 1.37 0.173 0.007 0.033 0.20 0.839 0.018 0.068 0.26 0.793

Term 0.448 0.022 20.24 0.000 0.348 0.017 20.68 0.000 0.464 0.037 12.52 0.000

Credit 0.282 0.055 5.09 0.000 0.307 0.043 7.08 0.000 0.348 0.090 3.87 0.000

High yield 0.122 0.027 4.45 0.000 0.021 0.021 1.01 0.315 0.060 0.041 1.45 0.150

Currency 0.506 0.019 26.44 0.000 0.113 0.012 9.21 0.000 0.285 0.030 9.46 0.000

Adjusted R-squared 94% 84% 77%

Observations 499 249 48

Swiss franc (CHF) Australian dollar (AUD) Canadian dollar (CAD)

Coef. Std. error t-stat. p-value Coef. Std. error t-stat. p-value Coef. Std. error t-stat. p-value

Intercept (net alpha) −0.010 0.041 −0.23 0.817 0.191 0.046 4.12 0.000 −0.078 0.088 −0.89 0.376

Term 0.464 0.022 21.02 0.000 0.385 0.023 16.66 0.000 0.380 0.045 8.37 0.000

Credit 0.325 0.056 5.82 0.000 0.308 0.058 5.30 0.000 0.170 0.116 1.46 0.146

High yield 0.028 0.027 1.06 0.292 0.098 0.029 3.42 0.001 0.093 0.057 1.63 0.106

Currency 0.569 0.016 34.73 0.000 0.024 0.016 1.52 0.130 0.633 0.041 15.43 0.000

Adjusted R-squared 93% 78% 79%

Observations 27 78 24

Global Government funds

U.S. dollar (USD) European euro (EUR) British pound (GBP)

Coef. Std. error t-stat. p-value Coef. Std. error t-stat. p-value Coef. Std. error t-stat. p-value

Intercept (net alpha) 0.132 0.066 1.99 0.049xx 0.072 0.075 0.96 0.340 0.094 0.069 1.35 0.178

Term 0.438 0.035 12.56 0.000 0.283 0.039 7.32 0.000 0.251 0.038 6.62 0.000

Credit 0.272 0.087 3.12 0.002 0.451 0.099 4.54 0.000 0.031 0.092 0.33 0.739

High yield 0.105 0.043 2.45 0.016xx −0.053 0.048 −1.10 0.275 −0.054 0.042 −1.29 0.199

Currency 0.353 0.030 11.69 0.000 0.474 0.028 16.92 0.000 0.372 0.031 12.03 0.000

Adjusted R-squared 80% 77% 77%

Observations 67 142 62

Swiss franc (CHF) Australian dollar (AUD) Canadian dollar (CAD)

Coef. Std. error t-stat. p-value Coef. Std. error t-stat. p-value Coef. Std. error t-stat. p-value

Intercept (net alpha) 0.015 0.040 0.37 0.713 0.253 0.075 3.36 0.001 -0.039 0.050 −0.77 0.444

Term 0.458 0.021 21.51 0.000 0.354 0.037 9.48 0.000 0.459 0.026 17.70 0.000

Credit 0.197 0.054 3.65 0.000 0.163 0.094 1.73 0.086x 0.069 0.066 1.04 0.303

High yield −0.042 0.026 −1.62 0.107 0.039 0.046 0.86 0.394 0.097 0.033 2.97 0.004

Currency 0.589 0.016 37.19 0.000 −0.082 0.026 −3.14 0.002 0.321 0.023 13.68 0.000

Adjusted R-squared 94% 54% 85%

Observations 51 20 57

Global Credit funds

U.S. dollar (USD) European euro (EUR) British pound (GBP)

Coef. Std. error t-stat. p-value Coef. Std. error t-stat. p-value Coef. Std. error t-stat. p-value

Intercept (net alpha) −0.024 0.043 −0.56 0.575 0.029 0.047 0.61 0.540 0.089 0.087 1.02 0.308

Term 0.448 0.023 19.67 0.000 0.439 0.024 18.13 0.000 0.561 0.048 11.80 0.000

Credit 0.677 0.057 11.86 0.000 0.542 0.062 8.71 0.000 0.328 0.115 2.85 0.005

High yield 0.140 0.028 4.97 0.000 0.093 0.030 3.10 0.002 0.144 0.053 2.73 0.007

Currency 0.069 0.020 3.49 0.001 0.090 0.018 5.15 0.000 0.060 0.039 1.55 0.124

Adjusted R-squared 91% 84% 65%

Observations 229 76 30

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Appendix A-3—Asset-weighted average monthly excess return was positive before accounting for factor exposures

Appendix A-4—On average, non-Australian Global Aggregate and Government bond fund managers took on more currency exposure than that of Australian global fund managers

Currency exposure

Note: Because of insufficient data, gross AUD returns and Global Credit funds denominated in CHF, AUD, and CAD were excluded from the analysis.Source: Vanguard calculations, based on data from Morningstar, Inc., and Bloomberg.

Notes: Equal-weighted EUR Global Aggregate funds were statistically significant to 5%. All other results were statistically significant to 1%.Source: Vanguard calculations, based on data from Morningstar, Inc., and Bloomberg.

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Page 16: Global active bond fund returns: a factor decompositionVanguard Research July 2018 Global active bond fund returns: a factor decomposition How much of a global active bond fund’s

© 2018 The Vanguard Group, Inc. All rights reserved. Vanguard Marketing Corporation, Distributor.

ISGGAB 072018

Vanguard Research

P.O. Box 2600 Valley Forge, PA 19482-2600

Connect with Vanguard® > vanguard.com

CFA® is a registered trademark owned by CFA Institute.

Appendix A-5—Average monthly net excess return factor decomposition (asset-weighted)

Source: Vanguard calculations, based on data from Morningstar, Inc., and Bloomberg.

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