# Redemption Runs in Canadian Corporate Bond Funds?

## Introduction

Mutual funds that manage fixed-income securities are growing: the amount of assets in these funds has doubled over the last decade. Focusing on Canadian corporate bond funds (CCBFs), Arora, Merali and Ouellet Leblanc (2018a) find that these investment vehicles direct an increasing share of domestic savings to corporate borrowers. Since CCBFs manage 8 per cent of outstanding corporate bonds issued in Canadian dollars, they play an important role in the Canadian financial system. However, they also face the risk of redemption runs, that is, of large and unexpected outflows.

In this note, we measure the asymmetry between investor inflows and outflows to gauge redemption run risk in CCBFs. Investor flows into and out of mutual funds are largely determined by fund performance (Chevalier and Ellison 1997). Funds that outperform their benchmark return are rewarded with inflows, whereas those that underperform are penalized with outflows. We find that outflows due to fund underperformance are larger than inflows due to outperformance. This asymmetric relationship between flow and performance is evidence of risk of redemption runs. In addition, we find that this asymmetry varies with time and across fund characteristics: outflows are greater during episodes of market volatility and in funds that are less liquid, as measured by their portfolio shares of cash and equivalents.

Mutual funds are aware of redemption run risk and employ several tools to mitigate it (Arora and Ouellet Leblanc 2018b). Nonetheless, the noted asymmetry suggests that CCBFs could remain vulnerable to redemption runs. This analysis of asymmetry in investor flows complements analysis of corporate bond fund assets by Arora, Merali and Ouellet Leblanc (2018a), which points to a potential increase in the likelihood of large redemptions. The vulnerability due to redemption run risk and its implications have also been discussed by the Financial Stability Board, the International Monetary Fund, the European Central Bank and the Bank of England (FSB 2017; IMF 2015; ECB 2017; BoE 2016).

## What causes redemption runs in corporate bond mutual funds?

Mutual funds perform liquidity transformation when they purchase illiquid corporate debt but provide daily cash redemptions to their investors. As previously mentioned, underperforming mutual funds experience outflows, while outperforming mutual funds experience inflows. The flow-performance relationship, in the presence of liquidity transformation, generates the risk of a redemption run.

When mutual funds underperform, investors may redeem their shares. Funds must pay these investors in cash within a short time frame. They can use liquidity buffers, such as cash and equivalents, to meet redemption demand. They can then rebuild these buffers by later offering less-liquid corporate bonds at a lower price to sell them quickly for cash. However, selling bonds at a discount depresses future performance of the fund. Additional forward-looking investors may choose to pre-emptively exit to avoid shouldering the liquidity discount. This new round of investor redemptions reignites the demand for in-cash payment in a short time frame and may eventually trigger a redemption run.

Although redemption runs represent a risk, they occur infrequently. Mutual funds employ a host of liquidity tools, such as redemption fees and lock-up periods, to discourage runs, and in an extreme scenario, can suspend redemptions altogether. However, we can detect whether funds are vulnerable to redemption run risk by analyzing the asymmetry of the flow-performance relationship. The degree of a fund’s asymmetry is an indicator of potential runs because larger outflows due to underperformance may indicate a higher probability of having to sell illiquid assets to raise cash quickly. In contrast, a symmetric flow-performance relationship can signal no risk of redemption runs, seen in more-liquid equity mutual funds, as documented by Goldstein, Jiang and Ng (2017).

## Is there a risk of redemption runs in corporate bond mutual funds?

Following Goldstein, Jiang and Ng (2017), we estimate a relationship between fund flows and fund performance (see Technical Appendix for details). Chart 1 shows that for underperformance of 2 per cent, Canadian corporate bond funds see 3.58 per cent in outflows, and for outperformance of 2 per cent, the inflows stand at only 0.43 per cent. This asymmetry in outflows versus inflows for the same level of performance is evidence of redemption run risk. This result is in line with the work of Goldstein, Jiang and Ng (2017) that analyzes US corporate bond mutual funds.

### Chart 1: The flow-performance relationship of Canadian corporate bond mutual funds is asymmetric

Note: AUM = assets under managment
Sources: Morningstar and Bank of Canada calculations Last observation: December 2016

## Does the risk of redemption run increase during volatile periods?

Corporate bond mutual funds face redemption run risk, but this risk can change when the probability of underperformance is greater, for instance, when market volatility is high (e.g., during the financial crisis in 2008 or the taper tantrum in 2013).

To test this hypothesis, we use the Chicago Board Options Exchange Volatility Index (VIX) to investigate how underperforming funds fare during volatile market conditions. Keeping with Goldstein, Jiang and Ng (2017), we focus on underperforming funds. Analysis of the subsample can result in different estimates than in Chart 1, but it allows for comparison with existing results in the United States.

Chart 2 shows that, when volatility is high, outflows following underperformance of 2 per cent increase from 1.30 to 3.77 per cent for CCBFs. This is evidence of increasing redemption run risk and is in line with the results of Goldstein, Jiang and Ng (2017) for US corporate bond mutual funds.

### Chart 2: The flow-performance asymmetry increases during higher market volatility

Note: AUM = assets under managment. See Technical Appendix for details.
Sources: Morningstar and Bank of Canada calculations Last observation: December 2016

## Do more-liquid funds face a lower risk of redemption runs?

While redemption run risk is present in CCBFs and increases during periods of market volatility, it also depends on the degree of liquidity transformation in the fund.

Holdings in cash and cash equivalents, called the liquidity ratio, are a good proxy for fund-level liquidity. Again, following Goldstein, Jiang and Ng (2017), we focus on underperforming funds. Here we replace the VIX with the liquidity ratio. The average effects shown in Chart 3 are different from those in Chart 2 and Chart 1, but can be compared with established results based on US mutual fund data.

Our results indicate that a higher level of liquid holdings reduces outflows after underperformance, consistent with decreased redemption run risk. Chart 3 compares outflows, in response to underperformance of 2 per cent, from funds with high liquidity ratios at the 75th percentile with those from funds with median liquidity ratios. In this example, the lower liquidity ratio increases outflows from 4.30 to 5.85 per cent.

Overall, the evidence is in line with the US results of Goldstein, Jiang and Ng (2017) and provides further empirical support for theoretical work in Zeng (2017), linking redemption run risk in corporate bond mutual funds with fund liquidity management.

### Chart 3: A higher liquidity ratio lowers the flow-performance asymmetry in Canadian funds

Note: AUM = assets under management. In our sample, 5 per cent is the median cash ratio, and 10 per cent is the 75th percentile cash ratio. See the Technical Appendix for details.
Sources: Morningstar and Bank of Canada calculations Last observation: December 2016

## Conclusion

We find that outflows due to fund underperformance are larger than inflows due to outperformance, and we interpret this asymmetry as evidence of redemption run risk in Canadian corporate bond mutual funds. The risk of redemption runs increases during periods of market volatility, but funds holding more liquidity can reduce this risk.

These results highlight important features of CCBF flows, complementing the work of Arora, Merali and Ouellet Leblanc (2018a) and Arora and Ouellet Leblanc (2018b). Future work can incorporate these findings in a larger stress-testing framework.

## Technical Appendix

### Data: fund selection

We define Canadian corporate bond funds (CCBFs) from the set of open-ended, Canadian-domiciled, active mutual funds.

Using Morningstar Direct monthly data from 2000 to 2016, we identify corporate bond funds by employing two filters:

(i) A subset of funds based on Morningstar categories (fixed-income fund, inflation-protected fund, long-term fund, short-term fund and high-yield fund)

(ii) A refinement of the subset through average lifetime asset allocations

For each fund we calculate average allocation to corporate bonds, government debt securities, equities and cash over the fund’s lifetime. We define corporate bond funds as having at least 40 per cent of their portfolio weight in corporate bonds and at most 40 per cent in equities over the fund’s lifetime. Our selection procedure yields 1,078 share classes of Canadian corporate bond funds. The unit of observation is a fund share class.

This definition is different from the one used by Arora, Merali and Ouellet Leblanc (2018a) and Arora and Ouellet Leblanc (2018b). In this note, we focus on a subset of CCBFs that hold a larger share of corporate debt and perform more liquidity transformation, since these funds are most likely to show the asymmetric flow-performance relationship.

### Data: flow-performance measurement

To analyze the flow-performance relationship of corporate bond funds, we need estimates of fund flows and fund performance. First, we estimate fund flows by calculating the change in total net assets (TNA), after controlling for monthly net fund returns (Equation 1):

$$Flow_{i,t}=\frac{TNA_{i,t}-TNA_{i,t-1} (1+R_{i,t} )}{TNA_{i,t-1} } \qquad (1)$$

Then, we calculate each fund’s idiosyncratic performance (alpha) over a rolling 12-month window, using a two-factor capital asset pricing model where we control for equity and bond market returns (Equation 2):

$$r_{i,t-12→t-1}=α_{i,t}+β_{i,t}^{bd} (Mkrt_{i,t-12→t-1}^{bd} )$$$$+β_{i,t}^{eq} (Mrkt_{i,t-12→t-1}^{eq} )$$$$+ε_{i,t} \qquad (2)$$

The backward-looking performance measure models the information set of an investor at time “t” when deciding whether to stay invested in the fund or redeem the shares. The investor in month “t” can make such a decision based only on past fund performance. Table 1 lists the sources for market factors used in the alpha estimation.

### Table 1: Data sources for the alpha estimation

Table 1: Data sources for the alpha estimation
Variable Source
Risk-free rates Name: Treasury 1-month
Code: CANSIM Table 176-0043
Time: Dec 1999 to Dec 2016
Equity market factor Name: SPTSX Composite
Code: Tot_ret_index_gross_dvds
Time: Jan 2000 to Dec 2016
Code: CAN0 Index
Time: Jan 2000 to Dec 2016
Note: SPTSX = S&P/TSX Composite Index, CANSIM = Canadian Socio-Economic Information Management System

The risk-free yields are lagged by one month since they represent the choice available to an investor at the beginning of the month of investing in either a risk-free or risky asset.

### Econometric analysis: finding redemption run risk in corporate bond mutual funds

To find redemption run risk, we consider the following regression model (Equation 3):

$$Flows_{i,t}=δ_{i,t}$$$$+β_1 Alpha_{i,t-12→t-1}$$$$+β_2 \{Alpha_{i,t-12→t-1} \times \Bbb{I} (Alpha_{i,t-12→t-1}<0)\}$$$$+β_3 \Bbb{I} (Alpha_{i,t-12→t-1}<0)$$$$+γ \times Controls_{i,t} +ε_{i,t}, \qquad (3)$$

where Controls are flow lagged by one period, Log(TNA), Log(Age) and calendar month fixed-effect dummies (February to December). Table 2 presents the results.

### Table 2: Finding redemption run risk.

Table 2: Finding redemption run risk. 1
Alpha 0.2151
(0.2582)
Alpha X (Alpha < 0) 0.9179*
(0.5206)
Alpha < 0 -0.0131***
(0.0018)
Controls Yes
Number of observations 50,586
R-squared 0.05

### Econometric analysis: redemption run risk under market stress

To analyze the dynamics of redemption run risk during periods of market stress, we build a market stress indicator using the VIX. The indicator takes on a value of 1 when the VIX level is above the sample period average, and 0 otherwise.

Then, we use the indicator in the following regression model (Equation 4):

$$Flows_{i,t}=δ_{i,t}$$$$+β_1 Alpha_{i,t-12→t-1}$$$$+β_2 \Bbb{I} (VIX_t<\overline{VIX})$$$$+β_3 \{ Alpha_{i,t-12→t-1 } \times \Bbb{I} (VIX_t<\overline{VIX})\}$$$$+γ \times Controls_{i,t}$$$$+ε_{i,t} ∀ Alpha<0 \qquad (4)$$

Table 3 presents the results.

### Table 3: Redemption run risk and market stress

Table 3: Redemption run risk and market stress
Alpha 0.6514
(0.5366)
Market stress 0.0195***
(0.0022)
Market stress X Alpha 2.2068***
(0.7553)
Controls Yes
Number of observations 31,376
R-squared 0.04

### Econometric analysis: redemption run risk and fund liquidity

To capture the effect of fund liquidity on flow-performance sensitivity, we use the following regression model (Equation 5):

$$Flows_{i,t}=δ_{i,t}$$$$+β_1 Alpha_{i,t-12→t-1}$$$$+β_2 Cash\%_{i,t}$$$$+β_3 \{ Alpha_{i,t-12→t-1} \times Cash\%_{i,t}\}$$$$+γ \times Controls_{i,t}$$$$+ε_{i,t} ∀ Alpha<0 \qquad (5)$$

Table 4 presents the results.

### Table 4: Redemption run risk and fund liquidity

Table 4: Redemption run risk and fund liquidity
Alpha 2.2461***
(0.4741)
Cash ratio -0.0290***
(0.0106)
Alpha X cash ratio -15.4376***
(5.0205)
Controls Yes
Number of Observations 31,376
R-squared 0.04

### Table 5: Summary statistics of Canadian corporate bond mutual funds

Table 5: Summary statistics of Canadian corporate bond mutual funds
Canadian bond funds Mean Std. dev. Minimum Maximum P1 P5 P10 P25 Median P75 P90 P95 P99 N
Excess return 0.25% 0.44% -4.08% 4.80% -0.86% -0.33% -0.18% 0.03% 0.24% 0.46% 0.71% 0.92% 1.53% 60283
Return 0.35% 0.43% -3.87% 4.81% -0.72% -0.23% -0.07% 0.13% 0.34% 0.56% 0.80% 0.99% 1.59% 60283
Alpha 0.01% 0.37% -2.77% 4.66% -0.80% -0.41% -0.27% -0.13% -0.04% 0.08% 0.39% 0.65% 1.39% 60283
Cash ratio (monthly) 7.05% 7.88% -4.86% 101.11% -0.69% 0.19% 0.91% 2.35% 4.87% 8.94% 15.87% 21.36% 35.38% 73142
Govt. ratio (monthly) 22.79% 19.99% -17.45% 100.39% 0.00% 0.00% 0.00% 1.80% 22.38% 40.63% 49.48% 53.67% 63.14% 73142
Corp. bond ratio (monthly) 65.13% 21.78% 0.00% 104.00% 17.12% 32.90% 38.45% 47.30% 61.72% 87.44% 93.17% 95.28% 98.08% 73142
Equity ratio (monthly) 0.80% 5.00% -2.83% 104.36% 0.00% 0.00% 0.00% 0.00% 0.00% 0.23% 1.75% 2.75% 9.88% 73142
Flows 1.21% 10.63% -31.76% 66.00% -31.65% -8.60% -4.77% -1.92% -0.11% 2.23% 7.74% 14.92% 65.54% 51699
Log(TNA) (in millions) 2.15 3.07 -13.82 9.67 -8.72 -3.26 -1.47 0.65 2.43 4.20 5.60 6.50 7.76 62138
Log(Age) (in years) 1.14 1.18 -2.48 3.92 -2.48 -1.10 -0.41 0.46 1.23 1.96 2.58 2.88 3.47 73021

Notes:
1) Flows are winsorized at the 1 per cent level to handle outliers, as is standard in the literature.
2) Data are adjusted to remove observations that do not fall in line with mutual fund leverage requirements. In Canada, as per NI 81-104, open-ended mutual funds are not allowed to borrow more than 5 per cent of their net asset value (NAV), and they are not allowed to short more than 20 per cent of their NAV.
3) The unit of observation is fund share class per month.

## Note

1. 1. For this and subsequent regression tables, standard errors are clustered at the fund share class level, and p-value significance stands as *10% **5% ***1%[]

## References

1. Arora, R., N. Merali and G. Ouellet Leblanc. 2018a. “Did Canadian Corporate Bond Funds Increase their Exposures to Risks?” Bank of Canada Staff Analytical Note 2018-7.
2. Arora, R. and G. Ouellet Leblanc. 2018b. “How do Canadian Corporate Bond Funds Meet Investor Redemptions?” Bank of Canada Staff Analytical Note 2018-14.
3. Bank of England (BoE). 2016. Financial Stability Report (November)
4. Chevalier, J. and G. Ellison. 1997. “Risk Taking by Mutual Funds as a Response to Incentives.” Journal of Political Economy 105 (6): 1167–1200.
5. European Central Bank (ECB). 2017. Financial Stability Review (May).
6. Financial Stability Board (FSB). 2017. Policy Recommendations to Address Structural Vulnerabilities from Asset Management Activities.
7. Goldstein, I., H. Jiang and D. T. Ng. 2017. “Investor Flows and Fragility in Corporate Bond Funds.” Journal of Financial Economics 126 (3): 592–613.
8. International Monetary Fund (IMF). 2015. Global Financial Stability Report (April).
9. Zeng, Y. 2017. “A Dynamic Theory of Mutual Fund Runs and Liquidity Management.” European Systemic Risk Board Working Paper Series No.42.

## Acknowledgements

With thanks to Chen Fan and Nadeem Merali for excellent research assistance. I am also thankful to Guillaume Bédard-Pagé, Jean-Sébastien Fontaine, Sermin Gungor, Guillaume Ouellet Leblanc, Jon Witmer and Jun Yang for helpful comments and suggestions. This research was performed using the Edith computing cluster resource at the Bank of Canada.

## Avis d’exonération de responsabilité

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