# On Fund Mapping Regressions Applied to Segregated Funds Hedging Under Regime-Switching Dynamics

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## Abstract

**:**

## 1. Introduction

- The presence of basis risk between underlying assets of segregated funds and their corresponding hedging instruments is assessed empirically. This fills an important gap in the literature as the presence of basis risk is overlooked in the majority of papers treating of variable annuities, with a few exceptions such as Ankirchner et al. (2014).
- Novel parallels between fund mapping-based hedges and minimal variance hedges are drawn. Such conceptual parallels indicate that fund mapping regressions are likely to produce downward biased estimates of capital requirements in the context of regime-switching models.
- The presence of such downward biases in this context are confirmed through simulation.

## 2. Assessment of the Basis Risk Magnitude for Segregated Funds

#### 2.1. Regime-Switching Model

#### 2.2. Estimation Results

## 3. Representation of Basis Risk Through Fund Mapping Regressions

## 4. Hedging of Variable Annuities

#### 4.1. Minimal Variance Hedging

#### 4.2. Fund Mapping Delta Hedging

#### 4.3. Links between Fund Mapping and Minimal Variance Hedging

#### 4.4. Impact of the Fund Mapping Constraints

#### 4.5. Impact of Neglecting the Error Term in the Fund Mapping Regression

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. The Trottier et al. (2018) Hedging Framework

## Appendix B. The Trottier et al. (2018) Simulation Setup

**Table A1.**Baseline parameters in monthly frequency used in simulations of Section 4.4 and Section 4.5.

Maturity (in months) | T | 120 |

Survival probability | ${}_{t}{p}_{660}$ | Projected CPM2014 |

Lapse rate | b | $0.34\%$ |

Total fee rate | ${\omega}_{tot}$ | $0.29\%$ |

Risk-free rate | r | $0.25\%$ |

GMMB guarantee | K | 100 |

Initial value of F and A | ${F}_{0}={A}_{0}$ | 100 |

Initial value of S | ${S}_{0}$ | 100 |

## References

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1. | See Proposition 3.3 of Trottier et al. (2018). |

2. | A negative number of long positions represents a short position. |

3. | There exists a very slight difference between the definition of ${\Delta}_{t}^{\phantom{\rule{-0.166667em}{0ex}}(\Pi )}$ and ${\Delta}_{t}$ which are two versions of the guarantee’s delta, see Appendix A. However this difference is negligible in practice, i.e., ${\Delta}_{t}^{\phantom{\rule{-0.166667em}{0ex}}(\Pi )}\approx {\Delta}_{t}$. It can thus be overlooked. |

4. | See Section 5.2 of the report “Reflection of Hedging in Segregated Fund Valuation. Document 212027” (http://www.cia-ica.ca/docs/default-source/2012/212027e.pdf) by the Canadian Institute of Actuaries. |

**Table 1.**List of funds considered for basis risk assessment. The three letters between brackets for each fund is an identifier for further referral.

[GCE] GWL Canadian Equity (GWLIM) BEL | |

Issuer: | Great-West Life |

Strategy type: | Canadian equity growth (active) |

[GCV] GWL Canadian Value (FGP) NL | |

Issuer: | Great-West Life |

Strategy type: | Canadian equity growth (active) |

[GCI] GWL Equity Index (GWLIM) BEL | |

Issuer: | Great-West Life |

Strategy type: | Canadian equity index (passive) |

[MPC] Manulife Canadian Small Cap Segregated Funds—Cap Category B | |

Issuer: | Manulife |

Strategy type: | Canadian equity small cap (active) |

[MRA] Manulife Canadian Growth Segregated Funds—Series R Category A | |

Issuer: | Manulife |

Strategy type: | Canadian equity growth (active) |

[MNA] Canadian Equity Segregated Funds—NAL/VISTA | |

Issuer: | Manulife |

Strategy type: | Canadian equity large cap (active) |

[RCE] RBC Canadian Equity GIF Series 1 | |

Issuer: | Royal Bank of Canada |

Strategy type: | Canadian equity growth (active) |

[AVL] Assumption/Louisbourg Canadian Equity Fund Series A | |

Issuer: | Assomption Vie |

Strategy type: | Canadian equity growth (active) |

[LCG] LL Canadian Equity Growth (CC&L) BEL | |

Issuer: | London Life |

Strategy type: | Canadian equity growth (active) |

[LCE] LL SRI Canadian Equity (GWLIM) BEL | |

Issuer: | London Life |

Strategy type: | Canadian equity growth (active) |

[RUS] RBC U.S. Equity GIF Series 1 | |

Issuer: | Royal Bank of Canada |

Strategy type: | US equity (active) |

[AUS] Assumption/Louisbourg U.S. Equity Fund Series A | |

Issuer: | Assomption Vie |

Strategy type: | US equity (active) |

GCE | GCV | GCI | MPC | MRA | MNA | RCE | AVL | LCG | LCE | RUS | AUS | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Mutual fund | ||||||||||||

${\mu}_{1}^{\left(F\right)}$ | 0.0083 | 0.0104 | 0.0091 | 0.0168 | 0.0139 | 0.0078 | 0.0100 | 0.0060 | 0.0113 | 0.0088 | 0.0050 | 0.0162 |

(0.0024) | (0.0022) | (0.0022) | (0.0034) | (0.0037) | (0.0021) | (0.0025) | (0.0030) | (0.0029) | (0.0026) | (0.0029) | (0.0055) | |

${\sigma}_{1}^{\left(F\right)}$ | 0.0330 | 0.0236 | 0.0321 | 0.0356 | 0.0375 | 0.0330 | 0.0297 | 0.0368 | 0.0308 | 0.0315 | 0.0306 | 0.0326 |

(0.0019) | (0.0019) | (0.0018) | (0.0026) | (0.0029) | (0.0018) | (0.0018) | (0.0021) | (0.0020) | (0.0018) | (0.0021) | (0.0045) | |

${\mu}_{2}^{\left(F\right)}$ | −0.0080 | −0.0110 | −0.0135 | −0.0206 | −0.0119 | −0.0105 | −0.0224 | 0.0023 | −0.0089 | −0.0094 | −0.0096 | −0.0031 |

(0.0104) | (0.0061) | (0.0119) | (0.0128) | (0.0097) | (0.0104) | (0.0125) | (0.0105) | (0.0064) | (0.0099) | (0.0049) | (0.0032) | |

${\sigma}_{2}^{\left(F\right)}$ | 0.0734 | 0.0493 | 0.0776 | 0.0971 | 0.0772 | 0.0760 | 0.0745 | 0.0783 | 0.0525 | 0.0664 | 0.0350 | 0.0375 |

(0.0081) | (0.0041) | (0.0085) | (0.0094) | (0.0061) | (0.0081) | (0.0089) | (0.0081) | (0.0048) | (0.0072) | (0.0037) | (0.0022) | |

TSX 60 index futures (for CAD funds) / S&P 500 index futures (for US funds) | ||||||||||||

${\mu}_{1}^{\left(S\right)}$ | 0.0085 | 0.0117 | 0.0092 | 0.0116 | 0.0113 | 0.0082 | 0.0106 | 0.0076 | 0.0100 | 0.0081 | 0.0102 | 0.0193 |

(0.0026) | (0.0025) | (0.0025) | (0.0024) | (0.0027) | (0.0024) | (0.0024) | (0.0025) | (0.0028) | (0.0027) | (0.0028) | (0.0036) | |

${\sigma}_{1}^{\left(S\right)}$ | 0.0348 | 0.0286 | 0.0345 | 0.0252 | 0.0288 | 0.0353 | 0.0293 | 0.0315 | 0.0310 | 0.0328 | 0.0297 | 0.0208 |

(0.0022) | (0.0023) | (0.0021) | (0.0018) | (0.0025) | (0.0020) | (0.0018) | (0.0018) | (0.0020) | (0.0019) | (0.0019) | (0.0026) | |

${\mu}_{2}^{\left(S\right)}$ | −0.0134 | −0.0114 | −0.0190 | −0.0109 | −0.0095 | −0.0178 | −0.0224 | −0.0078 | −0.0057 | −0.0084 | −0.0145 | −0.0028 |

(0.0127) | (0.0093) | (0.0146) | (0.0105) | (0.0074) | (0.0141) | (0.0130) | (0.0115) | (0.0074) | (0.0105) | (0.0062) | (0.0034) | |

${\sigma}_{2}^{\left(S\right)}$ | 0.0858 | 0.0764 | 0.0924 | 0.0849 | 0.0616 | 0.0938 | 0.0791 | 0.0856 | 0.0661 | 0.0761 | 0.0470 | 0.0397 |

(0.0097) | (0.0071) | (0.0104) | (0.0077) | (0.0055) | (0.0114) | (0.0093) | (0.0087) | (0.0055) | (0.0076) | (0.0042) | (0.0023) | |

Correlations | ||||||||||||

${\rho}_{1}$ | 0.9439 | 0.8727 | 0.9402 | 0.7349 | 0.8123 | 0.9001 | 0.9815 | 0.9016 | 0.9410 | 0.9366 | 0.9734 | 0.8208 |

(0.0090) | (0.0230) | (0.0091) | (0.0448) | (0.0415) | (0.0146) | (0.0034) | (0.0151) | (0.0109) | (0.0101) | (0.0054) | (0.0565) | |

${\rho}_{2}$ | 0.9068 | 0.7120 | 0.9069 | 0.9232 | 0.6585 | 0.7486 | 0.9824 | 0.9080 | 0.8684 | 0.9306 | 0.9292 | 0.9455 |

(0.0269) | (0.0584) | (0.0279) | (0.0210) | (0.0654) | (0.0716) | (0.0068) | (0.0252) | (0.0318) | (0.0226) | (0.0229) | (0.0090) | |

Transition matrix | ||||||||||||

${P}_{1,1}$ | 0.9767 | 0.9375 | 0.9788 | 0.9364 | 0.9272 | 0.9728 | 0.9749 | 0.9885 | 0.9754 | 0.9877 | 0.9848 | 0.9604 |

(0.0137) | (0.0284) | (0.0114) | (0.0254) | (0.0313) | (0.0130) | (0.0143) | (0.0084) | (0.0148) | (0.0091) | (0.0117) | (0.0360) | |

${P}_{2,1}$ | 0.0850 | 0.1129 | 0.0906 | 0.1202 | 0.1377 | 0.1386 | 0.1009 | 0.0287 | 0.0373 | 0.0297 | 0.0254 | 0.0074 |

(0.0527) | (0.0610) | (0.0507) | (0.0492) | (0.0545) | (0.0619) | (0.0578) | (0.0237) | (0.0237) | (0.0250) | (0.0205) | (0.0081) |

**Table 3.**Proportion $1-\sqrt{1-{\rho}^{2}}$ of the standard deviation of cash flow injections that can be eliminated through a local minimal variance hedge for a correlation between the mutual fund and the hedging asset of $\rho $.

$\rho $ | 0.65 | 0.7 | 0.75 | 0.8 | 0.85 | 0.9 | 0.95 | 1 |

$1-\sqrt{1-{\rho}^{2}}$ | 0.240 | 0.286 | 0.339 | 0.400 | 0.473 | 0.564 | 0.688 | 1 |

**Table 4.**Linear regression results for the fund mapping model (2) for each respective fund and the corresponding hedging instrument. Mutual fund descriptions are provided in Table 1. For Canadian equity funds, the hedging instrument is the TSX 60 index futures. For US equity funds, the hedging instrument is the S&P 500 index futures.

GCE | GCV | GCI | MPC | MRA | MNA | RCE | AVL | LCG | LCE | RUS | AUS | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

${\beta}_{0}$ | 0.0017 | 0.0010 | 0.0016 | 0.0009 | 0.0012 | 0.0022 | −0.0004 | 0.0016 | 0.0011 | 0.0012 | −0.0015 | −0.0008 |

(0.0012) | (0.0016) | (0.0012) | (0.0022) | (0.0028) | (0.0018) | (0.0007) | (0.0016) | (0.0013) | (0.0011) | (0.0010) | (0.0011) | |

${\beta}_{1}$ | 0.8159 * | 0.5321 * | 0.8052 * | 1.0822 * | 0.9188 * | 0.6921 * | 0.9485 * | 0.8837 * | 0.7938 * | 0.8605 * | 0.8342 * | 0.9197 * |

(0.0247) | (0.0314) | (0.0232) | (0.0438) | (0.0621) | (0.0350) | (0.0149) | (0.0307) | (0.0304) | (0.0240) | (0.0283) | (0.0307) | |

${\sigma}_{M}$ | 0.0175 | 0.0233 | 0.0172 | 0.0288 | 0.0403 | 0.0258 | 0.0079 | 0.0222 | 0.0180 | 0.0142 | 0.0107 | 0.0144 |

(0.0009) | (0.0011) | (0.0008) | (0.0015) | (0.0020) | (0.0013) | (0.0005) | (0.0011) | (0.0009) | (0.0007) | (0.0014) | (0.0017) |

**Table 5.**Calculation of the fund mapping parameters obtained under constraints (3) for the various funds described in Table 1. The difference compared to the unconstrained model (see Table 2) is given in brackets. Teal brackets indicate an improvement from the perspective of the insurer performing the hedge (i.e., higher mean, lower volatility, or higher correlation), and red brackets indicate a worsening (i.e., lower mean, higher volatility, or lower correlation).

GCE | GCV | GCI | MPC | MRA | MNA | RCE | AVL | LCG | LCE | RUS | AUS | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

First regime | ||||||||||||

${\mu}_{1}^{\left(F\right)}$ | 0.0086 | 0.0072 | 0.0090 | 0.0135 | 0.0116 | 0.0079 | 0.0097 | 0.0084 | 0.0090 | 0.0082 | 0.0070 | 0.0170 |

[+0.0003] | [−0.0032] | [−0.0001] | [−0.0033] | [−0.0023] | [+0.0001] | [−0.0003] | [+0.0024] | [−0.0023] | [−0.0006] | [+0.0020] | [+0.0008] | |

${\sigma}_{1}^{\left(F\right)}$ | 0.0333 | 0.0278 | 0.0327 | 0.0397 | 0.0482 | 0.0355 | 0.0289 | 0.0356 | 0.0305 | 0.0316 | 0.0270 | 0.0240 |

[+0.0003] | [+0.0042] | [+0.0006] | [+0.0041] | [+0.0107] | [+0.0025] | [−0.0008] | [−0.0012] | [−0.0003] | [+0.0001] | [−0.0036] | [−0.0086] | |

${\rho}_{1}$ | 0.8515 | 0.5469 | 0.8501 | 0.6872 | 0.5492 | 0.6872 | 0.9624 | 0.7813 | 0.8076 | 0.8937 | 0.9186 | 0.7985 |

[−0.0924] | [−0.3260] | [−0.0901] | [−0.0477] | [−0.2631] | [−0.2129] | [−0.0192] | [−0.1203] | [−0.1334] | [−0.0429] | [−0.0548] | [−0.0223] | |

Second regime | ||||||||||||

${\mu}_{2}^{\left(F\right)}$ | −0.0093 | −0.0050 | −0.0137 | −0.0109 | −0.0076 | −0.0101 | −0.0216 | −0.0053 | −0.0034 | −0.0060 | −0.0136 | −0.0033 |

[−0.0013] | [+0.0060] | [−0.0002] | [+0.0097] | [+0.0043] | [+0.0004] | [+0.0008] | [−0.0076] | [+0.0055] | [+0.0034] | [−0.0040] | [−0.0002] | |

${\sigma}_{2}^{\left(F\right)}$ | 0.0722 | 0.0469 | 0.0764 | 0.0963 | 0.0695 | 0.0699 | 0.0754 | 0.0788 | 0.0555 | 0.0670 | 0.0406 | 0.0393 |

[−0.0012] | [−0.0024] | [−0.0012] | [−0.0008] | [−0.0077] | [−0.0061] | [+0.0009] | [+0.0005] | [+0.0030] | [+0.0006] | [+0.0056] | [+0.0018] | |

${\rho}_{2}$ | 0.9702 | 0.8676 | 0.9743 | 0.9541 | 0.8148 | 0.9292 | 0.9946 | 0.9594 | 0.9461 | 0.9774 | 0.9650 | 0.9301 |

[+0.0634] | [+0.1556] | [+0.0674] | [+0.0309] | [+0.1563] | [+0.1806] | [+0.0122] | [+0.0514] | [+0.0777] | [+0.0468] | [+0.0358] | [−0.0154] |

**Table 6.**Calculation of the fund mapping parameters obtained under constraints (3) assuming no basis risk (i.e., ${\sigma}_{M}=0$) for the various funds described in Table 1. The difference compared to the unconstrained model (see Table 2) is given in brackets. Teal brackets indicate an improvement from the perspective of the insurer performing the hedge (i.e., higher mean, lower volatility, or higher correlation), and red brackets indicate a worsening (i.e., lower mean, higher volatility, or lower correlation).

GCE | GCV | GCI | MPC | MRA | MNA | RCE | AVL | LCG | LCE | RUS | AUS | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

First regime | ||||||||||||

${\mu}_{1}^{\left(F\right)}$ | 0.0086 | 0.0072 | 0.0090 | 0.0135 | 0.0116 | 0.0079 | 0.0097 | 0.0084 | 0.0090 | 0.0082 | 0.0070 | 0.0170 |

[+0.0003] | [−0.0032] | [−0.0001] | [−0.0033] | [−0.0023] | [+0.0001] | [−0.0003] | [+0.0024] | [−0.0023] | [−0.0006] | [+0.0020] | [+0.0008] | |

${\sigma}_{1}^{\left(F\right)}$ | 0.0284 | 0.0152 | 0.0278 | 0.0273 | 0.0265 | 0.0244 | 0.0278 | 0.0278 | 0.0246 | 0.0282 | 0.0248 | 0.0191 |

[−0.0046] | [−0.0084] | [−0.0043] | [−0.0083] | [−0.0110] | [−0.0086] | [−0.0019] | [−0.0090] | [−0.0062] | [−0.0033] | [−0.0058] | [−0.0135] | |

${\rho}_{1}$ | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |

[+0.0561] | [+0.1273] | [+0.0598] | [+0.2651] | [+0.1877] | [+0.0999] | [+0.0185] | [+0.0984] | [+0.0590] | [+0.0634] | [+0.0266] | [+0.1792] | |

Second regime | ||||||||||||

${\mu}_{2}^{\left(F\right)}$ | −0.0093 | −0.0050 | −0.0137 | −0.0109 | −0.0076 | −0.0101 | −0.0216 | −0.0053 | −0.0034 | −0.0060 | −0.0136 | −0.0033 |

[−0.0013] | [+0.0060] | [−0.0002] | [+0.0097] | [+0.0043] | [+0.0004] | [+0.0008] | [−0.0076] | [+0.0055] | [+0.0034] | [−0.0040] | [−0.0002] | |

${\sigma}_{2}^{\left(F\right)}$ | 0.0700 | 0.0407 | 0.0744 | 0.0919 | 0.0566 | 0.0649 | 0.0750 | 0.0756 | 0.0525 | 0.0655 | 0.0392 | 0.0365 |

[−0.0034] | [−0.0086] | [−0.0032] | [−0.0052] | [−0.0206] | [−0.0111] | [+0.0005] | [−0.0027] | [−0.0001] | [−0.0009] | [+0.0042] | [−0.0010] | |

${\rho}_{2}$ | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |

[+0.0932] | [+0.2880] | [+0.0931] | [+0.0768] | [+0.3415] | [+0.2514] | [+0.0176] | [+0.0920] | [+0.1316] | [+0.0694] | [+0.0708] | [+0.0545] |

**Table 7.**Results for the minimal variance hedge applied under the unconstrained model (top panel), under the fund mapping constraints (middle panel), and under the fund mapping constraints with ${\sigma}_{M}=0$ (bottom panel). Funds are described in Table 1. The statistics are for the discounted sum of injections: ${\sum}_{t=1}^{T}{e}^{-rt}{I}_{t}$.

GCE | GCV | GCI | MPC | MRA | MNA | RCE | AVL | LCG | LCE | RUS | AUS | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Unconstrained model | ||||||||||||

Mean | 3.13 | 6.78 | 3.39 | 6.10 | 3.07 | 2.91 | 8.00 | 1.42 | 8.24 | 6.23 | 14.31 | 10.48 |

Std.Dev. | 4.97 | 8.24 | 5.19 | 9.62 | 10.17 | 6.91 | 4.11 | 8.05 | 8.21 | 6.78 | 6.06 | 4.71 |

${\mathrm{CVaR}}_{0.70}^{\mathbb{P}}$ | 9.16 | 17.27 | 9.79 | 17.76 | 15.65 | 11.36 | 13.06 | 10.29 | 18.66 | 14.80 | 21.69 | 16.07 |

${\mathrm{CVaR}}_{0.80}^{\mathbb{P}}$ | 10.73 | 19.58 | 11.46 | 20.22 | 18.75 | 13.60 | 14.05 | 12.19 | 20.82 | 16.65 | 23.28 | 17.41 |

${\mathrm{CVaR}}_{0.90}^{\mathbb{P}}$ | 13.04 | 22.73 | 13.90 | 23.76 | 23.12 | 16.93 | 15.48 | 15.11 | 23.77 | 19.32 | 25.48 | 19.53 |

${\mathrm{CVaR}}_{0.95}^{\mathbb{P}}$ | 15.04 | 25.26 | 16.01 | 26.78 | 26.54 | 19.78 | 16.73 | 17.61 | 26.23 | 21.61 | 27.21 | 21.51 |

${\mathrm{CVaR}}_{0.99}^{\mathbb{P}}$ | 18.96 | 29.90 | 20.16 | 32.60 | 32.66 | 25.23 | 19.22 | 22.19 | 31.02 | 26.10 | 30.17 | 25.75 |

Fund mapping model | ||||||||||||

Mean | 2.46 | 4.32 | 2.71 | 2.83 | 1.67 | 0.84 | 7.47 | 2.34 | 3.73 | 3.62 | 10.77 | 8.70 |

Std.Dev. | 4.86 | 6.93 | 4.85 | 7.54 | 10.15 | 6.53 | 3.78 | 6.21 | 5.16 | 4.50 | 4.36 | 4.85 |

${\mathrm{CVaR}}_{0.70}^{\mathbb{P}}$ | 8.36 | 12.95 | 8.60 | 11.80 | 14.04 | 8.81 | 12.08 | 9.88 | 10.05 | 9.13 | 15.86 | 14.52 |

${\mathrm{CVaR}}_{0.80}^{\mathbb{P}}$ | 9.79 | 14.92 | 10.02 | 13.82 | 17.03 | 10.84 | 12.99 | 11.60 | 11.54 | 10.36 | 16.88 | 15.67 |

${\mathrm{CVaR}}_{0.90}^{\mathbb{P}}$ | 11.92 | 17.72 | 12.13 | 16.78 | 21.35 | 13.90 | 14.28 | 14.14 | 13.74 | 12.14 | 18.41 | 17.33 |

${\mathrm{CVaR}}_{0.95}^{\mathbb{P}}$ | 13.75 | 20.02 | 13.95 | 19.36 | 24.90 | 16.49 | 15.38 | 16.29 | 15.61 | 13.64 | 19.70 | 18.75 |

${\mathrm{CVaR}}_{0.99}^{\mathbb{P}}$ | 17.27 | 24.29 | 17.36 | 24.38 | 31.40 | 21.36 | 17.49 | 20.42 | 19.14 | 16.53 | 22.16 | 21.49 |

Fund mapping model without basis risk | ||||||||||||

Mean | 2.91 | 5.15 | 3.16 | 3.89 | 3.61 | 1.75 | 7.60 | 3.19 | 4.21 | 4.04 | 10.97 | 9.03 |

Std.Dev. | 2.01 | 2.15 | 2.13 | 2.26 | 1.65 | 1.68 | 2.71 | 2.89 | 2.10 | 2.45 | 3.02 | 2.97 |

${\mathrm{CVaR}}_{0.70}^{\mathbb{P}}$ | 5.41 | 7.63 | 5.79 | 6.58 | 5.65 | 3.85 | 10.88 | 6.77 | 6.81 | 7.11 | 14.27 | 11.91 |

${\mathrm{CVaR}}_{0.80}^{\mathbb{P}}$ | 5.97 | 7.96 | 6.38 | 7.23 | 6.04 | 4.37 | 11.40 | 7.54 | 7.27 | 7.73 | 14.70 | 12.18 |

${\mathrm{CVaR}}_{0.90}^{\mathbb{P}}$ | 6.86 | 8.45 | 7.31 | 8.31 | 6.62 | 5.18 | 12.18 | 8.75 | 7.95 | 8.67 | 15.19 | 12.53 |

${\mathrm{CVaR}}_{0.95}^{\mathbb{P}}$ | 7.70 | 8.89 | 8.19 | 9.35 | 7.16 | 6.00 | 12.91 | 9.86 | 8.57 | 9.53 | 15.50 | 12.81 |

${\mathrm{CVaR}}_{0.99}^{\mathbb{P}}$ | 9.61 | 9.90 | 10.14 | 11.69 | 8.42 | 7.71 | 14.45 | 12.03 | 9.88 | 11.29 | 16.03 | 13.37 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Trottier, D.-A.; Godin, F.; Hamel, E.
On Fund Mapping Regressions Applied to Segregated Funds Hedging Under Regime-Switching Dynamics. *Risks* **2018**, *6*, 78.
https://doi.org/10.3390/risks6030078

**AMA Style**

Trottier D-A, Godin F, Hamel E.
On Fund Mapping Regressions Applied to Segregated Funds Hedging Under Regime-Switching Dynamics. *Risks*. 2018; 6(3):78.
https://doi.org/10.3390/risks6030078

**Chicago/Turabian Style**

Trottier, Denis-Alexandre, Frédéric Godin, and Emmanuel Hamel.
2018. "On Fund Mapping Regressions Applied to Segregated Funds Hedging Under Regime-Switching Dynamics" *Risks* 6, no. 3: 78.
https://doi.org/10.3390/risks6030078