Additional regression analyses of the fund’s historical factor exposure

Below, we include results from additional regression analyses of the funds historical factor exposure.

Table 1 shows results from a multivariate regression where the fund’s benchmarks are included as an explanatory factor. As in our report, published 4 May¹, all relative returns, benchmarks and factor portfolios are measured in USD.

Table 1

Multifactor regression coefficients (t-values in parentheses). Significant (non-zero at 5% confidence) coefficients in bold type. Annualized intercept and intercept estimate bounds at a 95% confidence level are given at the bottom of the tables. R-squared is not adjusted for the number of factors in the model.

GPFG	Since inception	Last 10 years	Last 5 years
Benchmark	0.03 (5.4)	0.01 (1.9)	0.01 (1.2)
Term	-0.02 (-2.1)	0.00 (-0.2)	-0.03 (-1.8)
Credit Aa	0.04 (3.1)	0.09 (3.7)	-0.05 (-1.7)
Credit Baa	0.05 (4.2)	0.06 (3.1)	0.01 (0.2)
Credit Caa	0.00 (-1.1)	0.00 (-0.3)	0.00 (0.5)
Emerging	0.00 (1.0)	0.01 (1.1)	-0.01 (-1.7)
Value/Growth	-0.01 (-1.5)	0.01 (0.5)	-0.02 (-1.7)
Small/Large	0.02 (1.9)	-0.01 (-0.6)	0.03 (1.6)
Low Volatility	0.00 (-0.2)	-0.02 (-1.7)	-0.02 (-2.4)
% variability explained (R2)	44 %	57 %	45 %
Annualized intercept (alpha)	0.141% (1.0)	-0.0112% (-0.1)	0.1795% (1.1)
Intercept – Lower bound	-0.1447%	-0.4194%	-0.1612%
Intercept – Upper bound	0.4267%	0.397%	0.5203%

Equity portfolio	Since inception	Last 10 years	Last 5 years
Benchmark	0.01 (1.3)	0.00 (0.6)	0.00 (-0.3)
Emerging	0.01 (1.6)	0.01 (0.9)	-0.02 (-3.3)
Value/Growth	-0.04 (-4.4)	-0.03 (-1.8)	-0.03 (-2.3)
Small/Large	0.02 (1.7)	0.00 (0.2)	0.05 (2.6)
Low Volatility	-0.02 (-3.6)	-0.04 (-4.2)	-0.03 (-3.6)
% variability explained (R2)	28 %	44 %	52 %
Annualized intercept (alpha)	0.5232% (2.9)	0.3344% (1.7)	0.1305% (0.8)
Intercept – Lower bound	0.1638%	-0.0622%	-0.1801%
Intercept – Upper bound	0.8827%	0.731%	0.4411%

Fixed-income portfolio	Since inception	Last 10 years	Last 5 years
Benchmark	0.06 (6.3)	0.05 (3.3)	0.01 (0.9)
Term	-0.07 (-4.2)	-0.05 (-2.1)	-0.05 (-2.4)
Credit Aa	0.08 (3.9)	0.14 (3.9)	-0.03 (-0.6)
Credit Baa	0.11 (6.3)	0.15 (4.8)	-0.02 (-0.7)
Credit Caa	0.00 (-0.6)	0.00 (-0.3)	0.00 (0.2)
% variability explained (R2)	37 %	47 %	12 %
Annualized intercept (alpha)	0.0195% (0.1)	-0.1641% (-0.5)	0.2929% (1.2)
Intercept – Lower bound	-0.4161%	-0.8491%	-0.1803%
Intercept – Upper bound	0.4552%	0.5209%	0.7662%

In Table 2 we show the results for regression analysis where the relative returns and the fund’s benchmarks are measured in the fund’s currency basket, risk factor returns are in USD.

Table 2

Multifactor regression coefficients (t-values in parentheses). Significant (non-zero at 5% confidence) coefficients in bold type. Annualized intercept and intercept estimate bounds at a 95% confidence level are given at the bottom of the tables. R-squared is not adjusted for the number of factors in the model.

GPFG	Since inception	Last 10 years	Last 5 years
Benchmark	0.05 (5.2)	0.03 (2.0)	0.01 (1.2)
Term	-0.02 (-1.9)	0.00 (-0.1)	-0.03 (-1.8)
Credit Aa	0.03 (2.3)	0.08 (3.4)	-0.05 (-1.7)
Credit Baa	0.04 (2.9)	0.05 (2.8)	0.00 (-0.1)
Credit Caa	-0.01 (-2.4)	-0.01 (-0.5)	0.00 (0.4)
Emerging	0.01 (1.9)	0.01 (1.4)	-0.01 (-1.5)
Value/Growth	-0.01 (-1.6)	0.01 (0.5)	-0.02 (-1.8)
Small/Large	0.02 (2.3)	-0.01 (-0.6)	0.03 (1.6)
Low Volatility	0.00 (0.2)	-0.02 (-1.5)	-0.02 (-2.6)
% variability explained (R2)	44 %	57 %	45 %
Annualized intercept (alpha)	0.0075% (0.0)	-0.1114% (-0.5)	0.1409% (0.8)
Intercept – Lower bound	-0.2939%	-0.5412%	-0.2108%
Intercept – Upper bound	0.3088%	0.3184%	0.4925%

Equity portfolio	Since inception	Last 10 years	Last 5 years
Benchmark	0.01 (1.5)	0.01 (1.2)	0.00 (0.4)
Emerging	0.01 (1.7)	0.01 (1.1)	-0.02 (-3.0)
Value/Growth	-0.04 (-4.5)	-0.03 (-1.9)	-0.03 (-2.4)
Small/Large	0.02 (1.8)	0.01 (0.3)	0.05 (2.6)
Low Volatility	-0.02 (-3.2)	-0.04 (-3.8)	-0.02 (-3.2)
% variability explained (R2)	28 %	44 %	52 %
Annualized intercept (alpha)	0.4992% (2.7)	0.2779% (1.4)	0.0919% (0.6)
Intercept – Lower bound	0.1352%	-0.1272%	-0.2336%
Intercept – Upper bound	0.8632%	0.6829%	0.4174%

Fixed-income portfolio	Since inception	Last 10 years	Last 5 years
Benchmark	0.15 (3.7)	0.11 (1.7)	-0.09 (-2.6)
Term	-0.10 (-3.8)	-0.07 (-1.6)	0.02 (0.7)
Credit Aa	0.07 (3.4)	0.16 (4.2)	0.02 (0.5)
Credit Baa	0.10 (5.3)	0.14 (4.2)	0.01 (0.2)
Credit Caa	-0.01 (-0.8)	0.00 (0.2)	-0.01 (-0.5)
% variability explained (R2)	30 %	44 %	21 %
Annualized intercept (alpha)	-0.2603% (-1.0)	-0.3887% (-1.0)	0.433 (1.9)
Intercept – Lower bound	-0.7855%	-1.1567%	-0.0326%
Intercept – Upper bound	0.265%	0.3794%	0.8986%

In Table 3 we show the correlations between the factor returns and the fund’s benchmarks over the period.

Table 3

Correlation matrix between monthly factor returns

	Fund   benchmark	Equity   benchmark	Fixed   income benchmark	Term	Credit Aa	Credit Baa	Credit Caa	Emerging/ developed	Value/ Growth	Small/ Large
Low   volatility	-0.65	-0.78	-0.17	0.29	-0.32	-0.37	-0.38	-0.77	-0.52	-0.55
Small/Large	0.33	0.31	0.20	-0.11	0.19	0.30	0.16	0.39	0.74
Value/Growth	0.34	0.37	0.11	-0.19	0.19	0.31	0.23	0.35
Emerging/dev.	0.68	0.81	0.17	-0.26	0.31	0.38	-0.26
Credit Caa	20 %	40 %	-20 %	-0.16	0.23	0.30
Credit Baa	0.25	0.33	-0.07	-0.10	0.21
Credit Aa	0.20	0.31	-0.18	-0.37
Term	0.01	-0.23	0.51
Fix.inc.bench.	69 %	37 %
Equity bench.	0.91

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¹«Government Pension Fund Global Historical Performance Measurement»