Investment fund selection techniques from the perspective of Brazilian pension funds

Paula, Jéssica Santos de; Iquiapaza, Robert Aldo

doi:10.1590/1808-057x202113250

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Revista Contabilidade & Finanças

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Original Article • Rev. contab. finanç. 33 (88) • Jan-Apr 2022 • https://doi.org/10.1590/1808-057x202113250 copy

Investment fund selection techniques from the perspective of Brazilian pension funds

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

The aim of this article was to evaluate the effectiveness of investment fund selection techniques from the perspective of Brazilian pension funds. Asset liability management (ALM) and liability driven investment (LDI) strategies are usually adopted to guide pension fund managers in relation to strategic allocation in asset classes that should compose their investment portfolios and to the liquidity needed in each period, but not specifying in which assets to allocate resources from among the infinity of assets available in the financial market. This article contributes to tactical management in the fixed income and stock segments outsourced via funds and demonstrates that adopting simple indicators can increase investment performance. The article broadens the knowledge on pension fund investment decisions and creates confidence in the adoption of the Sharpe ratio as a technique for choosing investment funds. We analyzed the returns obtained by hypothetical portfolios built using the following techniques: (i) the Sharpe ratio; (ii) the alpha of a multifactor model; (iii) data envelopment analysis (DEA) efficiency; and (iv) the different combinations of these techniques. We considered information on 369 funds from 2013 to 2018, adopting 12 temporal windows for choosing and re-evaluating the portfolios. The returns obtained were compared with the mean actuarial goal of the benefits plans administered by the pension funds, by means of the unplanned divergence (UD). When outsourcing pension fund investments in fixed income and stock investment funds it was verified that the Sharpe ratio contributes significantly to pension fund performance, compared with other indicators and techniques or a combination of them.

Keywords:
pension funds; performance analysis; investment funds; data envelopment analysis; unplanned divergence

Indicator	Description	Formula
Sharpe ratio (Sharpe, 1966Sharpe, W. F. (1966). Mutual fund performance. The Journal of Business, 39(1), 119-138.)	Expected return ( ${\bar{R}}_{i}$ ) beyond the risk-free asset ( ${\bar{R}}_{f}$ ) divided by the risk that this runs (σ_i).	$S R = \frac{{\bar{R}}_{i} - {\bar{R}}_{f}}{σ_{i}}$
Jensen’s alpha (Jensen, 1968Jensen, M. C. (1968). The performance of mutual funds in the period 1945-1964. The Journal of Finance, 26(1), 389-416.)	Excess return in relation to the risk-free asset ( ${\bar{R}}_{f}$ ) and to the gain according to the risk incurred (β_i) in relation to the market portfolio ( ${\bar{R}}_{m}$ ).	$α_{i} = {\bar{R}}_{i} - {\bar{R}}_{f} - β_{i} ({\bar{R}}_{m} - {\bar{R}}_{f})$
M² (Modigliani & Modigliani, 1997Modigliani, F., & Modigliani, L. (1997). Risk-adjusted performance. Journal of Portfolio Management, 23(2), 45.)	Excess return of the fund when compared to the return on the market portfolio ( ${\bar{R}}_{m}$ ), after adjusting the fund’s return ( ${\bar{R}}_{i}$ ) to the market risk (σ_m), as if both had the same volatility.	$M ² = {\bar{R}}_{c} - {\bar{R}}_{m}$ , where ${\bar{R}}_{c} = \frac{σ_{m}}{σ_{i}} \times {\bar{R}}_{i} + (1 - \frac{σ_{m}}{σ_{i}}) \times {\bar{R}}_{f}$
Sortino ratio (Sortino & Van Der Meer, 1991Sortino, F. A., & van der Meer, R. (1991). Downside risk. Journal of Portfolio Management, 17(4) 27.)	Similar to the Sharpe ratio, differing only in the risk measure, as it uses the volatility occurring only in the returns below a certain reference value.	$θ = \frac{{\bar{R}}_{i} - {\bar{R}}_{f}}{\sqrt{\frac{1}{N} \sum_{i = 1}^{N} {[M i n (0; R_{i} - {\bar{R}}_{f})]}^{2}}}$
AR (appraisal ratio) (Treynor & Black, 1973)	Value added to the portfolio due to assuming a different risk from the market risk.	$A R = \frac{α_{i}}{σ_{ε}}$ , where α_i is the Jensen’s alpha and σ_ε is the non-systematic risk
Systemic beta	Measure of sensitivity of the fund’s return (R_i) in relation to the return of a market index (R_m).	$β_{i} = \frac{C o v (R_{i}, R_{m})}{V a r (R_{m})}$
Parametric VaR	Maximum potential variation measure of the value of a portfolio with a given probability in a predefined horizon.	VaR = z_{(1 - α)} ^* σ_I, where o (1 - α) is a quantile of the standardized normal distribution (N ~ (0,1)), 0 < α < 1 and σ_i is the fund’s volatility
Historical VaR	Similar to the parametric VaR, considering the histogram of expected returns.	VaR_a (X) = min {z\|Fx(z) ≥ 1 - α}, 1 - α is the confidence level, and VaR_a (X) is the percentile that results in the highest expected loss
Conditional VaR	Expected loss of an investment, given that this exceeds the VaR.	CVaR = E(X\|X > VaR), where X is the mean expected loss, that is, the mean expected returns of the fund above the VaR
UD	Deviation in the return on the investments (r_t) in relation to a target return (I_t).	UD = r_t - I_t = r_t - {[(1 + i)(1 + π_t)] - 1}, where i is the financial discount rate of the actuarial goal and π_t is the inflation rate indexed to the actuarial goal

ANBIMA classification
Fixed income segment	Stock segment
Fixed income pension	Dividend stocks
High duration fixed income^*	Indexed stocks
Low duration fixed income^*	Active index stocks
Free duration fixed income^*	Free stocks
Average duration fixed income^*	Sector stocks
Indexed fixed income	Small cap stocks
Simple fixed income	Sustainability/governance stocks
	Value/growth stocks
	Closed stocks
	Pension stocks

Performance indicators	Fixed income fund selection techniques
Performance indicators	SR	ALPHA	DEA	SR_ALPHA	SR_DEA	ALPHA_DEA	SR_ALPHA_DEA
Average return (%)	0.95	0.68	0.81	0.83	0.86	0.71	0.75
Standard deviation of returns (%)	0.46	1.26	0.61	0.91	0.51	1.00	0.81
Sharpe ratio	0.2659	-0.1163	-0.0300	0.0052	0.0715	-0.1125	-0.0705
Jensen’s alpha	0.0012	-0.0014	-0.0001	0.0001	0.0004	-0.0010	-0.0006
M²	0.0243	0.0012	0.0064	0.0086	0.0126	0.0015	0.0040
Sortino ratio	0.3692	-0.1360	-0.0402	0.0066	0.1063	-0.1321	-0.0840
AR	65.0281	-10.1152	-4.1281	2.0304	18.4684	-13.0827	-17.9058
Systemic beta	0.0219	0.0842	0.0370	0.0651	0.0324	0.0771	0.0606
Historical VaR 95%	0.0054	-0.0297	-0.0057	-0.0114	-0.0032	-0.0169	-0.0163
Parametric VaR 95%	0.0020	-0.0140	-0.0020	-0.0066	0.0002	-0.0093	-0.0078
Conditional VaR 95%	-0.0056	-0.0299	-0.0123	-0.0234	-0.0055	-0.0215	-0.0123

Performance indicators	Stock fund selection techniques
Performance indicators	SR	ALPHA	DEA	SR_ALPHA	SR_DEA	ALPHA_DEA	SR_ALPHA_DEA
Average return (%)	0.94	0.81	0.69	0.82	0.69	0.73	0.80
Standard deviation of returns (%)	4.60	4.85	4.38	4.76	4.15	4.25	4.28
Sharpe ratio	0.0252	-0.0035	-0.0316	-0.0006	-0.0318	-0.0219	-0.0063
Jensen’s alpha	0.0021	0.0007	-0.0005	0.0009	-0.0005	-0.0001	0.0006
M²	0.0098	0.0081	0.0064	0.0082	0.0063	0.0069	0.0079
Sortino ratio	0.0358	-0.0049	-0.0419	-0.0008	-0.0430	-0.0299	-0.0087
AR	3.8161	1.0963	-2.2490	1.4169	-1.6095	-0.2039	1.5186
Systemic beta	0.6555	0.6752	0.6843	0.6683	0.6264	0.6325	0.6279
Historical VaR 95%	-0.0674	-0.0697	-0.0737	-0.0697	-0.0702	-0.0755	-0.0736
Parametric VaR 95%	-0.0663	-0.0717	-0.0651	-0.0700	-0.0614	-0.0626	-0.0624
Conditional VaR 95%	-0.0965	-0.1103	-0.0914	-0.1111	-0.0818	-0.0839	-0.0880

Statistics	SR	ALPHA	DEA	SR_ALPHA	SR_DEA	ALPHA_DEA	SR_ALPHA_DEA
Positive UDs	46	40	37	43	41	38	37
Negative UDs	26	32	35	29	31	34	35
Mean (%)	0.06	-0.21	-0.08	-0.06	-0.02	-0.17	-0.08
Standard deviation (%)	0.51	1.27	0.65	0.92	0.55	1.01	0.65

Year	SR	ALPHA	DEA	SR_ALPHA	SR_DEA	ALPHA_DEA	SR_ALPHA_DEA
Return (%)	97.15	62.08	78.63	81.12	85.75	66.56	78.63
UD (%)	8.38	-26.69	-10.13	-7.65	-3.02	-22.21	-10.13

Statistics	SR	ALPHA	DEA	SR_ALPHA	SR_DEA	ALPHA_DEA	SR_ALPHA_DEA
Positive UDs	36	36	34	36	33	35	34
Negative UDs	36	36	38	36	39	37	38
Mean (%)	0.06	-0.08	-0.20	-0.06	-0.19	-0.15	-0.09
Standard deviation (%)	4.71	4.95	4.48	4.86	4.25	4.35	4.38%

Year	SR	ALPHA	DEA	SR_ALPHA	SR_DEA	ALPHA_DEA	SR_ALPHA_DEA
Return (%)	82.56	67.79	53.40	69.49	55.08	58.94	66.79
UD (%)	-6.21	-20.98	-35.37	-19.28	-33.68	-29.83	-21.98

Universidade de São Paulo, Faculdade de Economia, Administração e Contabilidade, Departamento de Contabilidade e Atuária Av. Prof. Luciano Gualberto, 908 - prédio 3 - sala 118, 05508 - 010 São Paulo - SP - Brasil, Tel.: (55 11) 2648-6320, Tel.: (55 11) 2648-6321, Fax: (55 11) 3813-0120 - São Paulo - SP - Brazil
E-mail: recont@usp.br

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