Volatility timing in CPF investment funds in Singapore: Do they outperform non-CPF funds?

Shen, Xiaoyi; Tsui, Albert K.; Zhang, Zhaoyong Article Volatility timing in CPF investment funds in Singapore: Do they outperform non-CPF funds? Risks Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Shen, Xiaoyi; Tsui, Albert K.; Zhang, Zhaoyong (2019) : Volatility timing in CPF investment funds in Singapore: Do they outperform non-CPF funds?, Risks, ISSN 2227-9091, MDPI, Basel, Vol. 7, Iss. 4, pp. 1-16, https://doi.org/10.3390/risks7040106 This Version is available at: https://hdl.handle.net/10419/257944 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ risks Article Volatility Timing in CPF Investment Funds in Singapore: Do They Outperform Non-CPF Funds? Xiaoyi Shen 1, Albert K. Tsui 1and Zhaoyong Zhang 2,* 1Department of Economics, National University of Singapore, Singapore 119077, Singapore; [email protected] (X.S.); [email protected] (A.K.T.) 2School of Business and Law, Edith Cowan University, Joondalup, WA 6027, Australia *Correspondence: [email protected] Received: 6 July 2019; Accepted: 10 October 2019; Published: 20 October 2019   Abstract: The purpose of this study is to examine the volatility-timing performance of Singapore-based funds under the Central Provident Fund (CPF) Investment Scheme and non-CPF linked funds by taking into account the currency risk effect on internationally managed funds. In particular, we empirically assess whether the funds under the CPF Investment Scheme outperform non-CPF funds by examining the volatility-timing performance associated with these funds. The volatility-timing ability of CPF funds will provide the CPF board with a new method for risk classification. We employ the GARCH models and modified factor models to capture the response of funds to market abnormal conditional volatility including the weekday effect. The SMB and HML factors for non-US based funds are constructed from stock market data to exclude the contribution of the size effect and the BE/ME effect. The results show that volatility timing is one of the factors contributing to the excess return of funds. However, funds’ volatility-timing seems to be country-specific. Most of the Japanese equity funds and global equity funds under the CPF Investment Scheme are found to have the ability of volatility timing. This finding contrasts with the existing studies on Asian, ex-Japan funds and Greater China funds. Moreover, there is no evidence that funds under the CPF Investment Scheme show a better group performance of volatility timing. Keywords: volatility timing; GARCH; weekday effect; currency risk exposure 1. Introduction1 The performance measure of funds has been an important topic in the past few decades. The conventional approach is to measure the performance of funds by calculating their absolute returns or reward-to-risk ratio (Sharpe 1966). Market timing has become an important measure to evaluate the performance of fund managers and an important skill for fund managers to make dynamical investment portfolio (Treynor and Mazuy 1966;Jensen 1972). In recent years the conditional models on return and volatility have become popular in studying the funds’ performance measure. Volatility timing is a trading strategy which focuses on the future volatility of the investment portfolio. Studies find that many portfolio managers behave like volatility timers, reducing their market exposure during periods of high expected volatility. In his seminal study of mutual fund volatility timing, Busse (1999) constructs a simple model that predicts that fund managers should time volatility counter-cyclically, i.e., they tend to decrease (increase) fund betas when conditional market volatility rises (falls). Chen and Liang (2007) propose a measure for timing return and volatility jointly that relates fund returns to the squared Sharpe 1 An earlier version of this paper with some preliminary findings was presented in the 20th International Congress on Modelling and Simulation (see Shen et al. 2013). Risks 2019,7, 106; doi:10.3390/risks7040106 www.mdpi.com/journal/risks Risks 2019,7, 106 2 of 16 ratio of the market portfolio to examine whether self-described market timing hedge funds have the ability to time the US equity market. They find evidence of timing ability at both the aggregate and fund levels, and report that timing ability appears relatively strong in bear and volatile market conditions. Jiang et al. (2007) find strong evidence of mutual fund timing ability by applying holdings-based tests. Fleming et al. (2001,2003), Marquering and Verbeek (2004) , and Tang and Whitelaw (2011) report that volatility timing can add value to investors’ portfolios, while Giambona and Golec (2009) show that compensation incentives partly drive fund managers’ market volatility timing strategies. Recently, Hallerbach (2012,2013) proves evidence that the volatility-targeting strategy improves the Sharpe ratio, and volatility weighting over time does improve the risk-return trade off.Cooper (2010) shows a similar finding that the Sharpe ratio of portfolios of equities and cash targeting constant risk is higher than that of buying and holding equities. Moreira and Muir (2017,2019) also find that volatility timing increases Sharpe ratios, and suggest that ignoring variation in volatility is very costly and the benefits to timing volatility are significantly larger than the benefits to timing expected returns. In contrast, Ferson and Mo (2016) report that the overall average timing of funds is negative or insignificant. However, most of these studies focus on the US funds and a few on the Asian-based funds. Most recently, Sherman et al. (2017) examined the market-timing performance of Chinese equity securities investment funds, and found that most funds do not time the market and 9% of the funds were statistically significant negative market timers. Yi et al. (2018) explores market timing abilities of Chinese mutual fund managers and find strong evidence that mutual funds can time the market volatility and liquidity. They show that only growth-oriental funds have the ability to time the market returns, and balance funds have the most significant volatility timing while growth funds have the most significant liquidity timing ability. Thus, the purpose of this study is to examine the volatility-timing performance of Singapore-based funds under the Central Provident Fund (CPF) Investment Scheme and non-CPF linked funds by taking into account of the currency risk effect on internationally managed funds.2 Given the strict entry criteria for the CPF Investment Scheme, it is an interesting question to ask if the CPF funds are “safer and better performed funds” as many people expected. In this study we empirically assess whether the funds under the CPF Investment Scheme outperform non-CPF funds by examining the volatility-timing performance associated with these funds. In particular, we employ GARCH models and modified factor models to capture the response of funds to the market abnormal conditional volatility including the weekday effect. SMB and HML factors for non-US based funds are constructed from stock market data to exclude the contribution of the size effect and the BE/ME effect. The volatility-timing ability of CPF funds will provide the CPF board with a new method for risk classification. Currently, the CPF board ranks funds’ cumulative return within the same risk classification, namely, (1) higher risk which includes funds invested in equities, (2) medium to high risk which includes funds in a mix of equities and bonds, (3) low to medium risk includes funds invested in income products and bonds, and (4) low risk includes funds invested in money market products. However, this method is too board to evaluate the funds’ market risk management and the impact on the returns of the funds. This is also the first study to apply the GARCH family models to the performance measure of the Singapore-based funds with the inclusion of currency risk to capture the characteristics of internationally managed funds. The results show that volatility timing is one of the 2 The CPF investment scheme was introduced in 1986 by the Singapore government in order to enhance CPF members’ funds for retirement. There are two accounts under the current CPF investment scheme, namely ordinary account (OA) and special account (SA). The instruments under CPF-SA are usually regarded to have higher risk than those under CPF-OA. CPF members can only invest in selected unit trusts, ETFs and investment-linked insurance products under the CPF-SA. The CPF board sets up strict admission criteria for investment products, especially for funds which tend to enter the CPF investment scheme. There are 28 fund management companies under the current CPF investment scheme, and 11 insurers under CPF Investment Scheme. Compared with the existing funds within the risk level under CPF Investment Scheme, new funds are required to have lower-than-median expense ratio. A good historical performance for at least three years is desirable. See also Koh et al. (2007). Risks 2019,7, 106 3 of 16 factors contributing to the excess return of funds. However, the funds’ volatility-timing seems to be country-specific. Most of the Japanese equity funds and global equity funds under CPF investment scheme are found to have the ability of volatility timing. This finding contrasts with the existing studies on Asian ex-Japan funds and Greater China funds. Moreover, there is no evidence that funds under CPF Investment Scheme show a better group performance of volatility timing. The rest of this study is organized as follows. Section 2discusses the models and the methodology used in this study. Section 3discusses the data sets, and Section 4analyzes the empirical results. Section 5concludes. 2. Methodology and the Model In this section we first discuss the volatility-timing model and then the methodology for conducting the empirical study. Treynor and Mazuy (1966) introduced a market-timing model to study whether mutual funds can outperform the market. Their model is based on the assumption that fund managers will shift to less-volatile assets when the market is bad and shift to more-volatile assets when the market is good. Therefore, a fund which can consistently outperform the market will have a “characteristic line” with steep slope when the market return is positive, or with a smooth slope when the market is negative. The slope of characteristic line describes the effective volatility of funds, which in turn contributes to the high return of funds. However, none of the 57 mutual funds in their sample is found to outperform the market. Sharpe (1966) extended this model by introducing a reward-to-risk ratio. Reward-to-risk ratio measures funds’ return in terms of risks. An alternative market-timing model was proposed by Henriksson and Merton (1981). Their main assumption is that fund managers predict when they believe market return will excess the risk-free rate. Measures of performance that attempt to accommodate market timing behavior typically model the ability to time the level of market factors, but not market volatility. Investors value market level timing because the positive covariance between a fund’s market exposure and the future market return boots the expected portfolio return for a given average risk exposure (Ferson and Mo 2016). Risk-averse investors value volatility timing when funds can reduce market exposure in anticipation of higher volatility. The negative covariance between a fund’s market exposure and volatility lowers the average volatility of the portfolio, and can do so without an average return penalty. Busse (1999) studies volatility timing behavior in US mutual funds, and finds evidence for the behavior in funds’ returns. Following Busse (1999), we specify the single-factor model as follows: Rpt =αp+βmpRmt +εpt (1) where Rpt is the excess return of individual fund at time tand Rmt is the excess return of market at time t, αp is the abnormal return of the fund, βmp is the exposure of the fund to the market risk, and εpt is the idiosyncratic return of the fund at time t. To account for volatility timing, a simplified Taylor series expansion is used to transfer the market beta into a linear function of the difference between market volatility and the time-series mean: βmpt =β0mp +γmp(σmt −σm). (2) By substituting Equation (2) into Equation (1), we can get the daily single-index volatility timing model as follows: Rpt =αp+β0mpRmt +γmp(σmt −σm)Rmt +εpt (3) where γmp is the volatility timing coefficient, which captures the relation between market volatility and fund return contributed to fund manager’s volatility-timing ability, and σmt is the standard deviation of the market index. Let Et−1(Rmt) be the expected return of market index conditional on the information set at time t − 1, if ∂Et−1(Rmt)/∂σmt ≤ 0, we expect a negative γmp if the fund manager is skillful at volatility timing. That is to say, when market volatility is higher than its time-series mean, a fund manager good at volatility timing can predict the increasing market volatility in advance and then Risks 2019,7, 106 4 of 16 adjust the assets from high volatile securities to low volatile securities. In other words, the individual fund with good volatility timing would be more sensitive to the market when the market is less volatile, while it would be less sensitive to the market when the market is more volatile. This process generates returns for the fund. On the other hand, if ∂Et−1(Rmt)/∂σmt > 0 for the market index, a positive volatility-timing coefficient is expected for a fund manager who is good at volatility timing. For a regional or global fund, the return is reported in a domestic currency on a daily basis while the actual trading in the foreign countries is invoiced and settled in foreign currencies. The domestically reported return is exposed to the currency risk. To correct the biased estimates of the market beta, we take account of the foreign exchange risk and follow Jensen (1968,1969); Lim (2005) and Jayasinghe et al. (2014a,2014b) to specify the currency-adjusted international CAPM model as follows: Et(RSG p,t+1−rfFC t+1) = βtEt(RFC mt ) + Et(∆sSG t+1−∆πSG t+1). (4) where RSG p,t+1 is the excess return of funds invested in foreign country but reported in Singapore dollars, rft is the risk-free rate in the foreign country, SSG t+1 is the spot exchange rate at time t+1, which is defined as the amount of Singapore Dollar per foreign currency, and πSG t+1 and πFC t+1 are the inflation rate at time t+1 for domestic country and foreign country, respectively. ∆sSG t+1=ln(SSG t+1)−ln(SSG t) is the nominal change of exchange rate, and ∆πSG t+1=πSG t+1−πFC t+1 refers to the inflation rate differential between Singapore and the foreign country. When we perform the empirical analysis, we proxy the inflation rate differential by the difference of their respective daily change of CPI transformed from the monthly CPI index. K-factor models have been used to capture the return of funds, which can be specified as follows; Rp,t+1=αpt + k X j=1 βpjtRj,t+1+εp,t+1(5) where Rp,t+1 is the excess return of fund pat time t+1, αpt is the extra return which is usually regarded as “Jensen’s alpha”, βpjt is the exposure of fund pto the risk factor jat time t, and εp,t+1 is the error term of fund pat time t+1. Assuming the error term is conditionally normal distributed, E(εp,t+1)Φt=0 and E(Rj,t+1εp,t+1)Φt=0 , where Φt is the information set at time t. Based on (5), the expected return of fund pbecomes: Et(Rp,t+1) = αpt + k X j=1 βpjtEt(Rj,t+1)(6) where Et(·) = E(·)Φt . Assuming that the factors from 1 to kare orthogonal, the conditional variance of fund pat time t is given by: σ2 t(Rp,t+1) = k X j=1 β2 pjtσ2 j,t+1+σ2 t(εp,t+1)(7) Instead of using the conventional moving-average volatility, we employ the conditional variance generated from the GARCH family to describe the market volatility. McAleer (2005) reviews a wide range of univariate and multivariate, conditional and stochastic, models of financial volatility, and McAleer and Medeiros (2008) discuss recent developments in modeling univariate asymmetric volatility. In this study we adopt a fitted exponential generalized autoregressive conditional heteroskedasticity (EGARCH) or GARCH with an adjusted mean equation and assumed error term to generate the conditional variance for different benchmark series. The exponential generalized autoregressive conditional heteroskedasticity (EGARCH) model proposed by Nelson (1991) has been widely used in the literature due to its capacity to capture asymmetry and possible leverage. Given that EGARCH is a discrete-time approximation to a continuous-time stochastic volatility process and also in logarithms, Risks 2019,7, 106 5 of 16 conditional volatility is guaranteed to be positive, but the model requires parametric restrictions to ensure that it can capture the (possible) leverage (Martinet and McAleer 2018). The EGARCH model also has relatively less restrictions on the parameters to ensure the non-negativity. To examine the impact of conditional volatility on returns, a conditional variance term can be added into the mean equation to contracture the EGARCH in mean model. In this study, we follow Ho et al. (2017,2018) and Qin et al. (2018) to extend the EGARCH-M (1,1) model by including other market factors such as size premium, value premium, and currency risk in the mean equations to examine the funds’ reaction to volatility timing. The proposed GARCH framework to estimate the volatility timing coefficients of funds are specified as follows: Rmt =ϕ0+ p X i=1 ϕiRm,t−i+εt− q X i=1 θiεt−i, where Rmt =rmt −rft (8) εmtεm,t−1,εm,t−2,. . . ∼N(0, σ2 mt)or t(0, σ2 mt)(9) ln σ2mt =a0+ s X i=1 αiεm,t−i+γiεm,t−i σm,t−i + m X j=1 βjln σ2 m,t−j(10) Or, σ2 mt =a0+ m X i=1 aiε2 m,t−i+ s X j=1 bjσ2 m,t−j(11) Rpt =αp+ K X k=1 βkpRkt +γmp(σmt −σm)Rmt +βctRct +εpt (12) where k= 1, 2, 3 and Rct =∆sSG t+1−∆πSG t+1−rft .R ct is the excess return of currency risk defined as the difference between deviations from PPP and risk-free rate. Equation (8) is the typical autoregressive generating process for market index. Equation (9) assumes the error term follows a conditional normal distribution with zero mean and conditional variance σ2 mt . Equations (10) and (11) accommodate the conditional variance in a GARCH or EGARCH framework. The choice of GARCH or EGARCH depends on the fitness of the time series. Equation (12) is the modified factor model to analyze the response of funds to abnormal market volatility. When we consider more factors in the model, we follow Fama and French (1993) to include terms that capture the differential dynamics of small cap stocks relative to large cap stocks (SMB) and high book-to-market stocks relative to low book-to-market stocks (HML) in addition to the market factor. Thus, when k=1, the excess return of the market index is the only factor considered except the excess return of exchange rate change; when k=2, the excess return of the market and HML are the loaded factors; when k=3, the excess return of the market, SMB and HML are included in the model besides the excess return of exchange rate change. 3. Empirical Analysis Data and Descriptive Statistics The funds chosen for this study were confined to those available in the Singapore fund market, regardless of whether they were managed offshore or domestically. Time series data were obtained from Bloomberg, while the categories of regional, country and global funds were from the IMAS Fund Information Service. Only equity funds were considered in this study because of the unavailability Risks 2019,7, 106 6 of 16 of benchmarks about bonds. Newly launched funds after 2006 were excluded because of their short duration. The daily return of funds was calculated as; Rfund,t=NAVt−NAVt−1 NAVt−1 where NAVt was the daily net asset value. We did not include dividends as a part of return, because the funds’ dividend was not easily available. Similarly, the daily returns of CPF funds were taken as a natural log to get a continuously compounded return. The excess return of CPF funds was defined as: Rpt =ln(NAVt NAVt−1 )−ln(1+r ft) Monthly CPI index data was obtained from CEIC. It was transformed to daily change from the monthly CPI index based on the following formula: πt=ln[(CPIm+1/CPIm)1/22] where CPIm was the monthly CPI index at month m+1 and πt was the daily continuously compounded CPI change. There were seven Japan equity funds under the CPF Investment Scheme and six non-CPF Japan equity funds. We used five funds under the CPF Investment Scheme and four non-CPF funds because the rest had insufficient numbers of observations. Similarly, we could only include seven CPF global equity funds and seven non-CPF global equity funds. In the case of the Asian ex-Japan equity fund, there were 15 funds under the CPF investment scheme and 10 non-CPF funds. Due to the data availability issue, we included in our dataset, only 10 CPF funds and four non-CPF Asian ex-Japan equity funds. Again, five out of eight CPF funds and two out of three non-CPF funds were included in the dataset for the Greater China equity funds. The excess return of each fund was calculated by following Fama and French (1993) three-factor asset-pricing model. The size premium (SMB) was the average return on the three small portfolios minus the average return on the three big portfolios, and the value premium (HML) was the average return on the two value portfolios (i.e., with high BE/ME ratios) minus the average return on the two growth portfolios (low BE/ME ratios). All data were daily and the sample period for the Japanese equity funds, global equity funds and Asian ex-Japan equity funds ranges from 1 January, 2000 to 31 December, 2006, and for the Greater China equity funds from 1 January, 2000 to 31 December, 2007. The descriptive statistics of the excess returns of these funds are summarized in Tables 1–4. Table 1. Descriptive statistics of the excess returns of Japan equity funds under the Central Provident Fund (CPF) Investment Scheme and non-CPF Japan equity funds. JPCPF1 JPCPF2 JPCPF3 JPCPF4 JPCPF5 JPNCPF1 JPNCPF1 JPNCPF1 JPNCPF1 Mean −0.017 −0.008 −0.025 −0.016 −0.002 −0.018 −0.021 0.002 −0.022 Median 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Max 5.561 5.849 6.952 17.450 5.999 5.914 7.434 5.899 6.971 Min −5.615 −6.234 −6.233 −18.834 −8.976 −9.106 −9.682 −6.418 −8.073 Std. Dev. 1.216 1.318 1.394 1.524 1.287 1.278 1.422 1.104 1.380 Skew. −0.072 −0.012 −0.071 −0.428 −0.415 −0.382 −0.570 −0.131 −0.298 Kurtosis 4.525 4.526 5.287 30.365 7.087 6.718 6.844 5.465 6.364 DF-Test −43.065 −40.866 −40.149 −45.356 −37.650 −36.005 −37.435 −41.343 −38.054 Obs 1824 1824 1824 1824 1824 1824 1824 1824 1824 Notes: JPCPF refers to Japan equity funds under the CPF Investment Scheme and JPNCPF refers to non-CPF funds. The number refers to the fund number. DF-test is the Dickey–Fuller Test. Obs stands for the number of observations. Risks 2019,7, 106 7 of 16 Table 2. Descriptive statistics of the excess returns of global equity funds under the CPF Investment Scheme and non-CPF global equity funds. (a) Global equity funds under CPF Investment Scheme GlCPF1 GlCPF2 GlCPF3 GlCPF4 GlCPF5 GlCPF6 GlCPF7 Mean 0.005 −0.010 −0.010 −0.004 −0.031 −0.021 −0.003 Median −0.004 −0.006 −0.006 0.052 −0.005 −0.008 −0.005 Max 4.775 5.511 6.612 6.825 5.603 6.990 7.871 Min −5.809 −5.995 −6.913 −6.913 −6.834 −5.641 −9.924 Std. Dev. 1.047 0.974 1.099 1.049 1.085 1.070 0.877 Skew. 0.039 −0.080 −0.033 −0.158 −0.218 0.207 −0.861 Kurtosis 5.432 7.032 6.217 6.598 6.660 7.514 19.373 DF-Test −38.696 −40.405 −38.795 −39.884 −37.258 −42.548 −38.743 Obs 1824 1824 1824 1824 1824 1824 1824 (b) Non-CPF global equity funds GNCPF1 GNCPF2 GNCPF3 GNCPF4 GNCPF5 GNCPF6 GNCPF7 Mean −0.023 −0.032 −0.015 0.022 −0.012 0.013 −0.009 Median −0.005 −0.005 0.020 0.029 −0.006 0.029 −0.006 Max 4.849 45.328 4.886 3.259 5.809 4.182 3.665 Min −4.576 −46.844 −7.675 −4.993 −5.894 −4.842 −6.973 Std. Dev. 0.981 1.914 1.117 0.591 1.039 0.768 0.866 Skew. −0.047 −0.773 −0.245 −0.402 −0.110 −0.197 −0.402 Kurtosis 5.889 370.245 5.931 8.991 5.873 6.275 6.690 DF-Test −37.647 −39.000 −42.275 −37.108 −41.031 −36.427 −38.399 Obs 1824 1824 1824 1824 1824 1824 1824 Notes: GlCPF refers to global equity funds under CPF Investment Scheme and GNCPF refers to non-CPF funds. The number refers to the fund number. DF-test is the Dickey–Fuller test. Obs stands for the number of observations. Table 3. Descriptive statistics of the excess returns of Asian ex-Japan funds under the CPF Investment Scheme and non-CPF Asia ex-Japan funds. (a) Asian ex-Japan equity funds under CPF Investment Scheme ACPF1 ACPF2 ACPF3 ACPF4 ACPF5 ACPF6 ACPF7 ACPF8 ACPF9 ACPF10 Mean 0.040 0.006 0.017 0.015 0.013 0.021 0.008 0.017 0.016 0.018 Median 0.044 −0.006 0.010 −0.007 −0.002 −0.006 −0.006 −0.007 −0.007 −0.006 Max 3.557 5.921 4.877 5.284 7.405 5.017 10.923 5.384 5.399 5.185 Min −6.549 − 13.636 −7.552 − 10.546 −8.666 −9.021 −12.44 −8.755 −8.087 −9.008 Std. Dev. 0.788 1.183 1.031 1.259 1.142 1.051 1.310 1.031 1.227 1.181 Skew. −0.961 −1.147 −0.505 −0.563 −0.304 −0.742 −0.759 −0.787 −0.497 −0.523 Kurtosis 10.071 16.735 7.007 7.566 7.404 8.060 14.087 10.197 6.258 7.323 DF-Test − 38.247 − 36.379 − 37.137 − 39.742 −39.84 −39.62 −41.52 −39.82 −39.08 −38.79 Obs 1824 1824 1824 1824 1824 1824 1824 1824 1824 1824 (b) Asian ex-Japan equity funds under CPF Investment Scheme ANCPF1 ANCPF2 ANCPF3 ANCPF4 Mean 0.018 0.004 0.006 0.013 Median −0.007 −0.006 −0.006 −0.006 Max 6.468 5.528 6.378 7.062 Min −12.579 −10.419 −9.111 −8.462 Std. Dev. 1.176 1.315 1.327 1.232 Skew. −0.946 −0.415 −0.262 −0.285 Kurtosis 12.900 7.199 6.532 6.698 DF-Test −39.934 −41.203 −37.223 −38.189 Obs 1824 1824 1824 1824 Notes: ACPF refers to Asian ex-Japan equity funds under the CPF Investment Scheme and ANCPF refers to non-CPF funds. The number refers to the fund number. DF-test is the Dickey-Fuller test. Obs stands for the number of observations. Risks 2019,7, 106 8 of 16 Table 4. Descriptive statistics of the excess returns of Greater China funds under the CPF Investment Scheme and non-CPF Greater China funds. GCCPF1 GCCPF2 GCCPF3 GCCPF4 GCCPF5 GCNCPF1 GCNCPF2 Mean 0.042 0.041 0.037 0.036 0.023 0.063 0.020 Median −0.005 −0.003 −0.006 −0.005 0.024 −0.004 −0.006 Max 7.523 4.157 5.961 6.290 4.668 8.627 5.867 Min −8.383 −8.729 −9.765 −10.466 −9.952 −8.482 −9.549 Std. Dev. 1.263 1.090 1.271 1.334 1.220 1.489 1.289 Skew. −0.362 −0.580 −0.355 −0.538 −0.836 −0.327 −0.409 Kurtosis 7.065 6.853 6.926 7.820 9.085 7.303 6.733 DF-Test −41.684 −43.071 −41.284 −41.611 −41.247 −24.186 −42.026 Obs 2085 2085 2085 2085 2085 2085 2085 Notes: GCCPF refers to Greater China funds equity funds under CPF Investment Scheme and GCNCPF refers to non-CPF funds. The number refers to the fund number. DF-test is the Dickey–Fuller Test. Obs stands for the number of observations. As it can be seen in Tables 1–4, overall the mean excess return for the Japan equity funds and the global equity funds was mostly negative, while for the Greater China funds and the Asian ex-Japan funds were positive, though all had a mean value around zero if measured in percentage terms. Comparatively the variation of the excess returns of Japan equity funds under the CPF Investment Scheme was greater than the non-CPF Japan equity funds. Similar results were found for the global equity funds. Japan equity funds also had the highest variation, while the global equity funds had the lowest, in comparison with the rest of the funds. The skewness suggests that the excess returns of Greater China funds and the Asian ex-Japan funds were the only two types of funds which were right-skewed, while the rest were generally more left-skewed. We used the stock index of the concerned country as the proxy for market index, and the major regional or global index used in the funds’ factsheets as the benchmark index of the invested market. Daily excess returns of markets were generated by: Rmt =ln(Pmt Pm,t−1 )×100 −ln(1+r ft)×100 where Pmt is the daily index of the market. MSCI Japan, MSCI world, MSCI Asian ex-Japan and MSCI Golden Dragon were chosen as the market benchmarks for Japan equity funds, global equity funds, Asian ex-Japan equity funds and Greater China equity funds, respectively. Figure 1presents the excess returns of these indexes. The excess return of currency risk was defined as the difference between deviations from PPP and the risk-free rate in the region or country in which funds were invested. Risks 2019, 7, x 8 of 16 Table 4. Descriptive statistics of the excess returns of Greater China funds under the CPF Investment Scheme and non-CPF Greater China funds. GCCPF1GCCPF2 GCCPF3GCCPF4 GCCPF5GCNCP F 1 GCNCPF 2 Mean 0.042 0.041 0.037 0.036 0.023 0.063 0.020 Median −0.005 −0.003 −0.006 −0.005 0.024 −0.004 −0.006 Max 7.523 4.157 5.961 6.290 4.668 8.627 5.867 Min −8.383 −8.729 −9.765 −10.466 −9.952 −8.482 −9.549 Std. Dev. 1.263 1.090 1.271 1.334 1.220 1.489 1.289 Skew. −0.362 −0.580 −0.355 −0.538 −0.836 −0.327 −0.409 Kurtosis 7.065 6.853 6.926 7.820 9.085 7.303 6.733 DF-Test −41.684 −43.071 −41.284 −41.611 −41.247 −24.186 −42.026 Obs 2085 2085 2085 2085 2085 2085 2085 Notes: GCCPF refers to Greater China funds equity funds under CPF Investment Scheme and GCNCPF refers to non-CPF funds. The number refers to the fund number. DF-test is the Dickey– Fuller Test. Obs stands for the number of observations. As it can be seen in Tables 1–4, overall the mean excess return for the Japan equity funds and the global equity funds was mostly negative, while for the Greater China funds and the Asian ex-Japan funds were positive, though all had a mean value around zero if measured in percentage terms. Comparatively the variation of the excess returns of Japan equity funds under the CPF Investment Scheme was greater than the non-CPF Japan equity funds. Similar results were found for the global equity funds. Japan equity funds also had the highest variation, while the global equity funds had the lowest, in comparison with the rest of the funds. The skewness suggests that the excess returns of Greater China funds and the Asian ex-Japan funds were the only two types of funds which were right-skewed, while the rest were generally more left-skewed. We used the stock index of the concerned country as the proxy for market index, and the major regional or global index used in the funds’ factsheets as the benchmark index of the invested market. Daily excess returns of markets were generated by: 100)1ln(100)ln( 1, ×+−×= − t tm mt mt rf P P R where mt P is the daily index of the market. MSCI Japan, MSCI world, MSCI Asian ex-Japan and MSCI Golden Dragon were chosen as the market benchmarks for Japan equity funds, global equity funds, Asian ex-Japan equity funds and Greater China equity funds, respectively. Figure 1 presents the excess returns of these indexes. The excess return of currency risk was defined as the difference between deviations from PPP and the risk-free rate in the region or country in which funds were invested. (a) (b) -8 -6 -4 -2 0 2 4 6 8 2000 2001 2002 2003 2004 2005 2006 Excess Return of MSCI Japan -6 -4 -2 0 2 4 6 2000 2001 2002 2003 2004 2005 2006 Excess Return of MSCI World Figure 1. Cont. 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