Statistical Analysis Assignment: Case Analysis of Australian Superannuation Funds

Question

Statistical Analysis Assignment - Case Study: Superannuation Funds @Nelson Perera 2019
Among the many investment choices available today, superannuation funds, a market basket of a portfolio of securities, is a common choice for those thinking about their retirement. The recent productivity commission report on productivity of superannuation was critical on the competitive nature of the industry.

Assume th+at you work as investment analyst for clients who decided to purchase superannuation funds for their retirement account. How would you go about making a reasonable choice among the many funds available today? The objective of your report is to provide general guidelines for clients to select a superannuation fund based on different characteristics.

The data file SUPERFUNDS2018 contains information regarding 11 variables from a sample of 168 superannuation funds. Please note that names of funds are omitted from this database. The variables are:

REGUCLA - Regulatory classification of the fund by APRA: 1 for Public Offer and 2 for Non Public offer

TYPE – type of the fund – 1 for Corporate, 2 for Retail, 3 for public and 4 for Industry

LICOWNER – Licensee Ownership type; 1 for Financial, 2 for Employer, 3 for Nominating, 4 for Public sector and 5 for other

OBJECTIVE – Licensee profit status: For Profit is noted as 1 and Non Profit is noted as 2

BASE – Membership base of the fund: 1 for corporate, 2 for general, 3 for government and 4 for Industry

BOARDSTU – Licensee board structure: 1 for gender equal and 2 gender non equal.

ASSETS – in thousands of dollars

NET – Net members benefit outflow ratio

INVESTEXPR – Investment expense ratio

OPEREXPRA – Operating expense ratio

ONERET – twelve-month return in 2018

THERET - three-year return – annualised return 2016 – 2018

FIVERET– annualised return 2014 – 2018 As an analyst you can use descriptive analytics (visualisation, presentation and descriptive statistics) and inferential statistics (hypothesis testing) for your analysis. You should analyse the performance variables (Expense ratios, Three year return, Five year Return and return 2018) based on funds characteristics (regulatory classification, type of the fund, licence ownership type, objective, board structure and base).

Please provide results of your analysis as a management report. Please follow the format given in the Moodle site.

Assignment Tasks:

1. Visually present data for the rate of return at based on funds characterises of licensee ownership structure. Calculate descriptive statistics for the rate of return at based on funds characteristics of licensee ownership structure. Comment on the location, shape and variability of those distributions.
2. Visually present data for the rate of return at based on funds characteristics of type of the fund. Calculate descriptive statistics for the rate of return at based on funds characteristics of type of the fund. Comment on the location, shape and variability of those distributions.
3. Visually present data for the rate of return at based on funds characteristics of objective. Calculate descriptive statistics for the rate of return at based on funds characteristics of objective. Comment on the location, shape and variability of those distributions.
4. Many investors believe that returns on funds with no profit motives are lower than return on funds with profit motive. Test this claim at 5 per cent significance level, in terms of 2018 return, 3-year return and 5-year return.
5. Many investors believe that investment expense ratio of funds with no profit motive are lower than investment expense ratio of funds with profit motive. Test this claim at 5 per cent significance level.
6. How did the different types of superannuation funds as categorised by their type (corporate, Retail, public and Industry) perform during 2018, the three-year period and the five-year period? Use 5% significance level.
7. Many investors believe that returns on funds with regulatory classification of public offer are lower than return on funds with regulatory classification of on Public offer. Test this claim at 5 per cent significance level, in terms of 2018 return and 3-year return.

Answer

1. Executive Summary
One-way ANOVA and t-test inferential analysis presented in this statistical analysis assignment are used to performance of superannuation funds in Australia on the basis of regulatory classification of the fund by APRA, type of the fund, licensee ownership type, licensee profit status. The data is drawn from the Nelson Perera, 2019 survey of 168 retirement funds in Australia. Knowledge of superannuation is defined, amongst other things, in terms of understanding expense ratio and market return for 2018, 2016-2018, and 2014-2018. In terms of specific understanding market returns of superannuation funds, graphical construction of boxplots to understand the shape of the distribution with location of descriptive measures. The statistical evidences suggest that corporate and retail funds have been found to be significantly less volatile and stable in terms of expected return relative to public sector and commercial funds. For non-profit licensees, there was a substantial gap in annualised returns over three and five years. Coprorate and industry-oriented funds have been slightly higher performing in three and five years. Thus, superior returns for long-term investment have been apparent. Non-public bid funds have been slightly better yielding than the publicly available funds in the long term. Finally, the cost ratio for non-profit - making policies was statistically smaller than that for profit-type accounts. The researcher concluded that investment for three years was the optimal timeline, but that five years would be a wiser option for a predictable and less uncertain investment term.

2. Introduction
There have now been almost three decades since Australia began to establish a compulsory scheme of private retirement pensions supplemented by a purposely broadly oriented public pension based on age and wage (Cummings, 2016). Beginning in the 1980s, the pension benefit was eventually applied to all workers until the 1992 Superannuation Garranty Fee was included in its expansion by compulsory company payments. This growing investment rate now has stabilised, which allows the self-employed to invest by tax reductions in the superannuation funds for those with substantial savings (Chant et al, 2014). This is a chance to bundle tax-efficient financing by means of income sacrificing, as well as a choice for all. Even today, Superannuation funds are always growning. Previous analyses indicate that success of mutual funds is diminished due to the expense and implementation uncertainties linked to big share transactions and lack of versatility in carrying out stock-selection ideas. de Zwaan et al (2015) considered the scale and efficiency of the funds closely linked in their analysis of the performance and costs of US pension fund domestic stock portfolios. Although investment in various portfolios provides cost benefits, the funds' productivity will depend upon the degree to which the dis-economies of their own equity portfolios can be mitigated or avoided.

The purpose of the study was to assess the performance of 168 superannuations funds based on type, licensee ownership, profit status, and expense ratio across a period of five years. Exploratory and inferential analyses have been utilized to classify the trend and performance disparities. The theoretical basis on which the statistical investigates are based have been stated in the form of a hypothesis.

2.1. Hypotheses
H1: Investors thought that gains from non-profit assets were considerably smaller than those of profitable funds in one year, three years and a five-year market return.

H2: It is believed that investment expense ratio are lower in funds with no profit motive compared to funds with profit motive.

H3: Market returns for one year, three years, and five years differed significantly for different types of superannuation funds categorised by their type.

H4: It was also believed that market returns on publicly offering funds with regulatory classifications are smaller than returns on non-publicly offered funds with a regulatory classification.

3. Business Problem
This research addresses a topic that is important to understanding the role of a retirement income fund in a pension benefit system to scale up economics of the retirement industry. A clearer understanding of this problem would be helpful for investors, considering the massive inflows and substantial mergers that have expanded the average size of the funds in recent years (Mackenzie, and McKerchar, 2014). This paper quantifies the value generated as the fund gets a greater performance based on their accrued types and categories. There are many explanations why superannuation schemes are able to capture economies of scale that are not collected from equities. One explanation for this is the possible cost savings from improved bargaining leverage with institutional investors (Basu, and Andrews, 2014). The willingness of superannuation funds to transfer capital from poor regions to regions with possible scale-related advantages may be another significant explanation. Donald et al (2014) found that, for defined-benefit pension funds, the funds are adjusting to change in size by moving into asset classes of scale and power-related bargaining – especially by increasing their allocation of alternative assets like private capital and land. They notice that this allocation change is related to strong positive cost and gross return economies. When investing in these asset groups, longer funds would certainly be able to reach more attractive fee rates (Mihaylov et al, 2015). This paper explores whether higher market return rates and lower investment expense ratios are present in bigger surviving funds for industries which differ in their investments in alternative asset classes.

4. Statistical Problem
Data on return rates are visually presented depending on the licensee ownership structure's signature funds, portfolio attributes of the investment form, and objective fund characteristics. Correspondingly, descriptive details have been calculated for return rate figures based on licensee ownership characteristics, investment attributes of the portfolio form, and objective fund characteristics.

Inferential studies are conducted to scrutinize claims of the investors who thought that investment yields of non-profit motive funds in one to three years and a five-year yield were considerably smaller than those of the profit motive funds. The investment cost ratio is compared between non-profit and profit-motivated funds to ascertain any existing disparity. Market returns are investigated for any substantial difference among one year, three years and five years of investment in all kinds of superannuation funds. Additionally, investor returns on funds with a statutory public offer classification has been compared with that of funds with a statutory public offer classification.

4.1. Methodology

4.1.1. Data Description
This research focuses on 168 pension funds operating in Australia, with at least 15 quarters of the related data for the period from 2014 to 2018. This funds constitute nearly the highest percentage of investments in APRA-regulated superannuation funds. Data are obtained from APRA’s statistical data collections on regulatory classification, type of the fund, licensee ownership type licensee profit status, membership base licensee board structure. Annual collections data are also obtained on the assets, net members benefit outflow ratio, investment expense ratio, operating expense ratio, and market returns for 2018, 2016 – 2018, and 2014 – 2018.

4.1.2. Study Design
Exploratory analyses with graphical support describes return rates depending on the licensee ownership structure's signature funds, portfolio attributes of the investment form, and objective fund characteristics. Inferential tests such as Student’s t-test and one-way ANOVA have been applied to comparatively scrutinize investment yields of funds based on objective and public offer classifications. The investment cost ratios are compared for licensee profit status to ascertain any existing disparity. ANOVA is used to ascertain difference among one year, three years and five years of investment in all kinds of superannuation funds.

5. Results of Analysis

5.1. Exploratory Investigation

5.1.1. Returns based on licensee ownership structure:
Average rate of return (RR) for superannuation funds for all licensee ownerships in 2016-2018 was relatively higher than annual average RR for 2018 and RR for the period 2014-2018. Few extreme outlier market RR are present in the graphical display of the distributions. Market returns are left skewed for 2018, 2016-2018, and 2014-2018. Volatility is observed to be higher in one year RR, followed by three and five years average returns. Shape of the distribution of five year return is markedly different from that of annual return in 2018 and average RR of 2016-2018.

Figure 1: Market Returns for one, three, and five years for financial licensee ownership

Figure 2: Market Returns for one, three, and five years for nominating licensee ownership

Figure 3: Market Returns for one, three, and five years for employer licensee ownership

Figure 4: Market Returns for one, three, and five years for public sector licensee ownership

Figure 5: Market Returns for one, three, and five years for other licensee ownership

5.1.1.1. One year scenario of market returns based on licensee ownership

Figure 6: Distribution of one year return based on licensee ownership

Based on the graphical presentation of market returns for 2018 we get that average market return in case of nominating ownership was higher than other licensees. From descriptive summary details in Table 1 was observe that spread of the market returns from financial fund is higher compared to others. Public fund due to presence of one outlier irregularity was highly negatively skewed, followed by other sector funds with above the par volatility. Considering one year scenario the nominating licensee ownership fund outperformed the rest.

Table 1: Descriptive Summary for One year rate of return based on licensee ownership

5.1.1.2. Three years scenario of market returns based on licensee ownership

Figure 7: Distribution of three years return based on licensee ownership

Based on the graphical presentation of market returns for 2016-2018 we get that average market return in case of public sector ownership was higher than other licensees. From descriptive summary details in Table 2 it was observe that spread of the market returns from financial fund is higher compared to others. Other sector fund due to presence outliers was highly negatively skewed, followed by financial sector fund and nominating licensee. Three year scenario reveals public sector funds as better choice than others. Spread of public and nominating licensee ownership funds were less compared to others.

Table 2: Descriptive Summary for three year rate of return based on licensee ownership

5.1.1.3. Five years scenario of market returns based on licensee ownership

Figure 8: Distribution of five years return based on licensee ownership

Figure 8 clearly shows the distribution of the of market returns for 2014-2018 for all the five licensees. The graph shows that the spread of the distribution for financial licensee fund was higher compared to rest four funds. Average market return in case of public sector ownership was higher than other licensees. From descriptive summary details in Table 3 it was observed that financial sector fund due to presence outliers was highly negatively skewed, followed by other and nominating sector funds. Five year scenario reveals public sector funds as better choice than others.

Table 3: Descriptive Summary for five year rate of return based on licensee ownership

5.1.2. Returns based on characteristics type

One year average RR for superannuation funds was relatively higher than that of three and five year periods. Five year average RR is highly left skewed relative to negative skewness of 2018 and 2016-2018 market RR. Volatility is observed to be higher in one year RR, followed by three and five years average returns. Shape of the distribution of five year return is markedly different from that of annual return in 2018 and average RR of 2016-2018.

Figure 9: Market Returns for one, three, and five years for corporate fund

Figure 10: Market Returns for one, three, and five years for corporate fund

Figure 11: Market Returns for one, three, and five years for public fund

Figure 12: Market Returns for one, three, and five years for industry fund

5.1.2.1. Comparative Analysis of one year market returns based on fund type

Figure 13: Distribution of one year return based on fund type

One year returns were highly volatile for retail sector with highest spread and volatility noted from the graphical presentation of market returns. Average market return for industry type fund is highest in 2018 with lowest volatility. Descriptive summary in Table 4 reveals the skewness and kurtosis of the distributions. It was observe that public fund has the most negative skewness due to presence of extremely negative return. One year scenario reveals industry sector funds as better choice than others. Spread of public and retail sectors were higher compared to others.

Table 4: Descriptive Summary for one year rate of return based on fund type

5.1.2.2. Comparative Analysis of three year market returns based on fund type

Figure 14: Distribution of three year return based on fund type

On the basis of the graphic overview of the 2016-2018 market return data, in case of retail sector we obtain the highest spread with most negative skewness. Average market gain was higher for corporate as well as industry type funds. It was observed in Table 5 that the distribution of market returns from retail sector is higher than other funds. Three years' example shows that industry fund performs the best.

Table 5: Descriptive Summary for three year rate of return based on fund type

5.1.2.3. Comparative Analysis of five year market returns based on fund type

Figure 15: Distribution of five year return based on fund type

On the basis of the graphic overview of the 2014-2018 market return data, in case of retail sector we obtain the highest spread with most negative skewness. Average market gain was higher for corporate and industry type funds. It was observed in Table 5 that the distribution of market returns from financial sector is right skewed due to some higher return figures. Five years' scenario shows that industry fund and the financial funds outperforms other two types.

Table 6: Descriptive Summary for five year rate of return based on fund type

5.1.3. Returns based on characteristics of objective
Average market return for 2016-2018 was relatively higher than average RR for 2018 and 2014-2018. Few outlier market RR are present in the graphical display of the distributions. Five year average RR is highly left skewed relative to negative skewness of 2018 and 2016-2018 market RR. Volatility is observed to be higher in one year RR, followed by three and five years average returns. Shape and location of the distribution of five year return is markedly different from that of annual return in 2018 and average RR of 2016-2018.

Figure 16: Market Returns for one, three, and five years for profit status

Figure 17: Market Returns for one, three, and five years for no-profit status

5.1.3.1. Comparative Analysis of one year market returns based on objective

Figure 18: Distribution of one year return based on objective

License profit status is found to have noteworthy impact on market returns in 2018. Profit intended funds performed badly compared to non-profit funds. However, the spread and negative skewness for no-profit fund was higher due to presence of extreme negative return. Correspondingly, the no-profit fund also has higher volatility.

Table 7: Descriptive Summary for one year rate of return based on objective

5.1.3.2. Comparative Analysis of three year market returns based on objective

Figure 19: Distribution of three year return based on objective

Three year average returns are higher for no-license profit fund with lower spread and negative skewness compared to profit sector funds. Correspondingly, the no-profit fund also has lower volatility. Hence, no-profit fund performed better in three year period. The spread of profit objective funds were higher with greater negative skewness.

Table 8: Descriptive Summary for three year rate of return based on objective

5.1.3.3. Comparative Analysis of five year market returns based on objective

Figure 20: Distribution of five year return based on objective

Five year average returns are considerably higher for no-license profit fund with lower spread and low negative skewness compared to profit sector funds. Correspondingly, the no-profit fund also has lower volatility. Hence, no-profit fund performed better in fivee year period. The spread of profit objective funds were higher with greater negative skewness.

Table 9: Descriptive Summary for five year rate of return based on objective

5.2 Inferential Analyses

5.2.1. Market returns on objective status
The no profit funds are significantly higher in profits compared to its complementary fund. The null hypothesis H1 is rejected based on statistical evidence that one year market returns for no-profit funds is significantly higher (t = -2.06, p < 0.05) than that of the profit objective funds, at 5% level of signiifcance. From Table 11 it can be noted that three year market returns for no-profit funds is also significantly higher (t = -8.76, p < 0.05) than that of the profit objective funds. Similar observation is available in Table 12 for five years return at 5a5 level of signiifcance (t = -8.41, p < 0.05).

Table 10: Two samples T-test with unequal variances to compare one year return based on objective

Table 11: Two samples T-test with unequal variances to compare three year return based on objective

Table 12: Two samples T-test with unequal variances to compare five year return based on objective

5.2.2. Investment Ratio Comparison
Investment expense ratio (IER) is higher in funds with no profit motive compared to funds with profit motive. There is enough statistical evidence at 5% level to reject H2. From Table 13, it can be concluded with evidence that investment expense ratio is not all lower in no-profit funds. On the contrary, IER for no-profit funds was significantly higher compare dto profit objective funds (t = -3.02, p < 0.05) at 5% level.

Table 13: Two samples T-test with unequal variances to compare investment ratio based on objective

5.2.3. Market returns comparison based on type of funds

5.2.3.1. One year return analysis based on fund type
Average one year return in 2018 for industry firm was highest with lowest standard deviation among all four types. Corporate funds performance was the second best followed by retail and public sector funds. The difference between these funds was statistically analysed using one-way ANOVA at 5% level. The overall model was statistically significant (F (3, 164) = 5.11, p < 0.05) enough to show at least one type of fund with statistically significantly different returns. In summary, it can be observed that industry fund gave significantly higher return in one year period compared to others.

Table 14: One-way ANOVA for one year return by type of funds

5.2.3.2. Three year return analysis based on fund type
Average three years return for 2016-2018 for industry and corporate firms were higher with industry type fund having lowest standard deviation among all four types. Corporate funds performance was the second best followed by public and retail sector funds. A one-way ANOVA at 5% level was significant (F (3, 164) = 24.17, p < 0.05) enough to show at least one type of fund with statistically significantly different returns. In summary, it can be observed that industry fund gave significantly higher return in one year period compared to retail and public funds.

Table 15: One-way ANOVA for three years return by type of funds

5.2.3.3. Five year return analysis based on fund type
Average five years return for 2014-2018 for corporate firms was higher with lowest standard deviation among all four types. Industry fund’s performance was the second best followed by public and retail sector funds. A one-way ANOVA at 5% level was significant (F (3, 164) = 23.44, p < 0.05) enough to show at least one type of fund with statistically significantly different returns. In summary, it can be observed that corporate fund gave significantly higher return in one year period compared to retail and public funds.

Table 16: One-way ANOVA for five years return by type of funds

5.2.4. Market returns comparison based on type of funds

5.2.4.1. One year return analysis based on APRA status
One year average return in case of regulatory classification for public offer was higher compared to that of the non-public offer. Table 17 with the two-sample t-test with unequal variances shows the difference between the two returns establishing that there was no statistical evidence (t = 0.198, p = 0.422) at 5% level for such conclusions.

Table 17: Two samples T-test with unequal variances to compare one year return based on regulatory classification

5.2.4.2. Three years return analysis based on APRA status
Three years average return in case of regulatory classification for non-public offer was higher compared to that of the public offer fund. Table 18 with the two-sample t-test with unequal variances shows the difference between the two returns establishing that there was enough statistical evidence (t = -5.16, p < 0.05) at 5% level for such conclusions.

Table 18: Two samples T-test with unequal variances to compare three year return based on regulatory classification

6. Conclusion and Implication
In light of the market returns of superannuation funds and the key objective variables, a valid portfolio was now easy for the researchers to build (Earl et al, 2015). Such groups of funds have gained particular attention because of the dramatic rise in the Australian surplus-annulation industry, in particular as their overall valuation increases (Charlton et al, 2013). Among the top performers for funding, corporate and industrial funds have been listed. Based on ownership of the licensee, nominating and employer funds held as better performers with lower volatility. A substantial factor in the success of the fund was APRA's legislation designation for public bid, and findings found to be compatible with prior research results (Arnold et al, 2014). In comparison to economic incentive goals, the operating cost percentage was found to be smaller in profit based funds than the non-profit category.

The present study investigates the role of regulatory classification of the fund by APRA, type of the fund , licensee ownership type, licensee profit status in determining perceptions of superannuation-holding in Australian financial market (Iskra, 2012). As far as basic knowledge of superannuation is concerned, most of the employees understand that companies are obligated to make donations on behalf of workers. It also shows that workers would make extra discretionary payments in lieu of those donations. They also realised that the government would not cover up the shortfall in support due to an absence of pension funds. A little over half of them knew that excess taxes were cheaper than other savings. However, only few of the participants appreciate the way they interpret their documents and appreciate the fund's approximate expenditure rate or the combination of funds they need to invest for retirement. Results from this study would prepare a guide map for investors to choose between funds with an eye on the expense ratio for obtaining higher returns.

7. References
Arnold, B.R., Bateman, H., Ferguson, A. and Raftery, A., 2014. The size, cost and asset allocation of Australian self-managed superannuation funds. CIFR Paper, (033).

Basu, A. and Andrews, S., 2014. Asset allocation policy, returns and expenses of superannuation funds: Recent evidence based on default options. Australian Economic Review, 47(1), pp.63-77.

Chant, W., Mohankumar, M. and Warren, G., 2014. MySuper: A new landscape for default superannuation funds. CIFR Paper, (020).

Charlton, K., Donald, S., Ormiston, J. and Seymour, R., 2013. Impact investments: perspectives for Australian superannuation funds.

Cummings, J.R., 2016. Effect of fund size on the performance of Australian superannuation funds. Accounting & Finance, 56(3), pp.695-725.

de Zwaan, L., Brimble, M. and Stewart, J., 2015. Member perceptions of ESG investing through superannuation. Sustainability Accounting, Management and Policy Journal.

Donald, M.S., Ormiston, J. and Charlton, K., 2014. The potential for superannuation funds to make investments with a social impact. Company and Securities Law Journal, 32(8), pp.540-551.

Earl, J.K., Gerrans, P., Asher, A. and Woodside, J., 2015. Financial literacy, financial judgement, and retirement self-efficacy of older trustees of self-managed superannuation funds. Australian Journal of Management, 40(3), pp.435-458.

Iskra, L., 2012. A technical note on Australian default superannuation investment strategies. Australasian Accounting, Business and Finance Journal, 6(2), pp.113-120.

Mackenzie, G. and McKerchar, M., 2014. Tax-aware investment management by public offer superannuation funds in Australia: attitudes, practices and expectations. Austl. Tax F., 29, p.249.

Mihaylov, G., Tretola, J., Yawson, A. and Zurbruegg, R., 2015. Tax compliance behaviour in Australian self-managed superannuation funds. eJTR, 13, p.740.