Methodology

We first use principal component analysis (PCA) to identify relevant factors from selected macroeconomic variables16_{. Essentially, PCA is a data reduction technique that reduces the}

number of variables from p to a smaller set of k derived orthogonal variables without much loss of information in the original p variables (Jolliffe, 2002). The k derived variables that account for most of the variation in the original variables are called principal components. The use of PCA has several advantages. First, it reduces the number of explanatory variables that allow us to consider a larger number of important factors, which may affect fund returns. Second, PCA addresses the problems of multicollinearity when used in conjunction with multiple regression analysis, as each principal component is orthogonal to each other. Although the estimated components may have no economic meaning, it is a good empirical way to explain the variance in the underlying data (Fifield et al., 2002).

Table 3.3: Eigenvalues and Proportions of Variance Explained by the Relative Components

Panel A: International variables Principal components 1 2 3 4 5 6 Eigenvalue 3.12 1.07 0.77 0.4 2 0.33 0.27 Proportion 0.52 0.18 0.13 0.0 7 0.06 0.05 Cumulative proportion 0.52 0.70 0.83 0.9 0 0.96 1.00 Panel B:

Domestic variables Principal components

1 2 3 4 5 6 7 Eigenvalue 2.23 1.88 1.02 0.7 7 0.58 0.28 0.24 Proportion 0.32 0.27 0.15 0.1 1 0.08 0.04 0.03 Cumulative proportion 0.32 0.59 0.74 0.8 5 0.93 0.97 1.00

16 _{The objective of PCA is to achieve parsimony and to reduce dimensionality by retaining the smallest number} of components that account for most of the variation in the original data, with little loss of information.

Panel C:

All variables Principal components

1 2 3 4 5 6 7 8 9 10 11 12 13 Eigenvalue 4.89 2.72 1.08 0.9 9 0.77 0.58 0.56 0.49 0.31 0.2 8 0.1 8 0.1 2 0.0 6 Proportion 0.38 0.21 0.08 0.0 8 0.06 0.04 0.04 0.04 0.03 0.0 2 0.0 1 0.0 1 0.0 0 Cumulative proportion 0.38 0.59 0.67 0.7 5 0.81 0.85 0.89 0.93 0.96 0.9 8 0.9 9 1.0 0 1.0 0 Notes: The table reports the results from applying a principal components analysis to three different sets of

macroeconomic variables for the quarterly returns of 24 fund categories over the period from 1998Q3-2013Q1. Panel A reports international variables, Panel B reports domestic variables, and Panel C reports all variables, including the international and domestic variables. The values in bold face indicate those principal components with eigenvalues greater than 1, and those principal components that account for a large portion of the variation in the data.

Tables 3.3 and 3.4 summarise the results by applying PCA to the international and domestic variables. Specifically, Table 3.3 reports the eigenvalues and proportions of variance explained by the principal components for each of three groups, the international variables group (Panel A), the domestic variables group (Panel B) and the all variables group (Panel C), which includes all international and domestic variables. The value in bold face in Table 3.4 indicates that the principal components, which are retained as inputs for further regression analysis, explain a major portion of the variability in the original macroeconomic variables. The Kaiser criterion is used to select principal components that should be retained17_{. For the}

international variables, two principal components are retained as they have eigenvalues greater than one. The first principal component, which has an eigenvalue, or variance of 3.12, explains 52% of total variance of all international variables. The second principal component, with an eigenvalue of 1.08, explains 18% of total variance of international variables. Together, these two principal components account for 70% of the variance of international variables. For the domestic variables, the three principal components retained explain 73% of the variance of domestic variables. Similarly, the three principal components retained for the all variables group explain 67% of the variance of all its variables.

Table 3.4: Factor Loadings for the Dominant Principal Components Panel A:

International variables Principal component 1 Principal component 2

Oil prices World inflation

Commodity prices US interest rate World industrial production

World market returns Panel B:

Domestic variables Principal component 1 Principal component 2 Principal component 3 Stock market prices Short-term interest rates Money supply

Foreign exchange rates GDP Current account balance CPI Panel C:

All variables Principal component 1 Principal component 2 Principal component 3

Oil prices GDP Money supply

World market returns World inflation World industrial Production CPI

Commodity prices Short-term interest rates Foreign exchange rates Current account balance Short-term interest rates

Stock market prices

Notes: The table summarises the results from applying a principal components analysis to two different sets of macroeconomic variables over the period 1998Q3-2013Q1. Panel A reports international variables; Panel B reports domestic variables. The factor loadings for those principal components have absolute values of more than 0.3, which indicates that they account for most of the variation in the data.

Table 3.4 summarises the significant factor loadings for the retained principal components from each group of international variables (Panel A) and domestic variables (Panel B). Following Stevens (1986), we report only those factor loadings that have an absolute value more than 0.318_{. The results in Table 4 indicate that the principal components predominantly}

18 _{Variables with more than 0.3 factor loadings indicate that they have large coefficients in each principal} component vector.

reflect variables from the stock market (MKT and WMKT), product market (GDP, CPI, WIDP and WCPI), foreign exchange market (TWI and CAB), money market (SIR, MON and USIR), and resources market (OIL and WCPM). These results are consistent with our expectation that managed fund returns have relationships with stock market returns and key economic indicators, as a large portion of fund assets are invested in the stock market and those key indicators reflect the shape of the economy.

The dominant principal components are then extracted and used as inputs into a regression analysis to explain the returns of 24 fund categories over the next K-quarter period (K=1, 2, 3, 4)19_{. Three regression models are considered. First, the quarterly returns of each fund category}

are regressed on two international principal components derived from the six international variables. The regression model is as follows:

!_",$6^ = __" + `<sub>></sub>YXa<sub>>,$</sub> + `_bYXa_b,$+ c_",$6^ (3.2) where !_",$6^ is :$d _{fund returns at time t+k, _}

" is an intercept, YXa>,$ is the first international principal component at time t, YXa_b,$ is the second international principal component at time t, `<sub>></sub> and `_b are factor loadings, and c_",$6^ is a random error term at time t+k.

Second, the quarterly returns of each fund category are regressed on three domestic principal components that are derived from seven domestic variables. The regression model is as follows:

!",$6^ = _" + `>eXa>,$+ `beXab,$ + `feXaf,$ + c",$6^ (3.3)

19 _{Since the objective is to examine the relationships between 24 different categories of funds and 13} macroeconomic variables, this study does not use panel regression analysis to explain the returns of 24 fund

where !_",$6^ is :$d _{fund returns at time t+k, _}

" is an intercept, eXa>,$ is the first domestic principal component at time t, eXa_b,$ is the second domestic principal component at time

t, eXa_f,$ is the third domestic principal component at time t, `<sub>></sub>, `_b and `_f are factor loadings, and c_",$6^ is a random error term at time t+k.

Third, the quarterly returns of each fund category are regressed on three principal components from the all variables group. The regression model is as follows:

!",$6^ = _"+ `>gXa>,$ + `bgXab,$+ `fgXa>,$ + c",$6^ (3.4) where !_",$6^ is :$d _{fund returns at time t+k, _}

" is an intercept, gXa>,$ is the first all variables principal component at time t, gXa_b,$ is the second all variables principal component at time

t, gXaf,$ is the third all variables principal component at time t, `>, `b, and `f are factor loadings, and c_",$6^ is a random error term at time t+k.

The estimation of regression models (3.2) allows us to understand the impact of the international factors on the domestic managed fund returns. The estimation of the regression model (3.3) helps us to understand which domestic factors are needed more for local managed funds. Model (3.4) can be used to identify both the incremental change in the explanatory power of the model and the international linkage between international and domestic macroeconomic factors, by reconstructing both the international and domestic variables

within one model20_{. We are particularly interested in whether the slope coefficient (`}

") is significantly different from zero.