Normalised Indexes — a better way of data visualisation for investment performance comparison
We received regularly performance reports on the investment of our mandatory provident funds (MPF). However, they are usually reported in cumulative rates of return for fixed periods, such as ‘in the past 3 months’, ‘in the past 1 year’, ‘in the past 5 years’, etc. People find the figures confusing as they cannot be compared between reports in different periods.
Moving Referencing Point of MPF Returns
Figure 1 shows an example of the common reporting format of MPF returns in cumulative rates of return in the past n-period. I extract the average return rates of several geographically categorised MPF investment funds, such as US Equity, Hong Kong Equity, etc. in the past three months, one year and three years provided by the HKIFA.
For the purpose of our discussion, I have gathered data from two recent reports, one is as at the end of October 2021 (20211031) and the other is as at the end of July 2021 (20210731). Each column provides the rates of return reported in these two periods. Take the past 3-month returns of US Equity as an example, the less positive rate of return in October than that in July does not necessarily imply a deterioration of the performance, as the referencing points for the two figures are different. The one reported on October 31, 2021 refers to the post-July 31 data point as the base, while the one reported on July 31, 2021 refers to the post-April 31 data point as the base. Since the price was rising in the end of July, the base value was increasing. The rate of return in October will be less than that in July even the absolute magnitudes of the increase in the two periods are the same. let’s say the prices are $100, $105.45 and $110.90 (increase by $5.45 in every three months), then the reported rates of returns in the past 3-month would be 5.45% and 5.17% respectively.
Worse still, such a presentation format does not provide a continuous picture of the performance. Investors cannot calculate the rates of return for other periods, such as the return in the past 2-year. The average of the returns in the past 1-year and 3-year does not necessarily reflect the return in the past 2-year. Imagine a scenario of the following prices in the past 4 years of a fund: $100, $200, $126.44, $169.96, then the rates of return in the past 1-year and 3-year are 34.35% and 69.96%, their average is about 52%, yet the actual rate of return in the past 2-year is -15%.
In other words, an ever moving point of reference renders the MPF performance data not comparable. The only comparable data, I suppose, is the “yearly” data as investors are quite used to comparing annual changes, as long as the annual rates of return are based on the same month of each year. Another commonly used metric is annualised return, which will be discussed separately in another article.
Normalised Indexes
It is a better way to compare the performance of funds continuously by means of plotting normalised indexes, as they are based on a fixed referencing point of time, which can be unmoving. Better still, the chart can show the continuous performance of each fund. Yet, it requires detailed data of the funds. Unfortunately, the daily price data of MPF funds are usually not available for detailed analysis.
Thus, I am showing the concept of normalised indexes by means of different stock market indexes. Figure 2 shows HKMA’s (2021) chart of normalised indexes of S&P 500 in the US, DAX in Germany, TOPIX in Japan, Hang Seng Index (HSI) in Hong Kong and CSI 300 in Mainland China, by fixing their price levels in the end of 2020 as 100.
Why Indexing and Normalising?
All indexes are calculated based on a reference point of time. For example, Hang Seng Index of Hong Kong stock market takes June 30, 1964 as the reference point (Trading Economics https://tradingeconomics.com/hong-kong/stock-market). Since the indexes of different stock markets have different referencing points of time, their index levels cannot be compared directly with each other. For example, the S&P 500 index in the United States today is 4697, while the Hang Seng Index was reported at 25049.
In order to compare their performance over time of different stock market indexes, a normalized index chart is usually plotted. For example, Figure 2 shows HKMA’s (2021) normalised index chart presented to the Legislative Council in October, which set all indexes to 100 at the end of 2020 (Normalised Index Level, 2020 year-end = 100). It provides a YTD (year-to-date, January — September, 2021) comparison.
From the normalized chart, it is easier to compare the performance of each stock market index. It does not only show a more than 10% increase for S&P500, DAX, and TOPIX and more than 10% decrease for CSI300 and HSI, but it also allows readers to see at a glance when the stock market index has outperformed or underperformed other stock markets. For example, TOPIX has soared by almost 10% since August, while HSI has several stepwise falls since June. CSI300, on the contrary, has fallen since March.
It is simple to convert a stock market index to a normalized index. Simply set the indexes at a certain point of time to 100 (in this example, in the end of 2020 the indexes are set to 100), and then calculate the subsequent time series data of the indexes proportionally. Detailed calculation method will be discussed separately in another article later.
Normalized index chart has shortcomings. The reference point can be arbitrary, and choosing different reference point can result in a very different chart.
Composite Index
The performance of a stock market index may not be comparable to the performance of a MPF fund, as the components of the portfolios can be very different even if they are investing in the same geographical stock market. The above is simply a demonstration of the data visualisation approach of using normalised index chart to compare the performance of the geographically categorised stock market as a whole. Stock market index is generally a composite index calculated by a weighted performance of multiple representative stocks. Thus, it is usually used to represent the overall performance of the stock market in the geographical city/country/region. For example, the Hang Seng Index “is a major stock market index which tracks the performance of around 50 largest companies listed in the Stock Exchange of Hong Kong. It is free floating, capitalization-weighted index.” (Trading Economics, https://tradingeconomics.com/hong-kong/stock-market)
The average return of a group of geographical designated MPF funds also has similar characteristics. Taking the return of the US Equity category of the MPF funds in Figure 1 as an example, the return is calculated based on the average returns of 11 funds that invest in the US stock market included in the samples of HKIFA. The average return does not represent the performance of a certain MPF fund, but it can reflect the overall performance of investing in the stock market in the region in that period.
Comparing Figures 1 and 2, the performance of the US stocks and European stocks have relatively higher rates of return than that of the Hong Kong stock in recent months. Figure 1 reports an annual return of about 40% in the US equity funds, while the annual return of the Hong Kong equity funds is only 4.3%. However, Figure 2 shows a more than 10% increase in the S&P 500 index and a 10% decrease in the HSI in the past 9 months. They show a big difference in the performance of a stock market index and a group of investment funds for the same region markets.
a Youtube (Cantonese version) is available at: https://youtu.be/CvBg2W8a4UE
