LYXOR CHINAH VERSUS LYXOR MSINDIA: PORTFOLIO RISK AND RETURN1

On a Saturday morning in late September 2015, Susie sat over her breakfast, which was rapidly turning cold, and reflected on the performance of her personal investment portfolio over the past seven years. She recalled that, after the financial crisis in 2008, she had been advised to avoid U.S. stocks and to put her savings in the emerging economies of India and China. At the time, she had chosen to allocate her funds to two exchange traded funds (ETF) invested in the equity markets of India and China, namely Lyxor ChinaH and Lyxor MSIndia, in the ratio of 60 per cent and 40 per cent respectively.

Lyxor ChinaH was an ETF invested in the public equity markets of China. The ETF invested in the stocks of large-cap companies operating across diversified sectors.2

Lyxor MSIndia was an ETF that invested in the public equity markets of India. The ETF invested in the stocks of large-cap and mid-cap companies operating across diversified sectors, and tracked the performance of the Morgan Stanley Capital International (MSCI) India Index.3

Although Susie had been satisfied with her portfolio performance over the past seven years, the high growth in these two emerging markets had fizzled out lately. However, the advice she had gathered from analysts' reports implied that she should stay invested in these markets, albeit with more attention to the volatile swings.

PORTFOLIO DIVERSIFICATION

Susie had enrolled in a corporate finance class on risk and return to improve her investment knowledge. During her classes, Susie learned that the risk of a portfolio was not simply a weighted average of the individual variances of the component assets. Rather, it was determined to a large extent by the comovement between the returns of the component assets. Consequently, Susie reasoned that diversification to include an asset that was imperfectly correlated with the existing components of her portfolio should reduce her risk without sacrificing returns, if she had understood correctly.

With this objective in mind, Susie started to search for an asset that was not correlated with Lyxor ChinaH or Lyxor MSIndia.

THE RECOVERING U.S. EQUITY MARKET

Susie wondered whether she should move some of her funds to U.S. equity. The U.S. economy appeared to have benefitted from the rounds of quantitative easing and was finally recovering from the doldrums. The U.S. unemployment data had improved and there was speculation that the Federal Reserve might raise interest rates.4 Surely, the fact that the United States was picking up at a time when China and India were slowing down was indicative of low correlation among the three economies.

FINANCIAL ANALYSIS

To confirm her belief, Susie decided to pick an ETF that tracked the U.S. equity market. She noticed that Lyxor United States Dow Jones Industrial Average (USDJIA) was invested in the public equity markets of the United States, in the stocks of companies operating across diversified sectors, excluding transportation and utilities sectors.5

She proceeded to gather past return data on Lyxor ChinaH, Lyxor MSIndia, and Lyxor USDJIA (see Exhibit 1). All three ETFs were listed on the Singapore Exchange. As a proxy for the market portfolio, Susie downloaded corresponding return data for Lyxor World (see Exhibit 1).

Lyxor World was an ETF that invested in the public equity markets of developed countries across the globe. It invested in the stocks of large-cap and mid-cap companies, and provided results that closely corresponded to the performance of the MSCI World Index.6

Susie's idea was to compare the mean returns and standard deviations of her existing portfolio with an alternative portfolio that would invest 40 per cent in China, 30 per cent in India, and 30 per cent in United States (see Exhibit 2). She hoped that the analysis would help her decide whether to diversify her portfolio or remain invested in China and India only.

In addition, she intended to compute the betas of Lyxor ChinaH, Lyxor MSIndia, and Lyxor USDJIA using their covariance with the market proxy, which would help her figure out their required returns, assuming a risk-free rate of 2.5 per cent and a market risk premium of 5.5 per cent. From there, she would be able to describe the systematic risk of her existing portfolio and the new portfolio, and their corresponding required returns.

Susie was excited to get started and to apply the financial concepts that she had gleaned from her corporate finance class. The class might have turned out to be her best investment yet.

EXHIBIT 1: ANNUAL RETURNS (%)

YEAR Lyxor ChinaH Lyxor MSIndia Lyxor USDJIA Lyxor World

2009 2.00 5.86 5.56 7.69

2010 4.25 22.40 6.11 5.79

2011 -29.40 -27.07 7.94 -3.28

2012 13.23 0.60 18.29 20.75

2013 8.86 -6.84 17.09 14.14

2014 2.31 33.87 14.20 15.06

2015 -2.96 -9.28 -4.71 -4.28

EXHIBIT 2: PORTFOLIO WEIGHTS (%)

Assets Existing Portfolio WeightsNew Portfolio Weights

Lyxor ChinaH 60 40

Lyxor MSIndia 40 30

Lyxor USDJIA 30

QUESTIONS

1. Using the annual data provided in Exhibit 1, of the case for LyxorChinaH and LyxorMSindia, calculate their mean return, standard deviation, covariance and correlation. with these numbers calculate the standard deviation, and return for susie's entire portfolio.
2. After adding LyxorUSDJIA , what is the portfolio's new standard deviation and return? How does the new portfolio compare with calculations in QUESTION 1.
3. Based on your data, should susie diversify her portfolio or remain invested in china and india?
4. Calculate the beta of Lyxor ChinaH Lyxor MSindia and Lyxor USDJIA. To calculate the covariance with the proxy , use Lyxor World return data shown in Exhibit 1. Assuming a risk free rate 2.5 percent and makrket risk premium of 5.5 percent. what are the required returns for each of three ETFs?