Define standard variation and interpret the different mean returns and standard deviations

Sarah was advised by her financial analyst to avoid U.S. stocks after the 2008 financial crisis and to put her savings in other economies. At the time, she had chosen to allocate her funds to two exchange traded funds (ETF) invested in the equity markets of Brazil and Russia, namely BRF for Brazil and RSX for Russia, in the ratio of 60 per cent and 40 per cent respectively.

Although Sarah 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.

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Sarah had enrolled in a corporate finance class on risk and return to improve her investment knowledge. During her classes, Sarah 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 co-movement between the returns of the component assets. Consequently, Sarah 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, Sarah started to search for an asset that was not correlated with BRF or RSX.


Sarah 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. Surely, the fact that the United States was picking up at a time when Brazil and Russia were slowing down was indicative of low correlation among the three economies.


To confirm her belief, Sarah decided to pick an ETF that tracked the U.S. equity market. She noticed that SPDR S&P 500 ETF (SPY) was invested in the public equity markets of the United States, in the stocks of companies operating across diversified sectors. She proceeded to gather past return data on RSX, BRF, and SPY (see Exhibit 1). As a proxy for the market portfolio, Sarah downloaded corresponding return data for World index (see Exhibit 1). World index was an ETF that invested in the public equity markets of developed countries across the globe. Sarah’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 Russia, 30 per cent in Brazil, 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 Russia and Brazil only. In addition, she intended to compute the betas of RSX, BRF, and SPY 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.


  RSX BRF SPY World index
2009 4.00% 7.86% 7.56% 9.69%
2010 6.25% 24.40% 8.11% 7.79%
2011 -27.40% -25.07% 9.94% -1.28%
2012 15.23% 2.60% 20.29% 22.75%
2013 10.86% -4.84% 19.09% 16.14%
2014 4.31% 35.87% 16.20% 17.06%
2015 -0.96% -7.28% -2.71% -2.28%

Source: Created by the authors.


Assets Existing Portfolio Weights New Portfolio Weights
RSX 60 40
BRF 40 30
SPY   30


Question 1: (30 marks)

  1. Using the annual return data provided in Exhibit 1 of the case for RSX, BRF, SPY and World index calculate their mean returns, Variance and standard deviations. Define standard variation and interpret the different mean returns and standard deviations.
  2. After that you need to calculate the covariance, and correlation for RSX, BRF.
  3. With these numbers, calculate the mean, variance and standard deviation for Sarah’s entire portfolio. (Note: RSX 60% and BRF 40%)

Question 2: (40 marks)

  1. Calculate the covariance and correlation coefficient for the three assets. (Russia-Brazil, Russia-US, US-Brazil). Define covariance and correlation coefficient and interpret the results.
  2. After adding SPY, what is the portfolio’s mean return, variance and standard deviation?
  3. Based on your data analysis, should Sarah diversify her portfolio or remain invested in Russia and Brazil only?

Question 3: (20 marks)

  1. Calculate the covariance and the betas of RSX, BRF, and SPY with the market proxy, use the World index return data shown in Exhibit 1 in the case.
  2. Using the calculated betas and assuming a risk free rate of 2.5 per cent and a market risk premium of 5.5 per cent, what are the required returns for each of the three ETFs? (Note: use the CAPM formula)

Question 4: (10 marks)

The “Brexit” is considered to be one of the top stories in the world lately. Discuss the main reasons behind the Brexit. Base your answer on relevant and reliable research. (750 to 1000 words)

******************End of questions******************


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