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.

PORTFOLIO DIVERSIFICATION

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.

THE RECOVERING U.S. EQUITY

MARKET

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.

FINANCIAL ANALYSIS

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.

EXHIBIT

1: ANNUAL 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.

EXHIBIT

2: PORTFOLIO WEIGHTS (%)

Assets

Existing Portfolio Weights

New Portfolio Weights

RSX

60

40

BRF

40

30

SPY

30

.

Question

1: (30

marks)

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.After that you need to calculate the

covariance, and correlation for RSX, BRF. 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)

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.After adding SPY, what is the portfolio’s mean

return, variance and standard deviation?Based on your data analysis, should Sarah

diversify her portfolio or remain invested in Russia and Brazil only?

Question

3: (20

marks)

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. 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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