[Solution]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…

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******************

Assignment status: Solved by our experts

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