a) CEMENCO Stock Return YEAR CEMENCO RETURN 2000 13.9% 2001 20.0% 2002 11.6% 200
ID: 2332542 • Letter: A
Question
a) CEMENCO Stock Return
YEAR CEMENCO RETURN
2000 13.9%
2001 20.0%
2002 11.6%
2003 2.8%
2004 3.6%
2005 -16.3%
2006 47.3%
2007 -12.7%
Find the Average Return and Risk (as measured by Standard Deviation) of CEMENCO since 2000.
b) You have a portfolio consisting of 20 percent CEMENCO stock ( = 0.81), 40 percent of Monrovia Breweries (Club Beer) stock (( = 1.67). How much market risk does the portfolio have? How does this compare with the general market?
c) Data from the last eight decades for S & P 500 index yield the following statistics: average excess return = 7.9%; Standard Deviation = 23.2%.
(i)To the extent that these averages approximated investor expectations for the period, what must have been the average coefficient of risk aversion? Formula: E (rm) – rf = 2m
(II)If the coefficient of risk aversion were actually 3.5, what risk premium would have been consistent with the market’s historical standard deviation?
d) A portfolio’s return is 12%, its standard deviation is 20% and the risk-free rate is 4%. Which of the following would make the greatest increase in the portfolio’s Sharpe ratio?
An increase of 1% in expected return?
A decrease of 1% in the risk-free rate?
A decrease of 1% in its standard deviation?
YEAR CEMENCO RETURN
2000 13.9%
2001 20.0%
2002 11.6%
2003 2.8%
2004 3.6%
2005 -16.3%
2006 47.3%
2007 -12.7%
Explanation / Answer
a) YEAR CEMENCO RETURN CEMENCO Stock Return 2000 13.90% 2001 20.00% 2002 11.60% 2003 2.80% 2004 3.60% 2005 -16.30% 2006 47.30% 2007 -12.70% Average Return = using excel function Average 8.77% Average Risk = using excel function STDEV 19.99% b) % invested Beta Beta x % invested CEMENCO stock 20.00% 0.81 0.162 Monrovia Breweries (Club Beer) 80.00% 1.67 1.336 Portfolio Beta 1.498 Market Beta is normally 1 but it is greater than 1 , the portfolio is more risky c) a) Coefficient of risk =7.9%/23.2%^2 1.47 b) Risk Premium = 3.5 x 23.2%^2 18.84% d) Sharpe Ratio = (Expected Return – Risk Free Return) / Standard Deviation SR = (12% - 4%)/20% 0.4 An increase of 1% in expected return SR = (13% - 4%)/20% 0.45 A decrease of 1% in the risk-free rate SR = (12% - 3%)/20% 0.45 A decrease of 1% in its standard deviation? SR = (12% - 4%)/19% 0.42 A 1 percentage point increase in expected return and 1 percentage point decrease in the riskfree rate will have the same impact of increasing Sharpe ratio from .40 to .45
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