Here are summary statistics on monthly returns for five U.S. common stocks, base
ID: 3181013 • Letter: H
Question
Here are summary statistics on monthly returns for five U.S. common stocks, based on 60 observations from January 1991 through December 1995.
Correlations:
Assume that these summary figures will still apply to future investments. Also assume that you may not make negative investments (such as short sales) in any of the stocks.
a. What portfolio (expressed as fractions of a dollar invested in each of the five stocks) would yield the highest expected monthly return?
b. What stock is the riskiest?
c. Let P be a portfolio with half the money invested in Merck and half invested in the riskiest stock. Will P be riskier than a portfolio with all the money invested in Merck?
d. What pair of stocks has the highest covariance (not necessarily the highest correlation)? What pair of stocks has the lowest covariance?
e. Consider two portfolios, one with equal amounts invested in the two stocks with the highest covariance, the other with equal amounts invested in the two stocks with the lowest covariance. Find the monthly expected returns and standard deviations (per dollar invested) in each portfolio.
Company Bristol Myers Ford IBM Merck US Airways Mean 0.017207 0.019168 0.002455 0.008826 0.009684 Std. dev. 0.061725 0.077009 0.080709 0.049723 0.159719Explanation / Answer
a)100% on Ford, it has the highest monthly return.
b)
US Airway, std=0.159719
c)
Var(0.5Merck+0.5USAirway)= 0.00783269>Var(Merck)
d)
Highest covariance: IBM and US airway, 0.00289
Lowest covariance: Ford and US airway, -0.00011
e)
E(0.5IBM+0.5US airway)= 0.0060695;
standard deviation is:
sqrt(Var(0.5IBM+0.5US airway)) =sqrt(0.25V(IBM)+0.25V(US)+2*0.5*0.5Cov))=0.09721111
2) (By the same way)For Ford and US airway: monthly expected return is 0.014426; standard deviation is: 0.08834591
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