J.P. Morgan Asset Management publishes information about financialinvestments. Over the past 10 years, the expected return for the S&P 500was 5.04% with a standard deviation of 19.45% and the expected returnover that same period for a core bonds fund was 5.78% with a standarddeviation of 2.13% (J.P. Morgan Asset Management, Guide to the Markets, Ist Quarter, 2012). The publication also reported that the correlation between the S&P 500 and core bonds is -.32. You are considering portfolio investments that are composed of an S&P 500index fund and a core bonds fund. a. Using the information provided, determine the covariancebetween the S&P 500 and core bonds.b. Construct a portfolio that is 50% invested in an S&P 500 indexfund and 50% in a core bonds fund. In percentage terms, what arethe expected return and standard deviation for such a portfolio? c. Construct a portfolio that is 20% invested in an S&P 500 indexfund and 80% invested in a core bonds fund. In percentage terms,what are the expected return and standard deviation for such aportfolio?d. Construct a portfolio that is 80% invested in an S&P 500 index fund and 20% invested in a core bonds fund. In percentage terms,what are the expected return and standard deviation for such aportfolio?e. which of the portfolios in parts (b), (c), and (d) has the largestexpected return? which has the smallest standard deviation? which of these portfolios is the best investment alternative?f. Discuss the advantages and disadvantages of investing in thethree portfolios in parts (b), (c), and (d). would you prefer investingall your money in the S&P 500 index, the core bonds fund, or one ofthe three portfolios? why?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
J.P. Morgan Asset Management publishes information about financial
investments. Over the past 10 years, the expected return for the S&P 500
was 5.04% with a standard deviation of 19.45% and the expected return
over that same period for a core bonds fund was 5.78% with a standard
deviation of 2.13% (J.P. Morgan Asset Management, Guide to the Markets, Ist Quarter, 2012). The publication also reported that the
index fund and a core bonds fund.
a. Using the information provided, determine the covariance
between the S&P 500 and core bonds.
b. Construct a portfolio that is 50% invested in an S&P 500 index
fund and 50% in a core bonds fund. In percentage terms, what are
the expected return and standard deviation for such a portfolio?
c. Construct a portfolio that is 20% invested in an S&P 500 index
fund and 80% invested in a core bonds fund. In percentage terms,
what are the expected return and standard deviation for such a
portfolio?
d. Construct a portfolio that is 80% invested in an S&P 500 index fund and 20% invested in a core bonds fund. In percentage terms,
what are the expected return and standard deviation for such a
portfolio?
e. which of the portfolios in parts (b), (c), and (d) has the largest
expected return? which has the smallest standard deviation? which of these portfolios is the best investment alternative?
f. Discuss the advantages and disadvantages of investing in the
three portfolios in parts (b), (c), and (d). would you prefer investing
all your money in the S&P 500 index, the core bonds fund, or one of
the three portfolios? why?
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