J.P. Morgan Asset Management publishes information about financial investments. Overthe 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 was5.78% with a standard deviation of 2.13% (J.P. Morgan asset Management, guide to theMarkets, 1st quarter, 2012). The publication also reported that the correlation betweenthe S&P 500 and core bonds is −.32. You are considering portfolio investments that arecomposed of an S&P 500 index fund and a core bonds fund.a. Using the information provided, determine the covariance between the S&P 500 andcore bonds.b. Construct a portfolio that is 50% invested in an S&P 500 index fund and 50% in a corebonds fund. In percentage terms, what are the expected return and standard deviationfor such a portfolio?c. Construct a portfolio that is 20% invested in an S&P 500 index fund and 80% investedin a core bonds fund. In percentage terms, what are the expected return and standarddeviation for such a portfolio?d. Construct a portfolio that is 80% invested in an S&P 500 index fund and 20% investedin a core bonds fund. In percentage terms, what are the expected return and standarddeviation for such a portfolio?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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, 1st quarter, 2012). The publication also reported that the
the S&P 500 and core bonds is −.32. You are considering portfolio investments that are
composed of an S&P 500 index fund and a core bonds fund.
a. Using the information provided, determine the
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?
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