Related questions with answers

We must determine the percentage of our money to be invested in stocks x and Let a = percentage of money invested in x and b = 1 − a = percentage of money invested in y. A choice of a and b is called a portfolio. A portfolio is efficient if there exists no other portfolio whose return has a higher mean return and lower variance, or a higher mean return and the same variance, or a lower variance with the same mean return. Let x be the mean return on stock x and y be the mean return on stock y. The variance of the annual return on one share of stock x is var x, and the variance of the annual return on one share of stock y is var y. Assume that the covariance between the annual return for one share of x and one share of y is cov(x, y). If we invest a% of our money in stock x and b% in stock y, the variance of the return is given by a2 var x+b2 var y+2abcov(x,y)a^{2} \text { var } x+b^{2} \text { var } y+2 a b \operatorname{cov}(x, y) Consider the following NLP:

maxz=ax+by s.t. a2varx+b2 var y+2abcov(x,y)va+b=1\begin{array}{c}{\max z=a \overline{x}+b \overline{y}} \\ {\text { s.t. } \quad a^{2} \operatorname{var} x+b^{2} \text { var } y+2 a b \operatorname{cov}(x, y) \leq v^{*}} \\ {a+b=1}\end{array}

where v* is a given non-negative number. a. Show that any solution to this NLP is an efficient portfolio. b. Show that as v* ranges over all non-negative numbers, all efficient portfolios are obtained.

Question

The price of a share of stock in XYZ Corporation was $74 two weeks ago. Seven weeks ago, the price was$59 a share.

a. Write a linear equation to find the price pp of a share of XYZ Corporation stock ww weeks from now.

b. Estimate the price of a share of stock five weeks ago.

Solution

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Recall that the slope intercept form of a linear function is given as follows.

y=mx+by=mx+b

where mm is the slope of the line and bb is the yy-intercept.

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