Question 1: Let X be the Price of Stock 1 and Y be the Price of Stock 2 in 1 yea

Question

Question 1: Let X be the Price of Stock 1 and Y be the Price of Stock 2 in 1 year. (20) Let X be ~N(15,100) and Y be ~N(20,100)

a) What is the that the Price of Stock 1 is less than or equal to $16 next year? (2.5)

b) What is the that the Price of Stock 2 is less than or equal to $18 next year? (2.5)

c) Assumeyoubuy5unitsofStock1ataPriceof$14and10unitsofStock2ataPriceof$17

today. What is the mean value of your Portfolio and its variance 1 year from now assuming that

both random stock Prices are independently distributed? (5)

d) Assume you still buy the same stock from Part c) today. What is the Probability that you have

made a profit of greater than 35$ next year? (5)

e) How does your result from c) change if the Covariance between X and Y= -0.5? Would you prefer

an independently distributed Portfolio or a negatively correlated Portfolio and Why? (1 sentence is enough) (5)

Question 2: Assuming that X ~ (42.6, 6.52) (10)
a) Find the x value such that 15% of the area below the curve lies to the right of x. (5)
b) Find the x values such that 92% of the area below the curve lies between x1 and x2. (5)

Explanation / Answer

a)

=normdist(16,15,sqrt(100),TRUE)

=0.539827837

b)

=normdist(18,20,sqrt(100),TRUE)

=0.420740291

c)

=(5*14/(5*14+10*17))^2*100+(10*17/(5*14+10*17))^2*100

=58.68055556

d)

=1-normdist(5*14+10*17+35,5*15+10*20,sqrt(58.6805556),TRUE)

=0.5

P.S.: I am allowed to answer only 4 questions

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