The first set of problem set 2 hints appears at http://derivatives.garven.com/2023/01/25/problem-set-2-helpful-hints/.
Here’s the second problem set 2 hint, based on the following questions:
Finance 4366 Student Question: “I am in the process of completing Problem Set 2, but I am getting stumped, are there any class notes that can help me with 1E and question 2? I am having trouble finding the correct formulas. Thank you.”
Dr. Garven Answer (for question 2): Yesterday, I provided some hints about problem set #2 @ http://derivatives.garven.com/2023/01/25/problem-set-2-helpful-hints/. Regarding question #2, here is what I wrote there: “The second problem involves using the standard normal probability distribution to calculate the probabilities of earning various levels of return by investing in risky securities and portfolios; see pp. 15-21 of the http://fin4366.garven.com/spring2023/lecture4.pdf lecture note for coverage of that topic.”
The inputs for this problem are all specified in parts A and B; in part A, expected return is 12% and standard deviation is 30%, whereas in part B, expected return is 7.5% and standard deviation is 15%. The probability of losing money in parts A and B requires calculating the z statistics for both cases. In part A, the z stat is z = (0-mu)/sigma= (0-12)/30, and in part B it is z = (0-mu)/sigma= (0-7.5)/15. Once you have the z stats, you can obtain probabilities of losing money in Parts A and B by using the z table from the course website (or better yet, your own z table).
Part C asks a different probability question – what the probability of earning more than 6% is, given the investment alternatives described in parts A and B. To solve this, calculate 1-N(z) using the z table, where z = (6-mu)/sigma.
Dr. Garven Answer (for question 1E): Regarding 1E – since returns on C and D are uncorrelated, this means that they are statistically independent of each other. Thus, the variance of an equally weighted portfolio consisting of C and D is simply the weighted average of these securities’ variances. See the http://fin4366.garven.com/spring2023/lecture3.pdf lecture note, page 9, the final two bullet points on that page. Also see the portfolio variance equation on page 13, which features two variance terms and one covariance term – Since C and D are statistically independent, the third term there (2w(1)w(2)sigma(12)) equals 0.