# Problem Set 2 due tomorrow at the beginning of class

As y’all are well aware, Problem Set 2 is due tomorrow at the beginning of class.  Last Thursday, I posted some (what I hope you will find to be) helpful hints for Problem Set 2.

# Problem Set 2 helpful hints

Problem Set 2 is available from the course website at http://fin4335.garven.com/fall2019/ps2.pdf; its due date is Thursday, September 12.

Problem Set 2 consists of two problems. The first problem requires calculating expected value, standard deviation, and correlation, and using this information as inputs into determining expected returns and standard deviations for 2-asset portfolios; see pp. 15-18 of the http://fin4335.garven.com/fall2019/lecture3.pdf lecture note for coverage of this topic. 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. 17-22 of the http://fin4335.garven.com/fall2019/lecture4.pdf lecture note for coverage of that topic.

# Today’s Finance 4335 Class Problem hints…

As promised, the Finance 4335 class problem set and solutions for problems 1-3 on that problem set are linked here:

I strongly encourage everyone to try tackling problems 4-5 prior to Thursday’s class meeting of Finance 4335.  Problem 4 involves finding the expected return and standard deviation for an equally weighted portfolio, whereas problem 5 involves finding the expected return and standard deviation for the least risky combination of assets and b.  The expected return and variance for these portfolios are:

Expected portfolio return:

$E({r_p}) = {w_a}E({r_a}) + {w_b}E({r_b})$

Variance of portfolio return:

$\sigma _p^2 = w_a^2\sigma _a^2 + w_b^2\sigma _b^2 + 2{w_a}{w_b}{\sigma _{ab}}$

In problem 4, equal weighting implies that ${w_a} = {w_b} = .5$. whereas in problem 5, the least risky combination of assets and can be determined by differentiating the variance equation above with respect to $w_a$, setting the resulting equation to 0, and solving for $w_a$ (see p. 17 of today’s lecture note for the math details); thus the lowest variance combination of assets and can be determined by setting ${w_a} = \displaystyle\frac{{\sigma _b^2 - {\sigma _{ab}}}}{{\sigma _a^2 + \sigma _b^2 - 2{\sigma _{ab}}}}$ and ${w_b} = 1 - {w_a}.$

# Problem Set 1 hint…

Problem Set 1 is due at the beginning of class on Tuesday, September 3. Here is a hint for solving the 4th question on problem set 1.

The objective is to determine how big a hospital must be so that the cost per patient-day is minimized. We are not interested in minimizing total cost; if this were the case, there would be no hospital because marginal costs are positive, which implies that total cost is positively related to the number of patient-days.

The cost equation C = 4,700,000 + 0.00013X2 tells you the total cost as a function of the number of patient-days. This is why you are asked in part “a” of the 4th question to derive a formula for the relationship between cost per patient-day and the number of patient days. Once you have that equation, then that is what you minimize, and you’ll be able to answer the question concerning optimal hospital size.