Math 458/558 Assignments

d=2012-05-22
Mon 8/31
Read: Chapter 1, Sec 6.1.

Wed 9/2
Read: Sec 6.2.
Homework:
L.1: Show that the sum of the weights is 1.
L.2: Show that the rate of return r for a portfolio is the weighted sum of the rates of return of the assets in the portfolio.

Fri 9/4
Read: Sec 6.3, 6.4.
Homework: Problems 6.3, 6.4, 6.5 from the text.
L.3: Show that E is linear, i.e. E[ax+by]= aE[x]+bE[y] for a,b constants and x,y random variables.
L.4: Show that cov(x,y)=E[xy]-E[x]E[y].

Wed 9/9
Read: Sec 6.5.

Homework Assignment #1 (30 pts):
L.2 (5 pts), L.4 (5 pts), 6.3 (10 pts), 6.5 (10 pts).
Due Friday, 9/18, at the beginning of class.

Fri 9/11
Read: Sec 6.6.

Mon 9/14
Homework: 6.6.
L.5: Show that when rho=0 the portfolio curve (for two assets) is convex to the left.

Wed 9/16
No assignment this day. Note HW1 is due Fri 9/18

Fri 9/18
Read: Sec 6.7, 6.8

Mon 9/21
Read: Sec 6.9.
Homework: 6.7, 6.8 (458 & 558);
Homework: 6.10 (558 only).

Wed 9/23
Read: Sec 7.1, 7.2.
Homework: 7.1.

Homework Assignment #2 (35 pts):
458: 6.6 (10 pts), 6.7 (15 pts), 6.8 (10 pts)
558: 6.7 (15 pts), 6.8 (10 pts), 6.10 (10 pts)
Due Friday, 10/2, at the beginning of class.

Fri 9/25
Read: Sec 7.3, 7.4.
Homework: 7.2, 7.4, 7.6.

Wed 9/30
No assignment this day. Note HW2 is due Fri 10/2

Fri 10/2
Read: Sec 7.5-7.6

Mon 10/5
Read: Sec 7.7
Homework: L.8 Stock Analysis

Wed 10/7
Homework: 7.7 (everyone), 7.8 (558 only).

Homework Assignment #3 (35 pts):
458: 7.2 (10 pts), L.8 (15 pts), 7.7 (10 pts)
558: 7.2 (10 pts), L.8 (15 pts), 7.8 (10 pts)
Due Wednesday, 10/21, at the beginning of class.

Fri 10/09
Review Ch 1, Sec. 6.1-6.5 and HW1, and sample test 1.

Mon 10/12
Review Sec. 6.6-6.10 and HW2. Note that test 1 is Wed 10/14

Wed 10/14
Test 1 is this day. No assignment.

Fri 10/16
Read: Sec 7.8.

Mon 10/19
Read: Sec 8.5, 8.6

Wed 10/21
Read: Appendix A.

Fri 10/23
Read: Sec 11.1-11.3
Homework: L.9 Prove that for the additive model, S(k) = (a^k)S(0)+ (a^(k-1)) u(0) + (a^(k-2))u(1) + ... + a u(k-2)+ u(k-1)

Mon 10/26
Read: Sec 11.4-11.7

Wed 10/28
Homework: 11.2, 11.3, 11.4.

Fri 10/30
Read: Sec 11.8
Homework: 11.7.

Mon 11/2
Read: Sec 11.9.
Homework: 11.1, 11.9.

Wed 11/4
Read: Sec 12.1-12.4.
Homework: 12.1, 12.2, 12.4.

Homework Assignment #4 (50 pts):
458: (10 pts each) L.9, 11.2, 11.7, 11.1, 12.1
558: (10 pts each) L.9, 11.4, 11.7, 11.9, 12.1
Due Wed 11/18, at the beginning of class

Fri 11/6
Read: Sec 12.5-12.6

Mon 11/9
Read: Sec 12.5-12.6.

Wed 11/11
Read: Sec 12.7 (on puts).
Homework: 12.5
L.10 Use a binomial lattice to find the value of a value of a six-month call option with strike price $52, Current price $55, interest rate 4%, standard deviation 0.25, and Delta t= 1 month.
L.11 Use a binomial lattice to find the value of a value of a six-month American put and a six-month European put option with the same parameters as in exercise L. 10.

Fri 11/13
Read: Sec 13.1, 13.2, 13.3, 13.5.
Homework: 13.2, 13.4
L.12 Use the Black-Scholes formulas to compute the values of a European call option and European put option with the same parameters as in Exercise L.10. (Show your work.)
Note: the value of a European put is given by
K exp(-r (T-t)) - S + CallEur
where CallEur is the value of a European call as given in the text, t is now and T is expiration (this follows from put-call parity)

Homework Assignment #5 (50 points):
12.4 (a,b) (10 points), 13.2 (15 points),L.11 (15 points), L.12 (10 points).
Due Fri 12/04, at the beginning of class.

Mon 11/16, Wed 11/18, Fri 11/20
There will be no further homework assignments for the term. During this period, please work on HW5.

Mon 11/23
Review Ch. 7, HW3, HW4 and look at sample test 2 over the break

Mon 11/30
Review HW4, work on sample test 2

Wed 12/02
Review Ch. 8

Fri 12/04
Review HW5, sample test 2 and write down and questions for instructor

Mon 12/07
Review sample test 2 and any material related to comments the instructor may make

Wed 12/09
Test 2 on this date

Fri 12/11
Last class: discussion of test 2, course overall, tie up any loose ends.