1. November 16, 2010MATH 2510: Fin. Math. 2 1 Hand-Outs, I Graded Course Works #2 (brown folder.) Nice work; more comments on Thursday. Course Work #3. Due (next) Thursday November 25 (green.) Student surveys; yellow. Fill out and give to me or Maths Taught Student Office. Attendence sheet (just the one.)

2. November 16, 2010MATH 2510: Fin. Math. 2 2 Hand-Outs, II Updated course plan (blue as usual.) Exercises for Thursday Nov. 17 Workshops. (Qs and As.) Commented table of the normal distribution. These slides. A few spares of CT1, Unit 14 w/ comments. Many spares of last week’s Workshop sol’ns.

3. November 16, 2010MATH 2510: Fin. Math. 2 3 CT1 Unit 14: Stochastic rates of return Rate of return each period, i t, is stochastic (or: random.) Returns are independent (actually not the worst assumption ever made.) We invest over the horizon 0 to n. What can we say about our time-n wealth? (Expected value, standard deviation, moments, distribution, …)

4. November 16, 2010MATH 2510: Fin. Math. 2 4 A single (£1) investment The central point of attack is the equation By raising it to powers (1 and 2 mostly; 3 and 4 in CW #3) and taking expectations we arrive at equations for moments in terms of i t -moments. (Nice w/ iid, manageble even if not.)

5. November 16, 2010MATH 2510: Fin. Math. 2 5 (£1) Annuity investment The central point of attack is the equation By raising it to powers (1 and 2 in particular) and taking expectations we arrive at recursive equations for moments.

6. November 16, 2010MATH 2510: Fin. Math. 2 6 Annuities w/ the iid returns In case of identically distributed returns we get with j = E(i) and v =´1/(1+j).

7. November 16, 2010MATH 2510: Fin. Math. 2 7 2nd moment of annuity wealth For the second moment we get This is easy the implement in e.g. Excel. (Go to file w/ Table 1.3.1.) (For non-identical i-distributions just put time-indices on j and s.)

8. November 16, 2010MATH 2510: Fin. Math. 2 8 Log-normal returns Another often used, none-too-bad assumption is A sum of independent, normally distributed random variables is itself normally distributed, and the central point of attack is

9. November 16, 2010MATH 2510: Fin. Math. 2 9 For single investment we can (when equipped w/ a table of the normal distribution function) find probabilities (for e.g. shortfall or outperformance) easily. A fact: For annuities the (log)normality assumption doesn’t really help much.