This is a closed-book examination. Answer all questions as directed. Mark your answers directly on the examination. There are no trick questions on the exam. There are some formulas from the course (including some you will not need) at the end of the exam. Good luck!
A. General Concepts Short Anwer: 20 points (Answer each question in no more than one sentence of ordinary length.)
There are lots of correct answers, e.g., any three of domestic equities, foreign equities, Treasury Bills, Municipal Bonds, Warrants, Real Estate, Corporate Bonds.
There are several good answers. Three are number of shares of each security, investment proportions in each security, and dollar investment in each security.
The main trade-off is between risk and return, where risk is measured by the variance and return by the mean.
ERISA, the Employee Retirement Income Security Act of 1974, is the main body of law regulating pension plans.
There are many good answers; the S&P 500 will probably be the most common answer.
Return = (45 + 2 - 50)/50 = -6%
Return = 40% x 10% + 60% x 1% = 4.6%
(315,000/300,000) x (495,000/500,000) - 1 = 3.95%
6% = 8%(1-t) or t=25%
A Simple Example in One Period
Riskless bond (interest rate is 50%):
100 --- 150
Stock (underlying portfolio):
|- 125 50 -| |- 50
Insured portfolio and put (floor = 95, insurance paid for separately):
|- 125 |- 0 ? -| ? -| |- 95 |- 45
r = 150/100 = 1.5, u = 125/50 = 2.5, d = 50/50 = 1
value = V_u(r-d)/(r(u-d)) + V_d(u-r)/(r(u-d)) = 0 x 2/9 + 45 x 4/9 = 20
stock = (0 - 45)/(2.5-1) = -30 or short $30 worth (= short .6 shares)
bond = 20 - (-30) = 50 or long $50 worth (= long .5 bonds)
stock = 50 (underlying) - 30 (put replication) = $20 long (equals .4 shares
long)
bond = 0 (underlying) + 50 (put replication) = $50 long (equals .5 bonds long)
false. Because of the luck of the draw, historical returns differ significantly from any reasonable estimate of expected return, and tend to lead to a prescription of going long and short extreme amounts.
false. Diversification means the variance is small. The expected return of a portfolio is always a weighted average of the individual stock returns, which means that the expected return of the portfolio is the expected return of a typical stock in the portfolio, practically by definition.
true. This is exactly one of the main results in the CAPM.
true. Costs are first order and the benefits of holding the optimal level of risk is second order.
false. The main point of the paper is that this and most other traditional answers to the question given by practitioners are fallacious.
SN(x ) - BN(x ), 1 2
2 2 x = log(S/B)/sqrt(s T) + sqrt(s T)/2 1
2 2 x = log(S/B)/sqrt(s T) - sqrt(s T)/2. 2
Binomial option pricing:
Value = p V + p V u u d d
r-d p = ------ u r(u-d)
u-r p = ------. d r(u-d)
Binomial replicating portfolio:
V - V u d stock = ------- u-d
uV - dV d u bond = --------- r(u-d)