1. PTS.) Let A and B be indegendem ewn‘rs with
PICA)
MB)
0.10.
0.60.
a. "What is P ( AME } 7’
0.06
b. “That ia P ( AME-C) “F
0.04
c. "What is the probabﬂhy that neiﬂler A nor B occurs r.’
0.36 1. PTS.) Ler X be a random variable with the ﬁlbxx'mg disuﬂjmi
Here are statistics for three companies‘ daily returns:
mean covariance
H Gii
Alpha Beta Gamma
Alpha 0.0011 0.0016 0.0001 0.0000
Beta 0.0010 0.0001 0.0004 0.0000
Gamma 0.0009 0.0000 0.0000 0.0004
Strictly speaking. these are the means and covariances
1. The current plice Ufa stock is S = $85.00. A call option with expiring exactly
T = 1 year from now with a strike price of K = $75.00 is now selling for
C = $20.00.
The present value of a guaranteed $100 payment at time T=l is $98.00.
a. (4 pts) If the
Mathematical Finance
Math 458/558
Adam S. Sikora
SUNY Bualo
Version: October 18, 2015
Syllabus.
(1) cash ows (eg. deposits, loans), value of money in time,
nancial transactions which do not involve risk
(2) Introduction to probability: probabilities, rand
T70 Chapter 6 MEAN~VAR|ANCE PORTFOLEO THEORY
EXERCISES
The single efﬁcient fund of risky assets F can be found by solving a system of
12 linear equations and n unknowns. When the soiution to this system is normaiized
so that its components sum to 1, the r
EXERCISES 35
EXERCISES
- -
— -=
1 inheritance) Suppose iii were invested in l7‘76 it 3 3 0 Interest compounded
(:2) Approximately how much would that investment be worth today: $l,000, $10,000,
$100,000, Dr $1,000,000"?
([1) What if the interest rate wer
EXERCiSES
EEEEEE
EXERCiSES 193
The beta of a por-tt‘oiio of stocks is equai to the weighted average of the betas of the
individual assets that make up the portfolio
One appiication of CAPM is to the evaluation of mutual fund performance The
Jensen index m
Problem 1
Suppose the market is complete. The stock price process, [Ethan is modeled by the Ito stochastic differential
equation as
db} =jJSEd1 + ﬂSgd-Bg
where [Ethan is the standard Brownian motion and ,u. and a" are constant positive teal numbers. The r