Problems for Ch 1
1. Graphically demonstrate the Fisher separation theorem for the case where an
individual ends up lending in financial markets. Label the following points on the
graph: initial endowment, Wo; optimal production investment, (Po, P1); opti
Solution to the Ch 4 assignments
Q1: (a) E[U(W)] = .5 ln 4,000 + .5 ln 6,000 = 8.4967825
Let U(W) = E[U(W)], i.e., ln (W) = 8.4967825. Then, W = $4,898.98
Thus, M RP = 5,000 - 4,898.98 = $101.02 ( <$125).
So, he would not buy the insurance for $125
(b) Gi
Solution to the Ch 5 assignments
Q1: (a)
Security A
Security B
Prob. distn.
State 1
30
20
/
State 2
10
40
/
prices
5
10
(b) pj denotes the price of pure security in state j. Solve
30 p1 + 10 p 2 = 5
20 p1 + 40 p 2 = 10
p1 = $0.1
p 2 = $0.2
Q2: (a) pi d
Solution to Ch 6 problem set
Q1:
a) E(X) = 9.0,
var(x) = 28,
E(Y) = 5.0,
Var(Y) = 50.8,
Cov(X,Y) = -1.2
b) E(R p ) = aE(X) + (1-a)E(Y)
2
2
2
Var(R p ) = a 2 x + 2ab cov( X , Y ) + (1 a ) y
% in X % in Y E(R p )
125
-25
10.0
100
0
9.0
75
25
8.0
50
50
7.0
2
Solution to Ch 7 problem set
Q1:
Yes. Given a riskless asset, two-fund separation obtains, and if you can observe any one
of the following: 1) the percent of the investors portfolio held in the market portfolio,
or 2) the of the investors portfolio, you c
Solution to the supplement Q for Ch7
(a) A zero-beta portfolio has zero covariance with the market portfolio, by definition.
Also, using matrix notation, the covariance between two portfolios is
cov = W1W2
where
W1 = the row vector of weights in the zero-
The solution to the Math Review (I) problem set
Q1:
E(X) = (a + b)/2 = 5.5
P(2< X < 6) =
6
V(X) = (b - a)2/12 = 25/12 = 2.083
61
2 f ( x)dx = 3 5dx =
63 3
=
5
5
Q2: The cumulative distn function for X is:
0,
1
,
F ( x ) = Pr ( X x ) = 3
1
,
2
1,
if _ x
WATER POLLUTION
Nery Garcia
This issue affects the community because it strips the good
water away from us for drinking, showers, cooking; making
it very unhealthy to use.
Households are local residents may gain jobs in purifying
the water for the commu
1
Module one Review
What is economics and how does it affect me?
Economics is a study of peoples choices and how it affects our lives
every day. Economics is your everyday life. (Doing chores at home,
using your cellphone, ordering pizza, shopping at a st
Garcia 1
Nery Garcia
Professor David Clark
Into to Humanities 1020 04B
February 29, 2015
Boccaccio Response Paper
This article is a detailed description of life during the middle ages. More specifically the
effects during and after the Black Death or the
Price
(In whole dollars)
10
12
14
16
18
20
22
24
26
Quantity
13600
11200
9200
7600
6000
4000
2400
1200
400
Sam Smith reveals that he wears contacts and he uses Alcon contact solution. He begins
to tell his fans that the Alcon company has better advancemen
Garcia 1
Nery Garcia
Economics with Financial Literacy
Mr. Benedict
August 22, 2016
02.03 Sharing with Uncle Sam
Career Name: Research scientist
Yearly Income: $90,000
Flat Tax
Some Americans are supporting switching to a flat income tax rate of 15%. How
Solution to the Ch 1 assignments
Q1: Assume the individual is initially endowed at A, with current income yo and endof-period income y1. Using the market rate rf, the PV of his endowment is his current
wealth wo: wo = y o +
y1
.
1 + rf
He will take on inv
Problems for Ch 7
Q1: In the CAPM, is there any way to identify the investors who are more risk
averse? Explain. How would your answer change if there were not a riskless asset?
Q2: Given risk-free borrowing and lending, efficient portfolios have no unsys
A supplementary problem for Ch 7
(This is optional, and you may not do it)
Q. Given the following var-cov matrix and expected returns vector (for assets X and
Y) for a two-asset world:
0
0.01
=
0.0064
0
X 1 0.2
X = 0.1
2
(a) What is the expected r
Ch 4.
Utility Theory under Uncertainty
The theory of choice
Ch 1 deals with choices of consumption and investment with capital markets under no
uncertainty. This chapter is concerned mainly with the foundation for the theory of
investor choice with uncert
Ch 5. State Preference Theory
Uncertain future states and complete markets
From now on, we deal with the optimal choice of investing in more than one risky
asset or security, i.e., the problem of portfolio decision making.
An individuals portfolio selecti
Ch 6. Objects of Choice
Using mean and variance as choice criteria in EU
EU for a continuous prob. distn. can be constructed in a manner similar to that for a
discrete case, which is introduced in the Review. The key point is on the equivalence
between a
Ch 7 CAPM and APT
The derivation of the CAPM
The market portfolio M must be an efficient portfolio in equil, i.e., it must lie on the
upper half of the mean-var investment opportunity set. Assume that asset returns
follow a normal distn., which is complet
Ch 10. Efficient Capital Markets: Theory
A. Definition of Efficiency
The capital market is a place in which funds are transferred from lenders who have
excess funds to borrowers who have productive opportunities.
A market is allocationally efficient when
Probability and Statistics Review ( I )
Random variable (denoted by a bold capital-case letter)
A random variable (RV) is not a sure thing but takes on more than one value with a
probability distribution. For a discrete RV denoted by X, it has n possible
Problems for the Review (I)
1. A uniform RV is denoted by X with a mass (3, 8). Draw its p.d.f and c.p.f. on two
separate graphs. Calculate E(X), V(X) and the prob. of X falling between (2, 6).
2. A RV, Y, has the following frequency distn:
Y
0
1
2
q
1/4
Problems for Ch 4
1. You have a logarithmic utility function, U(W) = ln (W), and you current level of
wealth is $5000.
(a) Suppose that you are exposed to a situation which results in a 50/50 chance
of winning or losing $1000. If you can buy insurance whi
Problems for Ch 5
1. Security A pays $30 if state 1 occurs and $10 if state 2 occurs. Security B pays
$20 if state 1 occurs and $40 if state 2 occurs. The price of security A is $5 and the
price of security B is $10.
(a) Set up the payoff table for securi
Problems for Ch 6
Q1: Given 2 RVs (X and Y) with the following distributions:
State probability State of nature Outcomes of X Outcomes of Y
.2
I
18
0
.2
II
5
-3
.2
III
12
15
.2
IV
4
12
.2
V
6
1
(a) Calculate the mean and variance of X and Y, and the covar
Ch 1 Introduction
We compare a world without capital markets to one with them in order to show that
no one is worse off while at least one individual is better off in a world with capital
markets.
Two periods: period o (today),
period 1 (tomorrow)
Endowme