HAAS SCHOOL OF BUSINESS
UNIVERSITY OF CALIFORNIA AT BERKELEY
UGBA 103 AVINASH VERMA
1.
SOLUTION TO Assume that the CAPM holds.
Portfolio a Ep
HOMEWORK 10
Securityk Portfolio q Rf
M (Market Portfolio)
Security j
Security i
p
[4 points each for a total of 4

Chapter 6 Solutions
2
6.1. Subproblems: Define an array of subproblems D(i) for 0 i n. D(i) will be the largest sum of a (possibly empty) contiguous subsequence ending exactly at position i. Algorithm and Recursion: The algorithm will initialize D(0) = 0

CS 170
Algorithms
Fall 2013
Satish Rao
HW 7
1. (20 pts.) A greedy algorithmso to speak The founder of LinkedIn, the professional networking site,
decides to crawl LinkedIns relationship graph to nd all of the super-schmoozers. (He gures he can make
more m

CS 170
Algorithms
Fall 2013
Satish Rao
HW 6
1. (10+5 pts.) Graph construction
Solution: We can construct a graph where the nodes are the states, and there is a directed edge from state
a to state b if by one crossing we get state b from a. We name the the

Solution to Midterm 2 Fall 2008 cs170
Problem 1 [60 points] 1. 0.55
0.3 0.1 0.05 2. True 3. 3
A B
1
S
1
4.
A
-5
B
20
S
22
Dijkstra outputs (S,A) and (S,B) as the final tree with shortest path distances of 20, and 22 respectively. In Dijkstra algorithm onc

CS 170
Algorithms
Fall 2013
Satish Rao
1. (11 pts.)
HW 3
Problem 2.5
a) T (n) = 2T (n/3) + 1 = (nlog3 2 ) by the Master theorem.
b) T (n) = 5T (n/4) + n = (nlog4 5 ) by the Master theorem.
c) T (n) = 7T (n/7) + n = (n log7 n) by the Master theorem.
d) T (

Chapter 2 Solutions
January 31, 2007
2
2.2. Consider b 2.3. a)
logb n
.
T (n)
=
3T 3k T
n + cn = = 3k T 2 n 2k + 2cn 3 2
k
n 2k
k-1
+ cn
i=0
3 2
i
=
=
-1
n For k = log2 n, T ( 2k ) = T (1) = d = O(1). Then:
T (n) = dnlog2 3 + 2cn as predicted by the Maste

Chapter 3 Solutions
2
3.1 The figure below gives the pre and post numbers of the vertices in parentheses. The tree and back edges are marked as indicated.
(1,12) (2,11) (3,10)
A
B
C
Tree Edge Back Edge
(13,18)
D
E
(5,6)
F
(4,9)
G
(14,17)
H
(15,16)
I
(7,8)

Chapter 1Solutions
February 2, 2007
2
1.1. A single digit number is at most b-1, therefore the sum of any three such numbers is at most 3b-3. On the other hand, a two-digit number can be as large as b2 - 1. It is enough to show that b2 - 1 3b - 3. Indeed,

CS 170
Algorithms
Fall 2012
1. (20 pts.)
HW 8
Satish Rao
Problem 6.4 (Corrupted text document)
(a) Subproblems: Dene an array of subproblems S(i) for 0 i n where S(i) is 1 if s[1 i] is
a sequence of valid words and is 0 otherwise.
Algorithm and Recursion:

HAAS SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA AT BERKELEY
UGBA 103 AVINASH VERMA
BRIEF TEACHING NOTE AND HOMEWORK 7
Let us first note that squared correlation, commonly referred to as "R-squared," between returns on Security i and those on the market p

HAAS SCHOOL OF BUSINESS
UNIVERSITY OF CALIFORNIA AT BERKELEY
UGBA 103
AVINASH VERMA
A:
VARIOUS CAPITAL BUDGETING CRITERIA: A BRIEF COMPARISON NET PRESENT VALUE [NPV] RULE Accept if NPV > 0 ; Between A and B, Choose A if NPV ( A) > NPV ( B ) . PAYBACK PERI

NAME: HAAS SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA AT BERKELEY UGBA 103
TAKE-HOME MID-TERM EXAMINATION JULY 23, 2009 TO JULY 27, 2009 DUE IN THE BOX OUTSIDE F494 AT 9AM ON JULY 27, 2009 SHOW WORK FOR PARTIAL CREDIT. EACH QUESTION HAS 12.5 POINTS.
1.
S

HAAS SCHOOL OF BUSINESS
UNIVERSITY OF CALIFORNIA AT BERKELEY
UGBA 103 AVINASH VERMA
SOLUTION TO HOMEWORK 9
1. Suppose the market portfolio is expected to earn a return a 12.5% with a standard deviation of 16%. The risk free asset yields a return of 4.5%.

HAAS SCHOOL OF BUSINESS
UNIVERSITY OF CALIFORNIA AT BERKELEY
UGBA 103 AVINASH VERMA
PRACTICE PROBLEMS ON OPTIONS
1. A nondividend paying asset is currently valued at $100. Its value over the next period can go up by a factor of 1.16 or go down by a factor

HAAS SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA AT BERKELEY
UGBA 103 Avinash Verma
UNCERTAINTY AND RISK IN FINANCE
This handout is intended to be a brief preview of the statistics that we shall be using in the course. Throughout this note, key words and

Mortgage Example from Class on 7/7/2009 Given: Annual Gross (pre-tax) Income Life of Mortgage Loan in Years Frequency of Payments (number of payments in a year) Tax Rate Assumed annual appreciation in real estate Quoted 30-year Fixed Rate Mortgage Rate (y

American Stocks in Table 5.7 on Page 101 of the Text
Stock Stock Price, P Income stocks Cummins Inc. $118.18 Dow Chemical $39.90 Growth Stocks Microsoft $29.86 Starbucks $35.42 Figures as of "the start of 2007" EPS Cost of Equity PVGO = P - EPS/r $12.03 $

Time
Cash Flows
YTM using IRR function
We are given these bond characteristics: n in years 25 c=C/M 4.50% M $1,000 C $45.00 And this price: P(0) $558.00 Price = P(t) 0 P(0) $558.00 P(1) 1 $563.22 2 P(2) $568.91 3 P(3) $575.11 4 P(4) $581.87 5 P(5) $589.23

HAAS SCHOOL OF BUSINESS
UNIVERSITY OF CALIFORNIA AT BERKELEY
UGBA 103
AVINASH VERMA
SOLUTION TO HOMEWORK 8
1.
(a) Identify two publicly traded stocks, (b) download the daily data on historical price of the identified stocks from www.finance.yahoo.com, (c)

HAAS SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA AT BERKELEY
UGBA 103 AVINASH VERMA
BRIEF TEACHING NOTE AND HOMEWORK 7
Let us first note that squared correlation, commonly referred to as "R-squared," between returns on Security i and those on the market p

CS 170, Fall 2013
HW 12 Solutions
Instructor: Satish Rao
Problem 1 (10 points)
We reduce from M -I
-S . Let (H, k ) be an instance of M -I
-S , where H
is an undirected graph. Suppose H = (V, E ). We construct a directed graph H = (V, E ) as follows.
For