Solutions to Problem Set 1
Foundations of Financial Markets
1. (a) You have sold 10,000 shares at the ask price of 102 1/2. You bought 4,000 shares
at a bid price 102 1/4. Thus, 6,000 shares are sold short (sold without already
owning the security). Your
Problem Set 4
Due Tuesday April 19 at the start of class.
1. All stocks below have the same expected return. Sort them depending on how much
you like them if you had to hold them:
(a) individually (i.e., the stock would form your entire portfolio). or
(b)
1. (a) Recall that the general formula for expected return for a two-security portfolio is:
E(Rp ) = w1 E(R1 ) + w2 E(R2 )
Also, the variance of return for a two-security portfolio is:
p2 = w12 12 + w22 22 + 2w1 w2 1 2 .
I know that E(RZ ) = .15, E(RY ) =
Foundations of Finance
HW 2: Solutions
1. A risk-free zero coupon bond pays $1,000 in six years.
(a) The risk-free rate is currently 10% effective annual. What should the current
price of the bond be?
The price of the bond should be its fair value: what i
Fixed income
Andre de Souza
First, a quick refresher
Effective rates
Annual Percentage Rates (APRs)
Moving from one to the other
Effective rate for a period
Tells you how much $1 will become if invested at
that rate for 1 such period.
E.g.: effective
Equity Valuation
Andre de Souza
1
Finding value of a firms equity
Valuation using balance sheet data
Valuing equity directly
Dividend Discount Model
Gordon growth model
Two-stage dividend discount model
Valuation ratios (e.g. P/E ratio)
2
Question t
Fair Values of risky
and riskfree assets
Andre de Souza
Fair Values
Assume there is a market in the background where
assets with various risks are being bought and sold
Among these is the riskfree asset
If you know the expected cashflows on any asset,
CAPM
Andre de Souza
Last class
Started by assuming all investors:
like more E(R) in their portfolios and hate more sigma of their
portfolios
have access to the same assets
agree on the E(R), sigma, and covariance of these assets
We drew mean-sigma di
CAPM continued,
performance evaluation,
and efficient markets
Andre de Souza
Three things to talk about
today
Some more CAPM
Performance Evaluation
Financial market efficiency
What does the CAPM say?
The market portfolio is the same as the tangency
po
Optimal portfolios
(continued)
Andre de Souza
So far
Talked about forming portfolios of
Two risky assets
One risky and one risk-free asset
What do these portfolios look like on mean-sigma
graphs?
Now:
Many risky assets
Many risky and one risk-free
Optimal Portfolios
Andre de Souza
Introduce notation
wA: weight of portfolio in asset A
E(RA): expected return of asset A
A (pronounced sigma A): standard deviation of
asset As return
2A: variance of asset As return
AB (pronounced rho A B): correlati
Risk and Return 1
Andre de Souza
1
Overview
Individual asset returns
Expected returns
Variance of returns
2
Returns
I buy a stock on 1 Jan 2001 for $70. On 31 Dec 2001,
It pays a dividend of $3
I sell it after receiving the dividend, for $85
We can
Trying to find E(R) and
Var(R) of portfolios
Rule for E(R) of portfolios
Given weights and E(R) of underlying assets
Rule for Var of portfolios
None yet
First need to calculate Covar between the two assets
Definition:
What is value for:
MSFT/IBM:
IBM
Fair value
How much would it cost to recreate this asset in
the marketplace?
Interest rate is 10% EA. I offer to sell you an asset
that pays $121 for sure in one year. What price will
you offer me for it?
PV of assets cashflows at market interest rate
HPR
You invest for a certain time
Holding period return (HPR)
How much you have at the end divided by how much you had
at the start
I buy a share of IBM at $150 today. One week later IBM
pays $12 per share dividend. Immediately afterwards I
sell the s
Financial Instruments
Andr de Souza
1
Overview
Real and financial assets
Use of financial assets
Important examples of financial
assets
2
Real vs Financial Assets
Real Assets
Assets used to produce goods and
services
Examples: factories, land, human
Present values and future
values
How much is:
$C invested now worth in T years?
$C borrowed now worth in T years?
How much:
Do I have to invest today to have $C in T years?
Do I have to borrow today to pay $C in T years?
What is r in these formulas
Foundations of
Financial Markets
Andre de Souza
Todays class
Administrative details
First topic: financial instruments and financial
markets
Professor and TA
Professor: Andre de Souza
Email: [email protected]
Phone: 212 998 0836
Office hours: W
Present Values and Future
Values
$1 today is not the same as $1 in one year
If I have $C today, and the annual interest rate is r, I can
invest that $C and have _ at the end of a year
If I reinvest, I will have $_ at the end of _ years
If I reinvest,
Lecture 21
Financial Intermediation
M&B 27
Credit Market
r
S by savers
r0
D by
borrowers
Q0
Credit
Q0
Credit Market
In theory, savers could
lend directly to borrowers.
r
S by savers
r0
D by
borrowers
Q0
Credit
Q0
Credit Market
In theory, savers could
lend
Lecture 23
The Subprime Mortgage Crisis
Calomiris & Khan, An Assessment of TARP
Assistance to Financial InsCtuCons,
J. Econ. Perspec-ves 29 (Spring 2015): 53-80,
hNp:/pubs.aeaweb.org/doi/pdfplus/10.1257/jep.29.2.53
F15
Lecture 25
Exchange Rate Regimes
Intl M System (briey)
M&B 33, 34.
FloaGng vs Fixed Exchange Rates
Major exchange rates were xed 1958 1973
Allowed to oat, 2/1973
$ conGnues to oat relaGve to Euro sin
F15
Lecture 24
Foreign Exchange Rates
M&B 32
Foreign Exchange (FX) M&B 32
Eurozone
UK
Switzerland
Mexico
ArgenFna
Brazil
Japan
China
S. Korea
etc.
Euro
Pound Sterling (LaFn librum)
S
F15
Lecture 22
Bank and Thri1 Deposit
Insurance and Regula:on
M&B 28
NEWS
Many Central Banks seCng nega:ve rates on reserve deposits:
ECB (European CB): -0.20% since late 2014, considering less.
Switzerland
F15
Lecture 18
War & Peace
M&B 25 War
M&B 26 Peace
Today Thru 1920s
The Great Depression
1929 through 1930s
What caused it?
Could the Great Recession of 2008 have been similar?
To understand the Great Depression is the Holy Grail of
macroeconomics.
- Ben