9/12/2011
Math 1140
Financial Mathematics
A) I had a great weekend.
B) I hate Monday mornings.
C) I am asleep now.
Lecture 9
Securities
Quiz
D) Just give me the quiz and
let me sleep.
E) I am eager to learn more
math.
Ana Nora Evans
403 Kerchof
AnaNEvans@virginia.edu
http://people.virginia.edu/~ans5k/
Math 1140 - Financial Mathematics
Promissory Notes
Discounting Non-interest-bearing Notes
In this type of problem
you are given the maturity
value, the sale date, the
due date, the discount
rate, and you are asked to
calculate the sale price.
A promissory note is legal document showing a
promise to pay agreement.
A note is non-interest-bearing if the maturity date
is specified instead of the principal and the
interest rate.
A note bears interest if it specifies the principal,
the term, and the interest rate.
Math 1140 - Financial Mathematics
Discounting Interest-bearing Notes
1) The borrower takes
out a loan from a
lender
2) The lender sells the
note to a third party
4
Discounting Interest-bearing Notes
Usually, the first
transaction bears simple
interest.
Step 1) Calculate the
Step 1) Use the future value
maturity value of the note formula
Step 2) Calculate the sale
price
The second transaction
uses discount interest.
3) The borrower pays
back the loan to the
third party
Math 1140 - Financial Mathematics
Use the discount proceeds
formula
P = S(1-dt)
Amount = maturity value of
the note
Term = the term from the
sell date to the date when
the note matures
Discount rate = discount
rate
3
Math 1140 - Financial Mathematics
Three transactions:
2
S = P(1+it)
Step 2) Use the discount
proceeds formula as in the
case of non-interest-bearing
notes.
P = S(1-dt)
5
Math 1140 - Financial Mathematics
6
1
9/12/2011
Example
Questions
A $1,000 promissory note, due
in 270 days bearing 5% interest
is sold after 130 days to a bank
charging 8% discount interest.
How much does the bank pay?
Math 1140 - Financial Mathematics
7
Math 1140 - Financial Mathematics
Securities Exchange Act of 1934
8
Securities
The term ‘‘security’’ means any note, stock, treasury stock, security
future, security-based swap, bond, debenture, certificate of interest or
participation in any profit-sharing agreement or in any oil, gas, or other
mineral royalty or lease, any collateral-trust certificate, preorganization
certificate or subscription, transferable share, investment contract, votingtrust certificate, certificate of deposit for a security, any put, call, straddle,
option, or privilege on any security, certificate of deposit, or group or
index of securities (including any interest therein or based on the value
thereof), or any put, call, straddle, option, or privilege entered into on a
national securities exchange relating to foreign currency, or in general, any
instrument commonly known as a ‘‘security’’; or any certificate of interest
or participation in, temporary or interim certificate for, receipt for, or
warrant or right to subscribe to or purchase, any of the foregoing; but
shall not include currency or any note, draft, bill of exchange, or banker’s
acceptance which has a maturity at the time of issuance of not exceeding
nine months, exclusive of days of grace, or any renewal thereof the
maturity of which is likewise limited.
9
Math 1140 - Financial Mathematics
Securities
A security is another form of ownership.
Debt securities
banknotes
promissory notes
treasury bills
Math 1140 - Financial Mathematics
10
Money Market
Equity securities (e.g. stock)
Derivatives
A derivative is a financial instrument whose
value depends on the values of other, more basic,
underlying assets.
The money market consists of financial institutions
and dealers in money or credit who wish to either
borrow or lend.
Participants borrow and lend for short periods of
time, typically up to thirteen months.
For example, a stock option is a derivative
whose value depends on the price of a stock.
Math 1140 - Financial Mathematics
11
Math 1140 - Financial Mathematics
12
2
9/12/2011
Secondary Market
Money market = fish market
A market where investors purchase securities or
assets from other investors, rather than from
issuing companies themselves.
Examples
New York Stock Exchange
NASDAQ
13
Math 1140 - Financial Mathematics
14
Math 1140 - Financial Mathematics
Secondary market = Whole Foods
Quiz
Solve as many problems as you can.
The quiz counts as 30 points class participation.
A clicker question is 2 or 3 points, so the quiz is the
equivalent to 10-15 clicker questions.
Math 1140 - Financial Mathematics
15
A) Monday 11:00-12:30
A) I received the email on
Friday about the review
session
B) Monday 1:00-2:30
C) Tuesday 11:00-12:30
D) Tuesday 3:30-5:00
B) I have never received an
email sent to
fall2011_math1140@coll
ab.itc.virginia.edu
16
Math 1140 - Financial Mathematics
Charge
Next time
Treasury bills and
certificates of deposit
First Exam (max 15 points):
26 September 2011 at 7pm
Location to be announced
Wednesday
Read section 2.5
Homework 4 is due.
Math 1140 - Financial Mathematics
17
Math 1140 - Financial Mathematics
18
3