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Investment
Analysis II
MGMT-6330 Investment Analysis II
Interest Rates, Forwards and Futures
Investment Analysis II - © 2012 Houman Younessi
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Investment
Analysis II
Interest and Interest Rates
(perhaps a review)
Interest is the fee paid by the borrower to the lender for the possession of
an asset for a fixed period of time.
Interest is usually calculated in terms of the percentage of monetary value
of the asset for a specific period of time (e.g. a year). This is called an
interest rate.
In investment finance we define interest rate as the relative return of
“risk-free” securities.
Investment Analysis II - © 2012 Houman Younessi
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Investment
Analysis II
Interest Rate Calculation
Simple Time Independent interest (usually simply called interest) is
the pure difference between the purchase price of the debt (the amount the
borrower must pay at maturity) and the face value of the amount borrowed
at contract time (principal) presented as a percentage with respect to the
face value.
Example: I borrowed $100 from my son and have agreed to pay him $110
“when he needs his money back”. What is the interest?
Answer: Maturity time is “when he needs his money back”, it is fixed but not
a constant. The interest is the pure difference the principal and purchase
price:
110 100
 0.1  10%
100
Note: Such interest is not time based. He may ask for his money back in ten years
(his loss) or tomorrow (mine)

Investment Analysis II - © 2012 Houman Younessi
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Investment
Analysis II
Interest Rate Calculation
Simple Time Normalized Interest (usually called simple interest RATE)
is the difference between the purchase price of the debt (the amount to
pay at maturity) and the face value of the amount borrowed at contract
time (principal) when the time from contract to maturity is fixed and predetermined; presented as a percentage of the face value.
Example: I borrowed $100 from my son and have agreed to pay him $110
in exactly one year. What is the interest rate?
Answer: Maturity time is exactly one year, it is fixed and constant. The
interest rate still is the pure difference the principal and purchase price:
P(t  m)  P(t  0) 110 100

 0.1  10%
P(t  0)
100
per annum
Note: Such interest rate is now time based. He can now only ask for his money
back in exactly one year

Investment Analysis II - © 2012 Houman Younessi
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Investment
Analysis II
Interest Rate Calculation
What if he wanted his money sooner, or I wanted to borrow the
money for longer than one year ?
There should be no problem. The interest rate may be calculated for any
period of time. These periods usually range from a day (overnight) to
multiple years (30 year loan). Each rate is calculated exactly the same.
Example: I borrowed $100 from my son and have agreed to pay him $110
in exactly 3 months. What is the interest rate?
P(t  m)  P(t  0) 110 100

 0.1  10%
P(t  0)
100
Per Quarter
Note: the numerical value of the rate is the same, but the actual rate is not the
same. This is 10% every three months

Investment
Analysis II
Interest rate calculation
What if he offered to lend me the money at 2.5% a quarter or 10% per
annum, which deal should I take?
There is no difference.
P(t  m)  P(t  0)(1 r )
P(t  m)  P(t  0)
r
P(t  0)
rP(t  0)  P(t  m)  P(t  0)
P(t  m)  P(t  0)(1 r )

P(t  90)  100(1 0.025)  102.5 100  2.5
So: P(t  180)  100(1 0.025)  102.5 100  2.5
P(t  270)  100(1 0.025)  102.5 100  2.5
P(t  360)  100(1 0.025)  102.5 100  2.5
$2.5 Per Quarter x 4 Quarters = $10 Per Annum
Note: I am not paying interest on the interest. I am borrowing $100, keeping it for 3
 with the $2.50 interest; then borrow $100 again, keep it
months, then return it along
for 3 months, then return it along with the $2.5 interest………(a total of four times)
Investment
Analysis II
Interest Rate Calculation
What if he realized that if I kept the money for a whole year and return the
principal and interest at the end of the year, at the end of the 3rd month, he is
actually lending me $102.5 and at therefore at the end of the 6th month I have
$102.5 (1+0.025)= $105.06 of his money and I should pay interest on that sum
for the third quarter and so on. At what effective annual rate have I borrowed
the $100?
This is called Compound Interest
P(t  m)  P(t  0)(1 r )
or in general:
P(t  90)  100(1 0.025)  102.5
P(t  180)  102.5(1 0.025)  105.06
P(t  270)  105.6(1 0.025)  107.68
P(t  m)  P(t  0)(1 r1)(1 r2 )(1 r3 )....(1 rn )
r  (1 r1 )(1 r2 )(1 r3 )....(1 rn )  (1 rn )n
P(t  360)  107.68(1 0.025)  110.38

Note: Now I am paying interest on interest and as such end up paying $0.38 more
Investment
Analysis II
Time Value of Money (Present and Future Value)
Because the notion of interest exists, money now, would be worth more than money
in the future (if interest rates are assumed to be more than zero).
One very good way of evaluating the value of various different payment
patterns is to determine their present value. The better investment
(ceteris paribus) is the one with a higher present value
If we know the interest rate, in a simple situation, the present value is the
future value divided by (1+r). So d=1/(1+r) is called the discount factor.
In the case of payments at a future different from a year, the rate is
expressed in its equivalent annual rate (r). If the payment takes place in
1/n years,
1
using simple interest rule the discount factor is: d 
The compound version is:
(1 r / n)
1
d
(1 r )
Investment Analysis II - © 2012 Houman Younessi
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n
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Investment
Analysis II
Investment Analysis II - © 2012 Houman Younessi
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Investment
Analysis II
What personal characteristics must board
members have?
They must be:
Competent – But know the limits of theory
Confident – But not overly so
Controlled (in control of their biases) – But not robots
also helps if they are:
Connected (informed of what is going on and able to exert some influence)
But not corrupt
Investment Analysis II - © 2012 Houman Younessi
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Investment
Analysis II
Over-confidence
Most people are over-confident, we are probably wired that way
We tend to take credit for our successes and blame our
failures on others or on bad luck
Investment Analysis II - © 2012 Houman Younessi
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Investment
Analysis II
In terms of trading, this means:
Most people over-trade (have higher turn-over than
necessary)
Even if you were right in selling
A and buying B (usually not the
case with over-confident
investors), the trading fees will
kill you
In the long-run, you
lose more than you
need to for the same
amount of return
intended
Most people take on more risk than
necessary
Investment Analysis II - © 2012 Houman Younessi
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Investment
Analysis II
Causes of over-confidence:
Illusions of :
Choice
Knowledge
Task familiarity
Outcome sequence
Availability of technology
Active involvement
Past success
Investment Analysis II - © 2012 Houman Younessi
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Investment
Analysis II
So, what have we learned?
You are not as good as you think you are
The world is not as simple as you think it is
XXXXX
Investment Analysis II - © 2012 Houman Younessi
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Investment
Analysis II
So, what must we do?
We must:
Know the theory and tools
Know ourselves
Know others
Know the environment
Know the market
Investment Analysis II - © 2012 Houman Younessi
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Investment
Analysis II
Theory and tools
QUIZ
Investment Analysis II - © 2012 Houman Younessi
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Investment
Analysis II
Financial Assets
Financial Asset: Current or future ability to purchase
Three forms:
Cash: Immediate or near immediate purchasing instrument
Contracts: A financial right or obligation set not necessarily through
a document
Securities: A document that confers upon its owner a financial claim
Note: Cash is arguably a form of security
Investment Analysis II - © 2012 Houman Younessi
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Investment
Analysis II
Financial Assets
Securities
Fixed Income
Cash
Contract
Equities
Fixed income: instruments that pay a fixed amount of money to their owners
Equity: A security that confers to its owner the right to a part of and a corresponding
portion of profits of an economic concern. An equity is sometimes called a
share
Investment Analysis II - © 2012 Houman Younessi
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Investment
Analysis II
Fixed Income
Bonds
…
Money-Market Accounts
Savings Accounts
Bond: A security purchased by its owner called the creditor; at an agreed amount
called the bond price that gives the owner the right to a fixed, pre-determined
payment called the nominal value (or face value, par vale or principal); at a
future, predetermined date called the maturity date (or simply maturity).
Investment Analysis II - © 2012 Houman Younessi
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Investment
Analysis II
Equities
Shares
Stocks
Stock: An equity issued by a company called the issuer and usually sold and
traded by a third party (such as an exchange) and purchased and held
by an owner called the stockholder.
Investment Analysis II - © 2012 Houman Younessi
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Investment
Analysis II
Contracts
Simple Contracts
Derivatives
Derivative: A contract whose payoff depends on the value of another financial
variable such as the price of a stock, price or maturity of a bond, an
exchange rate, or the price or another feature of another derivative)
Investment Analysis II - © 2012 Houman Younessi
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