Risk and Return Chapter 4
These notes are an expanded version of the notes used in ECBU 500D.
Very
important ideas have been added.
Therefore, you may see some overlap with them.
In this topic we will look at the risk and return from the point view of personal
investment.
This is important because corporations obtain funds by issuing financial
securities such as stocks and bonds to individuals.
The person who buys a stock or a
bond from a corporation expects a certain rate of return or profitability from these
financial assets.
This is known as the required return of the funds’ providers.
The
required return of the funds’ providers equals the cost of funds for the funds’ acquirer.
Basically if I borrow money from you and you charge me 10% interest rate on the loan,
then my cost of funds is 10% and your rate of return on the loan is also 10%.
So, lets look at risk and return of financial instruments and how they are measured.
To
begin we need to define these terms.
Return
on an investment is defined as the change in the value of the investment.
Investors expect positive returns from their investments.
However, sometimes
investments end up loosing value.
Risk
on an investment is defined as the probability that the actual outcome of the
investment does not equal the expected outcome.
Some may only worry about the
probability of loss.
However, in my definition I am including all deviations from the
expected outcome because an error in forecast or an economic condition that caused extra
return could also cause a reduction in return.
Risk and Return Analysis:
Return:
Rate of return is measured as a percentage.
For example, the return was 12%.
To
measure the return from an investment for a period, usually a year, we add the cash we
received from the investment during the year plus the value of the investment at the end
of the year to get out total return.
Then we subtract from that number the value of the
investment at the beginning of the year to get our return expressed in dollars.
To get the
rate of return we divide the return in dollars by the value of the investment at the
beginning of the year.
So, the equation is as follows:
0
0
1
1
1
P
P
CF
P
r

+
=
where:
r
1
is the return for year 1
P
1
is the market value of the investment at the end of year 1
P
0
is the market value of the investment at the beginning of year 1 or end of year 0
CF
1
is the cash flow from the investment during year 1.
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To illustrate the equation, lets assume that an investor purchased a security for $100 and
received $7 cash flow from the security in the form of interest payment during the year.
At the end of the year this investor sold the security for $105.
What was the investor’s
rate of return.
In this example
P
1
= $105,
CF
1
= $7, and
P
0
= $100.
Therefore:
%
12
100
12
100
100
112
100
100
7
105
0
0
1
1
1
=
=

=

+
=

+
=
P
P
CF
P
r
Expected return, E(r):
When evaluating the potential performance of a security, we have to look at the future
expected return.
Since we can’t predict the future with certainty, we forecast few
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 Spring '11
 Mehdi
 Management, Capital Asset Pricing Model

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