Chapter7 an introduction to risk and return

CHAPTER 7

An Introduction to
Risk and Return
History of Financial Market Returns
Rodel F. Falculan

Chapter Outline








Realized and Expected
Rates of Return & Risk

Objective.

A Brief History of Financial
Market Returns

Objective.

Geometric vs. Arithmetic
Average Rates of Return

Objective.

What Determines Stock
Prices?

Objective.

Calculate realized &

expected rates of return & risk.
Describe the historical

pattern of financial market returns.

Compute geometric &

arithmetic average rates of return.
Explain the efficient market

hypothesis and why it is important to stock
market.

Principles Applied


Principle 2 : There Is a Risk-Return
Tradeoff
“investing in higher risk investments
does not always result in higher
realized rates of return ( that’s why
they call it risk ), higher risk
investments are expected to realize
higher returns, on average”.

Principles Applied


Principle 4 : Market Prices Reflect
Information
“ help us understand the wisdom of
markets and how investors purchases
and sales of a security drive its price
to reflect everything that is known
about the security’s risk and expected
return”.

INTRO : “ TRUST FUND BABY ”
January, 1926, $100 – December, 2009
Long term bond
issued by the US gov’t

5.4%

$8,400

Portfolio of large
US stocks

9.8%

$259,200

Portfolio of the smallest
publicly traded firms

11.9%

$1.2M

INTRO : “ TRUST FUND BABY ”






First, how do we measure the risk and
return for an individual investment?
Second, what is the history of financial
market returns on various classes of
financial assets, including domestic and
international debt and equity securities as
well as real estate and commodities?
Finally, what returns should investors
expect from investing in risky financial
assets?

Calculating the Realized Return
from an Investment


Realized return or cash return
measures the gain or loss on an
investment.

from an Investment



Example 1 : You invested in 1 share
of Apple (AAPL) for $95 and sold a
year later for $200. The company did
not pay any dividend during that
period. What will be the cash return
on this investment?

from an Investment

Cash Return

= $200 + 0 - $95
= $105

from an Investment


We can also calculate the rate of
return as a percentage. It is simply
the cash return divided by the
beginning stock price.

from an Investment


Example 2: You invested in 1 share of
share Apple (AAPL) for $95 and sold a
year later for $200. The company did
not pay any dividend during that
period. What will be the rate of
return on this investment?

from an Investment



Rate of Return = ($200 + 0 - $95) ÷ $95

= 110.53%


Table 7-1 has additional examples on
measuring an investor’s realized rate of return
from investing in common stock.

from an Investment






Table 7-1 indicates that the returns
from investing in common stocks can
be positive or negative.
Furthermore, past performance is not
an indicator of future performance.
However, in general, we expect to
receive higher returns for assuming
more risk.

Calculating the Expected Return
from an Investment


Expected return - average of the
possible returns, where each possible
return is weighted by the probability
that it occurs.

Calculating the Expected Return
from an Investment



Expected Return
= (-10% × 0.2) + (12% × 0.3) +
(22% × 0.5)
= 12.6%

Measuring Risk


In the example on Table 7-2, the
expected return is 12.6%; however,
the return could range from -10% to
+22%.



This variability in returns can be
quantified by computing the
Variance or Standard Deviation in
investment returns.

Measuring Risk


Variance – average squared
difference between the individual
realized returns and the expected
return.



Standard deviation – square root of
the variance.

Calculating the Variance and Standard
Deviation of the Rate of Return on an
Investment


Let us compare two possible
investment alternatives:


(1) U.S. Treasury Bill –short-term debt

obligation of the U.S. Government. Assume this
particular Treasury bill matures in one year and
promises to pay an annual return of 5%. U.S.
Treasury bill is considered risk-free as there is no
risk of default on the promised payments.


(2) Common stock of the Ace Publishing
Company – an investment in common stock
will be a risky investment.

Investment




The probability distribution of an
investment’s return contains all
possible rates of return from the
investment along with the associated
probabilities for each outcome.
Figure 7-1 contains a probability
distribution for U.S. Treasury bill and
Ace Publishing Company common
stock.

Investment




The probability distribution for Treasury
bill is a single spike at 5% rate of return
indicating that there is 100% probability
that you will earn 5% rate of return.
The probability distribution for Ace
Publishing company stock includes
returns ranging from -10% to 40%
suggesting the stock is a risky
investment.

Investment


Using equation 7-3, we can calculate
the expected return on the stock to
be 15% while the expected return on
Treasury bill is always 5%.



Does the higher return of stock make
it a better investment? Not
necessarily, we also need to know the
risk in both the investments.

Investment


We can measure the risk of an
investment by computing the
variance as follows:

Investment
Investment
Treasury Bill
Common
Stock


Expected
Return
5%

Standard
Deviation
0%

15%

12.85%

So we observe that the publishing company
stock offers a higher expected return but also
entails more risk as measured by standard
deviation. An investor’s choice of a specific
investment will be determined by their attitude
toward risk.

A Brief History of Financial
Market Returns



We can use the tools that we
have learned to determine the
risk-return tradeoff in the
financial markets.

A Brief History of the Financial
Markets


Investors have historically earned
higher rates of return on riskier
investments.



However, having a higher expected
rate of return simply means that
investors “expect” to realize a higher
return. Higher return is not
guaranteed.

U.S. Financial Markets: Domestic
Investment Returns








Small stocks: shares of the smallest 20% of all
companies whose stock is traded on the public
exchanges. ( Firm size is measured using the market
capitalization of the company’s equity, which is equal to
the share price multiplied by the number of shares
outstanding. )
Large stocks: the Standard & Poor’s (S&P) 500 stock
index, which is a portfolio that consists large company
stocks such as Walmart (WMT), Intel (INTC), and
Microsoft (MSFT).
Gov’t bonds: 20-year bonds issued by the federal gov’t.
These bonds are typically considered to be free of the
risk of default or non-payment since the gov’t is the
most credit-worthy borrower in the country.
Treasury bills: short-term securities issued by the
federal gov’t that have maturities of one year or less.

U.S. Financial Markets: Domestic
Investment Returns
Small
Stocks

Large
Stocks

Gov’t
Bonds

Treasury
Bill

Compound annual return 11.9%

9.8%

5.4%

3.7%

Standard deviation

20.5%

9.6%

3.1%

32.8%

LESSONS LEARNED:

Lesson #1: The riskier investments have
historically realized higher returns.

Lesson #2: The historical returns of the higherrisk investment classes have standard deviations.



Arithmetic average may not always
capture the true rate of return
realized on an investment. In some
cases, geometric or compound
average may be a more appropriate
measure of return.



For example, suppose you bought a
stock for $25. After one year, the
stock rises to $30 and in the second
year, it falls to $15. What was the
average return on this investment?



The stock earned +20% in the first
year and -50% in the second year.



Simple average = (20%-50%) ÷ 2 =
-15%







However, over the 2 years, the $25
stock lost the equivalent of 22.54%
({($15/$25)1/2} - 1 = 22.54%).
Here, -15% is the simple arithmetic
average while -22.54% is the
geometric or compound average rate.
Which one is the correct indicator of
return? It depends on the question
being asked.



The geometric average rate of return
answers the question, “What was the
growth rate of your investment?”



The arithmetic average rate of return
answers the question, “What was the
average of the yearly rates of return?

Computing the Geometric or
Compound Average Rate of Return

Compute the arithmetic and geometric
average for the following stock.
Year

Annual Rate
of Return

Value of the
stock
$25

1

40%

$35

2

-50%

$17.50

0



Arithmetic Average = (40-50) ÷ 2 =
-5%



Geometric Average
= [(1+Ryear1) × (1+Ryear 2)]1/2 - 1
= [(1.4) × (.5)] 1/2 - 1
= -16.33%

Choosing the Right “Average”


Both arithmetic average geometric average are
important and correct. The following grid provides
some guidance as to which average is appropriate and
when:
Question being
addressed:
What annual rate of
return can we expect
for next year?
What annual rate of
return can we expect
over a multi-year
horizon?

Appropriate Average
Calculation:
The arithmetic
average calculated
using annual rates of
return.
The geometric
average calculated
over a similar past
period.

What Determines Stock Prices?


In short, stock prices tend to go up
when there is good news about future
profits, and they go down when there
is bad news about future profits.



Since US businesses have generally
done well over the past 80 years, the
stock returns have also been
favorable.

The Efficient Market Hypothesis


The efficient market hypothesis (EMH)
states that securities prices accurately
reflect future expected cash flows and are
based on information available to investors.



An efficient market is a market in which
all the available information is fully
incorporated into the prices of the
securities and the returns the investors
earn on their investments cannot be
predicted.



We can distinguish among three types
of efficient market, depending on the
degree of efficiency:
1.

2.

3.

The Weak-Form Efficient Market
Hypothesis
The Semi-Strong Form Efficient Market
Hypothesis
The Strong Form Efficient Market
Hypothesis

(1) The Weak-Form Efficient Market
Hypothesis asserts that all past
security market information is fully
reflected in security prices. This
means that all price and volume
information is already reflected in a
security’s price.

(2) The Semi-Strong-Form Efficient
Market Hypothesis asserts that all
publicly available information is fully
reflected in security prices. This is a
stronger statement as it includes all
public information (such as firm’s
financial statements, analysts’
estimates, announcements about the
economy, industry, or company.)

(3) The Strong-Form Efficient Market
Hypothesis asserts that all
information, regardless of whether
this information is public or private, is
fully reflected in securities prices. It
asserts that there isn’t any
information that isn’t already
embedded into the prices of all
securities.

Chapter7 an introduction to risk and return

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