Financial Management

Lecture 9

Dr. Harshit Rajaiya

Telfer School of Management
University of Ottawa
 Readings
• Readings: Chapter 12

2
 Outline
➢ Define a Security’s Return
• Historical Return and Expected Return

➢ Define a Security’s Risk (stand-alone risk)

• Variance and Standard Deviation

➢ How to Compute Expected Return and Standard Deviation

➢ Capital Market Efficiency

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 Measuring Returns
Pt Pt+1, Dt+1

t t+1

𝑃𝑡+1 +𝐷𝑡+1
➢ By definition: 𝑟𝑡:𝑡+1 = −1
𝑃𝑡

P1 − P0 + Income1 P1 − P0 Income1
r1 = = +
P0 P0 P0
Income Yield
(Dividend or Coupon)

Capital Gains Yield

4
 Historical Returns
Consider four broad asset classes:
➢ Cash
• Debt securities that are very liquid, very low-risk and very short-
term (e.g., T-bills)

➢ Bonds
• Debt instruments that have a longer maturity than cash (e.g.,
Government bonds)

➢ Large stocks
• Ownership of shares in publicly held large corporations (large
market capitalization)
➢ Small stocks
• Ownership of shares in publicly held small corporations (small
market capitalization)

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 Example – Calculating Returns
➢ You bought a stock for $35, and you received dividends
of $1.25. The stock is now selling for $40.

• What is your dollar return?

• Dollar return = 1.25 + (40 – 35) = $6.25

• What is your percentage return?

• Dividend yield = 1.25 / 35 = 3.57%

• Capital gains yield = (40 – 35) / 35 = 14.29%
• Total percentage return = 3.57 + 14.29 = 17.86%

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 The Importance of Financial Markets

➢ Financial markets allow companies, governments and individuals to

increase their utility
• Savers may invest in financial assets so that they can defer
consumption and earn a return to compensate them for doing
so
• Borrowers have better access to the capital that is available so
that they can invest in productive assets

➢ Financial markets also provide us with information about the returns

that are required for various levels of risk

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 Average Returns
1957 – 2014
Arithmetic Average
Investment
Return (%)
Canadian common stocks 10.30
U.S. common stocks (Cdn $) 11.73
Long bonds 8.57
Small stocks 12.81
TSX Venture stocks 7.16
Inflation 3.82
Treasury bills 5.88

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 Risk Premiums

➢ The “extra” return earned for taking on risk

➢ Treasury bills are considered to be risk-free
➢ The risk premium is the return over and above
the risk-free rate

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 Average Returns and Risk Premiums
1957 – 2014
Investment Arithmetic Average return (%) Risk Premium (%)
Canadian common stocks 10.30 4.42
U.S. common stocks (Cdn $) 11.73 5.85
Long bonds 8.57 2.69
Small stocks 12.81 6.93
TSX Venture stocks 7.16 1.28
Inflation 3.82 −2.06
Treasury bills 5.88 0.00

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 Variance/Standard Deviation: Measures of
Risk
▪ The spread of a return distribution is a measure of how much an observed
return may deviate from its mean value

▪ We usually use the standard deviation (σ) to represent the spread of a normal
distribution
❑ Standard deviation is the square root of variance

Probability distributions
are used to describe If Normal distribution:
returns by listing all 68% of obs within ± 1σ
possible returns and
their probabilities 95% of obs within ± 2σ
99.7% of obs within ± 3σ

-3σ -2σ -σ r +σ +2σ +3σ

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 Probability Distributions

Stock A

Stock B

-30 -15 0 15 30 45 60

Returns (%)

The tighter (i.e., more peaked) the probability distribution, the more likely it is
that the actual returns will be close to the expected value (so it less risky)

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Calculating Variance and Average Returns –
Historical Case
➢ Variance & standard deviation are measures of total risk

T and

 (R − R )
t
2
 2 = variance =  2

2 = t =1  = standard deviation
T −1 R = arithmetic average
T = the number of data points (i.e. sometimes referred to as " N" )

➢ In common parlance, we talk in terms of standard deviation

• Variance is denominated in “squared units” which is hard to interpret

• Arithmetic average return (the mean):

( R1 +  + R T )
R=
T 13
Calculating Variance and Average Returns –
Historical Case
“Ex-post” variance & standard deviation are
measures of total risk:
Standard deviation of returns

( R − R ) 2
+ ( R − R ) 2
+  + ( R − R ) 2
 = 2 = 1 2 T
T −1
Where the average return (arithmetic mean):

( R1 +  + RT )
R=
T
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 Example – Variance and Standard
Deviation
Year Actual Average Deviation from Squared
Return Return the Mean Deviation
1 .15 .105 .045 .002025
2 .09 .105 -.015 .000225
3 .06 .105 -.045 .002025
4 .12 .105 .015 .000225
Totals .42 .00 .0045

Variance = .0045 / (4-1) = .0015 Standard Deviation = .03873

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Why Do We Care about Historical Returns

➢ When we invest, we care about the future not the past

➢ One strategy to forecast the future is to investigate the

past:
• Use historical average return to estimate expected future return
• Use historical standard deviation to estimate future standard
deviation

➢ Note: Not the only method, we can also look at models

that we will learn in the next lectures

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 Can we trust historical data?
➢ Historical data is helpful but should be used carefully
“Data Mining”
➢ Which data sample & frequency to use?
• 1 year, 5 years, 30 years, 100 years?

➢ “Difficult” to estimate expected return accurately

• Variance is more persistent → “easier” to estimate

➢ “Easier” to forecast average annual rate of return over longer time

periods
• Say, 5 to 10 years compared to just 1 year

➢ Note: Using historical data for individual stocks is almost guaranteed to fail. It
simply projects winners to continue winning and loser stocks to continue
losing. This approach is more appropriate at market-wide level with rich
history of data.

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 More on Average Returns

➢ There are many different ways of calculating

returns over multiple periods

➢ Two methods are:

• Arithmetic Average Return
• Geometric Average Return

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 Arithmetic vs. Geometric Average
Example
➢ You invested $100 in a stock five years ago. Over the
last five years, annual returns have been 15%, -8%,
12%, 18% and -11%. What is your average annual rate
of return? What is your investment worth today?

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 Calculating Arithmetic Average
15 + (−8) + 12 + 18 + (−11)
Arithmetic Average Return = RA =
5

R A = 5.2

• The return in an average year was 5.2%.

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 Calculating Geometric Average

➢ FV=$100(1+.15)(1-.08)(1+.12)(1+.18)(1-.11)
➢ FV=$124.44

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 Calculating Geometric Average
➢ What equivalent rate of return would you have to earn
every year on average to achieve this same future
wealth?

$124.44 = $100  (1 + RG ) 5
1
RG = 1.2444 5
−1
RG = 4.47%

➢ Your average return was 4.47% each year. Notice that

this is lower than the arithmetic average. This is because
it includes the effects of compounding.
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 Geometric Average

➢ The general formula for calculating the

geometric average return is the following:

Geometric Average Return = (1 + R 1 ) (1 + R 2 ) ...  (1 + R T ) − 1

1
T

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Geometric vs. Arithmetic Average Returns
1957-2014
Average Return

Investment Arithmetic (%) Geometric (%) Standard deviation (%)

Canadian common stocks 10.30 9.01 16.50
U.S. common stocks (Cdn $) 11.73 10.42 16.94
Long bonds 8.57 8.16 9.78
Small stocks 12.81 9.83 25.96
TSX Venture stocks 7.16 −2.69 44.35
Inflation 3.82 3.77 3.10

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Geometric vs. Arithmetic Average Returns
Which one is better?

Arithmetic average is a better forward-looking measure of average expected

future return. The arithmetic average could be used to give an indication as to
what future returns would be on a stock.

Geometric average is a better historical measure of average expected return,

as it takes into account the effects of compounding. It could be used to show
how an investment portfolio increased in value over a period of time

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 What is an efficient market?
➢ An efficient market is one where the market price is an
unbiased estimate of the true value of the investment.

➢ Implicit are several key concepts –

• Market efficiency does not require that the market price be

equal to true value at every point in time. All it requires is that
errors in the market price be unbiased (prices can be greater or
less than true value, if these deviations are random).
•
• Randomness implies that there is an equal chance that stocks
are under or over valued at any point in time. If the deviations
of market price from true value are random, it follows that no
group of investors should be able to consistently find under or
over valued stocks using any investment strategy.

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The Efficient Market Hypothesis (EMH)

➢ Information is widely and cheaply available to all

investors.

➢ The efficient market hypothesis states that prices react

quickly and unambiguously to new information.
Security prices are reflecting all relevant and ascertainable information.

➢ Important lesson:
You can trust the market prices because they impound available information about the
value of a security.

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 Reaction of the Stock Price to New Information
in Efficient and Inefficient Markets

Stock
Overreaction to “good
Price
news” with reversion
Delayed
response to
Efficient market response to “good news”
“good news”

semi-strong -30 -20 -10 0 +10 +20 +30

Days before (-) and after (+) announcement

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The Different Types of Efficiency
➢ Weak Form
• Security prices reflect all information found
in past prices and volume.
➢ Semi-Strong Form
• Security prices reflect all publicly available
information.
➢ Strong Form
• Security prices reflect all information—
public and private.

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Fama vs Thaler: Are Markets Efficient?

Nobel Laureate Eugene Fama Nobel Laureate Richard Thaler

https://www.youtube.com/watch?v=bM9bYOBuKF4

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 The Evidence
➢ The record on the EMH is extensive, and some debate
remains, although academics tend to support the EMH (in the semi-
strong form)
➢ Studies fall into three broad categories:
1. Are changes in stock prices random? Are there profitable
“trading rules”? (Weak-Form Test)
2. Event studies: Does the market quickly and accurately respond
to new information? (Semi-Strong Form Test)
3. The record of professionally managed investment firms. (Semi-
Strong Form Test)

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 Weak Form Tests – Examining Technical Analysis

➢ Tests for serial correlation of returns

• e.g., successive price changes
• ++-+--+-+---++ …..
• Test for return predictability to see if you can make money

– e.g., Technical analysis

• Trading rules based on patterns of price and
volume
• Results
– Markets are weak form efficient
– You can’t use the past pattern of prices to predict future prices (i.e., prices
follow a random walk)

Note: There is some evidence of return predictability (i.e., momentum effect)

although unclear if it profitable after trading costs and after adjusting for risk
(e.g., evidence of momentum crashes).
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 Event Study Results
➢ Over the years, event study methodology has been applied to many
events including:
• Dividend increases and decreases
• Earnings announcements
• Mergers
• Capital spending
• New issues of stock
➢ The studies generally support the view that the market is semi-strong
form efficient, so it is impossible to make superior returns by trading
the stock after the news.
➢ Markets rapidly and accurately reflect information in the price of the
firm’s stock and may even have some foresight into the future.

Note: There is some evidence of return predictability with respect to a ‘post-earning

announcement drift’ where the price stock with good earnings tend to drive upward
even after the announcement, and vice versa.
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 Event Studies: Dividend Omissions
Cumulative Abnormal Returns for Companies Announcing
Dividend Omissions
Cumulative abnormal returns (%)

1 0.146 0.108 0.032

-0.483
0
-1 -0.244 Efficient market
-0.72
-2 response to “bad news”
-3
-3.619 -4.563 -4.685
-4 -4.898

-5
-4.747 -4.49
-5.015
-6 -5.183
-5.411
-7
-8
-8 -6 -4 -2 0 2 4 6 8
Days relative to announcement of dividend omission
S.H. Szewczyk, G.P. Tsetsekos, and Z. Santout “Do Dividend Omissions Signal Future Earnings or Past Earnings?” Journal of Investing (Spring 1997)

The Abnormal Return on a given stock for a particular day is calculated by subtracting the
market’s return on the same day (RM) from the actual return (R) on the stock for that day:
AR= R – Rm
The abnormal return can be also calculated using CAPM:
AR= R – (a + bRm) 34
 The Record of Mutual Funds
➢ If the market is semi strong-form efficient, then no matter what
publicly available information mutual-fund managers rely on to
pick stocks, their average returns should be the same as those
of the average investor in the market.

➢ We can test efficiency by comparing the performance of

professionally managed mutual funds with the performance of a
market index.

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The Record of Mutual Funds

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 The Strong Form of the EMH
➢ One group of studies of strong-form market efficiency investigates
insider trading.

➢ Several studies support the view that insider trading is abnormally

profitable.

➢ Thus, strong-form efficiency does not seem to be substantiated by

the evidence.

➢ Takeaway: If you have inside information which is not illegal (most

of the time it is but check with your lawyer *for a fee) you may be
able to beat the market.

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 Real World Implications
➢ If market is efficient, why exert effort and pay the price to trying to
beat it?

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 Evidence Contrary to Market Efficiency
(Anomalies)
➢ Stock Market Crashes & Speculative Bubbles
➢ Post-Earnings Announcement Drift: Investors under react to the
earnings announcements

➢ The New-Issue Puzzle (IPOs): On average the investors who receive

new issues receive an immediate capital gain, but these early gains
often turn into losses

➢ Size effect
• Small firms appear to outperform big firms, after adjusting for risk.

➢ Value (low market/book ratio) versus glamour (high market/book ratio)

• Low market-to-book equity firms appear to outperform.
Anecdotes?

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 Summary

➢ You should know that:

• Risky assets earn a risk premium
• Greater risk requires a larger required reward
• In an efficient market, prices adjust quickly and
correctly to new information
• The three levels of market efficiency are strong form
efficient, semi strong form efficient, and weak form
efficient.

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