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Transcript
Chapter 6
The Returns and Risks from
Investing
Learning Objectives
•
•
•
•
Define “return” and state its two components.
Explain the relationship between return and risk.
Identify the sources of risk.
Describe the different methods of measuring
returns.
• Describe the different methods of measuring
risk.
• Discuss the returns and risks from investing in
major financial assets in the past.
Asset Valuation
• Asset valuation is a function of both
return and risk




At the centre of security analysis
Return is the reward for undertaking the
investment
The realized risk-return tradeoff is based on
the past
The expected future risk-return tradeoff is
uncertain and may not occur
Return Components
• Returns consist of two elements:

Yield: Periodic cash flows such as interest or
dividends (income component of the security’s
return)
•
•

“Yield” measures relate income return to a price for
the security
Issuer makes the payments in cash to the security
holder
Capital Gain (Loss): Price appreciation or
depreciation
•
The change in price of the security over some period
of time
• Total Return = Yield + Capital Gain (Loss)
Example: Calculating yields and price
changes
• Assume that an investor buys 100 shares of a
stock for $40, holds it for one year and then sells
it at $50. During that year the investors receives
a dividends of $0.01 per share every 4 months.
• Calculate the yield and the capital gain (loss) for
the investor.
Risk
• Risk is the chance that the realized (actual) return
for an investment will be different from the expected
return
• Investors are concerned that the realized return will
be less than the expected return
• The greater the variability between the expected
and realized return, the greater the risk
• Although, investors may receive on average their
expected returns on risky assets in the long-run,
they fail to do so in the short-run
Risk Sources
• Interest Rate Risk

Affects market value
and resale price
• Market Risk


Purchasing power
variability
• Business Risk
Tied to debt financing
• Liquidity Risk

Overall market
effects
• Inflation Risk

• Financial Risk
Time and price
concession required to
sell security
• Exchange Rate Risk
• Country Risk

Potential change in
degree of political
stability
Risk Sources
• Interest Rate Risk
• Is the variability in a security’s return resulting from
changes in the level of interest rates
• Affects bonds more directly than common stocks and is
a major risk faced by bondholders
• Market Risk
• Is the variability in returns resulting from fluctuations in
the overall market
• All securities (especially common stocks) are exposed
to market risk
Risk Sources
• Inflation Risk
• Also known as purchasing power risk
• Is related to interest rate risk since interest rates
generally rise as inflation increases (inflation premiums)
• Business Risk
• The risk of doing business in a particular industry or
environment
• For example, Shell Canada faces unique problems as a
result of developments in the global oil situation
Risk Sources
• Financial Risk
• Is associated with the use of debt financing by
companies (financial leverage)
• The larger the proportion of assets financed by debt
(as opposed to equity), the larger the variability in
returns, the larger the risk
• Liquidity Risk
• Is the risk associated with the particular secondary
market in which the security trades
• A T-bill has little or no liquidity risk, whereas a small
OTC stock may have a large liquidity risk
Risk Sources
• Exchange Rate Risk
• Is the variability in returns on securities caused by
currency fluctuations
• Also called currency risk
• Country Risk
• Also called political risk
• With more investors investing internationally, the
political, and therefore economic, stability and viability
of a country’s economy need to be considered
Risk Types
• Two general types:

Systematic (market) risk
•
•

Pervasive, affecting all securities, cannot be
avoided
Interest rate or market risk or inflation risk
Non-systematic (non-market) risk
•
Unique characteristics specific to a security
• Total Risk = General Risk + Specific Risk
=Market Risk + Issuer Risk
= Systematic Risk + Non-Systematic
Risk
Measuring Returns
• Total Return (TR) compares performance over
time or across different securities
• Total Return is a percentage relating all cash
flows received during a given time period,
denoted CFt +(PE - PB), to the start of period
price, PB
CFt  (PE  PB )
TR 
PB
Measuring Returns
• CF_t = cash flows during measurement period t
(Cash flows for a bond comes from interest payments
received, and for a stock it comes from dividends
received)
• P_E = ending or sale price
• P_B = beginning or purchase price
CFt  (PE  PB )
TR 
PB
Measuring Returns
• The total return concept is valuable as a
measure of return because:
1- It is all-inclusive, measuring the total return per
dollar of the original investment
2- It facilitates the comparison of assets returns
over a specified period, whether the comparison
is of different assets (stocks vs. bonds) or
different securities within the same asset
(several common stocks)
Measuring Returns
• Total Return can be either positive or negative

When calculating a cumulative wealth index or a
geometric mean (cumulating or compounding),
negative returns are a problem
• A Return Relative solves the problem because it is
always positive
CFt  PE
RR 
 1  TR
PB
Example: Total return and return
relative
• Problem 4 pg 181
• Calculate the TR and return relative for:
• A preferred stock bought for $70 per share, held
one year during which $5 per share dividend are
collected, and sold for $63
• A bond with a 12% coupon rate bought for $870,
held for two years during which interest is
collected, and sold for $930
Measuring Returns
• To measure the level of wealth created by an
investment rather than the change in wealth,
returns need to be cumulated over time
• Cumulative Wealth Index, CWIn, over n
periods, =
CWI  WI (1  TR )(1  TR )...(1  TR )
n
0
1
2
n
Measuring Returns
• CWI_n = the cumulative wealth index as of the
end of period n
• WI_0 = the beginning index value, typically $1
(The cumulative effect of returns over time are
measured given some stated beginning amount,
such as $1)
• TR_1…n = the periodic TRs in decimal form
Example: Cumulative wealth index
Year
1999
2000
2001
2002
2003
TR%
31.42598
7.52756
-12.60567
-12.32439
26.32534
Calculate the cumulative wealth index for the
S&P/TSX Index total returns shown above (assume
that the beginning index value is equal to $1)
Example in book pg 163
Measuring Returns
• The values for the cumulative wealth index can
be used to calculate the rate of return for a given
period
• TR_n = (CWI_n / CWI_n-1) – 1
• Example
Use the CWI in years 2002 and 2003 to calculate
TR for year 2003. (pg 164)
Measuring International Returns
• International returns include any realized
exchange rate changes

If foreign currency depreciates, returns are
lower in domestic currency terms and vice
versa
• Total Return in domestic currency =
End Val. of For.Curr. 

RR  Begin Val. of For.Curr.   1


Example: International Returns
• (Pg 164 & 165) Consider a Canadian investor
who invests in US Steel (which trades on NYSE)
at $30 US when the value of the US dollar stated
in Canadian dollars is $1.37. One year later, US
Steel is at $33 US and the stock paid a dividend
of $0.20 US. The US dollar is now at $1.4, which
means that the Canadian dollar depreciated
against it.
• Calculate the TR to the Canadian investor in US
dollars
• Calculate the TR to the Canadian investor in
Canadian dollars after currency adjustment
Measures Describing a Return
Series
• TR, RR, and CWI are useful for a given, single
time period
• What about summarizing returns over several time
periods (i.e., a series of returns)?

Arithmetic mean and geometric mean
• Arithmetic mean, or simply mean, is the sum of
each of the values being considered divided by the
total number of values
X

X
n
Arithmetic Mean
• When should the arithmetic mean be used when
talking about stock returns?
• Arithmetic mean should be used when describing
the average rate of return without considering
compounding
• It is the best estimate of the rate of return for a
single period, such as a year
Geometric Mean
• Geometric mean is the compound rate of return
over time
• When should the geometric mean be used when
talking about stock returns?
• It is a better measure of the change in wealth
over more than a single period
• Over multiple periods the geometric mean
indicates the compound rate of return or the rate
at which the invested dollar grows, taking into
account the variability in returns.
Arithmetic Versus Geometric
• Arithmetic mean does not measure the
compound growth rate over time


Does not capture the realized change in
wealth over multiple periods
Does capture typical return in a single period
• Geometric mean reflects compound,
cumulative returns over more than one period
Geometric Mean
• Geometric mean defined as the n-th root of the
product of n return relatives minus one, or G =
(1  TR1)(1  TR2 )...(1  TRn )
1/ n
1
Example: Arithmetic and Geometric
Mean
Year
TR%
1987
6.23
1988
10.62
1989
21.20
1990
-14.81
• Calculate the arithmetic and geometric mean
Arithmetic and Geometric Mean
• The geometric mean will always be less than the
arithmetic mean (unless the values are identical)
because it reflects the variability of the returns
• The spread between the two depends on the
dispersion of the distribution
• Difference between Geometric mean and
Arithmetic mean depends on the variability of
returns (standard deviation), s
1  G  1  X   s
2
2
2
Inflation-Adjusted (Real) Returns
• Returns measures are not adjusted for
inflation (since they are nominal returns)


Purchasing power of investment may change
over time
Consumer Price Index (CPI) is a possible
measure of the rate of inflation (IF)
TR IA
1  TR 


1
1  CPI
Example: Inflation-Adjusted Returns
• (Pg 169) For the period from April 1, 1995 to March
31, 2004, the total return for small-cap Canadian
common stocks for the entire period was 9% and
the rate of inflation was 1.9%.
• Calculate the real (inflation-adjusted) total return
for small-cap common stocks
• How much is a basket of consumer goods
purchased for $1 in April 1995 worth in March
2004?
Measuring Risk
• Risk is the chance that the actual outcome will be
different than the expected outcome (i.e.,
dispersion or variability of returns)
• Standard Deviation measures the deviation of
returns from the arithmetic mean of the
observations
  X  X
s  
 n1
2



1/ 2
Standard Deviation
•
•
•
•
s = standard deviation
X = each observation in the sample
¯X = the mean of the observations
n = the number of returns in the sample
  X  X
s  
 n1
2



1/ 2
Standard Deviation
• Standard deviation is a measure of the total risk
of an asset or portfolio
• It is considered to be a reliable measure of
variability because all the information in a
sample is used
• It can be combined with the normal distribution
to provide useful information about the
dispersion or variation in returns.
Standard Deviation
Example: Standard Deviation
Year
1999
2000
2001
2002
2003
TR%
31.42598
7.52756
-12.60567
-12.32439
26.32534
• Calculate the standard deviation for the years
1999 to 2003. (Problem 16 pg 182)
Risk Premiums
• Premium is additional return earned or expected
for additional risk

Calculated for any two asset classes
• Risk premium is the part of the security’s return
above the risk-free rate of return
• The risk premiums are measured as the geometric
difference between pairs of return series
Risk Premiums
• Equity risk premium is the difference between
stock returns and risk-free rate of return
• Equity Risk Premium, ERP, =


 1  TRCS

1



1  RF 


or,
TRCS  RF
Risk Premiums
• Bond horizon premium is the difference
between the return on long term government
bonds and the risk-free rate as measured by
the returns on T-bills
• Bond Horizon Premium, BHP, =



 1  TRGB

1  TR
TB


 1


Risk Premiums
• Bond default premium is the difference between
the return on long term corporate bonds and on
long-term government bonds
• Bond Default Premium, BDP, =



 1  TRCB

1  TR
GB


 1


The Risk-Return Record
• Since 1938, cumulative wealth indexes show stock
returns dominate bond returns
 Stock standard deviations also exceed bond standard
deviations
• Annual geometric mean return for the time period
between 1938 and 2003 for Canadian common stocks is
10.32% with standard deviation of 16.36%
• The smaller differences between the geometric and
arithmetic means for bonds (6.07% & 6.46%), T-bills
(5.2% & 5.28%), and inflation (3.97% & 4.05%) reflect
the much lower levels of variability in these series
Annual Total Returns for Major
Financial Assets (1938-2003)
Series
Geometric
Mean
Arithmetic
Mean
Standard
Deviation
Canadian
Common
Stocks
10.32%
11.53%
16.36%
US Common
Stocks
12.09%
13.5%
17.67%
Long-term
Government of
Canada Bonds
6.07%
6.46%
9.39%
91-Day
Government
Canada Bonds
5.20%
5.28%
4.36%
Inflation (CPI)
3.97%
4.05%
3.63%
The Risk-Return Record
• G = the geometric mean of a series of asset returns
• ¯X = the arithmetic mean of a series of asset returns
• s = the standard deviation of the arithmetic series of
returns
Thus, if we know the arithmetic mean of a series of asset
returns and the standard deviation of the series, we
can approximate the geometric mean of this series.
1  G  1  X   s
2
2
2