Chapter 6Charles P. Jones, Investments: Analysis and Management,
Twelfth Edition, John Wiley & Sons
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Function of both return and risk◦ At the center of security analysis
Historical risk-return relationships useful indicators◦ No guarantee future will be like the past◦ Also no reason to assume that relative
relationships will be much different in the future than they are now
◦ Especially useful in the long-run
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Returns consist of two elements:◦ Yield
Periodic cash flows such as interest or dividends Measures return relative to purchase or current price
◦ Capital gain (loss)
The change in price of the asset Total Return =Yield + Price Change Investors sometimes focus only on yield
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For comparing 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
P
)P(PCF TR
B
BEt
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Total Return can be either positive or negative◦ When cumulating or compounding, negative returns
are problem A Return Relative solves the problem
because it is always positive
TR P
PCF RR
B
Et
1
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To measure return in dollars and reflect compounding returns over a time period, given a specific initial investment, use Cumulative Wealth Index
Cumulative Wealth Index, CWIn, over n periods =
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) nTR)...(TR)(TR( WI 121110
International investments subject to exchange rate risk◦ When you buy a foreign asset, you must use the
foreign currency, so you must first exchange home currency
◦ If foreign currency depreciates, returns lower in domestic currency terms
Total Return in domestic currency =
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rr. of For.CuBegin Val..f For.CurrEnd Val. o
RR 1
TR, RR, and CWI are useful for a given, single time period
What about summarizing returns over several time periods?
Arithmetic mean, or simply mean,
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nX
X
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
Over multiple periods, the geometric mean shows the true average compound growth rate
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Defined as the n-th root of the product of n return relatives minus one, or G =
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)TR)...(TR)(TR( /nn 1111 1
21
Return measures are nominal, i.e., are not adjusted for inflation◦ Purchasing power of investment may change over
time◦ Nominal return = real return + expected inflation
rate◦ Consumer Price Index (CPI) is possible measure of
inflation
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CPITR
TRIA 111
Risk and return are opposite sides of the same coin
Risk is the chance that the actual outcome from an investment will differ from the expected outcome
Investors willing to assume large risks may gain large returns, but they may also lose money
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Risk
Interest Rate Risk◦ Affects income return
Market Risk◦ Recession, war, etc.
Inflation Risk◦ Purchasing power
variability Business Risk
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Financial Risk◦ Tied to debt financing
Liquidity Risk◦ Marketability of
security in secondary market
Currency Risk◦ Exchange Rate Risk
Country Risk◦ Political stability
Risk arises from variability of outcomes Variance and standard deviation measure
variability Standard Deviation is simply the square
root of the variance
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nXX
s
/212
1
Returns for Major Asset Classes
Spread in Returns for Major Asset Classes, 1962-2011
200
-60
Inflation Treasury bills
Corporate bonds
Treasury bonds
S&P 500 Small stocks
Two general types:◦ Systematic (general) risk
Pervasive, affecting all securities, cannot be avoided Interest rate or market or inflation risks
◦ Nonsystematic (specific) risk Unique characteristics specific to issuer
Total Risk = General Risk + Specific Risk
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Premium is additional return earned or expected for additional risk◦ Calculated for any two asset classes
Equity risk premium is the difference between stock and risk-free returns◦ Stocks versus Treasury bills◦ Stocks versus Treasury bonds
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Equity Risk Premium, ERP, =
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1TR
CS 1 RF
1
From 1926 - 2010, geometric average annual return was 9.6% for S&P 500
Arithmetic mean was 11.4% Standard deviation was 19.9% Smaller common stocks show greater risks
and returns than large common stocks in that period
T-bills showed lowest risk and return
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Cumulative wealth index can be decomposed into◦ Dividend component: cumulative dividend yield
(CDY)◦ Price change component: (CPC)
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Cumulative Wealth Indexes
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