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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