Returns and Risk

Returns and Risk

 Realized Returns—expect (after the fact) return



 Expected Return- estimated return



 Investment Decision—trade off between risk (expected) and return (expected)







Trade-Off Between Risk and Return



 Required Return = Risk free rate + Risk premium

 Required Return = Cost of Capital to Firm

 Two components of Required Return:

 Risk-free rate

 Risk premium





First step in the investment decision process

 Knowledge of long-term return (actual) and risk (actual)



The past is a good guidepost but

Don’t use it as a hitching post



 Historical returns play a large part in estimating future unknown returns





Return

 Objective of investor: Maximize Wealth

 Micro-basis—maximize expected returns given a level of risk

 Components of Return

 Yield—income component

 Dividend Yield

 Current Yield

 Capital gain (loss) [ Price Change]

 Change on price of a security over some period

 Total Return for period = Yield over period + Price Change over period







5-1

Risk

 the chance that the actual outcome from an investment will differ from the expected

outcome

 Greater the variability----the greater the risk





Sources of Risk:

1. Interest Rate Risk

 security prices move inversely to interest rates

 bonds more directly affected



2. Market Risk

 variability in returns resulting from fluctuations in the overall market

 common stock affected more than bonds

 Market risk components:

 Recessions, wars, structural change in the economy, and changes in consumer

preferences



3. Inflation Risk

 purchasing power risk

 with unexpected inflation, the real return (inflation-adjusted) involves risk even when

the nominal return is certain (fixed)

 Fisher equation



4. Business Risk

 risk associated with a particular industry or environment

 risks associated with the business cycle

 factors that affect the business cycle

 monetary policy, changes in technology, changes in supply of raw materials



5. Financial Risk

 debt financing

 financial leverage







6. Liquidity Risk



5-2

7. Exchange Rate Risk (Currency Risk)

 variability in returns on securities caused by currency fluctuations



8. Country Risk (Political Risk)



Types of Risk

 Systematic (Market)

 Nonsystematic (Company)

 Total Risk= Systematic Risk + Nonsystematic Risk









Holding Period Return

(Total Return)





(Any Cash pymts received over the period)  (Price change over the period)

TR 

Price at beginning of the period





Any Cash pymts received over the period Price change over period

TR  

Price at beginning of the period Pr ice at beginning of the period



TR  Period' s Yield  Period' s Price Change









5-3

Return Relative

 Total return for an investment for a given time period stated on the basis of



RR  1  TR





CFt  PE

Return Relative 

PB





Cumulative Wealth Index

 Measures the cumulative effect of returns over time, typically on the basis pf a $1 invested

 Measures the level rather than the changes in wealth





CWI n  WI 0 [(1  TR1 )(1  TR 2 )...(1  TR n )]





CWI n  Yield X Price Change





CWI n

TR n  1

CWI n 1









5-4

International Returns

 Convert cashflows into US dollars and therefore experience currency or exchange rate risk





Ending Value of foreign currency

Total Return in Domestic Terms  [ RR * ] 1

Beginning Value of foreign currency

 Example: Buy foreign company stock @ 175.86 pesos (1 peso=.29) and sell after 2 years @ 250 pesos (

1 peso=.27) No dividends



Geometric Mean = 19.23%

Geometric Mean in $ = [1.1923 * (.27/.29)] –1 =11.01%





TR= ( 250/175.86 ) - 1 = 42.2%



TR in $ = [ 1.422 * (.27/.29)] –1 = 32.4%





Annual Returns



 Arithmetic Mean

 Measures the central tendency of a distribution



X

X

n

 Geometric Mean (compounded return)







G  [(1  TR1 )(1  TR 2 )...(1  TR n )]1 / n  1

G  (CWI n )1 / n  1

where WI0  $1





5-5

 measures the annual compound rate of growth over time

 uniform rate at which the $ actually grows over time (per period)

 measures the realized change in wealth over multiple periods

 reflects the variability of returns

 always 1 more risky than market

β j 15% then undervalued - good buy



Prices:

D1 = 5

5 + 50

P1 = 50 Pe = = 47.83

(1 + .15)

Kj = .15



If actual market price

Pm > 47.83 Over Valued (sell)



Pm < 47.83 Under Valued (buy)









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 The SML can shift in a parallel fashion due to changes in expected

inflation.

 The SML can change its slope due to a change in consumer

confidence.

 The SML can shift and change its slope simultaneously.





CAPITAL ASSET MARKET LINE



 Recall SML:









(E(K m) - R f )

E(K j) = R f + Cov(K j , K m)



2

m





Cov: (ρj m σj σm)









 Capital Market Line considers Total Risk



 If ρ(Kj, Km) = 1 then SML reduces to CML





 jm  j m

j =

m

2





if ρj m = 1 then



i

j =

m









5-18

and





CML







(E(Km) - R f )

E(K j) = R f + j

m



E(K j) = R f +  j (E(K m) - R f )









5-19