Risk And Return

Risk and Return ….Two sides of the Investment Coin

Introduction Investment Financial Assets Real assets Both are characterized by return and risk. Valuation of Financial Assets is a function of

return and risk.

Return It is the reward for undertaking the

investment. Components of Return:  Interest/

Dividend  Capital appreciation( depreciation)

Types of Return Realized Return: It is the certain return that an investor has actually obtained from his investment at the end of the holding period. Expected Return: It is the uncertain future return that an investor expects to receive/get from his investment.

Concepts of Risk 

Definition of Risk

v Risk is the possibility of the actual outcome being different from the expected outcome. It includes both down side and upside potential Difference between Risk & Uncertainty v Certainty is the situation where 100% probability is known on happening or non happening of an event v Risk is the situation where we know there are number of specific , probable outcomes but not sure about which one will actually happen v Uncertainty is a situation where we do not know even the probable outcomes 

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Business Entities are Exposed to Many Risks  Interest Rate Risk  Exchange Risk

 Marketability Risk  Credit Risk

 Liquidity Risk  Default Risk

 Operational Risk  Environmental Risk

 Internal Business Risk  External Business Risk

 Production Risk  Events of God

 Financial Risk  Market Risk

 AND MANY RISKS



6



Elements of Risk/Sources and Types of Risk The variation in return is caused by a number

of factors and these factors constitute the elements of risk. Factors: External Factors (Uncontrollable)  Systematic Risk Internal Factors (Controllable)  Unsystematic

Risk

 

Total Risk = Systematic Risk + Unsystematic Risk

Systematic Risk It refers to the portion of total variability in

security returns caused by changes in system-wide factors such as economic, political and social factors. Components: Interest Rate Risk  Market Risk  Inflation Risk  Exchange Rate Risk  Liquidity Risk  Country Risk 

Interest Rate Risk It refers to the variation in bond or debenture

prices caused due to the variation in market interest rates. It directly affects debt securities and indirectly affects the shares. 

Market Risk It refers to the variability in returns from

securities caused by the volatility of the stock market.

Purchasing Power Risk It refers to the variation in investor returns

caused by inflation. Its impact is uniformly felt on all securities in the market.

Liquidity Risk It is associated with the particular secondary

market (Stock Exchange) in which a security trades. Liquidity risk of securities results from the inability of a seller to dispose them off except by offering price discounts and commissions.

Unsystematic Risk This risk is unique or peculiar to a company

or industry and affects it in addition to the systematic risk. Sources: The operating environment of the Company  Business Risk  The financing pattern adopted by the Company  Financial Risk 

Business Risk It is a function of the operating conditions

faced by a company and is the variability in operating income caused by the operating conditions of the company.

Financial Risk It is associated with the use of debt financing

by companies. It is the variability in cash flows because of various factors

Measuring Return and Risk Can we measure Risk? Historical Return and Risk 



Measuring Return  Statistical Tools  Measuring Risk  Statistical tools

Expected Return and Risk Measuring Expected Return  Measuring expected Risk 

 

Historical Return The return on an investment for a given period

is:

Cash Payment Received during the period + price change over the period  R= Price of the investment at the beginning or

R=

C + ( PE − PB ) PB

Where C = Cash payment received during the period PE = Ending price of the Investment PB = Begining price of the Investment

Statistics to measure Return The two most popular summery statistics are Arithmetic Mean Geometric Mean

Statistics to measure Return 

Arithmetic Mean

 

R=

∑R

i

N



where Ri = i th value of the total return ( i =1, 2, ....n)



N = No. of total returns



Limitations:  When

% changes in value over time are involved,  When we want to know the average compound rate of growth that has actually occurred over multiple periods.

Contd….. Suppose an investor purchased a stock in year

1 for Rs 50 and it rose to Rs 100 by year end. Then the stock went from Rs 100 at the start of year 2 to Rs 50 at the end of that year. What is the return on stock over 2 years period?

Statistics to measure Return 

Geometric Mean It is defined as the nth root of the product

resulting from multiplying a series of returns together. GM = [ (1 + R1 ) (1 + R2 )......(1 + Rn )]



where Ri = total return for period i ( i = 1, 2, ....n) n = number of time periods

1

n

−1

Measuring Risk The most commonly used measures of

Variability or Risk in finance are 

Standard Deviation



n

 

or

δ=

2 ( R − R ) ∑ i i =1

  

Variance

δ

2

N

Measuring Expected Return and Risk 

Expected Return Develop the probability distribution. It is the probability weighted average of all

the possible returns. 

n

E ( R ) = ∑ Ri Pi i =1

where Ri = return from security under state i Pi = probabilit y that the state i n = no. of possible states of the world

Measuring Expected Return and Risk Expected Risk



It is the variance or standard deviation of the

probability distribution of possible returns. 

E (δ ) =

n

∑ Pi [ Ri − E ( R)]

2

i =1

where Ri = return from security under state i Pi = probabilit y that the state i E ( R ) = Expected Return on security i n = no. of possible states of the world

Measuring Market Risk The Market risk of a security can be measured by

relating that security’s variability variability in the stock market index.

with

the

 A higher variability would indicate higher market

risk and vice versa.

It is measured by a statistical measure called Beta

Statistical Tools Correlation Method  Regression Method 

Measuring Beta 

Correlation Method

   

rimδ iδ m βi = δ m2

Where



  



Rim= correlation coefficient between the returns of stock iand the returns of the market index δi = S.D of returns of stock i δm = S.D of returns of the market index δm2 =variance of market returns



Measuring Beta 

Regression Method  The regression model postulates a linear relationship

between a dependent variable (security’s return) and an independent variable (market return)

    

Y = α + βX

Where Y = dependent variable X = independent variable α and β are constants



 β : measures the change in the dependent variable in

response to unit change in the independent variable.  α : measures the value of the dependent variable even when the independent variable has zero value. 

Cont….. The formula used for the calculation of α and β

are:

α =Y − β X



nΣXY −(ΣX )( ΣY ) β= nΣX 2 −(ΣX ) 2

  

  

Where n = number of items Y = mean value of the dependent variable scores X = mean value of independent variable scores Y = dependent variable scores X = independent variable scores