FINANCIAL CALCULATION OF RISK AND RETURN

You already know about the meaning of finance,  now know the meaning of calculation of risk and return.

Calculation means quantification(amount) of numbers.

FIRST WE SHOULD ANALYSE THE RISK AND THEN  QUANTIFY THE RISK.

RISK ANALYSIS :

Risk can be said as  possible variation(positive or Negative)of actual return from the expected return. 

Variability of returns between actual and expected is known as Risk .

Elements of risk can be classified in to two types 

one  type  is     -      systematic risks 

another  type is  -  unsystematic risks

Systematic risks can be divided in to :

Interest rate risk

Purchasing power risk 

Market risk

Unsystematic risk can be divided in to :

Business risk 

Financial risk

Systematic Risk :

Systematic risks arises due to dynamic nature of society the changes occur in the

Socio - economic , Political systems constantly.

These changes have a  significant influence on the performance of companies and their buy on their companies shares, debentures, bonds returns.

Impact  of   Socio - Economic, Political  changes is system - Wide factors and 

That portion of total variability  is  in companies   shares, debentures,bonds caused by such system wide factors returns is referred to as systematic risk.

Systematic risk can be further subdivided into

Interest Rate Risk : 

This risk  arises due to variability in the interest rates from time to timeand particularly affects  debt instruments like bonds and debentures as they carry fixed coupon rates of interest.

Change in interest rateestablishes  an inverse relationship in the prices of bonds & debentures and long term bonds are more vulnerable to interest rate risk  while cash and cash equivalents are less vulnerable.

Purchasing Power Risk : 

This risk also knownInflation risk ,it affects the purchasing poweradversely and is more inflationary conditionsespecially in respect of bonds and fixed incomefinancial instruments.

Purchasing power risk is however,less in flexible income financial instruments like equity shares, preference shares,as rise in dividend income offsets increase in the rate of Inflation and provides advantage of  capital gains.

Market Risk  :      

Market  risk affects prices  of any  particular share moving up (or) down consistently for some  time periods  in line  with other shares in the market. 

A general rise in share prices is referred to as a bullish trend, whereas a general fall in share prices is referred to as a bearish  trend .

The share market moves between the bullish phases and the bearish phases.

The market movements can be easily seen in movement of share price indices such as the BSE sensitive index, NSE index.

Unsystematic Risk :   

Sometimes the returns from a security of any company may vary because of certain factors particular to that company. Variability in returns of financial instruments of a company on

 on account of these factors, it is known as unsystematic risk.

Unsystematic risk can be further subdivided into

Business Risk :  This risk arises due to sale and purchase of financial instruments affected  by 

business cycles , technological changes  etc..

Business cycles affect all types of financial instruments .

There is cheerful movement in boom due to bullish trend in share prices whereas bearish 

trend in depression brings down fall in the prices of all types of financial instruments.

Flexible Income financial instruments  are more affected than fixed rate financial instruments during depression due to decline in their market price.

Financial Risk  : 

This  arises  due  to changes in the capital structure  of the company. It is also known as leveraged risk and  expressed in terms of debt - equity ratio . Excess of debt  to equity in the capital structure indicates that the company is highly geared.

Although a leveraged  company earning per share is more, dependence  on borrowings exposes it to the risk of winding up for  its inability to honour its commitments towards lenders/creditors . This risk is known as leverage or financial risk.

Diversification of Risk : 

Due to the above the total risk of an individual security  consists of two risks: systematic risk and unsystematic risk. 

It should be noted that by combining  financial instruments in a portfolio the unsystematic risk can  be  avoided or cancelled out which is attached to any  particular financial instruments.

 That's why the creation  of  portfolios is required to diversify the risks.

Risk & Return:

An Intelligent investor would attempt to anticipate the kind of risk that he/she is likely to face & would also attempt to estimate the extent of risk associated with different Investment proposals.

In other words an attempt to  measure or quantify the risk of each investment under consideration before making the final selection

Thus quantification of risk is necessary for Analysis of any investment.

As risk is attached with return cannot be measured without references to return

The return depends up on the cash flows to be received from the Investment

For equity investment cash flows will be generally dividends & capital gains.

Calculation (Quantification) of Return:

Return = Forecasted dividends +Forecasted                                                                        end of share price

                           Initial investment      

EXPLANATION:

XBAR(x̄), SUMMATION ∑, PROBABILITY(P) are  statistical representatives of some concepts .

where as  (Sigma) σ,    (Alpha)α, (Beta)   β  are Greek Alphabet symbols used to represent some concepts.

Calculation of Expected Return:

When probabilities of possible returns are known

Expected Return of the Investment is the probability weighted average of all the possible returns.

If possible returns are denoted by Xi     

andthe related probabilities are p(Xi), 

Expected Return may be represented as (x̄) 

(X BAR)

                       n

         (x̄)   =   ∑ Xi   P(Xi)

                     i = 1

x̄          =      Expected Return

∑          =     Summation

n          =     Number  of  possible returns

i           =      Return  of financial instrument

Xi        =       Possible returns

P(Xi)   =      Probabilities of possible returns

When historical returns are known

                             n

            (x̄)      =     ∑        X1 +X2+X3........Xi

                             i=1                 n

x̄          =      Expected Return

∑          =     Summation

n          =     Number  of  possible returns

i           =      Return  of financial instrument

Xi        =      Possible returns

Calculation of Risk : 

As risk is attached with every return hence calculation of only expected return is not sufficient for decision making.

Therefore risk aspect should also be considered

along with the expected return

The most popular measure of risk the variance or standard deviation of the probability distribution of possible returns.

                             n

                     σ2 =∑ {(Xi-x̄)2]  P(Xi)}

                            i=1

σ2        =  Variance of financial instrument

σ          =    Standard deviation (SD) of {financial    

                            .                                      instrument}   

∑          =     Summation

n          =     Number  of  possible returns

i           =      Return  of financial instrument

Xi        =      Possible returns

x̄          =      Expected Return

P(Xi)   =     Probabilities of possible returns

Standard Deviation of the return will be the positive square root of the variance and is 

generally represented by σ.

Measurement of Systematic Risk:

As discussed earlier, systematic risk is the variability in financial instruments returns caused by changes in the economy or the market and all financial instruments are affected by such changes to some extent. 

Some financial instruments exhibit greater variability in response to market changes and some may exhibit less response. 

Financial instruments that are more sensitive to changes in factors are said to have higher systematic risk. 

The average effect of a change in the economy can be represented by the change in the 

share market index.

The systematic risk of a financial instrument can be measured by relating the financial instruments variability ,vis-à-vis variability in the sharemarket index. A higher variability would indicate higher systematic risk and vice versa.

The systematic risk of a  is measured by a statistical measure which is called Beta (β).

The main input data required for the calculation of beta of any financial instruments are the historical data of returns of the individual financial instruments and corresponding return of a representative market return (share market

index). 

There are two statistical methods 

correlation method and the regression method, 

which can be used for the calculation of Beta. 

Correlation Method :

Correlation measures the extent to which two variables are related. 

In respect to Beta, it means how market returns and security returns are related.

Using this method beta (β) can be calculated from the historical data of returns by the following formula:

            βi  = r im σi σm

                              σm2 

Where

rim = Correlation coefficient between the returns of the s QQhare i and the returns of the market  index.

σi = Standard deviation of returns of stock i 

σm= Standard deviation of returns of the market index.

Regression Method : 

The regression model is based on the postulation (assumed to be true) that there exists a linear relationship between a dependent variable and an independent variable. 

The model helps to calculate the values of two constants, namely alfa (α) and beta (β).

β measures the change in the dependent variable in response to unit change in the independent variable,

while α measures the value of the dependent variable even when the independent variable has zero value. 

The formula of the regression equation is as follows:

                  Y = α + βX 

where

Y = Dependent variable  (return of individual                                                           financial instrument)

X = Independent variable(return of market index)

                  α = Y - βX

The formula used for the calculation of α and β are given below.

     β   =             n∑XY- (∑X)(∑Y)

                             n∑X2   (∑X)2

where

n = Number of items.

Y = Dependent variable scores.

X = Independent variable scores.

For the purpose of calculation of β, the return of the individual financial instrument is taken as the dependent variable and the return of the market index is taken as the independent variable.

Here it is very important to note that a financial instrument can have betas that are positive, negative zero.

• Positive Beta-indicates that financial instrument return is dependent on the market return and moves in the direction in which market moves.

• Negative Beta- indicates that financial instrument return is dependent on the market return but moves in the opposite direction in which market moves.

• Zero Beta- indicates that  financial instrument return is independent of the market return.

Further as beta measures the volatility of a financial instruments returns relative to the market, the larger the beta, the more volatile the financial instruments.

• A beta of 1.0 indicates that financial instrument has risk as that of the market. 

• A share with beta greater than 1.0 has above average risk i.e. its returns would be more 

volatile than the market returns. 

For example, when market returns move up by 6%, a share with beta of 2 would find its returns moving up by 12% (i.e. 6% x 2). Similarly, decline in market returns by 6% would produce a decline of 12% (i.e. 6% x 2) in the return of that financial instrument.

• A share with beta less than 1.0 would have below market risk. Variability in its returns would 

be less than the market variability. 

Beta is calculated from historical data of returns to measure the systematic risk of a financial instrument.

It is a historical measure of systematic risk. In using this beta for investment decision making, the investor is assuming that the relationship between the financial instrument variability and market variability will continue to remain the same in future also.