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Chapter -5Risk & Return

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This chapter mainly deals with risk & return in the investment of common stocks.

However, the same technique may also be applied to the capital investment projects.

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Return (Profit):It is calculated by: cash received over the period in

the form of dividend or interest plus change in market price,

Rate of Return:Rate of return is a Return (profit) on an investment over a period of

time, expressed as a proportion of the original investment.

Formula:

Cash received (e.g. Dividend ) + Capital Gain (Ending price of share - Beginning price

of share) Beginning price of a share

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Risk:The chance(percentage) that an investment's actual return

will be different than expected return. Risk includes the possibility of losing some or all of the original investment.  

Probability(Pi):It is defined as percentage of chance that may occur against

a particular possible return on a given task/investment. Possible return(Ri):It is defined as, possible outcome that may occur against a

particular probability on a given task/investment.

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Expected return(R): [On a Single type of investment]. It is the most likely return from the all possible returns against a particular event/task.

Formula: (When data is given in probability distribution):

_Expected Return=R= R1 X P1 + R2 X P2+..+ Rn X Pn

Where as, R1 to Rn = Possible returns, P1 to pn = Probability against each

returns

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Average return(R): (when data is in historical form):

It is the most likely return from the all possible returns against a particular event/task. 

Formula: [On a Single type of investment]

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Average return =R = R1 +R2 + .. +RN

N

Where as, R1, R2,…. Rn = actual returnsWhere as, N = number of years

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Risk measurement:The risk in an investment can be measured

quantitatively by using two statistical methods. These are as under:

1. Standard Deviation [SD] 2. Coefficient of variation [CV]

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1.Standard Deviation [SD]It is defined as the, dispersion of a set of data from its expected

return or from average rate of returnIn accounting terms, it is the variability of cash flows around the

expected return. The Standard deviation shows that how much the data in a certain

collection are scattered around the expected return or from average rate of return. It is an absolute value of dispersion. 

A low standard deviation means that the data are tightly clustered; a high Standard deviation means that they are widely scattered.

 The higher the standard deviation, the higher the risk of investment.

The lower the Standard deviation, lower the risk of investment.

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Standard when the data is in probability distribution:

 

Formula:

_ _ _ [(R1 -R )2 X P1 + (R2 -R )2 X P2 + ..+ (Rn -R )2 X Pn ]1/2

Where as, n= Total number of probabilities.

2. Coefficient of variation [CV]It is the ratio of the standard deviation to the expected return. It is a

relative measure of dispersion. 

Formula:

Coefficient of variation [CV] = Standard deviation Expected return  

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Standard deviation when the data is in historical form: _ _ _ _

Standard deviation =[(R1 – R)2 + (R2 – R )2 +(R1 – R)2 ..+ (Rn –R )2]1/2

N-1

Where as, N= number of years.

Coefficient of variation [CV]= Standard deviation Average return

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Portfolio Investment(Diversification):It is defined as, Investment in two or more

securities or assets.

 Expected return on portfolio investment

Expected return on investment “A” X proportionate weight of A + Expected return on investment B X proportionate weight of “B” …..+ Expected return on investment “N” X proportionate weight of “N” = xxx

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Types of Risk:Risks are two types:

1. Systematic RiskIt is also called non diversifiable risk. Or unavoidable risk

i.e. those risk, which cannot be eliminated through diversification.

Examples are Inflation, War, International incidence, political events, etc.

 2. Un Systematic RiskIt is also called diversifiable risk. Or avoidable risk i.e. those

risk which can be eliminated through diversification.Examples are Firm’s specific events, which may be

controllable, such as Strikes, Lawsuits, Loss due to any key factor, et

Total Risk = Systematic risk + Unsystematic risk

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The Capital – Asset Pricing Model:In this model, a security expected (Required)

return is equal to the risk free rate plus Market risk premium based on the systematic risk of the security. Market risk premium is represented by (Rm - Rf). It is the additional return that investors reasonably expect for investing in the stock market rather than depositing in a fixed deposit account.

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The required return of stock j will be computed by the given formula:

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Rj = Rf + (Rm - Rf )βj

Where as, Rm = Expected return for the market portfolio

Rf = Risk free rate (i.e., Guaranteed interest rate on a fixed deposit account in a bank).

β = It is an index of a stock’s systematic or unavoidable risk relative to the market portfolio.

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Required return and stock prices:The Capital Asset Pricing Model provides us to

determine us an opportunity to compute the required rate of return on a security. Moreover, this required rate of return may be used to calculate intrinsic value (discounted value)of a share of stock. The intrinsic value of stock can be now calculated by the perpetual dividend growth model.

Formula:  P = . D1 . Ke- gWhere as, D1 = Dividend expected after one year, Ke = Required rate of return, g = growth rate in

dividend

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……The end…,…