return and risk - the basis of investment

8/13/2019 Return and Risk - The Basis of Investment

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Return and RiskThe Basis of

Investment Decisions

Gayatri Mohanty


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Return: Why invest?

Cash has an opportunity cost and by holding cash the

opportunity of earning return on the cash is foregone.Also inflation reduces the purchasing power of cash over

a period of time.

So, when an investor invests his money in some

investment alternative forgoing his present consumption,it is important that after the period for which he invests

his money he should get a return that will compensate for

the risk assumed by him.

There is also a need to understand the differencebetween the expected return (a rate of return that the

investor expects to earn at the end of the investing

period) and the realized return (the actual return earned

by him).


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Historical and Expected Return

Calculation of Historical Return:

The total return on an investment for a given period

is calculated as:Cash payment received Price change over

during the period (Dividends) + the period (Capital appreciation)

Price of the investment at the beginningTotal Return =

C + (PEPB)

PBR =

Where;C= Cash payment received during the year

PE= The ending price of the investment

PB= The beginning price of the investment


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Historical and Expected Return Calculat ion o f Expected Return: The weighted average of all the

possible returns multiplied b y their respective probabilities.

As denoted by the above formula, simply take the probability of each

possible return outcome and multiply it by the return outcome itself. For

example, if you knew a given investment had a 50% chance of earning

a 10% return, a 25% chance of earning 20% and a 25% chance of

earning -10%, the expected return would be equal to 7.5%:

= (0.5) (0.1) + (0.25) (0.2) + (0.25) (-0.1)

= 0.075

= 7.5%

Although this is what you expect the return to be, there is no guarantee

that it will be the actual return.

n

i

PiRiRE

1

)(


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Expected Return The table below provides a probability distribution for the returns

on stocks Aand BState Probability Return On Return On

Stock A Stock B

1 20% 5% 50%

2 30% 10% 30%3 30% 15% 10%

4 20% 20% -10%

The state represents the state of the economy one period in the

future i.e. state 1 could represent a recession and state 2 a

growth economy.

The probability reflects how likely it is that the state will occur.

The sum of the probabilities must equal 100%.

The last two columns present the returns or outcomes for stocks

Aand Bthat will occur in each of the four states.


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Expected Return

In this example, the expected return for stock A

would be calculated as follows:

E(R)A = 0.2(5%) + 0.3(10%) + 0.3(15%) +0.2(20%) = 12.5%

Now you try calculating the expected return for stock

B!


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Expected Return

Did you get 20%? If so, you are correct.

If not, here is how to get the correct answer:

E(R)B= 0.2(50%) + 0.3(30%) + 0.3(10%) + 0.2(-10%) = 20%

So we see that Stock Boffers a higher expectedreturn than Stock A.

However, that is only part of the story; we haven't

considered risk.


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Real Return and Nominal Return

The returns that we have discussed so far are the

nominal returns and not the real return . So, what is the difference between the two?

Real return is a rate of return which has taken into

account the rate of inflation prevailing in the system.

As we all know that Rs.100 today will not have the

same value after say 10 years. Similarly, a return that

we will earn on an investment after some years will not

have the same value as it may have today. So, today

when we are making our investment decisions we needto understand that what will be the real return that we

are going to get from the investment in the future. So,

we need to adjust the inflation against the nominal

return to get the real return from the investment.


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Real Return and Nominal Return

Real returns are the gain or loss on yourinvestments, after factoring in the effects

of inflation. Nominal returns don't factor in

inflation.1 + Nominal Return

1 + Inflation Rate

- 1Real Return =

For e.g.: The total return for an equity stock during a year was 18.5 percent.The rate of inflation during that year was 5.5 percent. Thus the real

(inflation-adjusted) total return was:

1.185

1.055- 1 = 0.123 or 12.3 percent


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Risk

Concept o f Risk:

The actual returns that an investor receives from a

stock may vary from his expected return and the this

probability of variance itself is the risk.

Risk is expressed in terms of variability of return.

An investor before investing in securities must properly

analyze the risks associated with these securities.

Sometimes the term risk and uncertainty are used

interchangeably but in case of uncertainty the possibleevents and probabilities of their occurrence are not

known, whereas in case of risk they are known. So,

risk and uncertainty are different from each other.


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Risk

So, risk is explained theoretically as thefluctuation in returns from a security. A security

that yields consistent returns over a period of

time is termed as riskless securityor riskfree

security.Risk is inherent in all walks of life. Since an

investor cannot foresee the future definitely, so

risk always prevails for an investor and he needs

to assess it and accordingly invest depending

upon his preference for the level of risk.


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Business Entities are Exposed to

Many Risks

Interest Rate Risk

Exchange Risk

Liquidity Risk

Default (Credit) RiskInternal Business

Risk

External BusinessRisk

Financial Risk

Market Risk

Marketability Risk

Operational Risk

Environmental Risk

Production RiskPolitical Risk

Events of God

Portfolio RiskAnd many more


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Types of Risks

Systematic Risk

Unsystematic Risk


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Systematic Risk

It is the risk that is caused by external factors suchas economic, political and sociological conditions.

It affects the functioning of the entire market.

Since these risks arise due to external factors they

are beyond the control of the company affected, andhence are uncontrollable or referred to asundiversifiable risk.

They are of three types:

Market riskInterest rate risk

Purchasing power risk


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Market Risk Jack Clark Francis, Ph.D., Professor of Economics and

Finance at Bernard Baruch College in New York has definedmarket risk as that portion of the total variability of returnsthat is caused by the alternating forces of bull and bearmarkets.

When the stock market moves upwards, it is known as bull

market. On the other hand, when the stock market movesdownwards, then it is known as bear market.

The two forces that affect the market are:

Tangible events: Earthquake, war, political uncertainty anddecrease in the value of money are some of the examples of tangible

events.

Intangible events:It is related to market psychology. Political unrestor fall of government affects the market sentiments. Inflow of foreignfunds may make the market psychology positive.


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Interest Rate Risk It is the risk caused by the variations in the market interest rates.

Prices of debentures, bonds, etc. are mainly affected by the interest

rate risk (as demand for bonds and debentures varies directly with theups and downs of the interest rates). As interest rates (on public sector

bonds) rise, bond prices fall and vice versa.

The rationale being that as interest rates increase, the price of the

bonds have to fall in order to make the yield of the particular bond more

attractive for the investor lest he shall invest elsewhere. If interest rates increase, the cost of borrowed funds also increase

thereby decreasing the distributable profits of the companies and

hence the stock prices also fall.

The causes of interest rate risk are as follows:

Changes in the governmentsmonetary policy

Changes in the interest rate of treasury bills

Changes in the interest rate of government bonds


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Purchasing Power Risk(Inflation Risk) Variations in returns are caused by the loss of purchasing power of currency.

So, the purchasing power risk is the probable loss in the purchasing power of the

returns to be received in the future. This is related to the interest rate risk as a

change in interest rate ultimately leads to a change in inflation rate as well.

There are mainly two types of inflation:

Demand-pull inflation: The demand for goods and services remains higher

than the supply.

Cost-push inflation: There is a rise in price due to the increase in the cost ofproduction.

Real future value =

Real Rate of Return =

where r= Rate of Return

IR= Inflation Rate

Nominal future value

1.0 Inflation Rate

1.0 r 1.0

1.0 IR


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Unsystematic Risk

It is a type of risk which is unique, specific

and related to a particular industry.Managerial inefficiency, changes in

preferences of the consumers, availability of

raw material, labour problems, etc. aresome of the causes of unsystematic risk.

These risks are however diversifiable andcan even be reduced to negligible

proportions.These are of two types: Business risk

Financial risk


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Business RiskIt is the risk that is caused by the inefficiency of a

company to manage its growth or stability of

earnings.It can be classified as: Internal bu siness risk (Operat ion al Risk): It is the risk that is

associated with the operational efficiency of a company:

(1)Fluctuations in the sales

(2)Research and Development(3)Personnel Management

(4)Fixed Cost

(5)Single Product

External busin ess r isk: It is the risk that is the result ofoperating conditions imposed on the firm by the externalenvironment:

(1)Social and regulatory factors

(2)Political risks

(3)Business cycle


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Financial Risk It is associated with the capital structure of the company, which

consists of equity and borrowed funds.

The use of debt financing by the company to finance a largerproportion of assets causes larger variability in returns to theinvestors in the faces of different business situation.

During prosperity the investors get higher return than the averagereturn the company earns, but during distress investors faces

possibility of vary low return or in the worst case erosion of capitalwhich causes the financial risk.

The larger the proportion of assets finance by debt (as opposed toequity) the larger the variability of returns thus lager the financialrisk.

A financial risk can be avoided by analyzing the capital structure ofthe company, however it is the cost a company has to pay if itchooses to take advantage of f inanc ial leverage.

The payment of interest affects the eventual earnings of the

company.


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Minimizing Risk Exposure

Market Risk Protection1. Study price behavior of stocks, avoid cyclical

stocks.

2. Measure risk of stocks by standard deviation

and beta etc. The NSE News bulletin providesthe beta values of stocks. Calculate the level of

risk associated with a stock and choose stocks

depending upon your risk tolerance.

3. Be prepared to hold stocks through adversities,

and time purchase and sales correctly.


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Interest Rate Risk Protection1. Hold securities till maturity, avoid selling during

periods of fall in interest rate.

2. Invest in treasury bills and bonds of short term

maturity and reinvest the money when theprevailing interest rates are favorable.

3. Invest in bonds of different maturity dates to

have liquidity for investment over a wide horizonof time.


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Inflation Risk Protection

1. Bonds and debentures with fixed interest are

not helpful in hedging against inflation.

2. Invest in short term securities and avoid long

term investments during high inflation as therising CPI will undo all real benefits of a long

term investment.

3. Diversify into real estate, precious metals,

arts and antiques or securities. Though a

perfect hedge against inflation is not

guaranteed but yes, the loss exposure can

be minimized.


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Protection against Business and Financial

Risks1.Analysis of strengths and weaknesses of the

industry to which the company belongs.

2.Analysis of profitability trend of the company.Companies with inconsistency in earnings are

better avoided.

3.Analysis of the capital structure of the

company. During a boom investment in ahighly levered company may be recommended

but not during recession.


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Risk Measurement Total Risk = General risk + Specific risk

= Systematic risk + Unsystematic risk

An efficient measurement of risks provides an appropriate

quantification of risk.

Standard deviation is used as a tool for measuring the

risk, which is a measure of the variables around its mean.

The following formula is used to calculate standard

deviation:

2

2

1

1

1

n

t

t

R Rn

Standard deviation = Variance

Where; = Standard Deviation or risk

n = Number of observations

Rt = Return for period t

R = Average return


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Example

The rate of return of equity shares of Wipro

Ltd., for past six years are given below:

Year 1 2 3 4 5 6

Rate ofReturn (%)

12 18 -6 20 22 24

Calculate the average rate of return, standard

deviation and variance.(consider the data to be representing the entire

population)


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Solution

Average rate of return = 15%

Variance = 102.33

SD = 10.11%

M f S t ti Ri k


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Measure of Systematic RiskThe systematic risk is calculated by (beta), ameasure of the volatility of a security or a portfolio in

comparison to the market as a whole. Beta is used inthe capital asset pricing model (CAPM), a model thatcalculates the expected return of an asset based onits beta and expected market returns.

where; Rj= Return on security j

Ke= Cost of equity (i.e. of security j)Rf= Risk free rate of return

Rm= Market rate of return

j= Beta or the systematic risk of security j

jfmfej )RR(RkR


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Measure of Systematic Risk

The security return is calculated as

Todays security return = X 100

Todays market return =

and the return on security is given by:

Ri= i+ iRm+ ei

Where Ri = Return on stock ii = Intercept i = Slope (beta) of stock i Rm= Return of the market index

=

Yesterdays price

Todays price Yesterdays Price

Todays index Yesterdays

indexYesterdays index

X 100


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Calculation of

n XY (X)(Y)

nX2 - (X)2

=

= yx


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ExampleDate NSE index (X) Bajaj Auto Stock

Prices (Y)

October 5 904.95 597.80

October 6 845.75 570.80

October 7 874.24 582.95

October 8 847.95 559.85October 9 849.10 554.60

October12 835.80 545.10

October13 816.75 519.15

October14 843.55 560.70October15 835.55 560.95

October16 839.50 597.40

Calculate the .


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Solution

IndexReturn (X)

X2 Bajaj AutoStock

Return (Y)

XY

-6.54 42.77 -4.52 29.56

3.37 11.36 2.13 7.18

-3.01 9.06 -3.96 11.92

0.14 0.02 -0.94 -0.13

-1.57 2.46 -1.71 2.68

-2.28 5.20 -4.76 10.85

3.28 10.76 8.00 26.24

-0.95 0.90 0.04 -0.04

0.47 0.22 6.50 3.06

Total -7.09 82.75 0.78 91.32


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Answers

= 1.19

= 1.02


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Interpretation of

+ ve (1, more than one, less than one)

- ve

= 1 > 1< 1


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Practical Problems

1. Assume that you are a portfolio managerand have to advise your client between thesecurities of two companies the returns on

the securities are given below:

On the basis of risk and return which

security will you choose?

Probability Security A Security B

0.5 4 0

0.4 2 3

0.1 0 3


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Solution

Security A is to be chosen.

Reason:

SecurityA

SecurityB

Risk () 1.327 1.5

ExpectedReturn E(R)

2.8 1.5

P ti l P bl


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Practical Problems

2. Following data give the market return and

the Sun Companys scrips return for aparticular period:

Index Return

(Rm)

Scrip return (Ri)

0.50 0.30

0.60 0.60

0.50 0.40

0.60 0.50

0.80 0.60

0.50 0.30

0.80 0.70

0.40 0.50

0.70 0.60

Calculate the

beta of the Sun

Companysscrip.

Also calculatethe scrip return if

the market

return is 2.


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Solution

= 0.75

=0.05

Scrip return when market return is 2 = 1.55


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Question

3. Mr. Mohan wants to buy Ant company

stock which is currently selling at Rs 60

without dividend payment. There is equal

probability for the Ant stock to be sold at Rs65 and Rs 80 during the next year. What is

the expected return and risk if 300 shares

are bought? Transaction cost is ignored.


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Solution

3. = (56.25)1/2= 7.5

(a) Expected Return

E(r) = 12.5 300 = Rs. 3750(b) If 300 shares are bought,

Risk= 7.5 300 = Rs. 2250.

return and risk - the basis of investment

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