Return and Risk – The Basis of Investment Decisions :

:- Ved Prakash panda

Security analysis is built around the idea that investors are concerned with two principal properties inherent in securities. The return that can be expected from holding a security and the risk.

Return The returns on the investment can

be broken in to two parts. 1.Dividend yield-The reward

investor gets by owing this asset over the holding period

2. Capital gain-The gain investor makes upon selling the asset after the holding period.

Total return=Dividend yield+Capital gain Total % return=(Dividend+capital

gain)/Initial investment ={D1+(p1-p0)}/p0 =(D1/p0)+{(p1-p0)/p0} Where D1-Dividend P0-Initial investment P1-Selling price

Example The current market price of a

share is rs 300.An investor buys 100 shares. After one year he sells these shares at a price of rs 360 and also receives the dividend of Rs 15 per share. Find out his total return ,% return, dividend yield and capital gains.

Solution Initial investment=300x100=30000 Dividend earned=15x100=1500 Capital gain=(360-300)x100=6000 Total return=1500+6000=7500Total %return=(7500/30000)x100=25%Dividend yield=(15/300)x100=5%Capital gain=(60/300)=20%

Risk Risk in holding securities is

generally associated with the possibility that realized returns will be less than the return that was expected.

Risk is generally of two types- Systematic Risk. Unsystematic Risk

Systematic Risk Systematic Risk is also known as

undiversified or uncontrollable risk. It refers to that portion of total variability in return caused by factors affecting the prices of all securities. Economic, political and sociological changes are sources of systematic risk.

Unsystematic Risk Unsystematic Risk is also known as

diversified or controllable risk. It is the portion of total risk that is unique to a firm or industry .

Factors such as management capability ,Consumer preferences, labour strikes cause variability of returns in a firm .

Unsystematic factors are largely independent of factors affecting securities markets in general. Because these factors affect one firm, they must be examined for each firm.

MARKET RISK_ Market risk refers to the variability of returns due

to fluctuation in the securities market. Market risk is caused by investor reaction to tangible as well as intangible events. Expectation of lower corporate profit in general may cause the larger body of common stocks to fall in price.

The basis for the reaction is a set of real, tangible events like depression, war,politics.

Intangible events are related to market psychology The initial decline in the market can cause the fear and all investors make for the exit.

Interest Rate Risk Interest Rate Risk refers to the uncertainty of

future market values and of the size of future income, caused by fluctuations in the general level of interest rates.

The root cause of interest rate risk lies in the fact that, as the rate of interest paid on government securities rises or falls .The rate of returns demanded on alternative investment, such as stocks and bonds issued in the private sector, rise or fall.

PURCHASING _POWER RISK Purchasing power risk refers to the

impact of inflation or deflation on an investment .Rising prices on goods and services are normally associated with what is referred to as inflation ,and falling prices on goods and services are termed deflation.

Rational investors should include in their estimate of expected return an allowance for purchasing power risk

BUSINESS RISK CAN BE Internal Business Risk External Business Risk. Internal Business Risk is largely associated

with the efficiency with which a firm conducts its operations within the broader operating environment imposed upon it.

External Business Risk is the result of operating conditions imposes upon the firm by circumstances beyond its control.

Financial Risk Financial risk is associated with the way in

which a company finances its activities .We usually take financial risk by looking at the capital structure of a firm .

The presence of borrowed money of debt in the capital structure creates fixed payment in the form of interest that must be sustained by the firm.

Financial risk is avoidable risk to the extent that management have the freedom to decide to borrow or not to borrow funds. A firm with no debt financing has no financial risk.

Liquidity risk Liquidity risk arises when an asset

cannot be liquidated easily in the secondary market.

ASSIGNING RISK ALLOWANCES One way of Quantifying risk and building a required rate

of return would be to express the required rate as comprising risk less rate plus compensation for individual risk factors.

R= I + P + B + F + M+O Where, I = Real interest rate (Risk less Rate) P=Purchasing Power Risk Allowance. B=Business Risk Allowance. F= Financial Risk Allowance. M= Market Risk Allowance. O= Allowance for Other Risk.

Starting Predictions “Scientifically.” Security analysis can not be expected to predict

with certainty whether a stock’s price will increase or decrease or by how much. Analysist can not understand political and socioeconomic forces completely enough to permit predictions that are beyond doubt or error.

This existence of uncertainty does not mean that analysis is value less. It does not mean that analysis must strive to provide not only careful and reasonable estimates of return but also some measure of the degree of uncertainty associated with these estimates of return.

R=∑PO Variance = ∑ P (O-R) 2

s.d = √variance R=Expected return P=probability O= Outcome

Suppose that stock A, in the opinion of the analysist, could provide returns as follows.

Returns (%) Likelihood 7 1 chance in 20. 8 2 chances in 20. 9 4 chances in 20. 10 6 chances in 20. 11 4 chances in 20. 12 2 chances in20. 13 1 chance in20. A likelihood of four chances in twenty is 4/20 or .20. .The total of

the probabilities assigned to individual events in a group of events must always equal 1.00.

Return (%) Probability.

7 .05 8 .10 9 .20 10 .30 11 .20 12 .10 13 .05 Security analysis use the probability distribution of return

to specify expected return as well as risk .This expected return is the weighted average of the returns .If we multiply each return by its associated probability and add the results together, we get a weighted average return or expected average return.

(1) (2) Return (%) Probability 1*2 7 .05 .35 8 .10 .80 9 .20 1.80 10 .30 3.00 11 .20 2.20 12 .10 1.20 13 .05 .65 10.00%

The expected average return is 10%.The expected return lies at the center of the distribution .Most of the possible outcomes lie either above or below it.

The spread of possible returns about the expected return can be used to give us a proxy of risk. Two stocks can have identical expected returns but quite different spread or dispersions and thus different risks.

Consider Stock B -: (1) (2) 1*2 Return (%) Probability 9 .30 2.7 10 .40 4.0 11 .30 3.3 1.00 10.0 Stock A and B have identical expected average

returns of 10%.But the spreads for stocks A and B are not same .The range of outcome from high to low return is wider for stock A than B .

Stock A Stock BReturn minus expected return( 1

Difference squared (2

Probability(3) 2*3

(4)

Return minus expected

return (5)

Difference

squared (6)

Probability (7) 6*7

7-10= -3 9 .05 .458-10= -2 4 .10 .409-10=-1 1 .20 .20 9-

10=1 1 .30 .3010-10=0 0 .30 0 10-10=0 0 .40 011-10=1 1 .20 .20 11-10=1 1 .30 .3012-10=2 4 .10 .4013-10=3 9 .05 .45

1.00 2.10 1.00 .60variance

2.10 .60

Variance of A 2.10 Variance of B .60 Standard deviation of A 1.45

Standard deviation of B .77

The variability of return around the expected

average return is thus a quantitative descripition of risk .The total variance is the rate of return on a stock around the expected average return that includes both systematic & unsystematic risk.

Beta Beta is a statistical measure of risk .and capital

asset pricing model (capm) links risk (beta) to the level of required return.

Total risk=diversifiable risk + non diversifiable risk

Studies have shown that by carefully selecting as few as 15 securities for a portfolio diversifiable risk can be almost entirely eliminated. Non diversifiable risk is unavoidable and each security possesses its own level of non diversifiable risk ,measured using the beta coefficient.

Beta measures non diversifiable risk. Beta shows how a price of a security responds to market forces. The more responds to the price of a security is to changes in the market, the higher will be its beta. Beta is calculated by relating the returns on a security with the returns of the market

Market return is measured by the average return of a large sample of stocks such as BSE or NSE index. The beta for overall market is equal to 1.00.

Beta can be positive or negative. However all betas are positive and most betas lie somewhere between .4 and 1.9. Stocks having betas of less than 1 will of course be less responsive to changing returns in the market and therefore are considered less risky .

CAPITAL ASSET PRICING MODEL(CAPM) CAPM uses beta to link formally

the notions of risk & return. CAPM can be viewed both as a mathematical equation & graphically, as the security market line,(SML).

Assumptions of CAPM Investors are risk averse. They take decision based

upon risk and return assessment. The purchase or sale of a security can be undertaken

in infinitely divisible units. Purchase and sale by a single investor can not affect

prices. There are no transaction costs. There are no taxes. Investor can borrow and lend freely at a risk less rate

of interest. Investors have homogeneous expectations - they

have identical, subjective estimate of the means, variances among returns.

Rs = Rf+ Bs (Rm-Rf) Where, Rs- The return required on the investment Rf- The return that can be earned on a risk-free

investment Bs-Beta of the security Rm-The average return on all securities (BSE, NSE

index) Ex. – Find the required rate of return when beta is1.2 ,

risk free rate is 4% & the market return is expected to be 12 %.

Rs= 4 % + [1.20 x (12%-4%)] =4 % + [1.20 x 8%] = 4% + 9.6 % = 13.6 %

Ex. – Find the required rate of return when beta is 1 and also when beta is 1.5 and 2 risk free rate is 4% & the market return is expected to be 12 %.

The investor should therefore require 13.6% return on this investment as compensation for the non diversifiable risk assumed, given the security’s beta of 1.2 if the beta were lower say 1.00, the required return would be 12%[4% +{1.00x(12%-4%)}]

And if the beta had been higher say 1.50 the required return would be 16% {4% + [1.50 x (12%-4%)]}.CAPM reflects a positive mathematical relationship between risk return since the higher the risk (BETA) the higher the required return.

SECURITY MARKET LINE When the capital asset pricing model (CAPM) is

depicted graphically, it is called the security Market Line (SML).Plotting CAPM; we would find that the SML is a straight line. It tells us the required return an investor should earn in the marketplace for any level of systematic (beta) risk. The CAPM can be plotted by using Equation.

Make beta zero and the required return is 4% [4+0(12%-4%)].

Using a 4% risk-free rate and a 12% market return, the required return is 13.6% when beta is 1.2.

Increase the beta to 2.0, & the required return equals 22% [4% +[2.0* (12%-4%)]] & so on.

We end up with the combinations of risk (beta) & required return. Plotting these values on a graph (with beta on the horizontal axis & required returns on the vertical axis); we would have a straight line. The SML clearly indicates that as risk (beta) increases the required return increases & vice versa.

THE SECURITY MARKET LINE (SML)

THE SECURITY MARKET LINESML

E(r)

rrf

rM

EVALUATING RISK In the end investors must some how relate the

risk perceived in a given security not only to return but also their own attitudes towards risk. Thus, the evaluation process is not one in which we simply calculate risk & compare it to a maximum risk level associated with an investment offering a given return.

The individual investor typically tends to want to know of the amount of perceived risk is worth taking in order to get the expected return & whether a higher return’s possible for the same level of risk.

In the decision process investors evaluate the risk-return behavior of each alternative investment to ensure that the return expected is “reasonable” given its level of risk.

If other vehicles with lower levels of risk provide greater returns, the investment would not be deemed acceptable. An investor would select the opportunities that offer the highest returns associated with the level of the risk they are willing to take.

Capital Market Line (CML)

A line used in the capital asset pricing model that plots the rates of return for efficient portfolios, depending on the risk-free rate of return and the level of risk (standard deviation) for a particular portfolio.

Efficient portfolio A portfolio is efficient when it is expected to

yield the highest return for the level of risk accepted or the smallest portfolio risk for a specified level of expected return.

To build an efficient portfolio an expected return level is chosen, and assets are substituted until the portfolio combination with the smallest variance at the return level is found.

As this process is repeated for other expected returns ,set of efficient portfolios is generated.

The CML is derived by drawing a tangent line from the intercept point on the efficient frontier to the point where the expected return equals the risk-free rate of return.