Security Analysis &

Portfolio Management “RISK & RETURN”

By

B.Pani M.Com,LLB,FCA,FICWA,ACS,DISA,MBA

9731397829 bpani2001@yahoo.co.in

Risk

Probability of loss or injury.

In investment sense, it can be defined as the chance that the actual outcome from an investment will differ from the expected outcome.

Classification of Risk

M arket risk p urchas ing p ow er risk in terest ra te risk

S ystem atic r iskor

U ndiv ers if iab le R isk

B usiness risk F inanc ia l R isk

U nsystem atic R iskor

D iv eris fiab le risk

R isk

Systematic Risk

Risk Attributable to broad macro factors affecting all securities.

Interest rate risk

The variability in the security’s return resulting from the changes in the interest rates

Market Risk

The variability in a security’s returns resulting from fluctuations in the aggregate market. It occurs due to basic sweeping changes in the expectations of the investor.

Purchasing power risk

Purchasing power risk is the uncertainty of the purchasing power of the amounts received.

Unsystematic risk

It is that portion of the total risk that is unique or peculiar to a particular security.

Business Risk

It is a function of the operating conditions faced by a firm and the variability these conditions inject into operating income and expected dividends.

Financial Risk

It is associated with the way in which the company finances its activities with the use of debt.

Attitude towards risk

• The relationship of a person’s certainty equivalent to the expected monetary value of a risk investment defines his attitude towards risk

Certainty equivalent less than expected value means risk averse

Certainty equivalent equals to expected value means risk neutral

Certainty equivalent more than expected value means risk loving

N

Systematic Risk (not under the control of the investor)

Total risk

Unsystematic risk

Reduced through diversification

ReturnReturn : It is the primary motivating forces that drives

investment. It represents the reward for undertaking the investment.

In security analysis we are primarily and particularly concerned with returns from investors perspective.

The return of an investment consists two components : (i) Current return (ii) Capital return.

(i) Current return: Periodic cash flow (income) such as dividend and interest. This can be zero or positive.

(ii) Capital return: The price appreciation or price changes. This can be zero, positive and negative also.

Thus Total Return = Current return + Capital return

Historical Return

• Historical capital return excluding Dividend.

Period : 0 1 2 3 4

Price : 100 110 108 130 115

Solution: R1 = (P1-P0)/P0 =(110 -100)/100 =0.10=10%

R2 = (P2 - P1)/P1=(108 -110)/ 110 = -0.018 = (-)1.8%

Similarly, R3= 20.37% and R4 = (-)11.54%

Average return=(10 – 1.8 + 20.37 – 11.54)/4= 4.26%

• Historical capital return including Dividend.

Period : 0 1 2 3 4

Price : 100 110 108 130 115

Dividend: 5 7 8 3

Solution:R1 = (P1-P0)+D1/P0 =(110 -100)+5/100 =0.15=15%

R2 = (P2-P1)+D2/P1=(108 -110)+7/ 110 = 0.45 =4.5%

Similarly, R3= 27.77% and R4 = (-)9.23%

Average return = 9.51%

This return will give the investors an insight or the prediction about the future return.

Measuring Expected ReturnWhen we invest in a stock we try to anticipate the

future streams return based on the past performance of the stock. It may be -5%, 15% or 35%.

Further the likely hood of these possible returns can vary. Hence we should think in terms of probability distribution.

The probability of an events represents the likelihood of its occurrence. For example there is a 70% chance that the price of the stock will increase and 30% chance that the price of the stock will not increase during the next fortnight.

The expected return would be E(R) = (0.25*36)+(0.50*26)+(0.25*12) = 25%

The risk of the stock :

σ2 =∑Pi *[Ri – E(R)]2

=(36-25)2 *0.25 + (26-25)2 * 0.50 + (12-25)2 * 0.25

= 73%

SD = 8.54%

Economic scenario

Probability of occurrence

Return from stock A(%)

Boom 0.25 36

Stagnation 0.50 26

Recession 0.25 12

Historical Risk• The majority of investors tend to emphasize

the return. They also tend to view the risk in subjective as well as comparative term.

Suppose you are evaluating two shares A & B for investment. You have collected data of return earned for the last 5 years.

Stock A: 30% 28% 34% 32% 31%Stock B: 26% 13% 48% 11% 57%You have to choose one stock among these two.

In this context of security analysis, we interpret risk essentially in the terms of the variability of the security return. The most common measures of riskyness of security is SD and Variance of return.

Given below returns of two stocks X and Y.Period Return of stock X(%) Return of stockY(%)

1 -6 4

2 3 6

3 10 11

4 13 15

5 16 19

Calculate which stock is more risky ?

Mean of X = 36/5 = 7.2 =X Mean of Y = 55/5 =11=YVariance of X = ∑(X- X)2/(n -1)= 310.80/(5-1)= 77.7 and the S.D

=√77.7=8.815

Period X Y (X – X) (Y – Y)

(X – X)2 (Y – Y)2

1 -6 4 -13.2 -7 174.24 492 3 6 -4.2 -5 17.64 253 10 11 2.8 0 7.84 04 13 15 5.8 4 33.64 165 16 19 8.8 8 77.44 64

Sum 36 55 310.84 154

Reduction of risk through Diversification

Security Analysis: Measuring risk & return.

Portfolio Mgt: minimize risk or maximize return.

Example:

Concept of Covariance: the degree to which the return of two securities vary or change together.

Concept of Correlation: the degree of relationship between two variables.

Measuring Historical Risk

The most commonly used measure of risk is standard deviation.

σ2 = Σ(Xi - X)2

N-1Where

σ2 = the variance of a set of values

Xi = each value in the set

X = the mean of the number of observation

n = number of observations

Illustration: Calculation of Risk

Year Total Return(%) (Xi)

Xi - X (Xi – X)2

1970 3.511971 14.121972 18.721973 -14.501974 -26.031975 36.921976 23.641977 -7.161978 6.391979 18.19

Calculate standard deviation. (Ans. 19.00%)

Measuring Expected Risk

σ2 = Σ (Xi - E(X))2 *Pi

Where

σ2 = the variance of a set of values

Xi = each value in the set

E(X) = the expected mean of the number of observation

n = number of observations

i=1

n

Illustration: Calculate Expected Risk

EconomicConditions

Rate ofreturn(%)

Probability

Growth 18.5 0.25

Expansion 10.5 0.25

Stagnation 1 0.25

Decline -6 0.25

Risk and return of a portfolio

• Expected return on a portfolio is simply the weighted average of the expected returns on the assets comprising the port folio

E(Rp)=Σwi E (Ri)

N

Systematic Risk (not under the control of the investor)

Total risk

Unsystematic risk

Reduced through diversification

• Empirical studies suggest that the bulk of the benefit of diversification in the form of risk reduction is achieved by forming a portfolio of about ten securities

• Thereafter the gain from diversification tends to be negligible

BetaIt measures the security’s performance in relation to

market.

Beta shows how the price of a security responds to market forces, the more responsive the price of a security is to change in the market, the higher will be its beta.

Beta can be positive or negative. However nearly all betas are positive and most betas lie somewhere between 0.4 to 1.9.

Measurement of Beta = Covariance of security & the market return/ variance of market return.

Beta (β)Beta is the relative measure of systematic risk. It measures the sensitivity of the return of the security vis-à-vis the market return.

β = Cov(X,Y)/ Var(X)

where X = Return on the market

Y= Return on individual security

It can also be calculated by the following formulae

β = (NΣX*Y -ΣX*ΣY ) /( NΣX2 - (ΣX)2)

where N = number of observation.

Interpretation of beta

β > 1 --------------------------- Aggressive Securities

β< 1----------------------------- Defensive securities

Explain why the beta of the market is 1

Illustration: Calculation of BetaTime period Return on

Security XReturn on MarketIndex

1 10 112 8 73 -4 -24 22 85 8 96 -11 -57 14 128 12 119 -9 310 12 10

Calculate beta and identify whether security X is an aggressive or a defensive security. What will be your investment decision in deflationary times?

Risk Break - Up

Total Risk of a security = σ2

Systematic Risk of a security = β2σ2 m

where β = Beta of an individual security

σ2 m= Variance of the market portfolio

Write the formulae of Unsystematic risk

Other risk calculations

Semi-variance or downside risk

Semi-variance is defined in analogy to variance, but using only returns below the mean. If the returns are symmetric – i.e., the return is equally likely to be x percent above and below the mean- the semi-variance is exactly one-half of the variance.

One approach defines downside risk as the square root of the semi-variance.

Target Semi-variance

A generalized semi-variance that focuses on returns below a target instead of just below the mean.

Problems associated with the measure of downside risk

• The statistical properties of semi-variance is not well known.

• It is computationally challenging for large portfolio construction problems.

Relative risk

If a investment manager is being compared to a performance benchmark, then the difference between the manager’s portfolio return Rp and the benchmark's return RB is of crucial importance. The difference is

called active return Rpa. Correspondingly, the active risk

is defined as the standard deviation of active return:

ψP = STD{Rpa }= STD{Rp - RB}

This is also called tracking error.