Risk and Return

Variability or uncertainty

Of returns

Gains received by Way of income+ increase in Market value

REALIZED RETURN & EXPECTED RETURN

Historic or realized return as in case of a bank deposit at a fixed rate of interest.

EXPECTED RETURN

Have to be sufficiently high to offset the risk or uncertainty.

Invest in Equity or not

MEANING OF CASH

Periodic cash receipts by way of interest,

Dividends. Eg. Yield on a 10% bond of

Rs. 900 is 11.11%

The appreciation/depreciation in the price of the asset. i.e. difference between purchase & sale price of assets.

Components Of Return

Objectives :How to calculate

Return ?What are itscomponents

How do we Measure risk

What is

Portfolio ?

What is Capital asset Pricing model ?

What is risks ?

What are its

Components ?

Therefore RETURNS are measured as -

• Shares of company A were purchased for Rs.3580 and were sold for Rs.3800 after one year and dividend of Rs.35 was paid for the year how much is rate of return ?

%12.73580

)35803800(35

Regular cash

flowCapital appreciationIn value of security

Initial capitalInvested.

How to measure return?

1

1)(

t

tt

P

PPDk

t

Dividend regular cash

flow

Change in the value of stock over t

-time

Value of stock in beginning

PROBABILITIES & RULES• A probability can never be

larger than 1• The sum total of probability

must be equal to 1• A probability can never be

negative• Certain to occur P=1 never

occur P=0• Probability should be mutually

& collectively exhaustive.

Let us take the case of HLL from 1991-1998

Year Share price (Pt)

Dividend per share

Capital gain Pt -Pt-1 / Pt-1

Dividend Yield (%)

Rate of return (%)

1991 24.75 -

1992 55.50 6.3 124.24 25.46 149.70

1993 86.25 8.4 55.41 15.14 70.54

1994 88.50 12.00 2.61 13.91 16.52

1995 93.60 15.00 5.76 16.95 22.71

1996 121.20 18.75 29.49 20.03 49.52

1997 207.60 25.50 ? ?

1998 249.60 33 ? ?

71.29 21.0420.23 15.90

92.33

36.12

HLL’s Annual Rates of Return

149.70

70.54

16.52 22.71

49.52

92.33

36.13

52.64

7.29 12.95

0.00

20.00

40.00

60.00

80.00

100.00

120.00

140.00

160.00

1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

Year

Tota

l Re

turn

(%

)

Expected returns

The anticipated income over some future period and may be subject to certain risk or uncertainty is expected return.

Suppose in case of Alpha Ltd, following information –

1. 20% chance of 50% return

2. 30% chance of 40% return

3. 25% chance of 30% return

4. 25% chance of 10% return

=(0.20 x 0.50)+(0.30 x 0.40) +(0.25 x 0.30)+ (0.25 x 0.10)

= 32%

Uncertainty of return is Risk components

Market risk

Liquidity risk

Interest rate riskinverse

Inflation risk

Business risk

Financial risk

Calculation of risk• Probability Distribution

• Range

• Variance

• Standard deviation

Say if following data is given to you ,of Alpha ltd.,

Probability distribution method – graphical method

PR

OB

AB

ILIT

Y

RETURN

Probability Rate of return

0.1 50%

0.2 30%

0.4 10%

0.2 -10%

0.1 -30%

Since the dispersion is near the y axis and not spread over the risk in this company is very low.

Say if following data is given to you ,of Beta ltd.

Probability distribution method – graphical method

PR

OB

AB

ILIT

Y

RETURN

Probability Rate of return

0.1 70%

0.2 50%

0.4 10%

0.2 -30%

0.1 -50%

Since the dispersion is far from the y axis and spread over the risk in this company is very high

Range

It is the difference between the highest and the lowest value of rate of return

It is based on only two extreme values.Range for Ala ltd = 50% –( -30%)

= 80%Range for Beta ltd= 70% - (-50%)

=120%. So beta is more risky

Variance

It is the sum of the squared deviation of each possible rate of return from the expected rate of return multiplied by the probability that the rate of return occurs.

)(2

1rri

n

i

iP

Standard Deviation

It is the square root of variance of the rate of return explained initially.

Standard deviation = Variance

)(2

1rri

n

i

iP

Sources Of Risk

• Interest Rate Risk-Security prices move inversely to interest rates.

• Market Risk- Variability of returns due to fluctuations in security markets. (Equity most affected)

• Inflation Risk-Reduction in purchasing power.

Directly related to interest rate risk.

Sources Of Risk

• Business Risk-Carrying on a business in a particular environment. The risk is transferred to the investors.

• Financial Risk- greater the debt financing, greater the risk.

• Liquidity Risk- Security which can be bought or sold easily, without significant price concession, is considered liquid. The greater the uncertainty about the time element & price concession, the greater the liquidity risk.

Treasury bills have ready markets lesser liquidity risks

Calculate risk in Alpha ltd. -

Outcomes Return (ki%) Pi

1 50% 40 1600 0.1 160

2 30% 20 400 0.2 80

3 10% 0 0 0.4 0

4 -10% -20 400 0.2 80

5 -30% -40 1600 0.1 160

Total 480

)( kki 2)( kki 2

kkPi

=√ 480 = 21.9%)(

2

1rri

n

i

iP

How to reduce risk ?

• If I invest in a company trading in sunglasses my normal observation would be that I experience good profits in summer and loss in rains

• If I invest in a company trading in raincoats I would experience good profits during rainy season and losses during summers.

PortfolioPortfolioGroup of asset so

that the total risk

reduces

Group of asset so

that the total risk

reduces

Keep all types of assets like – Keep all types of assets like – equity,equity,

- bond, saving - bond, saving accountaccount

- real estate- real estate - bullions- bullions - collectibles and - collectibles and

other other assets. assets.

I have to invest in two I have to invest in two companiescompanies

• There are two companies – Company A and Company B .

• The return from Company A is 12% and Company B is 18%

• The standard deviation of A is 16% and 24%• Then how much will I invest in A and how

much in B ie. The weights assigned to each will decide my total risk and return factor

What will be the return and risk What will be the return and risk if I invest 50:50 in company A if I invest 50:50 in company A

and company Band company B

A . 15 % return and 20 % risk

B. 15 % return and 4 % risk

C. 15 % return and 14.42 % risk

The answer will depend on the relationship between Company A and Company B

Formula to calculate risk in Formula to calculate risk in portfolio is – standard deviation portfolio is – standard deviation

of the portfolioof the portfolio

2 2 2 2 2

2 2 2 2

2 Co var

2 Cor

p x x y y x y xy

x x y y x y x y xy

w w w w

w w w w

Standard deviation ofThe security

Standard deviation ofThe security

Relationship of

The two securities

Total Risk can be reduced Total Risk can be reduced through diversificationthrough diversification

Perfectly positively co-relatedPerfectly positively co-related – ex. Two – ex. Two leading companies in pharmaceutical industry.leading companies in pharmaceutical industry.

Portfolio risk will be calculated as the addition of Portfolio risk will be calculated as the addition of the risk of the securities in the portfolio.the risk of the securities in the portfolio.

Say, in given case Say, in given case

=(0.5*16)=(0.5*16)22 + (0.5*24) + (0.5*24)22 + 2 + 2 *0.5*16*0.5*24* 1*0.5*16*0.5*24* 1

= 0.5*16 + 0.5*24= 0.5*16 + 0.5*24

= 20%= 20% No advantage of diversification No advantage of diversification

2 2 2 2 2

2 2 2 2

2 Co var

2 Cor

p x x y y x y xy

x x y y x y x y xy

w w w w

w w w w

Risk can be reduced Risk can be reduced through diversificationthrough diversification

Perfectly negatively co-relatedPerfectly negatively co-related – ex. Two – ex. Two companies in raincoat and sunglass industry.companies in raincoat and sunglass industry.

Portfolio risk will be calculated as the difference Portfolio risk will be calculated as the difference of the risk of the securities in the portfolio.of the risk of the securities in the portfolio.

Say, in given case Say, in given case

=(0.5*16)=(0.5*16)22 + (0.5*24) + (0.5*24)22 - 2 *0.5*16*0.5*24* - 2 *0.5*16*0.5*24* 11

= 0.5*16 - 0.5*24= 0.5*16 - 0.5*24

= 4%= 4% Huge advantage of diversification Huge advantage of diversification

2 2 2 2 2

2 2 2 2

2 Co var

2 Cor

p x x y y x y xy

x x y y x y x y xy

w w w w

w w w w

Risk can be reduced Risk can be reduced through diversificationthrough diversification

Perfectly not co-relatedPerfectly not co-related – ex. Two – ex. Two companies in steel and fertilizer industry.companies in steel and fertilizer industry.

Portfolio risk will be calculated by following Portfolio risk will be calculated by following method.method.

Say, in given case Say, in given case

=(0.5*16)=(0.5*16)22 + (0.5*24) + (0.5*24)22 + 2 + 2 *0.5*16*0.5*24* 0*0.5*16*0.5*24* 0

=(0.5*16)=(0.5*16)22 + (0.5*24) + (0.5*24)22

= 14.42%= 14.42% Advantage of diversification to some extent Advantage of diversification to some extent

2 2 2 2 2

2 2 2 2

2 Co var

2 Cor

p x x y y x y xy

x x y y x y x y xy

w w w w

w w w w

RISKRISK DIVERSIFIABLE/ DIVERSIFIABLE/

unique riskunique risk

NON – NON – DIVERSIFIABLE DIVERSIFIABLE or systematic or systematic riskrisk

Changes in government policies – monetary policy, fiscal policy, foreign policy, corporate taxes

War

Earthquake, floods, rains, tsunamis etc.

Strikes

Increase in competition

Technical breakdown or obsolescence

Inadequate raw material

Change in management.

Loss of a big contract etc.

Hence though initially the risk gets diversified, due to some systematic or market risk the

diversification cannot completely negate the risk

Number of securities in portfolio

Ris

kRisk Reduction through diversification.

Non – diversifiable Risk

Diversifiable Risk

The effect reduces with

No change in market risk

Increase in the portfolio size

Similarly if we calculate Return of Alpha– 12% and Beta – 18% and std. deviation –

Alpha -16% and Beta – 24% Portfolio Risk, p (%) Correlation

Weight Portfolio

Return (%) +1.00 -1.00 0.00 0.50 -0.25

Alpha Beta Rp p p p p p 1.00 0.00 12.00 16.00 16.00 16.00 16.00 16.00 0.90 0.10 12.60 16.80 12.00 14.60 15.74 13.99 0.80 0.20 13.20 17.60 8.00 13.67 15.76 12.50 0.70 0.30 13.80 18.40 4.00 13.31 16.06 11.70 0.60 0.40 14.40 19.20 0.00 13.58 16.63 11.76 0.50 0.50 15.00 20.00 4.00 14.42 17.44 12.65 0.40 0.60 15.60 20.80 8.00 15.76 18.45 14.22 0.30 0.70 16.20 21.60 12.00 17.47 19.64 16.28 0.20 0.80 16.80 22.40 16.00 19.46 20.98 18.66 0.10 0.90 17.40 23.20 20.00 21.66 22.44 21.26 0.00 1.00 18.00 24.00 24.00 24.00 24.00 24.00

Minimum Variance Portfolio wL 1.00 0.60 0.692 0.857 0.656 wR 0.00 0.40 0.308 0.143 0.344 2 256 0.00 177.23 246.86 135.00

(%) 16 0.00 13.31 15.71 11.62

If we plot the data on a graph

0

5

10

15

20

0 5 10 15 20 25 30

Porfolio risk (Stdev, %)

Po

rtfo

lio r

etu

rn,

%

Cor = - 1.0

Cor = - 0.25

Cor = + 1.0

Cor = + 0.50

Cor = - 1.0

alfa

betaEfficient frontier

Inefficient

frontier

We will now try to analyze more of diversifiable (market risk) and

non- diversifiable risk• For this we will try to find relation between

market risk and specific risk of the security

• We try to analyse the responsiveness of security to general market and measure how extensively the return of security vary with changes in market return.

Calculation of risk of a stock/ portfolio with respect to market

• We try to fit a line to find the systematic relationship (linear) between the return of security and the return of market.

• As per model of William Sharpe it is expressed as –

mjjj kk

Return on Security J

Relation between the market security and the

security k

Return above

market at all times

Calculation of beta • Beta refers to the regression co-efficient

between the market security and the portfolio returns.

Capital Asset Pricing Model

• The capital asset pricing model (CAPM) is a model that provides a framework to determine the required rate of return on an asset and indicates the relationship between return and risk of the asset.

• Assumptions of CAPM– Market efficiency– Risk aversion and mean-variance optimisation – Homogeneous expectations – Single time period – Risk-free rate 

Capital Asset Pricing Model

)( fmjfj kkkk

Security Market Line

• For a given amount of systematic risk (), SML shows the required rate of return

= (covarj,m/2

m)

SLM

E(Rj)

Rm

Rf

1.00

j f m f jE(R ) = R + (R ) – R β

Defensive securities

EX

PE

CT

ED

/

RE

QU

IRE

D R

AT

E O

F

RE

TU

RN

ON

Y A

XIS

RISK PREMIUM FOR UNCERTAINTY

Aggressive securities

Beta

1.0

Km

Rf

SML

Defensive securities

EX

PE

CT

ED

/

RE

QU

IRE

D R

AT

E O

F

RE

TU

RN

ON

Y A

XIS

RISK PREMIUM FOR UNCERTAINTY

Aggressive securities

Beta

1.0

Km

Rf

SMLX

Y

Types of investors – based on risk

• A risk-averse investor will choose among investments with the equal rates of return, the investment with lowest standard deviation. Similarly, if investments have equal risk (standard deviations), the investor would prefer the one with higher return.

• A risk-neutral investor does not consider risk, and would always prefer investments with higher returns.

• A risk-seeking investor likes investments with higher risk irrespective of the rates of return. In reality, most (if not all) investors are risk-averse.