Risk & Return

tainty r e c n u lity or i b a i r a V rns Of retu

Risk and Return

Gains received b y 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 OF Return CASH Components 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.

Objectives : How to calculate Return ? What are its components

How d o we Measu re risk

t is a h W o? i l o f t Por

Wha t is Cap ital a Prici ng m sset odel ?

W ha W t Co ha is r m t a isk po re s ne its ? nt s?

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 ?

sh a c lar u g Re flow

35 + (3800 −3580) = 3580 Initial capital = 7.12% Invested.

Capital appreciation In value of security

How to measure return? Dividend regular cash flow

Change in the value of stock over t -time

Dt + ( Pt − Pt − 1) k= Pt − 1 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 1992 1993 1994 1995 1996 1997 1998

24.75 55.50 86.25 88.50 93.60 121.20 207.60 249.60

6.3 8.4 12.00 15.00 18.75 25.50 33

124.24 55.41 2.61 5.76 29.49 ? 71.29 ?20.23

25.46 15.14 13.91 16.95 20.03 ? 21.04 ?15.90

149.70 70.54 16.52 22.71 49.52 92.33 36.12

HLL’s Annual Rates of Return 160.00

149.70

Total Return (%)

140.00 120.00

92.33

100.00

70.54

80.00

52.64

49.52

60.00

36.13

40.00

16.52

20.00

22.71 7.29

12.95

2000

2001

0.00 1992

1993

1994

1995

1996

1997

Year

1998

1999

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 Business risk

Liquidity risk

Inflation risk k

Financial ris

Interest rate risk inverse

Calculation of risk • • • •

Probability Distribution Range Variance Standard deviation

Probability distribution method – graphical method

given to you ,of Alpha ltd., Probability

0.1 0.2 0.4 0.2 0.1

Rate of return

50% 30% 10% -10% -30%

PROBABILITY

 Say if following data is

RETURN

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

Probability distribution method – graphical method

given to you ,of Beta ltd. Probability

0.1 0.2 0.4 0.2 0.1

Rate of return

70% 50% 10% -30% -50%

PROBABILITY

 Say if following data is

RETURN

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.

n

∑ P (r − r ) i

i =1

i

2

Standard Deviation  It is the square root of variance of the rate of

return explained initially. Standard deviation =

σ=

Variance n

∑ P (r − r ) i

i =1

i

2

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. Pi

Pi  k −k  2

Outcomes

Return (ki%)

1 2 3 4

50% 30% 10% -10%

40 20 0 -20

1600 400 0 400

0.1 0.2 0.4 0.2

160 80 0 80

5

-30%

-40

1600

0.1

160

Total

480

σ=

n

∑ Pi ( r i − r ) i =1

2

(ki − k )

( ki − k ) 2

=√ 480 = 21.9%

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.

set so s a f o p Grou tal risk o t e h t t tha reduces

■

Portfolio

Keep all types of assets like – equity, ■

account ■ ■ ■

other ■

- bond, saving - real estate - bullions - collectibles and assets.

I have to invest in two companies • 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 if I invest 50:50 in company A and 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 portfolio is – standard deviation of the portfolio Standard deviation of The security

Relationship of The two securities

   w   w  2 wx wy Co varxy 2 p

2 x

2 x

2 y

2 y

  w   w  2 wx wy x y Corxy 2 x

2 x

2 y

2 y

Total Risk can be reduced through diversification ■

■

■

Perfectly positively co-related – ex. Two leading companies in pharmaceutical industry. Portfolio risk will be calculated as the addition of the risk of the securities in the portfolio.  p2   x2 wx2   y2 wy2  2 wx wy Co varxy Say, in given case   x2 wx2   y2 wy2  2 wx wy x y Corxy

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

= 20%

No advantage of diversification

Risk can be reduced through diversification ■ ■

■

Perfectly negatively co-related – ex. Two companies in raincoat and sunglass industry. Portfolio risk will be calculated as the difference of the risk of the securities in the portfolio. Say, in given case  2   2 w2   2 w2  2 w w Co var p

x

x

y

y

x

y

xy

  x2 wx2   y2 wy2  2 wx wy x y Corxy

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

= 4%

Huge advantage of diversification

Risk can be reduced through diversification ■ ■ ■

Perfectly not co-related – ex. Two

companies in steel and fertilizer industry. Portfolio risk will be calculated by following method. Say, in given case 2 2 2 2 2  p   x wx   y wy  2 wx wy Co varxy

  x2 wx2   y2 wy2  2 wx wy x y Corxy

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

= 14.42% Advantage of diversification to some extent

RISK ■

DIVERSIFIABLE/ unique risk ■

Strikes Increase in competition Technical breakdown or obsolescence

NON – DIVERSIFIABLE or systematic risk

Change in management.

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

Loss of a big contract etc.

War

Inadequate raw material

Earthquake, floods, rains, tsunamis etc.

Hence though initially the risk gets diversified, due to some systematic or market risk the diversification cannot completely negate the risk

Risk Reduction through diversification. The effect reduces with

Risk

Diversifia ble Risk

No change in market risk

Non – diversifiable Risk

Increase in the portfolio size Number of securities in portfolio

Similarly if we calculate Return of Alpha– 12% and Beta – 18% and std. deviation – Alpha -16% and Beta – 24% Weight

Alpha 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 wL wR σ2 σ (%)

Beta 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Portfolio Return

Portfolio Risk, σp Correlation

Rp σp σp σp 12.00 16.00 16.00 16.00 12.60 16.80 12.00 14.60 13.20 17.60 8.00 13.67 13.80 18.40 4.00 13.31 14.40 19.20 0.00 13.58 15.00 20.00 4.00 14.42 15.60 20.80 8.00 15.76 16.20 21.60 12.00 17.47 16.80 22.40 16.00 19.46 17.40 23.20 20.00 21.66 18.00 24.00 24.00 24.00 Minimum Variance Portfolio 1.00 0.60 0.692 0.00 0.40 0.308 256 0.00 177.23 16 0.00 13.31

σp 16.00 15.74 15.76 16.06 16.63 17.44 18.45 19.64 20.98 22.44 24.00

σp 16.00 13.99 12.50 11.70 11.76 12.65 14.22 16.28 18.66 21.26 24.00

0.857 0.143 246.86 15.71

0.656 0.344 135.00 11.62

If we plot the data on a graph 20

Portfolio return, %

Cor = - 1.0

Efficient frontier beta

Cor = - 0.25

Cor = + 0.50

15

Cor = + 1.0 Cor = - 1.0

10

alfa

ent i c i f f e In r frontie

5

0 0

5

10

15

20

Porfolio risk (Stdev, %)

25

30

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 Relation between the expressed as – Return on Security J

market security and the security k

kj = αj + βjkm 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

kj = kf + βj (km − kf )

Security Market Line • For a given amount of systematic risk (β), SML shows the required rate of return E(Rj)

E(R j ) = R f +  (R m ) – Rβf  SLM

Rm Rf

0

1.0

β = (covarj,m/σ 2 m)

j

EXPECTED / REQUIRED RATE OF RETURN ON Y AXIS

SML

RISK PREMIUM FOR UNCERTAINTY

Km

Rf

Defensive securities

Beta 1.0

Aggressive securities

EXPECTED / REQUIRED RATE OF RETURN ON Y AXIS

X

SML

RISK PREMIUM FOR UNCERTAINTY

Km

Y

Rf

Defensive securities

Beta 1.0

Aggressive securities

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.