Risk & Return
Transcript of Risk & Return
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.