2. Introduction
• Return is the motivating force for making an
investment
• Risk is inherent to all investment decisions
• For a financial manager, risk means:
“uncertainty in future cash flows”
• Risk should be measured, and
• Discount rate should be adjusted to measure returns
• Understanding the risk-return relationship is very
important– helps in decision making
3. Return
• Enables comparison of alternative options
of investment
• Measures past performance
• Helps in estimating future
• Two Types:
– Historical or Realized return or Holding period
return
– Expected return
4. Income receivedIncome received on an investment plus
any change in market pricechange in market price (if being(if being
traded)traded), usually expressed as a percent of
the beginning market pricebeginning market price (initial(initial
value)value) of the investment.
DDtt + (PPtt - P- Pt-1t-1 )
PPt-1t-1
R =
Defining Return
5. Rate of Return of a Stock
• Returns from holding a stock
– Dividend(s)
– Capital Gain/ Loss
6. The stock price for Stock A was Rs. 1010 per
share 1 year ago. The stock is currently
trading at Rs. 9.509.50 per share, and shareholders
just received a Rs. 1 dividendRs. 1 dividend. What return
was earned over the past year?
1.001.00 + (9.509.50 - 10.0010.00 )
10.0010.00RR = = 5%5%
Example
7. Return of a Bond/ Debenture
• Returns of holding a Bond/ Debenture
– Interest (annually, semi-annually, quarterly,
etc.)
– Change in the price (if being traded in a
market)
8. 14% Rs. 1,000 IDBI debenture was purchased
for Rs. 1050 and was sold when the price of
the security raised to Rs. 1080 at the end of
one year. What return was earned over the
past year?
140140 + (1,0801,080 – 1,0501,050)
1,0501,050RR = = 16.2%16.2%
Example
9. Return: Single Asset
• Rate of return =
Current yield + Capital gain/loss yield
• Current yield or Dividend yield
Annual Income/ Beginning price
• Capital gain (loss) yield
(End price – Beginning price) / Beginning
price
10. Illustration
Assume that IPCL was trading at Rs. 142 per
share one year back. It declared a dividend of
60% and the price now is Rs. 176.
Compute the returns: current yield and capital
gain yield on IPCL stocks.
Current yield: 4.23%
Capital gain yield: 23.94%
11. Expected Return
• Return in a future period
• Future is uncertain
• If possibilities of returns and their chance of
occurrence can be defined i.e. probability of
outcomes…
12. Expected Rate of Return
• It is the weighted average of all possible
returns multiplied by their respective
probabilities
R = expected return
Ri = return for the i th possible outcome
pi = probability associated with Ri
n = no. of possible outcome
R = ∑ pi Ri
n
i = 1
13. Illustration
Probability distribution of rate of return on stocks of
Bharat Foods and Oriental shipping
State of Probability of Rate of Return (%)
Economy Occurrence ABC XYZ
Boom 0.20 25 30
Normal 0.50 15 8
Recession 0.30 10 -5
ABC Ltd R = 15.5%
XYZ Ltd R = 8.5%
14. What rate of return do you expect on yourWhat rate of return do you expect on your
investment (savings) this year?investment (savings) this year?
What rate will you actually earn?What rate will you actually earn?
Does it matter if it is a bank FD or equity share?Does it matter if it is a bank FD or equity share?
The variability of returns from thoseThe variability of returns from those
that are expected.that are expected.
The possibility that actual outcome will differThe possibility that actual outcome will differ
from expected outcomefrom expected outcome
Defining Risk
15. Sources of Risk
• Interest rate risk
– Change in level of interest rates
– Security prices move inversely to interest rates
• Market risk
– Fluctuations in the securities market
• Inflation risk
– Purchase power risk
16. Sources of Risk…
• Business Risk
– Industry, Environment
• Financial Risk
– Use of debt financing
• Liquidity Risk
– Transaction of a asset/ conversion
17. Measures of Risk
(Variability of Return)
• Range
– Maximum & Minimum value
• Variance / Standard deviation (historical)
var = σ2
= 1/n Σ (Ri – R)2
σ = √σ2
• Variance (expected return)
σ2
= Σ Pi (Ri – R)2
18. Illustration (historical)
Johnson & Nicholson has the following dividend per share
(DIV) and market price per share (MP) for the period 2003-
2008s
Year DIV MP
2003 1.53 31.25
2004 1.53 20.75
2005 1.53 30.88
2006 2.00 67.00
2007 2.00 100.00
2008 3.00 154.00
What are the annual rate of returns for the last five years? How
risky is the share?
19. Solution
• R04 = - 28.07%
• R05 = 56.2%
• R06 = 123.4%
• R07 = 52.2%
• R08 = 57%
• Mean Return = 52.0%
∀ σ2
= 2,330.63
∀ σ = 48.28
• The standard deviation of J&N’s share of returns is
quite high.
• The share is very risky.
25. Risk & Expected Rate of Return
Expected return: is the weighted average of
all possible returns multiplied by their
respective probabilities
R = expected return
Ri = return for the i th possible outcome
pi = probability associated with Ri
n = no. of possible outcome
R = ∑ pi Ri
n
i = 1
26. Variance
• Variance of an asset’s return is the sum of
the squared deviations of each possible rate
of return from the expected rate of return
multiplied by their probabilities
• Variance (expected return)
σ2
= Σ Pi (Ri – R)2
27. Illustration
• Probability distribution of rate of return on stocks
of Bharat Foods and Oriental shipping
State of Probability of Rate of Return %
Economy Occurrence Bharat Foods Oriental shipping
Boom 0.30 25 40
Normal 0.50 20 10
Recession 0.20 15 -20
Bharat Foods R = 20.5%
Oriental Shipping R = 13.0%
28. Risk of Expected Returns
State of
Economy
pi Ri pi Ri Ri – R (Ri – R)2
pi(Ri–R)2
Boom 0.30 25 7.5 4.5 20.24 6.075
Normal 0.50 20 10.0 -0.5 0.25 0.125
Recession 0.20 15 3.0 -5.5 30.25 6.050
R = Σ pi Ri = 20.5 Σ pi (Ri – R)2
= 12.25
σ = [Σ pi (Ri – R)2
]1/2
= (12.25)1/2
= 3.5%
Expected returns of Bharat Foods’ Stock
29. Risk of Expected Returns
State of
Economy
pi Ri pi Ri Ri – R (Ri – R)2
pi(Ri–R)2
Boom 0.30 40 12 27.0 729.0 218.7
Normal 0.50 10 5 -3.0 0.25 4.5
Recession 0.20 -20 -4 -33.0 1089.0 217.8
R = Σ pi Ri = 31.0 Σ pi (Ri – R)2
= 441.0
σ = [Σ pi (Ri – R)2
]1/2
= (441.0)1/2
= 21.0%
Expected returns of Oriental Shipping’s Stock
30. Why Standard Deviation (σ)?
• Standard deviation is a measure of
dispersion around the average (expected)
value
• Standard deviation considers every possible
event and assigns equal weight to its
probabilities
• Easy to calculate, widely accepted
31. Certainty EquivalentCertainty Equivalent (CECE) is the amount
of cash someone would require with
certainty at a point in time to make the
individual indifferent between that
certain amount and an amount
expected to be received with risk at the
same point in time.
Risk Attitudes
32. Certainty equivalent > Expected value
Risk PreferenceRisk Preference
Certainty equivalent = Expected value
Risk IndifferenceRisk Indifference
Certainty equivalent < Expected value
Risk AversionRisk Aversion
Most individuals are Risk AverseRisk Averse.
Risk Attitudes
33. Portfolio
• A portfolio refers to a group of assets owned by
an investor
• Assets in which an investor has made investments
• Why Portfolio?
– It is possible to construct a portfolio in such a way that
the total risk of the portfolio is less than the sum of the
risk of individual assets
– To reduce risk, investors hold a diversified portfolio
(equity capital, bonds, real estate, FDs, Bulion, etc.)
34. RP = Σ ( Wj )( Rj )
RP is the expected return for the portfolio,
Wj is the weight (investment proportion) for the jth
asset in the portfolio,
Rj is the expected return of the jth
asset,
m is the total number of assets in the portfolio.
m
j=1
Portfolio (Expected) Return
35. Portfolio Risk: Standard
Deviation
• Standard deviation = √ variance
• Variance of the portfolio (2-security case)
σσ22
PP = ω= ω22
xxσσ22
xx + ω+ ω22
yyσσ22
yy +2ω+2ωxxωωyyσσxxσσyyCorCorxyxy
36. m
j=1
m
k=1
σσPP = Σ Σ Wj Wkσjk
Wj is the weight for the jth
asset in the portfolio,
Wkis the weight for the kth
asset in the portfolio,
σjkis the covariance between returns for the jth
and
kth
assets in the portfolio.
Portfolio Risk: Standard
Deviation
37. σσ jk = σ jσ k rr jk
σjis the standard deviation of the jth
asset in the
portfolio,
σkis the standard deviation of the kth
asset in the
portfolio,
rjkis the correlation coefficient between the jth
and
kth
assets in the portfolio.
What is Covariance?
39. TotalTotal
RiskRisk
Unsystematic riskUnsystematic risk
Systematic riskSystematic risk
STDDEVOFPORTFOLIORETURN
NUMBER OF SECURITIES IN THE PORTFOLIO
Factors such as changes in nation’s
economy, tax reform, Inflation
or a change in the world situation.
Total Risk = Systematic Risk +
Unsystematic Risk
40. TotalTotal
RiskRisk
Unsystematic risk or DiversifiableUnsystematic risk or Diversifiable
Systematic risk or Non-DiversifiableSystematic risk or Non-Diversifiable
STDDEVOFPORTFOLIORETURN
NUMBER OF SECURITIES IN THE PORTFOLIO
Factors unique to a particular company
or industry. For example, the death of a
key executive or loss of a govt. contract.
Total Risk = Systematic Risk +
Unsystematic Risk
41. CAPM is a model that describes the
relationship between risk and expected
(required) return; in this model, a security’s
expected (required) return is the risk-free raterisk-free rate
plus a premiuma premium based on the systematic risksystematic risk
of the security.
Capital Asset Pricing Model
(CAPM)
42. CAPM: Expected Return
• The expected rate of return of a security:
Expected return = Risk-free rate + Risk premium
Risk premium =(Mkt return – Risk-free rate) x Beta
Ri= Rf + (Rm – Rf) βi
βi= COVim/ σ2
m
Ri= αi + βiRm + εI(Characteristic Regression
Line)
43. 1. Capital markets are efficient.
2. Homogeneous investor expectations
over a given period.
3. Risk-freeRisk-free asset return is certain
(use short- to intermediate-term
Treasuries as a proxy).
4. Market portfolio contains only
systematic risksystematic risk (use SENSEX or similar as a
proxy).
CAPM Assumptions
44. An index of systematic risksystematic risk.
It measures the sensitivity of a stock’s
returns to changes in returns on the market
portfolio.
The betabeta for a portfolio is simply a
weighted average of the individual stock
betas in the portfolio.
What is Beta?
45. Beta Calculation
Beta =
N ΣXY – (Σ X) (ΣY)
N ΣX2
– (ΣX)2
Where
X = return of market
Y = return of stock
