This slide discuss about the risk,return, CAPM, APT, Sharpe Ratio, Treynor Ratio, Fama decomposition etc. it has lots of charts for support.

1. Security Analysis
&
Portfolio Management
Muruganandan. S
Assistant Professor
Department of Humanities
PSG College of Technology
Coimbatore

2. Risk
Risk is the deviation from expected return
What is expected Return?
Historical average return
What is Deviation and How to measure?
Standard deviation of the return

3. Components of Risk
Total Risk = Systematic Risk + Unsystematic Risk

4. Systematic Risk
The portion of an individual asset’s total
variance attributable to the variability of the
total market.
In other words, the changes in the price of the
security is due to changes in the market factor
i.e. Macroeconomic factors like interest rate,
inflation etc..

5. Unsystematic risk
• When variability of the return occurs due to
such firm known as firm specific risk or
unsystematic risk
• This may be due to
1. Operating environment of the company (Business
risk)
2. Financing pattern adopted by the company (financial
risk)

6. Portfolio Means
Group of Securities held together is called
Portfolio
Diversification
The process of creating portfolio is called as
diversification
It is an attempt to minimise the RISK

7. Diversification of Risk

8. Optimum Portfolio Means….
 A Number of portfolio can be constructed from the given
securities
 Rational investors attempt to find efficient
portfolio/Optimal portfolio
 Efficient/ Optimal Portfolio: A portfolio which gives
maximum return for given level of risk or minimum risk for
given level of return.

9. Feasible set of portfolio
• With limited securities – construct large
number of portfolio by altering the proportion
of investments..
• This is known as portfolio opportunity set….
• Each portfolio in opportunity set has expected
return & risk
Portfolio No A B
1 10% 90%
2 20% 80%
3 50% 50%
4 40% 60%

10. Efficient set of portfolio
• Not all portfolio in opportunity set likes the
investors….. Because
• All portfolio in opportunity set will not give
the……..
Highest return for given level of risk & low risk for given
level of return
The portfolio which gives the highest return for
given level of risk or low risk for given level of
return is known as Efficient portfolio…

11. Expected return and SD of some
portfolio

12. Feasible set of portfolio
North-West Boundary of shaded area are more
efficient than any other portfolio

13. Efficient frontier
• The shaded boundary is call Efficient frontier
• The efficient frontier is a concave curve in the
risk-return space that extends from the
minimum variance to maximum return

14. • risk averse investors like to hold the portfolio in lower left hand
segment
• Risk takers hold the portfolio in upper portion of the efficient
portfolio.
• The optimal portfolio for an investor would be one at the point
of tangency B/w Efficient Frontier and indifference curve.

15. Limitation of the Markowitz model
• Large number of data
• Complexity in computation required
• Little use in practical
So, index model is introduced

16. Single index model
All stocks are affected by the movement in stock market
The co-movement of the stock may studied with the help
of Regression Analysis
Market goes down - most share price goes down vice
versa Hence return of the security may be calculated by
𝑅𝑖 = 𝛼𝑖 + 𝛽𝑖 𝑅 𝑚 + 𝜀𝑖
Where
𝑅𝑖 is return of security I
𝑅 𝑚 is the return of market index
𝛼𝑖 is component of the security return that is independent to
market performance.
𝛽𝑖 is the constant the measure the expected changes in the Ri
given changes in 𝑅 𝑚
𝜀𝑖 is the error term

17. Return & Risk under single index model
𝑅𝑖 = 𝑎𝑖 + 𝐵𝑖 𝑅 𝑚
Return of the security is combination of two component
i.e. 𝑎𝑖 specific return component and market related
return component 𝐵𝑖 𝑅 𝑚
Total risk = market related risk + Specific risk
𝜎𝑖
2
= 𝛽2
𝜎2
𝑚 + 𝜎𝑒𝑖
2
𝜎𝑖
2 = variance of the security
𝛽 beta coefficient of individual security
𝜎𝑒𝑖
2 = variance of residual return
𝜎 𝑚
2
= variance of market return

18. Multi-index model
𝑅𝑖 = 𝛼𝑖 + 𝛽𝑖 𝑅 𝑚 + 𝛽1 𝐹𝑖 + 𝛽2 𝐹2 + 𝜀𝑖
The changes in the return of the security is
based on the two additional factor eg. Interest
rate and inflation
This model try to identify non-market factors
that cause security to move together also into
the model

19. How to interpret the single index model
𝑅 𝑝 = 2.3 + 0.85𝑅 𝑚 + 𝜀 𝑝
For each unit of changes in the market return the
security return will incorporate 0.85 per cent
changes.
But, the security itself gives the return of 2.3 per
cent.
If 𝑅 𝑚 is +1 then the 𝑅 𝑝 = 2.3 +0.85= 3.15
if 𝑅 𝑚 is -1 then the Rp = 2.3-0.85= 1.45
β < 1= lower sensitive to the market
β>1= higher sensitive to the market
β value of the market is always one

20. CAPM
• Extension of the Markowitz model
• It includes the risk free assets.
Assumptions:
 Investors are risk averse individuals who maximize the expected utility of
their end of period wealth.
 Investors have homogenous expectations (beliefs) about asset returns
 Asset returns are distributed by the normal distribution
 There exists a risk free asset and investors may borrow or lend unlimited
amounts of this asset at a constant rate
 All assets are perfectly divisible and priced in a perfectly competitive
marked.
 Information available to all investors at free of cost
 All investors are price takers

21. Efficient Frontier (EF) with Risk free
Assets
• Portfolio theory deals with risky assets
• But, RF also available, then what is RF.
• Risk free asset is one whose return are certain like
Government Security.
• Variability of that security is ZERO
• Investor can include this RF with his portfolio.
• The efficient frontier arising from a feasible set of
portfolio of risky asset is concave in shape.
• When the riskless security included into the portfolio
the shape of EF transform into a straight line

22. Tangent

23. Risk-Return with Leverage
Return of the portfolio with RF
𝑅 𝑝𝑜𝑟𝑡𝑓𝑜𝑖𝑙𝑖𝑜 = 𝜔𝑅 𝑟𝑖𝑠𝑘𝑦 𝑠𝑒𝑐𝑢𝑟𝑖𝑡𝑦 + 1 − 𝜔 𝑅𝐹
Risk of the portfolio with RF
𝜎 𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 = 𝜔𝜎𝑟𝑖𝑠𝑘𝑦 𝑠𝑒𝑐. + (1 − 𝜔)𝜎𝑟𝑓
But the SD of Rf is Zero hence
𝜎 𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 = 𝜔𝜎𝑟𝑖𝑠𝑘𝑦 𝑠𝑒𝑐.
If ω = 1; fully invested in risky assets
If ω < 1; fraction of the fund invested in risky asset
and remaining invested in risk free assets
If ω > 1; borrowed at the risk free rate and invested
in risky assets

24. EF with Risk less Lending and Borrowing

25. Security Market line
Total risk = Systematic Risk + Unsystematic risk
In well diversified portfolio, unsystematic risk tends
to become zero.
Hence, only the relevant risk is systematic risk. i.e
market risk which is measured by β
𝑅𝑖 = 𝑅𝑓 + 𝛽𝑖( 𝑅 𝑚 − 𝑅𝑓)
Rf is reward for Waiting
( 𝑅 𝑚 − 𝑅𝑓) Reward for taking the risk is called as
risk premium

26. SML
• A risk free asset has an expected return equivalent to RF with
zero beta
• The market portfolio M has a beta coefficient of 1
• A straight line joint these two point is known as Security
Market Line

27. CAPM
The relationship between risk and return
established by the security line is known as the
capital asset pricing model.
𝑅𝑖 = 𝑅𝑓 + 𝛽𝑖( 𝑅 𝑚 − 𝑅𝑓)

28. Pricing of Security with CAPM

29. Relaxing the Assumption
Differential Borrowing and Lending

30. Zero Beta Model
• If the market portfolio (M) is mean-variance
efficient (i.e., it has the lowest risk for a given
level of return among the attainable set of
portfolios), an alternative model, derived by
Black, does not require RFR.
• Within the set of feasible alternative portfolios,
several portfolios exist where the returns are
completely uncorrelated with the market
portfolio.
• The beta of these portfolios with the market
portfolio is zero.

31. Zero beta …..
• Among several Zero-beta portfolio you should select
the one with minimum variance.
• This zero beta portfolio does not have Systematic risk
• But it have unsystematic risk
• The combinations of this zero-beta portfolio and the
market portfolio will be a linear relationship in return
and risk.
• Covariance between zero beta portfolio and market
portfolio is similar to mkt portfolio Vs RFR
• Assuming that the return on ZERO beta portfolio is
greater than the RFR
• Then the equation for ZERO-BETA portfolio CAPM is
𝐸(𝑅𝑖) = 𝐸(𝑅 𝑧) + 𝛽𝑖[𝐸(𝑅 𝑚) − 𝐸(𝑅 𝑧)]

32. Zero beta Portfolio

33. If there is a transaction cost

34. Empirical tests of CAPM
• The theory should not be judged on the basis of
its assumptions
• But, how well it explains the relationships that
exist in the real world.
• When testing the CAPM there are two major
questions.
How stable is the measure of systematic risk (beta)?
Is there a positive linear relationship as hypothesized
between beta and the rate of return on risky assets?

35. Stability of Beta
• The risk measure was not stable for individual
stocks but the stability of the beta for
portfolios of stocks increased dramatically.
• Further, the larger the portfolio of stocks (e.g.,
over 50 stocks) and the longer the period (over
26 weeks), the more stable the beta of the
portfolio.
• How many month considered for the
calculation of the beta also play an important
role.

36. Stability of Beta
• Chen concluded that portfolio betas would be biased if
individual betas were unstable, so he suggested a Bayesian
approach to estimating these time-varying betas.
• Carpenter and Upton considered the influence of the
trading volume on beta stability and contended that the
predictions of betas were slightly better using the volume-
adjusted betas. This impact of volume on beta estimates is
related to small-firm effect which noted that the beta for
low-volume securities was biased downward as confirmed
by Ibbotson, Kaplan, and Peterson.20
• To summarize, individual betas were generally volatile over
time whereas large portfolio betas were stable. Also, it is
important to use at least 36 months of data to estimate
beta and be conscious of the stock’s trading volume and
size.

37. • Reilly and Wright examined over 1,100 securities
for three no overlapping periods and confirmed
the difference in beta found by Statman.
• They also indicated that the reason for the
difference was the alternative time intervals (i.e.,
weekly versus monthly observations) and the
security’s market value affected both the size and
the direction of the interval effect.
• Therefore, when estimating beta or using a
published source, you must consider the return
interval used and the firm’s relative size.

38. Relationship between Systematic risk
and return
• Effect of Skewness on the relationship
• Effect of size, B/E ratio and Leverage
• Effect of book to market value:
A study by Fama and French attempted to evaluate the
joint roles of market beta, size, E/P, financial leverage,
and the book-to-market equity ratio in the cross section
of average returns on the NYSE,AMEX, and Nasdaq
stocks

39. Why APT
• (1) markets are not particularly efficient for extended
periods of time or
• (2) market prices are efficient but there is something
wrong with the way the single-factor models such as
the CAPM measure risk.
• Hence, the academic community searched for an
alternative asset pricing theory to the CAPM that was
reasonably intuitive, required only limited
assumptions, and allowed for multiple dimensions of
investment risk.
• The result was ARBITRAGE PRICING THEORY (APT),
which was developed by Ross in the mid-1970s and has
three major assumptions

40. Assumptions of APT
1) Capital markets are perfectly competitive.
2) Investors always prefer more wealth to less wealth
with certainty.
3) The stochastic process generating asset returns can
be expressed as a linear function of a set of K risk
factors (or indexes).

41. Basics of APT
As the theory assumes that the stochastic process generating
asset returns can be represented as a K factor model of the form

42. Similar to the CAPM model, the APT assumes that the unique
effects (ei) are independent and will be diversified away in a
large portfolio.

43. Factor Models
• There are broadly three types of data that can
be employed in quantitative analysis of
financial problems: time series data, cross-
sectional data, and panel data.
Time series data
Time series data, as the name suggests, are data that have
been collected over a period of time on one or more
variables.
Time series data have associated with them a particular
frequency of observation or collection of data points.

45. Problems that could be tackled using
time series data
• How the value of a country’s stock index has
varied with that country’s macroeconomic
fundamentals
• How the value of a company’s stock price has
varied when it announced the value of its
dividend payment
• The effect on a country’s exchange rate of an
increase in its trade deficit

46. Cross-sectional data
• Cross-sectional data are data on one or more
variables collected at a single point in time. For
example, the data might be on:
A poll of usage of Internet stockbroking services
A cross-section of stock returns on the New York Stock
Exchange(NYSE)
A sample of bond credit ratings for UK banks.
• Problems that could be tackled using cross-
sectional data:
The relationship between company size and the return to
investing in its shares
The relationship between a country’s GDP level and the
probability that the government will default on its sovereign
debt.

47. Panel data
• Panel data have the dimensions of both time
series and cross-sections
• The daily prices of a number of blue chip
stocks over two years
Company Year Dividend
ABC 2013 50
2014 45
XYZ 2013 52
2014 48

48. Portfolio Revision
Portfolio Management Deals with:
1. Security Analysis
Each secretary has its own risk-return profile. Eg. Bond,
Shares, ADR and GDR etc.. Fundamental & Technical Analysis
2. Analysis and Selection of Portfolio
No of portfolio can be constructed by changing the
security or proportion of different security.
Different portfolio constructed first analysed and
selected the Optimal Portfolio.

49. Revision of Portfolio
Portfolio Management is continuous process .
Changes in Capital Market – Revision of Portfolio.
Replace the overpriced Security for Under priced
security
Evolution of portfolio
– Evaluation of Risk & Return of the portfolio over a
given period of time

50. Portfolio Revision Strategies
Constant Rupee Value Plan
 investors have two portfolio
 aggressive – equity
 conservative – bond and debentures
Keep the aggressive portfolio value as same
When equity price increase –
sold out the equity – invest in bond
When equity price fall –
sold out bond- invest in equity

51. Constant Ratio Plan
• Two portfolio constructed
– Aggressive portfolio
– Conservative Portfolio
• The ratio between the investment in
conservative and aggressive portfolio kept
constant
1:1
1:1.5

52. Dollar Cost Averaging
• Invest the constant sum of rupees on ever
particular interval in the particular share. Eg.
Every month Rs. 1500.
• Price fluctuation will be averaged due to
purchase the security at different p[rice both
up and low value.

53. Risk Adjusted Portfolio Performance
Measures
• Sharpe Ratio
• Treynor Ratio
• Jensen Measure
• Fama Decomposition of the total return.

54. Sharpe Ratio (Reward-to-Variability)
• Sharpe ratio is referred to as the reward to
variability ratio.
• It is the ratio of risk premium to the variability
of return/ risk as measured by the standard
deviation.
𝑆ℎ𝑎𝑟𝑝𝑒 𝑅𝑎𝑡𝑖𝑜 =
𝑟 𝑝−𝑟 𝑓
𝜎 𝑝

55. Treynor Ratio (Reward-to-volatility Ratio)
• The performance measure developed by Jack
Treynor is referred to as Treynor Ratio or
Reward to Volatility Ratio.
• It is the ratio of risk premium to the volatility
of return as measured by the portfolio.
𝑇𝑟𝑒𝑦𝑛𝑜𝑟 𝑅𝑎𝑡𝑖𝑜 =
𝑟 𝑝−𝑟 𝑓
𝛽 𝑝

56. Treynor Vs Sharpe Ratio
• Sharpe ratio use Standard Deviation as Measure
of Risk; Treynor ratio use Beta as a measure of
risk ….
• If the portfolio is well diversified (does not
contain any unsystematic risk) the two measures
gives identical ranking – because the total
variance of the portfolio is only the systematic
risk……
• If the portfolio is not well diversified, ranking
based on the Treynor ratio may higher, but much
lower ranking on the basis of Sharpe ratio.

57. Jensen Differential Measure
• The Jensen measure is based on the capital asset
pricing model (CAPM).
• All versions of the CAPM calculate the expected
one-period return on any security or portfolio by
the following expression
CAPM ------ E(𝑅 𝑝) = 𝑅𝑓 + 𝛽 𝑝(E(𝑅 𝑚) − 𝑅𝑓)
The differential Return Calculated as
𝛼 𝑝 = 𝑅 𝑝 − 𝐸(𝑅 𝑝)
This will apply in CAPM
𝐸(𝑅 𝑝) =𝑅 𝑝 − 𝛼 𝑝
𝑅 𝑝 − 𝛼 𝑝= 𝑅𝑓 + 𝛽 𝑝(E(𝑅 𝑚) − 𝑅𝑓)
𝑅 𝑝 − 𝑅𝑓= 𝛼 𝑝+ 𝛽 𝑝(E(𝑅 𝑚) − 𝑅𝑓) Final Jensen Model

58. Fama’s Decomposition of Performance
Total return = Risk free return + Excess Return
Excess Return = Risk Premium + Return from Stock
Selection
Risk Premium = Return for Bearing Systematic risk +
Return for bearing diversifiable
risk
Return on portfolio = Risk free return + Return for
Bearing Systematic risk +
Return for bearing
diversifiable risk + Return
from Stock Selection