Cycle 6 PM Session 4.ppt

PAN African e-Network Project
MFM
Portfolio Management
Semester – IV
Session - 4
By – Suraj Prakash

REVIEW OF LAST LECTURE
• Single Index Model
• Efficient Market Hypothesis
• Portfolio Management Framework
• Introduction to portfolio revision and
rebalancing

CONTENTS
• Portfolio Revision, rebalancing contd…
• Performance Measurement
• Performance Evaluation of Mutual Funds
• Problems with Performance Measurement

Constant Proportion
Portfolio Insurance
• A constant proportion portfolio
insurance (CPPI) strategy requires the
manager to invest a percentage of the
portfolio in stocks:
$ in stocks = Multiplier x (Portfolio value – Floor value)

Constant Proportion
Portfolio Insurance (cont’d)
Example
A portfolio has a market value of $2 million. The
investment policy statement specifies a floor value of
$1.7 million and a multiplier of 2.
What is the dollar amount that should be invested in
stocks according to the CPPI strategy?

Constant Proportion
Example (cont’d)
Solution: $600,000 should be invested in stock:
$ in stocks = 2.0 x ($2,000,000 – $1,700,000)
= $600,000
If the portfolio value is $2.2 million one quarter later,
with $650,000 in stock, what is the desired equity
position under the CPPI strategy? What is the ending
asset mix after rebalancing?

Constant Proportion
Example (cont’d)
Solution: The desired equity position after one
quarter should be:
$ in stocks = 2.0 x ($2,200,000 –
$1,700,000)
= $1,000,000
The portfolio manager should move $350,000 into
stock. The resulting asset mix would be:
$1,000,000/$2,200,000 = 45.5%

Rebalancing Within the
Equity Portfolio
• Constant proportion
• Constant beta
• Change the portfolio components
• Indexing

Constant Proportion
• A constant proportion strategy within an
equity portfolio requires maintaining the
same percentage investment in each stock
• Constant proportion rebalancing requires
selling winners and buying losers

Constant Proportion (cont’d)
Example
A portfolio of three stocks attempts to invest approximately one
third of funds in each of the stocks. Consider the following
information:
Stoc
k
Price Shares Value % of Total Portfolio
FC 22.00 400 8,800 31.15
HG 13.50 700 9,450 33.45
YH 50.00 200 10,000 35.40
Total $28,25
0
100.00

Constant Beta Portfolio
• A constant beta portfolio requires maintaining
the same portfolio beta
• To increase or reduce the portfolio beta, the
portfolio manager can:
– Reduce or increase the amount of cash in the
portfolio
– Purchase stocks with higher or lower betas than the
target figure
– Sell high- or low-beta stocks
– Buy high- or low-beta stocks

Change the
Portfolio Components
• Changing the portfolio components is
another portfolio revision alternative
• Events sometimes deviate from what the
manager expects:
– The manager might sell an investment turned
sour
– The manager might purchase a potentially
undervalued replacement security

Indexing
• Indexing is a form of portfolio management that
attempts to mirror the performance of a market
index
– E.g., the S&P 500 or the DJIA
• Index funds eliminate concerns about
outperforming the market
• The tracking error refers to the extent to which
a portfolio deviates from its intended behavior

Window Dressing
• Window dressing refers to cosmetic
changes made to a portfolio near the end
of a reporting period
• Portfolio managers may sell losing stocks
at the end of the period to avoid showing
them on their fund balance sheets

Contributions to the Portfolio
• Periodic additional contributions to the
portfolio from internal or external sources
must be invested
• Dividends:
– May be automatically reinvested by the fund
manager’s broker
– May have to be invested in a money market
account by the fund manager

When Do You Sell Stock?
• Introduction
• Rebalancing
• Upgrading
• Sale of stock via stop orders
• Extraordinary events
• Final thoughts

Rebalancing
• Rebalancing can cause the portfolio
manager to sell shares even if they are not
doing poorly
• Profit taking with winners is a logical
consequence of portfolio rebalancing

Upgrading
• Investors should sell shares when their
investment potential has deteriorated to
the extent that they no longer merit a place
in the portfolio
• It is difficult to take a loss, but it is worse to
let the losses grow

Change in Client Objectives
• The client’s investment objectives may
change occasionally:
– E.g., a church needs to generate funds for a
renovation and changes the objective for the
endowment fund from growth of income to
income
• Reduce the equity component of the portfolio

Change in Market Conditions
• Many fund managers seek to actively time
the market
• When a portfolio manager’s outlook
becomes bearish, he may reduce his
equity holdings

Introduction
• Performance evaluation is a critical aspect
of portfolio management
• Proper performance evaluation should
involve a recognition of both the return and
the riskiness of the investment

Introduction
• As portfolio managers, how can we evaluate the
performance of our portfolio?
• We know that there are 2 major requirements of
a portfolio manager’s performance:
1. The ability to derive above-average returns
conditioned on risk taken, either through
superior market timing or superior security
selection.
2. The ability to diversify the portfolio and
eliminate non-systematic risk, relative to a
benchmark portfolio.

PERFORMANCE EVALUATION RATE OF
RETURN METHODS
1. ARITHMETIC MEAN
2. IRR
3. GEOMETRIC MEAN

Example
Year Market value of
the portfolio
(Rs)
Dividend and
interest income
(Rs)
Rate of return
0 100,000
1 105,000 10,000 10,000 + (105,000 – 100,000)
= 15%
100,000
2 95,000 10,000 10,000 + (95,000 – 105,000)
= 0.0%
105,000
3 120,000 10,000 10,000 + (120,000 – 95,000)
= 36.8%
95,000
4 140,000 12,000 12,000 + (140,000 – 120,000)
= 26.7%
120,000
5 150,000 12,000 12,000 + (130,000 – 140,000)
= 15.7%
140,000

A.M : (15.0 + 0.0 + 36.8 + 26.7 + 15.7) / 5 = 18.8%
10,000 10,000 10,000 12,000 12,000 +
150,000
IRR :100000 = + + + +
(1+r) (1+r)2 (1+r)3 (1+r)4 (1+r)5
r ≃ 17.65%
GM : [ (1.15) (1.00) (1.368) (1.267) (1.157)] 1/5 - 1 ≃ 18.2%
Example

IRR
PERIOD
1 2 3 4
RATE OF RETURN EARNED 10% 30% 20% -
PORTFOLIO A
1. BEGINNING VALUE BEFORE
INFLOW OR OUTFLOW 10,000 11,000 14,300 17,160
2. INFLOW (OUTFLOW) - - - (17,160)
3. AMOUNT INVESTED 10,000 11,000 14,300 -
4. ENDING VALUE 11,000 14,300 17,160 -
PORTFOLIO B
1. BEGINNING VALUE BEFORE
INFLOW OR OUTFLOW 10,000 11,000 3,900 4,680
2. INFLOW (OUTFLOW) - (8,000) - (4,680)
3. AMOUNT INVESTED 10,000 3,000 3,900 -
4. ENDING VALUE 11,000 3,900 4,680 -
17,160
A : 10,000 = r = 19.72%
(1+r)3
8,000 0 4680
B : 10,000 = + + r = 15.27%
(1+r) (1+r)2 (1+r)3
IRR REFLECTS INVESTMENT PERFORMANCE AS WELL AS THE EFFECT OF CONTRIBUTIONS AND
WITHDRAWALS .. TOTAL EXPERIENCE OF A FUND (a) INVESTMENET PERFORMANCE & (b) CASH
FLOWS.
G.M : [(1.10) (1.30) (1.20)] 1/3 - 1 = 0.1972 OR 19.72%

• Sharpe and Treynor measures
• Jensen measure (Alpha)
• Performance measurement in practice
Traditional
Performance Measures

Security Market Line based
Performance Measures
• Treynors ratio
• Jensens ratio (Alpha)

Treynor Portfolio Performance
Measure

A risk-adjusted measure of return that divides a
portfolio's excess return by its beta.
• The Treynor Measure is given by
Treynor Measure
The Treynor Measure is defined using the average rate of return
for portfolio p and the risk-free asset.
p
f
p
p
r
R
=
T



Treynor Index
• Treynor’s Index is the slope of a straight line
going through the risk-free rate of return. The
Treynor Index may also be defined as the risk
premium earned per unit of risk taken, where beta
is the risk measure.
• Evaluation of Past Returns:

The Treynor Index:
A Graphical Illustration
-2.5
2.5
7.5
12.5
17.5
22.5
0 0.5 1 1.5 2 2.5
Expected Return
Beta Coefficient
A
B
C
SML
TA > TB > TC

Treynor Measure
A larger Tp is better for all investors, regardless of
their risk preferences.
Because it adjusts returns based on systematic risk, it is
the relevant performance measure when evaluating
diversified portfolios held in separately or in
combination with other portfolios.
p
f
p
p
r
R
=
T



Treynor Measure
• Beta measures systematic risk, yet if the portfolio is not
fully diversified then this measure is not a complete
characterization of the portfolio risk.
• Hence, it implicitly assumes a completely diversified
portfolio.
• Portfolios with identical systematic risk, but different total
risk, will have the same Treynor ratio!
• A portfolio negative Beta will have a negative Treynor
measure.

Jensen Portfolio Performance
Measure

• Alpha is a risk-adjusted measure of superior
performance
• This measure adjusts for the systematic risk of
the portfolio.
• Positive alpha signals superior risk-adjusted
returns, and that the manager is good at
selecting stocks or predicting market turning
points.
Jensen’s Alpha
  t
p
t
f
p
p r ,
,
t
M,
t
f,
t
p, R
r
R 

 





• Alpha represents the return differential
between the return of the portfolio and the
return predicted by the CAPM adjusted for
the systematic risk of portfolio (p).
• Unlike the Sharpe Ratio, Jensen’s method
does not consider the ability of the
manager to diversify, as it is only accounts
for systematic risk.
Jensen’s Alpha

The Treynor Ratio and Jensen's Alpha are related
to the systematic risk component implied by the
Sharpe-Lintner Model. There are 2 problems
with the application of these two performance
measures:
1) Is the systematic risk the appropriate risk
measure for an investor?
2) Does the Sharpe-Lintner Model regard all
relevant information in predicting a securities or
portfolios expected return?
Jensen’s Alpha

Capital-market-line based performance
measures
• The sole measure of risk is total risk which
is equivalent to the statistical measure of
standard deviation or σ. The two traditional
measures based thereon are the Sharpe
Ratio and the RAP (Risk-Adjusted
Performance) measure.

Sharpe Portfolio Performance
Measure

• Similar to the Treynor measure, but uses the
total risk of the portfolio, not just the
systematic risk.
• The Sharpe Ratio is given by
• The larger the measure the better, as the
portfolio earned a higher excess return per
unit of total risk.
Sharpe Measure
p
f
p
p
r
R
=
S



Sharpe Measure
It adjusts returns for total portfolio risk, as opposed
to only systematic risk as in the Treynor
Measure.
Thus, an implicit assumption of the Sharpe ratio is
that the portfolio is not fully diversified, nor will it
be combined with other diversified portfolios.
It is relevant for performance evaluation when
comparing mutually exclusive portfolios.
Sharpe originally called it the "reward-to-variability"
ratio, before others started calling it the Sharpe
Ratio.

• Treynor’s measure uses Beta and hence examines
portfolio return performance in relation to the SML.
• Sharpe’s measure uses total risk and hence examines
portfolio return performance in relation to the CML.
• For a totally diversified portfolio, both measures give
equal rankings.
• If it is not a diversified portfolio, the Sharpe measure
could give lower rankings than the Treynor measure.
• Thus, the Sharpe measure evaluates the portfolio
manager in terms of both return performance and
diversification.
Comparison of Sharpe and Treynor

Comparison of Sharpe and Treynor
Sharpe and Treynor measures are similar in a way, since
they both divide the risk premium by a numerical risk
measure. The total risk is appropriate when we are
evaluating the risk return relationship for well-diversified
portfolios. On the other hand, the systematic risk is the
relevant measure of risk when we are evaluating less
than fully diversified portfolios or individual stocks. For a
well-diversified portfolio the total risk is equal to
systematic risk. Rankings based on total risk (Sharpe
measure) and systematic risk (Treynor measure) should
be identical for a well-diversified portfolio, as the total
risk is reduced to systematic risk. Therefore, a poorly
diversified fund that ranks higher on Treynor
measure, compared with another fund that is highly
diversified, will rank lower on Sharpe Measure.

Price of Risk
• Both the Treynor and Sharp measures, indicate
the risk premium per unit of risk, either
systematic risk (Treynor) or total risk (Sharpe).
• They measure the price of risk in units of excess
returns per each unit of risk (measured either by
beta or the standard deviation of the portfolio).
T
=
r
R p
p
f
p 

p
p
f
p S
r
R 



Information Ratio
• Using a historical regression, the IR takes on the
form
• where the numerator is Jensen’s alpha and the
denominator is the standard error of the
regression. Recalling that
Note that the risk here is nonsystematic risk, that could, in theory,
be eliminated by diversification.


 p
p
IR 
  t
p
t
f
p
p r ,
,
t
M,
t
f,
t
p, R
r
R 

 





Information Ratio
• Excess return represents manager’s ability to use
information and talent to generate excess returns.
• It is a ratio of portfolio returns above the returns of a
benchmark (usually an index) to the volatility of those
returns. The information ratio (IR) measures a portfolio
manager's ability to generate excess returns relative to a
benchmark, but also attempts to identify the consistency
of the investor. This ratio will identify if a manager has
beaten the benchmark by a lot in a few months or a little
every month. The higher the IR the more consistent a
manager is and consistency is an ideal trait.
ER
b
p
p
R
R
=
IR



• A high IR can be achieved by having a high return in the
portfolio, a low return of the index and a low tracking
error.
For example:
Manager A might have returns of 13% and a tracking
error of 8%
Manager B has returns of 8% and tracking error of 4.5%
The index has returns of -1.5%
Manager A's IR = [13-(-1.5)]/8 = 1.81
Manager B's IR = [8-(-1.5)]/4.5 = 2.11
Manager B had lower returns but a better IR. A high ratio
means a manager can achieve higher returns more
efficiently than one with a low ratio by taking
on additional risk. Additional risk could be achieved
through leveraging.
Information Ratio

• The information ratio is often used to gauge the skill
of managers of mutual funds, hedge funds, etc. In
this case, it measures the active return of the
manager's portfolio divided by the amount of risk
that the manager takes relative to the benchmark.
The higher the information ratio, the higher the active
return of the portfolio, given the amount of risk taken,
and the better the manager. Top-quartile investment
managers typically achieve information ratios of about
one-half.1 There are both ex ante expected and ex post
observed information ratios.
• Generally, the information ratio compares the returns of
the manager's portfolio with those of a benchmark such
as the yield on three-month Treasury Bills or an equity
index such as the S&P 500.
Information Ratio

• The information ratio is similar to the Sharpe ratio but,
whereas the Sharpe ratio is the 'excess' return of an
asset over the return of a risk free asset divided by the
variability or standard deviation of returns, the
information ratio is the 'active' return to the most relevant
benchmark index divided by the standard deviation of
the 'active' return or tracking error.
• Some hedge funds use Information ratio as a metric for
calculating a performance fee.
• One of the main criticisms of the Information Ratio is that
it considers arithmetic returns and ignores leverage. This
can lead to the Information Ratio calculated for a
manager being negative when the manager produces
alpha to the benchmark and vice-versa. A better
measure of the alpha produced by the manager is the
Geometric Information Ratio.3
Information Ratio

Fama Model
• The Eugene Fama model is an extension of Jenson
model. This model compares the performance,
measured in terms of returns, of a fund with the required
return commensurate with the total risk associated with
it. The difference between these two is taken as a
measure of the performance of the fund and is called
net selectivity.
• The net selectivity represents the stock selection skill of
the fund manager, as it is the excess return over and
above the return required to compensate for the total risk
taken by the fund manager. Higher value of which
indicates that fund manager has earned returns well
above the return commensurate with the level of risk
taken by him.

• Required return can be calculated as: Ri = Rf +
Si/Sm*(Rm - Rf)
• Where, Sm is standard deviation of market
returns. The net selectivity is then calculated by
subtracting this required return from the actual
return of the fund.
Fama Model

The Fama-French Three Factor Model
• The Fama-French Three Factor Model is used to explain
differences in the returns of diversified equity portfolios.
It's a model that compares a portfolio to three distinctive
types of risk found in the equity market to assist in
categorizing returns. Prior to the three-factor model, the
Capital Asset Pricing Model (CAPM) was used as a
"single factor" way to explain portfolio returns.
• However, several shortcomings of the CAPM model exist
when compared to realized returns, and the affect of
other risk factors have put this model under criticism.
The assumption of a single risk factor limits the
usefulness of this model.

• In June 1992, Eugene F. Fama and Kenneth R. French published a
paper that found that on average, a portfolio’s beta only explains
about 70% of its actual returns. For example, if a portfolio was up
10%, about 70% of the return can be explained by the advance of all
stocks and the other 30% is due to other factors not related to beta.
• "Beta," the measure of market exposure of a given stock or portfolio,
which was previously thought to be the be-all/end-all measurement
of stock risk/return, is of only limited use. Fama/French showed that
this parameter did not explain the returns of all equity portfolios,
although it is still useful in explaining the return of stock/bond and
stock/cash mixes.
• The return of any stock portfolio can be explained almost entirely by
two factors: Market cap ("size") and book/market ratio ("value").
Therefore, a portfolio with a small median market cap and a high
book/market ratio will have a higher expected return than a portfolio
with a large median market cap and a low book/market ratio

• To represent the market cap ("size") and
book/market ratio ("value") returns, Fama and
French modified the original CAPM with two
additional risk factors: size risk and value risk.
• The Fama and French equation:
– E(rA) = r(f) + βA(E(rm) - rf) + sASMB + hAHML
• where SMB is the "Small Minus Big" market capitalization
risk factor and
• HML is the "High Minus Low" value premium risk factor
• SMB, Small Minus Big, measures the additional
return investors have historically received by
investing in stocks of companies with relatively
small market capitalization. This additional
return is often referred to as the “size premium.”

• HML, which is short for High Minus Low, has been
constructed to measure the “value premium” provided to
investors for investing in companies with high book-to-
market values (essentially ,the value placed on the
company by accountants as a ratio relative to the value
the public markets placed on the company, commonly
expressed as B/M). (Note terminology usage as
mentioned above.)
• The key point of the model is that it allows investors to to
weight their portfolios so that they have greater or lesser
exposure to each of the specific risk factors, and
therefore can target more precisely different levels of
expected return.

• A factor model that expands on the capital
asset pricing model (CAPM) by adding size and
value factors in addition to the market risk factor
in CAPM. This model considers the fact that
value and small cap stocks outperform markets
on a regular basis. By including these two
additional factors, the model adjusts for the out
performance tendency, which is thought to make
it a better tool for evaluating manager
performance

• One powerful feature of the Three Factor Model is that it
provides a way to categorize mutual funds by size and
value risks, and therefore predict expected return
premiums. This classification provides two main benefits.
Classifying funds into style buckets
• Funds (and their fund managers) can be compared by
placing them in specific "buckets" based on the style of
asset allocation chosen in their portfolios. For this
purpose, funds are often plotted on a 3x3 matrix,
demonstrating the relative amount of risk represented by
different strategies.
• The mutual fund rating company Morningstar is the
biggest resource for classification. Funds are separated
horizontally into three groups through a B/M ranking
(value ranking) and vertically based on a ranking of
market capitalization (size ranking).

Relevance of various models
• Among the above performance measures, two
models namely, Treynor measure and Jenson
model use systematic risk based on the premise
that the unsystematic risk is diversifiable.
• These models are suitable for large investors
like institutional investors with high risk taking
capacities as they do not face paucity of funds
and can invest in a number of options to dilute
some risks. For them, a portfolio can be spread
across a number of stocks and sectors.

However, Sharpe measure and Fama model that consider
the entire risk associated with fund are suitable for small
investors, as the ordinary investor lacks the necessary
skill and resources to diversified. Moreover, the selection
of the fund on the basis of superior stock selection ability
of the fund manager will also help in safeguarding the
money invested to a great extent. The investment in
funds that have generated big returns at higher levels of
risks leaves the money all the more prone to risks of all
kinds that may exceed the individual investors' risk
appetite
Relevance of various models

Which Portfolio is Best?
• It depends.
• If P or Q represent the entire portfolio, Q would
be preferable based on having higher sharp ratio
and a better M2.
• If P or Q represents a sub-portfolio, the Q would
be preferable because it has a higher Treynor
ratio.
• For an actively managed portfolio, P may be
preferred because it’s information ratio is larger
(that is it maximizes return relative to
nonsystematic risk, or the tracking error).

Performance Evaluation
of Mutual Funds

Evaluating fund managers
As shown, the Three-Factor Model allows classification of
mutual funds and enables investors to choose exposure
to certain risk factors. This model can be extended to
measure historical fund manager performance to
determine the amount of value added by management.
• A new variable, alpha ("α") is added to the equation and
the terms rearranged in a form that can be used for
regression analysis.
– E(rA) - r(f) = α + βA(E(rm) - rf) + sASMB + hAHML
• where α is "effective return" as defined in the
CAPM equation
• Historical data is utilized in a multivariate regression
analysis to determine the value of alpha. A positive alpha
indicates that the fund manager is adding to the value of
the portfolio versus a result of exposure to the HML or
SMB factors. In other words, the three-factor model can
help determine the effectiveness of a fund manager.

ANNUAL RETURNS FOR THREE MUTUAL FUNDS AND A
MARKET INDEX

PERFORMANCE EVALUATION OF
THE THREE FUNDS
Rp - Rf
TREYNOR MEASURE :
p
17.1 - 8.6
FUND A : = 7.1
1.20
14.5 - 8.6
FUND B : = 4.9
0.92
13.0 - 8.6
FUND C : = 4.8
1.04
11.0 - 8.6
MARKET INDEX : = 2.4
1.0

Rp - Rf
SHARPE MEASURE :
p
17.1 - 8.6
FUND A : = 0.302
28.1
14.5 - 8.6
FUND B : = 0.299
19.7
13.0 - 8.6
FUND C : = 0.193
22.8
11.0 - 8.6
MARKET INDEX : = 0.117
20.5
JENSEN MEASURE : Rp - [Rf + p (RM - Rf )]
FUND A : 17.1 - [8.6 + 1.20 (2.4)] = 5.62
FUND B : 14.5 - [8.6 + 0.92 (2.4)] = 3.69
FUND C : 13.0 - [8.6 + 1.04 (2.4)] = 1.90
MARKET INDEX : O (BY DEFINITION)

PROBLEMS WITH
PERFORMANCE
MEASUREMENT

•QUANTIFICATION .. FUNCTION ONLY PARTLY
AMENABLE
• SHORT-TERMISM
• CULT OF MARKET-TIMING
•DIETZ & KIRSCHMAN: “FOR ACCURACY OF
COMPUTATIONS, PERFORMANCE SHOULD BE
COMPUTED AS OFTEN AS PRACTICED, BUT RESULTS
SHOULD NOT BE TAKEN AS SIFNIFICANT BY THE
INVESTOR OR THE INVESTMENT MANAGER UNTILA
REASONABLE PERIOD OF TIME, SUCH AS A MARKET
CYCLE FOR EQUITIES OR AN INTEREST RATE CYCLE
FOR FIXED INCOME SECURITIES, HAS ELAPSED”

SUMMING UP
• Portfolio management is a complex process or activity that may
be divided into seven broad phases.
• Investment objectives are expressed in terms of return and risk.
• The strategic asset-mix decision (or policy asset-mix decision) is
the most important decision made by the investor.
• Investors with greater tolerance for risk and longer investment
horizon should tilt the asset mix in favour of stocks
• The four principal vectors of an active portfolio strategy are :
market timing, sector rotation, security selection, and the use of
a specialised concept.
• A passive portfolio strategy calls for creating a well-diversified
portfolio at a pre-determined level of risk and holding it
relatively unchanged over time.

• The factors commonly considered in selecting bonds are : yield
to maturity, risk of default, tax shield, liquidity, and duration.
• Three broad approaches are employed for stock selection :
technical analysis, fundamental analysis, and random selection.
• Motives of trading are cognitive and emotional.
• Portfolio revision involves portfolio rebalancing and portfolio
upgrading
• The key dimensions of performance evaluation are rate of
return and risk.
• Treynor measure, Sharpe measure, and Jensen measure are
three popularly employed performance measures.
SUMMING UP

Thank You
Please forward your query
To:surajamity@yahoo.com

Cycle 6 PM Session 4.ppt

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