L1 flashcards portfolio management (ss12)

The Portfolio Approach to Investing
Well Diversified Single Security
 Less likely to lose their
investment
 Reduce the total risk of a
portfolio
 Reduce overall portfolio
volatility
 Greater probability of losing
their investment
 Unsystematic risk
 Flat portfolio
Study Lesson 12, Reading 43

Types of Investors
 Individual Investors
 Short-term goals of individual investors can be children’s
education expenses, or lumpy purchases
 Long term goals can be retirement plans paid such as a
defined benefit contribution plan.
 Under a defined benefit contribution plan, the employee
receives a fixed cash pension payment at the time of
retirement

Types of Investors
 Institutional Investors
 Includes commercial banks, investment banks, insurance
companies, asset management companies, etc.
 Endowment funds by universities
 Banks invest in excess financial reserves

The Portfolio Management Process
An Investment Policy Statement maps out an investors needs
and restrictions. It is designed to allow investment advisors to
make investment recommendations which suit that particular
investor’s objectives.

Stages in Developing an
Investment Policy Statement
 Step 1: Planning. Understanding the client’s goals and
preparing the IPS.
 Step 2: Execution. Deciding the asset
allocation, undertaking security analysis, and portfolio
construction.
 Step 3: Feedback. Monitoring and rebalancing of
portfolio, measurement, and reporting performance.

Mutual Funds
 It is a pool of investment capital from individuals and
institutions that is managed by a fund manager.
 Two types of mutual funds: open-end and closed-end
 Open-end funds: when new investors invest by investing
capital with asset managers at the latest net asset value.
 Closed-end funds: when new investors can only gain
exposure to the fund by purchasing existing shares in the
fund from another investor.
 Mutual funds exist for investments in money
markets, bonds, stocks, and balanced funds.

Mutual Funds
 Money Market Funds: Investments in high-quality, short
term, corporate or government debt.
 Bond Funds: Invest in all types of rated debt from low to high
quality debt and does not have a maturity restriction.
 Stock Market Funds: Invest in a portfolio of equity securities.
Can be either Active or Passive
 Balanced Funds: Invest in a portfolio across a range of asset
classes and securities.

Measures of Investment Returns:
Calculating Returns
 The Holding Period Return of an investment in a single security
is calculated as:
Where: D is the dividend, P is the price, t-1 is the date of the
initial investment, and t is the date the investment is exited or
the measurement end date.

Calculating Returns
 The HPR of an investment over three years can be
calculated as:

Money Weighted Return
 The money weighted return weights the returns achieved by
each asset in a portfolio by the weight of capital invested in
each security. The formula is identical to the IRR formula:

Annualizing Returns
 Investors can annualize return measures using the following
formula:
 In the formula above, c is the number of periods in the
investment horizon. For example, if quarterly returns are being
annualized, c=4.

Returns of a Portfolio
 The return of a portfolio can be calculated by weighting
returns generated by the portfolio:
 Where w is the weight, R is the return, and i represents a
single security in the portfolio.

Arithmetic vs. Geometric Returns
 The arithmetic average of investment returns is simply the
mean of the returns over a number of periods.
 The geometric average returns need to be calculated over a
sequential period of investment.
 For example, assume the returns on an investment portfolio
over 5 periods were 90%, 10%, 20%, 30% and -90%. Using the
geometric average returns formula ([(1.9 x 1.1 x 1.2 x 1.3 x 0.1)
^ 1/5] – 1), the geometric return can be calculated as -20.1%.

Characteristics of Major Asset Classes
 Equities: Investing in equities or stocks is an investment in a
security representing an ownership interest in a business.
 Fixed Income: Fixed Income securities provide a return in the
form of fixed periodic payments (coupons) and the eventual
return of principal at maturity.
 Cash and Cash Equivalents: Assets such as cash or those that
can be converted into cash immediately

Geometric Mean Return
 Average of returns over a number of period.
 The geometric mean return can be calculated as:
 where is the return of period ‘t’ , and T is the total number of
periods.
 Gross return is the returns calculated before any deduction of
expenses is made and Net Return is what the investor
eventually earns after all the expenses are accounted for.

Variance of a Portfolio
 Variance is an indicator of the historical riskiness of returns of
a various asset. High variance in historic returns signals a high
risk investment.
 where R is return over period ‘t’, and T is the total number of
periods, while is average of T returns, supposing T represents
the population of returns.

 If a sample is provided, then the following formula is used to
calculate the sample variance:
 The Standard Deviation of an asset’s returns is square root of
the variance.

 The variance of portfolio can be calculated using the
following formula:
 Covariance measures the tendency for returns of two assets
to move in the same direction at the same time. It is
calculated using the following formula:

Risks Aversion and Its Implications
For Portfolio Selection
 Risk aversion is the willingness of an investor to accept risk in
the pursuit of higher returns.
 Risk-Seeking investors
 Risk-Neutral investors
 Risk-Averse investors
 Risk tolerance is the opposite of risk aversion.

 Each investor has a Utility Function which helps investment
advisors select investments which maximise the investor’s
utility. The Utility Function is calculated as:
U = utility of one investment
E(r) = expected return
= investment’s variance
A =risk aversion measure of an investor

 The following chart highlights the different indifference curves
for different types of investors:

Return of a Portfolio
 The return of a portfolio can be calculated as the weighted
average of the returns of each asset which makes up the
portfolio. It can be calculated as:

Risk of a Portfolio
 The risk of a portfolio can be measured
by the variance and standard deviation of returns.
 The variance of returns of a portfolio can be calculated as:
 The standard deviation of a two asset portfolio can be
calculated as:

Covariance and Correlation
 In order to calculate the variance and standard deviation of a
multi-asset portfolio, we need to consider the covariance of
returns between the assets.
 The covariance of returns can be calculated as:
Cov (R1, R2) = p12σ1σ2
 Where p12 is correlation of R1, R2; p12 =+1: The returns of two
assets are exactly the same through; p12 = -1: The returns of
two assets are exactly inverse of each other through time; p12
= 0: The returns of two assets are not related to each other.

Risk and Return of a
Portfolio with >2 Assets
The return of a multiple asset portfolio can be calculated as:
Assuming all assets have an equal variance and equal
correlation, the equation above can be restated

Impact of Portfolio Risk of Investing in
Less Than Perfectly Correlated Assets
An investor can reduce the total risk of a portfolio by combining
assets in a portfolio which have a correlation of returns <1. This
is the key driver of the benefits of Diversification.
How Diversification Benefits are Achieved
The lower the correlation between the assets, the greater the
diversification benefits.

Minimum-Variance and Efficient
Frontiers of Risky Assets and the
Global Minimum-Variance Portfolio

Minimum-Variance and Efficient
Frontiers of Risky Assets and the
Global Minimum-Variance Portfolio
 The leftmost point on the minimum-variance frontier is known
as the global minimum-variance portfolio. This is the portfolio
of risky assets with the lowest possible risk (ie standard
deviation).
 The Markowitz Efficient Frontier is the minimum-variance
portfolio at all points above the Global Minimum Variance
Portfolio.
 As an investor moves along the Markowitz Efficient
Frontier, the return for each unit of risk decreases.

Optimal Portfolio of Risk-Free
and Risky Assets

Optimal Portfolio of Risk-Free and
Risky Assets
 A risk-free asset lies on the Y-axis.
 An investor can combine the risk free asset with a portfolio of
risky assets, in order to reach a satisfactory risk/return trade
off.
 All points on the efficient frontier can be grouped with the
risk-free asset to highlight the potential portfolio
combinations.
 In the following chart, CAL (P) dominates CAL (A) given it has a
higher return for a given level of risk.
 Investors risk preferences can be illustrated by the use of
indifference curves.

The Capital Allocation Line

The Capital Allocation Line
 The Capital Allocation Line (CAL) graphs the potential risk and
return portfolios that an investor can achieve by combining a
portfolio of risky and risk-free assets.
 The CAL can also be known as the "reward-to-variability ratio".
 The Optimum Risky Portfolio falls at the intersection of an
indifference curve and the capital allocation line

Implications of Combining a Risk-
Free Asset With a Portfolio of Risky
Assets
 The Capital Asset Pricing Model can be used to predict the
expected return of an optimised risky portfolio.
 While different investor’s have different risk preferences, the
CAPM assumes homogeneity of expectations

The Capital Market Line
 The Market Portfolio contains all available risky assets that
have a value attached to them and are tradeable.
 A Capital Allocation Line (CAL) maps of potential risk and
return profiles of portfolios which combine a risk-free asset
and a risky portfolio.
 The Capital Market Line (CML) is a special case of a Capital
Allocation Line (CAL) where the risky asset is the market
portfolio.

The Capital Market Line

Systematic vs. Non-Systematic Risk
 Systematic risk is the market risk that an investor assumes by
investing in risky assets. It is driven by fluctuations in economic
conditions etc.
 Non-systematic risk is specific to an industry or asset class.
 Total Risk = Systematic Risk + Non-Systematic Risk

No Additional Return For Bearing
Non-Systematic Risk
 Given that systematic risk is diversifiable, investors are not
rewarded for bearing this type of risk.
 This suggests that investors are better off investing in a fully
diversified portfolio in order to maximize the risk/return trade
off.

Return Generating Models
 The quality of the estimated returns depends solely on the
quality of inputs and how robust the prediction model is.
 Multi-factor models estimate returns by attributing returns to
more than one risk factor.
 One type of multifactor model is a macroeconomic model
which estimates returns by considering a range of economic
factors.
 “Fama and French models” multifactor models typically
contain 3 or 4 factors that contribute to returns.
 Single-index model only uses one factor.

The Market Model
 The market model is an example of a single factor model.
 The market model can be expressed as:

Beta
Calculating and Interpreting Beta
 Beta measures the sensitivity of an asset to fluctuations in the
market.
 Variances and correlation used in the calculation of beta are
estimates from historic returns.
 An asset with a positive beta suggests that returns of the
underlying asset tend to move in the same direction as the
market. A negative beta suggests that returns generated by
the asset tend to be inverse to returns achieved by the
market, leading to low systematic risk.

Beta
Calculating and Interpreting Beta
 A single-index model also known as the Capital Asset Pricing
Model (CAPM) can be used to calculate beta:
 The market model can also be used to estimate beta (by
rearranging the following formula):

Capital Asset Pricing Model
 Assumptions:
 Investors are risk averse, that they know balance of risk-return
trade off.
 Frictionless markets are markets with no transactional costs or
taxes, hence borrowing and lending happens at risk-free rate.
 Single period planning by investors is where an investor makes an
investment for a single period.
 The homogenous belief of investors is that every investor has the
same method to analyse.
 Investments are divisible infinitely.
 Price taking investors are investors who do not dictate pricing, thus
trading does not affect pricing of the underlined asset.

The Security Market Line
 A graphical representation of the CAPM where the expected
return is plotted on the y-axis and the beta is plotted on x-axis.

Application of the CAPM
 The risk and hence expected return of an investment
opportunity can be calculated using the CAPM.
 The CAPM can be used to estimate the appropriate discount or
hurdle rate to be used in capital budgeting .

The Sharpe Ratio and Treynor Ratios
 Indicators of risk adjusted returns based on the CAPM.
 Sharpe Ratio: Treynor Ratio:

The M2 Ratio
 The M2 is an extension of the Sharpe ratio.
 It suggests that a portfolio that outperforms the market on a
risk adjusted basis will have a positive M2 and a negative M2 if
it underperforms.
 The M2 can be calculated as:

The Information Ratio
 Measures portfolio returns above the returns of a benchmark,
relative to the volatility of those returns.
 Measures a portfolio manager's ability to generate
excess returns relative to a benchmark, but also attempts to
identify the consistency of the relative performance.
 The Information Ratio can be calculated as:
 A large information ratio suggests that the investor is able to
generate positive risk adjusted returns.

The Information Ratio
 Measures portfolio returns above the returns of a
benchmark, relative to the volatility of those returns.
 Measures a portfolio manager's ability to generate
excess returns relative to a benchmark, but also attempts to
identify the consistency of the relative performance.
 The Information Ratio can be calculated as:
 A large information ratio suggests that the investor is able to
generate positive risk adjusted returns.

 The key objective of the Investment Policy Statement (IPS) is to
outline the investor’s objectives, and willingness/ability to take
risk.
 The IPS of an investor must be reviewed on a regular basis.
 The objectives of the investor need to be explained in terms of
both risks and rewards.
 For each client, the IPS should be well defined, and all
constraints regarding liquidity, taxation, time
period, regulatory and other unique needs should be
addressed.

Major Components of IPS
 Introduction
 Statement of Purpose.
 Statement of Responsibilities
 Procedures
 Investment objectives
 Investment Constraints.
 Investment Guidelines
 Evaluation and review
 Appendices

Risk and Return Objectives
 Risk tolerance should be stated in the Investment Policy
Statement.
 Risk objective should be stated whether they are
fixed, variable, or a mixture of both.
 The return objective defines how much an investor wants to
earn.
 The return objective should be realistic, and return
expectations should be managed considering the investor’s
risk profile.

An Investor’s Financial Risk
Tolerance: Willingness Vs. Ability To
Take Risk
 Risk bearing ability can be broken down into three major
components:
 Time range
 Expected cash flows
 The ratio of wealth to liabilities.

Investment Constraints
 The Investment Policy Statement (IPS) of an investor should
consider its investment constraints.
 There are 5 baskets of financial constraints:
 Liquidity
 Time Horizon
 Taxation
 Legal & Regulator
 Unique Circumstances

Strategic Asset Allocation
Investors can strategically alter the weight of the investment
portfolio across different asset classes in order to benefit from
the returns of asset classes at different points of the economic
cycle.

Asset Classes
 Traditional asset classes include:
 Bonds
 Equities
 Cash
 Real estate
 Alternative asset classes include:
 Commodities
 Hedge funds
 Private equity.

How Strategic Asset Allocation or
Translates into an Actual Portfolio
 An investor considers long-term capital market expectations
and its Investment Policy Statement (IPS) to form its Strategic
Asset Allocation.
 When investors choose between assets with similar expected
return profiles, they tend to select the least risky asset. If
assets with similar risk profiles are presented, investors choose
the asset with the highest return.

How Strategic Asset Allocation or
Translates into an Actual Portfolio
 The following formula calculates the expected utility of an
investor’s portfolio as the expected returns of the
portfolio, adjusted for the portfolio’s risk levels and risk
aversion.
= Expected utility of investor portfolio
 = Portfolio’s expected return
 = Portfolio return’s standard deviation
 = The risk aversion of investor is measured by .

L1 flashcards portfolio management (ss12)

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