1. 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
2. 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
Study Lesson 12, Reading 43
3. 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
Study Lesson 12, Reading 43
4. 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.
Study Lesson 12, Reading 43
5. 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.
Study Lesson 12, Reading 43
6. 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.
Study Lesson 12, Reading 43
7. 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.
Study Lesson 12, Reading 43
8. 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.
Study Lesson 12, Reading 44
9. Measures of Investment Returns:
Calculating Returns
The HPR of an investment over three years can be
calculated as:
Study Lesson 12, Reading 44
10. Measures of Investment Returns:
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:
Study Lesson 12, Reading 44
11. Measures of Investment Returns:
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.
Study Lesson 12, Reading 44
12. Measures of Investment Returns:
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.
Study Lesson 12, Reading 43
13. Measures of Investment Returns:
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%.
Study Lesson 12, Reading 43
14. 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
Study Lesson 12, Reading 44
15. 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.
Study Lesson 12, Reading 44
16. 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.
Study Lesson 12, Reading 44
17. Variance of a Portfolio
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.
Study Lesson 12, Reading 44
18. Variance of a Portfolio
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:
Study Lesson 12, Reading 44
19. 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.
Study Lesson 12, Reading 44
20. Risks Aversion and Its Implications
For Portfolio Selection
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
Study Lesson 12, Reading 44
21. Risks Aversion and Its Implications
For Portfolio Selection
The following chart highlights the different indifference curves
for different types of investors:
Study Lesson 12, Reading 44
22. 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:
Study Lesson 12, Reading 44
23. 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:
Study Lesson 12, Reading 44
24. 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.
Study Lesson 12, Reading 43
25. 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
Study Lesson 12, Reading 43
26. 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.
Study Lesson 12, Reading 43
28. 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.
Study Lesson 12, Reading 44
30. 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.
Study Lesson 12, Reading 44
32. 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
Study Lesson 12, Reading 45
33. 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
Study Lesson 12, Reading 45
34. 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.
Study Lesson 12, Reading 45
36. 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
Study Lesson 12, Reading 45
37. 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.
Study Lesson 12, Reading 45
38. 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.
Study Lesson 12, Reading 45
39. The Market Model
The market model is an example of a single factor model.
The market model can be expressed as:
Study Lesson 12, Reading 45
40. 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.
Study Lesson 12, Reading 45
41. 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):
Study Lesson 12, Reading 45
42. 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.
Study Lesson 12, Reading 45
43. 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.
Study Lesson 12, Reading 45
44. 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 .
Study Lesson 12, Reading 45
45. The Sharpe Ratio and Treynor Ratios
Indicators of risk adjusted returns based on the CAPM.
Sharpe Ratio: Treynor Ratio:
Study Lesson 12, Reading 45
46. 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:
Study Lesson 12, Reading 45
47. 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.
Study Lesson 12, Reading 45
48. 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.
Study Lesson 12, Reading 45
49. Investment Policy Statement
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.
Study Lesson 12, Reading 46
50. Major Components of IPS
Introduction
Statement of Purpose.
Statement of Responsibilities
Procedures
Investment objectives
Investment Constraints.
Investment Guidelines
Evaluation and review
Appendices
Study Lesson 12, Reading 46
51. 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.
Study Lesson 12, Reading 46
52. 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.
Study Lesson 12, Reading 46
53. 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
Study Lesson 12, Reading 46
54. 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.
Study Lesson 12, Reading 46
55. Asset Classes
Traditional asset classes include:
Bonds
Equities
Cash
Real estate
Alternative asset classes include:
Commodities
Hedge funds
Private equity.
Study Lesson 12, Reading 46
56. How Strategic Asset Allocation or
Investment Policy Statement
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.
Study Lesson 12, Reading 46
57. How Strategic Asset Allocation or
Investment Policy Statement
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 .
Study Lesson 12, Reading 46