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- 1. The Portfolio Approach to InvestingWell Diversified Single Security Less likely to lose theirinvestment Reduce the total risk of aportfolio Reduce overall portfoliovolatility Greater probability of losingtheir investment Unsystematic risk Flat portfolioStudy Lesson 12, Reading 43
- 2. Types of Investors Individual Investors Short-term goals of individual investors can be children’seducation expenses, or lumpy purchases Long term goals can be retirement plans paid such as adefined benefit contribution plan. Under a defined benefit contribution plan, the employeereceives a fixed cash pension payment at the time ofretirementStudy Lesson 12, Reading 43
- 3. Types of Investors Institutional Investors Includes commercial banks, investment banks, insurancecompanies, asset management companies, etc. Endowment funds by universities Banks invest in excess financial reservesStudy Lesson 12, Reading 43
- 4. The Portfolio Management ProcessAn Investment Policy Statement maps out an investors needsand restrictions. It is designed to allow investment advisors tomake investment recommendations which suit that particularinvestor’s objectives.Study Lesson 12, Reading 43
- 5. Stages in Developing anInvestment Policy Statement Step 1: Planning. Understanding the client’s goals andpreparing the IPS. Step 2: Execution. Deciding the assetallocation, undertaking security analysis, and portfolioconstruction. Step 3: Feedback. Monitoring and rebalancing ofportfolio, measurement, and reporting performance.Study Lesson 12, Reading 43
- 6. Mutual Funds It is a pool of investment capital from individuals andinstitutions 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 investingcapital with asset managers at the latest net asset value. Closed-end funds: when new investors can only gainexposure to the fund by purchasing existing shares in thefund from another investor. Mutual funds exist for investments in moneymarkets, bonds, stocks, and balanced funds.Study Lesson 12, Reading 43
- 7. Mutual Funds Money Market Funds: Investments in high-quality, shortterm, corporate or government debt. Bond Funds: Invest in all types of rated debt from low to highquality 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 assetclasses and securities.Study Lesson 12, Reading 43
- 8. Measures of Investment Returns:Calculating Returns The Holding Period Return of an investment in a single securityis calculated as:Where: D is the dividend, P is the price, t-1 is the date of theinitial investment, and t is the date the investment is exited orthe measurement end date.Study Lesson 12, Reading 44
- 9. Measures of Investment Returns:Calculating Returns The HPR of an investment over three years can becalculated as:Study Lesson 12, Reading 44
- 10. Measures of Investment Returns:Money Weighted Return The money weighted return weights the returns achieved byeach asset in a portfolio by the weight of capital invested ineach 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 followingformula: In the formula above, c is the number of periods in theinvestment horizon. For example, if quarterly returns are beingannualized, 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 weightingreturns generated by the portfolio: Where w is the weight, R is the return, and i represents asingle 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 themean of the returns over a number of periods. The geometric average returns need to be calculated over asequential period of investment. For example, assume the returns on an investment portfolioover 5 periods were 90%, 10%, 20%, 30% and -90%. Using thegeometric 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 asecurity representing an ownership interest in a business. Fixed Income: Fixed Income securities provide a return in theform of fixed periodic payments (coupons) and the eventualreturn of principal at maturity. Cash and Cash Equivalents: Assets such as cash or those thatcan be converted into cash immediatelyStudy 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 ofperiods. Gross return is the returns calculated before any deduction ofexpenses is made and Net Return is what the investoreventually 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 ofa various asset. High variance in historic returns signals a highrisk investment. where R is return over period ‘t’, and T is the total number ofperiods, while is average of T returns, supposing T representsthe population of returns.Study Lesson 12, Reading 44
- 17. Variance of a Portfolio If a sample is provided, then the following formula is used tocalculate the sample variance: The Standard Deviation of an asset’s returns is square root ofthe variance.Study Lesson 12, Reading 44
- 18. Variance of a Portfolio The variance of portfolio can be calculated using thefollowing formula: Covariance measures the tendency for returns of two assetsto move in the same direction at the same time. It iscalculated using the following formula:Study Lesson 12, Reading 44
- 19. Risks Aversion and Its ImplicationsFor Portfolio Selection Risk aversion is the willingness of an investor to accept risk inthe 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 ImplicationsFor Portfolio Selection Each investor has a Utility Function which helps investmentadvisors select investments which maximise the investor’sutility. The Utility Function is calculated as:U = utility of one investmentE(r) = expected return= investment’s varianceA =risk aversion measure of an investorStudy Lesson 12, Reading 44
- 21. Risks Aversion and Its ImplicationsFor Portfolio Selection The following chart highlights the different indifference curvesfor different types of investors:Study Lesson 12, Reading 44
- 22. Return of a Portfolio The return of a portfolio can be calculated as the weightedaverage of the returns of each asset which makes up theportfolio. It can be calculated as:Study Lesson 12, Reading 44
- 23. Risk of a Portfolio The risk of a portfolio can be measuredby 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 becalculated as:Study Lesson 12, Reading 44
- 24. Covariance and Correlation In order to calculate the variance and standard deviation of amulti-asset portfolio, we need to consider the covariance ofreturns 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 twoassets are exactly the same through; p12 = -1: The returns oftwo 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 aPortfolio with >2 AssetsThe return of a multiple asset portfolio can be calculated as:Assuming all assets have an equal variance and equalcorrelation, the equation above can be restatedStudy Lesson 12, Reading 43
- 26. Impact of Portfolio Risk of Investing inLess Than Perfectly Correlated AssetsAn investor can reduce the total risk of a portfolio by combiningassets in a portfolio which have a correlation of returns <1. Thisis the key driver of the benefits of Diversification.How Diversification Benefits are AchievedThe lower the correlation between the assets, the greater thediversification benefits.Study Lesson 12, Reading 43
- 27. Minimum-Variance and EfficientFrontiers of Risky Assets and theGlobal Minimum-Variance PortfolioStudy Lesson 12, Reading 44
- 28. Minimum-Variance and EfficientFrontiers of Risky Assets and theGlobal Minimum-Variance Portfolio The leftmost point on the minimum-variance frontier is knownas the global minimum-variance portfolio. This is the portfolioof risky assets with the lowest possible risk (ie standarddeviation). The Markowitz Efficient Frontier is the minimum-varianceportfolio at all points above the Global Minimum VariancePortfolio. As an investor moves along the Markowitz EfficientFrontier, the return for each unit of risk decreases.Study Lesson 12, Reading 44
- 29. Optimal Portfolio of Risk-Freeand Risky AssetsStudy Lesson 12, Reading 44
- 30. Optimal Portfolio of Risk-Free andRisky Assets A risk-free asset lies on the Y-axis. An investor can combine the risk free asset with a portfolio ofrisky assets, in order to reach a satisfactory risk/return tradeoff. All points on the efficient frontier can be grouped with therisk-free asset to highlight the potential portfoliocombinations. In the following chart, CAL (P) dominates CAL (A) given it has ahigher return for a given level of risk. Investors risk preferences can be illustrated by the use ofindifference curves.Study Lesson 12, Reading 44
- 31. The Capital Allocation LineStudy Lesson 12, Reading 45
- 32. The Capital Allocation Line The Capital Allocation Line (CAL) graphs the potential risk andreturn portfolios that an investor can achieve by combining aportfolio 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 anindifference curve and the capital allocation lineStudy Lesson 12, Reading 45
- 33. Implications of Combining a Risk-Free Asset With a Portfolio of RiskyAssets The Capital Asset Pricing Model can be used to predict theexpected return of an optimised risky portfolio. While different investor’s have different risk preferences, theCAPM assumes homogeneity of expectationsStudy Lesson 12, Reading 45
- 34. The Capital Market Line The Market Portfolio contains all available risky assets thathave a value attached to them and are tradeable. A Capital Allocation Line (CAL) maps of potential risk andreturn profiles of portfolios which combine a risk-free assetand a risky portfolio. The Capital Market Line (CML) is a special case of a CapitalAllocation Line (CAL) where the risky asset is the marketportfolio.Study Lesson 12, Reading 45
- 35. The Capital Market LineStudy Lesson 12, Reading 45
- 36. Systematic vs. Non-Systematic Risk Systematic risk is the market risk that an investor assumes byinvesting in risky assets. It is driven by fluctuations in economicconditions etc. Non-systematic risk is specific to an industry or asset class. Total Risk = Systematic Risk + Non-Systematic RiskStudy Lesson 12, Reading 45
- 37. No Additional Return For BearingNon-Systematic Risk Given that systematic risk is diversifiable, investors are notrewarded for bearing this type of risk. This suggests that investors are better off investing in a fullydiversified portfolio in order to maximize the risk/return tradeoff.Study Lesson 12, Reading 45
- 38. Return Generating Models The quality of the estimated returns depends solely on thequality of inputs and how robust the prediction model is. Multi-factor models estimate returns by attributing returns tomore than one risk factor. One type of multifactor model is a macroeconomic modelwhich estimates returns by considering a range of economicfactors. “Fama and French models” multifactor models typicallycontain 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. BetaCalculating and Interpreting Beta Beta measures the sensitivity of an asset to fluctuations in themarket. Variances and correlation used in the calculation of beta areestimates from historic returns. An asset with a positive beta suggests that returns of theunderlying asset tend to move in the same direction as themarket. A negative beta suggests that returns generated bythe asset tend to be inverse to returns achieved by themarket, leading to low systematic risk.Study Lesson 12, Reading 45
- 41. BetaCalculating and Interpreting Beta A single-index model also known as the Capital Asset PricingModel (CAPM) can be used to calculate beta: The market model can also be used to estimate beta (byrearranging the following formula):Study Lesson 12, Reading 45
- 42. Capital Asset Pricing Model Assumptions: Investors are risk averse, that they know balance of risk-returntrade off. Frictionless markets are markets with no transactional costs ortaxes, hence borrowing and lending happens at risk-free rate. Single period planning by investors is where an investor makes aninvestment for a single period. The homogenous belief of investors is that every investor has thesame method to analyse. Investments are divisible infinitely. Price taking investors are investors who do not dictate pricing, thustrading 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 expectedreturn 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 investmentopportunity can be calculated using the CAPM. The CAPM can be used to estimate the appropriate discount orhurdle 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 arisk adjusted basis will have a positive M2 and a negative M2 ifit 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 managers ability to generateexcess returns relative to a benchmark, but also attempts toidentify the consistency of the relative performance. The Information Ratio can be calculated as: A large information ratio suggests that the investor is able togenerate positive risk adjusted returns.Study Lesson 12, Reading 45
- 48. The Information Ratio Measures portfolio returns above the returns of abenchmark, relative to the volatility of those returns. Measures a portfolio managers ability to generateexcess returns relative to a benchmark, but also attempts toidentify the consistency of the relative performance. The Information Ratio can be calculated as: A large information ratio suggests that the investor is able togenerate positive risk adjusted returns.Study Lesson 12, Reading 45
- 49. Investment Policy Statement The key objective of the Investment Policy Statement (IPS) is tooutline the investor’s objectives, and willingness/ability to takerisk. The IPS of an investor must be reviewed on a regular basis. The objectives of the investor need to be explained in terms ofboth risks and rewards. For each client, the IPS should be well defined, and allconstraints regarding liquidity, taxation, timeperiod, regulatory and other unique needs should beaddressed.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 AppendicesStudy Lesson 12, Reading 46
- 51. Risk and Return Objectives Risk tolerance should be stated in the Investment PolicyStatement. Risk objective should be stated whether they arefixed, variable, or a mixture of both. The return objective defines how much an investor wants toearn. The return objective should be realistic, and returnexpectations should be managed considering the investor’srisk profile.Study Lesson 12, Reading 46
- 52. An Investor’s Financial RiskTolerance: Willingness Vs. Ability ToTake Risk Risk bearing ability can be broken down into three majorcomponents: 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 shouldconsider its investment constraints. There are 5 baskets of financial constraints: Liquidity Time Horizon Taxation Legal & Regulator Unique CircumstancesStudy Lesson 12, Reading 46
- 54. Strategic Asset AllocationInvestors can strategically alter the weight of the investmentportfolio across different asset classes in order to benefit fromthe returns of asset classes at different points of the economiccycle.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 orInvestment Policy StatementTranslates into an Actual Portfolio An investor considers long-term capital market expectationsand its Investment Policy Statement (IPS) to form its StrategicAsset Allocation. When investors choose between assets with similar expectedreturn profiles, they tend to select the least risky asset. Ifassets with similar risk profiles are presented, investors choosethe asset with the highest return.Study Lesson 12, Reading 46
- 57. How Strategic Asset Allocation orInvestment Policy StatementTranslates into an Actual Portfolio The following formula calculates the expected utility of aninvestor’s portfolio as the expected returns of theportfolio, adjusted for the portfolio’s risk levels and riskaversion.= 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

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