Course 3: Module 9. Portfolio Management
Holding Period Return
((Terminal Value - Initial Value) + Cashflows) / Initial Value. This method's major weakness is it fails to take the time value of money into account.
The optimal portfolio is
the one that lies in the indifference basket that offers the investor the highest return with the lowest uncertainty.
Ranking portfolios' average rates of return can make an efficient low-risk portfolio appear to do poorly. To evaluate a portfolio adequately, its risk must be considered with its rate of return.
-- Sharpe's index of portfolio performance measures the risk premium per unit of risk. The Sharpe ratio considers total risk, as measured by standard deviation, for the appropriate risk statistic. -- Treynor uses beta coefficients and average returns to derive an index number suitable for ranking the desirability of assets in Beta-E(r) space. Some analysts prefer the Treynor ratio because systematic risk is more relevant than total risk in certain applications and because the Treynor measure can be used to compare individual assets and portfolios. The Treynor ratio has the disadvantage that its values can be sensitive to the market index used to estimate the investments' betas. -- Jensen's alpha measures risk-adjusted returns and is useful for evaluating the performance of both portfolios and individual assets. Alpha is used to compare risk premiums over systematic risks. However, the Alpha is not quite as easy to use for rankings as the other one-parameter performance measures. The Treynor, Sharpe, and Alpha investment performance measures tend to rank mutual funds similarly. Additional tools are available to analyze a portfolio's returns through time and determine if the portfolio manager possesses market-timing skills. Considering the low fees associated with most indexed mutual funds, and the fact that index funds perform better than the majority of actively managed mutual funds, passive investing should not be ignored.
If you own both Stock A and Stock B equally, what is the risk if the correlation coefficient is 0.6? 30-40% 1-10% 10-20% 15-20% 20-30%
20-30% When the correlation coefficient is 1.0, you can average the risk (15% + 45%) / 2 = 30%. Thus, the maximum risk can be no more than 30%.
Which of the following indexes measures the stock performance of small companies? S&P 500 Wilshire 5000 Russell 3000 Russell 2000
4. Small cap stocks generally have market caps of $300 million to $2 billion. The value range of the Russell 2000 range between $175 million to $1.6 billion. The Russell 3000 covers 98% of U.S. market capitalization, and the Russell 2000 covers the bottom 8% of the Russell 3000 index. The Wilshire covers around 6,300 stocks (all publicly traded U.S. equities including all the micro-caps), but since it is market (value) weighted, the 500 largest stocks in the Wilshire 5000 represent about 70% of the index, which makes it a poor measure of small companies.
Assume the returns on a managed portfolio are regressed against the returns on a market index. The resulting alpha shows which of the following? The amount of unsystematic risk in the portfolio. The degree of diversification in the portfolio. The return added to the portfolio by the portfolio manager. The amount of the portfolio's price movement explained by the market.
Alpha indicates how the portfolio manager performed.
Information Ratio
Also known as an appraisal ratio, the information ratio is another widely used performance measure. It measures a portfolio's average return in excess of a benchmark portfolio, divided by the standard deviation of those excess returns.
According to the CAPM, which of the four is the most efficient? Asset A has a return of 14%; beta=1.25; standard deviation=18% Asset B has a return of 10%; beta=1.15; standard deviation=14% Asset C has a return of 19%; beta=1.45; standard deviation=24% Asset D has a return of 17%; beta=1.25; standard deviation=21%
Asset D has a return of 17%; beta=1.25; standard deviation=21% Based on the information provided, the risk assessment investment statistic under the CAPM that details relative efficiency is Coefficient of Variation, which is Standard Deviation, divided by return. Since the risk measure is the numerator, the lower the result the better the risk-return relationship; that is, it is more efficient. The CV for asset D is 1.235 which is the lowest. Simply, for every unit of return (for which Asset D has 17), there is 1.235 units of risk. Asset A, B, and C have CV of 1.286, 1.4 and 1.263, respectively.
The formula sheet for the CFP® certification examination has the following formula for determining covariance:
COV = SDi X SDj X corr. coeff.ij Be ready to solve for correlation coefficient, if you are given standard deviations of each asset and the covariance. You would have to algebraically rearrange to: corr. coeff.ij = COV / SDi X SDj
Time-weighted Return
Calculates the return for the amount prior to a change caused by deposit or withdrawal. The individual returns are added together. It is more accurate than annualized returns.
correlation coefficient
Closely related to covariance is the statistical measure known as correlation coefficient. In fact, when it comes to diversification, the correlation coefficient is the most important statistic. Correlation coefficients always lie between -1.0 and +1.0. A value of +1.0 represents perfect positive correlation. A value of -1.0 represents perfect negative correlation.
Which measure includes methods that are used when deposits or withdrawals occur sometime between the beginning and end of the investment interval? Time-weighted returns The geometric mean The arithmetic mean Dollar-weighted returns
Dollar-weighted returns The dollar-weighted return (or internal rate of return) is the method that helps in situations when deposits or withdrawals occur sometime between the beginning and end of the period.
Annualized Returns
Either add the returns of the quarters together, or add 1 to each quarterly return, then multiply the four figures, and finally subtract 1 from the resulting product. This could be misleading because it does not consider how long each dollar was in the investment.
Markowitz asserts that investors should base their portfolio decisions solely on two variables. Initial and terminal wealth Non-satiation and marginal utility Variance and covariance Expected returns and standard deviations
Expected returns and standard deviations According to Markowitz, the investor should view the rate of return associated with any portfolio by considering the random variables of expected (or mean) value and standard deviation.
Expected return and standard deviation:
Expected returns can be determined based on the terminal versus initial value or a weighted sum of the securities' expected return. The risk (standard deviation) of a portfolio can be determined using the double summation method, which examines the securities' covariance and correlation.
Please select the best of the 3 Mutual Funds below.
Fund #2 Since each of the list funds have a high R2, the fund that should be selected is the one with the highest alpha (Fund #2). If all the R2s were low, then Fund #3 should be selected (highest Sharpe number). If no Alpha was given and all the R2s were high, then Fund #3 should be selected (highest Treynor number). R2 measures diversification. A R2 of 1 or 100 indicates movements in the S&P 500. The Jensen/Alpha and Treynor formulas and concepts can only work with a diversified portfolio. Sharpe is used with low R2.
The Sharpe index does which of the following? Assumes the portfolio is well-diversified. Assumes the portfolio is not diversified. Compares the actual return to the expected return. Standardizes performance by the portfolio's Beta coefficient. I, III, IV I, II II II, III
II Answers I, III and IV refer to the Jensen index.
Which two investments would not have low correlations? I. Equity investments II. Preferred stocks III. Real estate IV. Bonds II, III III, IV I, III I, II II, IV
II and IV Fixed income securities, like preferred stock and bonds, have low correlations with other asset classes shown. However, they are in the same asset class - fixed income securities.
Investment policy statements
Investment policy statements determine the investment objectives and investable wealth of the investor
The following two assumptions are implicit in portfolio selection.
Non-satiation: People will always prefer more money than less money. If there were two portfolios that have the same risk, but varying return, investors will choose the one with the higher expected return. Risk-averse: People will less likely take a bet when there is an alternative to make the same amount of money with more certainty. Investors will choose the portfolio with the smaller standard deviation.
Probability Analysis
Probability analysis looks at the actual performance of a portfolio in comparison to its expected outcomes. When selecting securities for a portfolio, certain assumptions are made as to the expected return. These assumptions are accompanied by the probability of attaining the expected return. Probability analysis uses standard deviation, variance, coefficient of determination, beta and alpha to determine the risk adjusted return of the portfolio. When looking back at the actual return over a period, one can compare how a portfolio did in comparison to the expected outcome of the period.
Stan has really been interested in a new OTC stock fund. He has had a devil of a time deciding which performance ratio to use. The three performance measures are given on the internet site, but he cannot decide whether or not it is diversified. Finally, he found out correlation to the market(R). If the R is 7, which performance measure should he use? Sharpe Jensen/alpha Treynor Modern portfolio theory
R2 = 0.7 x 0.7 = 0.49 The number is below 60, so you use Sharpe.
Investors will less likely make an investment when there is an alternative to make the same amount of money with more certainty. This statement assumes that investors are: Risk-averse Risk-seeking Risk-neutral
Risk-averse It is assumed that investors are risk-averse, which means that the investor will choose a portfolio with a smaller standard deviation. Risk-averse investors are willing to forego some expected terminal wealth (that is, accept lower expected returns) in exchange for less risk.
CAPM-based measures of portfolio performance are:
Sharpe ratio Treynor ratio Jensen's ratio
Which portfolio is riskier when correlation is considered? 50% in the S&P 500 index and 50% in the Russell 2000 index. 50% in the S&P 500 index and 50% in the EAFE index.
The S&P 500 and the EAFE index will have a lower correlation.
What will show the relevancy of the benchmark?
The coefficient of determination (R-squared). For example, a certain stock may move with a broad market index. However, if an industry factor causes the stock to drop, the rest of the market may move forward without it.
Initial and terminal wealth:
Used to calculate the rate of return and help to decide the expected returns and standard deviations for portfolios.
Which of the following indexes is the broadest measure of the market? EAFE Wilshire 5000 S&P 500 Russell 2000
Wilshire 5000
Performance measures
are important in evaluating the performance of a portfolio manager and the securities within a portfolio. Risk-adjusted measures such as the Sharpe Ratio, the Treynor Ratio, the Information Ratio, and the Jensen alpha measurement are used to evaluate the performance of a portfolio. Benchmarks for a portfolio should also be set so that the portfolio's performance can be matched with the performance of a relevant index.
The Modern Portfolio Theory explores
how risk-averse investors construct portfolios in order to optimize expected returns against market risk. In fact, MPT quantifies diversification.
Monte Carlo simulations
is a probability analysis tool. It is a computer assisted statistical analysis of probable outcomes. _______ _____ _____ are performed on computer software to determine expected portfolio returns and the likelihood of receiving those returns. However, statistics do not factor in what people may be driven to do by their emotions at various market environment conditions. Therefore, it is important to position the simulation results as what they are: statistical trials.
Covariance
is a statistical measure of the relationship between two random variables. That is, it is a measure of how two random variables, such as the returns on securities i and j, "move together." A positive value for covariance indicates that the securities' returns tend to move in the same direction. For example, a better-than-expected return for one is likely to occur along with a better-than-expected return for the other. A negative covariance indicates a tendency for the returns to offset one another. For example, a better-than-expected return for one security is likely to occur along with a worse-than-expected return for the other. A relatively small or zero value for the covariance indicates that there is little or no relationship between the returns for the two securities.
The basic problem facing each investor is
to determine the type of risky securities to own. Investors must select the optimal portfolio from a set of possible portfolios that has the perfect combination of the best return and the most certainty, otherwise known as the portfolio selection problem. The solution to this problem is to follow the Modern Portfolio Theory (MPT) approach to investing, put forth in 1952 by Harry M. Markowitz.
The Beta of a stock is -0.5. What is the correlation coefficient if the stock has a standard deviation of 10% and the market has a standard deviation of 8%? -0.4 -0.6 0.625 0.75
-0.4 The correlation coefficient has to be negative. The formula will be given, but you must be able to adjust the formula to solve for the missing part. Correlation Coefficient = (Beta x SDM) / SDS Correlation Coefficient = (-0.5 x 0.08) / 0.1
Your client wants you to analyze two funds based on the information below. Which risk adjusted performance measure would be used if the risk free rate is 5%? Fund X using Sharpe Black/Scholes Fund X using Jensen Fund Y using Treynor
1. When the R2s are low, you must use Sharpe. Sharpe X is higher than Sharpe Y. Black/Scholes is an option valuation model.
Portfolio diversification is most effective when the correlation coefficient is Greater than zero Positive Less than one Less than zero
4. When the correlation coefficient is greater than zero, it indicates the securities in the portfolio are moving in tandem. Whereas, when the correlation coefficient is zero, the movement of one security in comparison to the other in the portfolio is not predictable. When the correlation coefficient is less than zero, the movement of one security as against the other is exactly opposite, indicating the most diversified situation.
Harry is very concerned about U.S. Government debt. He subscribes to a newsletter that indicates a default of government debt. The newsletter spells out the government having to keep the money printing presses running 24 hours a day, 7 days a week to keep up. He cannot sleep at night and he currently has 100% of his investable assets in a money market fund paying minimal interest. Which asset allocation would you suggest? 25% in equity REITs, 25% in an international fund, 50% in a gold fund. 50% in gold bullion, 25% in natural resources, 25% in cash. 25% in Canadian bonds, 25% in a global fund, 50% in real estate LPs. 100% in a short position on government bonds.
50% in gold bullion, 25% in natural resources, 25% in cash. For a riverboat gambler shorting government bonds is the best answer, but Harry won't do it. The mix of REITs, an international fund and a gold fund is not a bad answer, but the correct answer is better.
If an investor invests 50% in IBM which returned 20%, 30% in Texaco which returned -10% and 20% in Motorola which returned 5%, what was the portfolio's rate of return? 14% 8% 8.45% 9.11%
8% The investment in IBM is 50% of the portfolio, so the return of 20% times the portfolio weight of 50% yields a contribution to the portfolio return of 10% (50% weight x 20% return). Calculate the same for Texaco (30% weight x -10% return = -3%), and the same for Motorola (20% weight x 5% return = 1%). Adding the three together generates the portfolio return (10% + -3% + 1% = 8%).
In selecting benchmark portfolios for comparison, the client should be certain that they represent ... The best possible portfolio construction available The best but not necessarily a feasible portfolio Alternative portfolios that could have been chosen instead of the one chosen Portfolios of varying degrees of risk
Alternative portfolios that could have been chosen instead of the one chosen Comparing the returns obtained by the investment manager with appropriate alternative portfolios that could have been chosen for investment helps evaluate portfolio performance. In selecting the benchmark portfolio, the client should be certain that they are relevant, feasible, and known in advance, meaning that they should represent alternative portfolios that could have been chosen for investment instead of the portfolio being evaluated.
Dollar-weighted Return (Internal Rate of Return)
Breaks up the holding period so that the market value of the account after a change will be compounded by the amount of time it was earning the interest. It is the best way to measure an individual investor's results.
In the case of a risk-averse investor, the portfolio on the indifference curve that is farthest _____________ would be the one selected for investment.
In the case of a risk-averse investor, the portfolio on the indifference curve that is farthest northwest would be the one selected for investment.
Which of the following is true about Dow Theory? The theory uses EMH principles. It is a method that identifies the top of a bull market and the bottom of a bear market. Primary price movements are based on Modern Portfolio Theory. The most important price movement is day-to-day fluctuations.
It is a method that identifies the top of a bull market and the bottom of a bear market. Dow theory contradicts Modern Portfolio Theory and EMH. It is based on trends, not day to day fluctuations.
Based on prior exam questions released by CFP Board, it is necessary to know:
Negatively correlated assets are NOT "necessary" to reduce risk (low positive are great). While the portfolio return will always be a straight-forward function of relative asset return and asset weight, the ONLY time the same will be true for standard deviation is if the correlation coefficient between the assets is perfect positive (+1.0). This is the only time the portfolio standard deviation can be calculated in the same manor as portfolio return.
Of the four following funds, which will provide the optimum risk-adjusted return for an investor? Funds #1 and #2 Fund #1 Fund #2 Fund #3 Funds #3 and #4
On a risk-adjusted basis, Funds #1 and #2 (12%) do better than Funds #3 and #4 (10%).
Sharpe Ratio
Ranking portfolios' returns averaged over several years is oversimplified because such rankings ignore risk. Thus, what is needed is an index of portfolio performance, which is determined by both the return and the risk. William F. Sharpe devised the reward-to-variability index of portfolio performance, denoted SHARPEp. This defines a single parameter portfolio performance index that is calculated from both the risk and return statistics.
Risk-adjusted performance measures
Risk-adjusted performance measures can be used to evaluate the risk and appropriate returns from investments.
Explain the relationship that leads to the concept of indifference curves:
Risk-averse investors are willing to forego some expected terminal wealth (that is, accept lower expected returns) in exchange for less risk. Thus, various combinations of expected terminal wealth (or expected returns) and risk will produce the same level of expected utility for an investor.
Investment Policy Statements
Setting investment policy involves determining the investor's objectives and the amount of their investable wealth. Because there is a positive relationship between risk and return for sensible investment strategies, it is not appropriate for an investor to say that his or her objective is to "make a lot of money." What is appropriate for an investor in this situation is to state that the objective is to attempt to make a lot of money while recognizing that there is some chance that large losses may be incurred. Investment objectives should be stated in terms of both risk and return Once an investment policy is created, it can be used as a recipe to create a portfolio of securities. The rationale for each investment decision for a portfolio should find its roots from the investment policy statement. The statement will also serve as the scope of performance measurements. For example, one cannot compare investment performance with small company stocks if they were ruled out of the portfolio based on the investment policy.
The correlation coefficient squared is known as
The correlation coefficient squared is known as the coefficient of determination in the statistical-world, but commonly known as R squared in the every-day world. The R squared is another extremely important statistic, in that it tells you the degree to which a fund or a portfolio is diversified. Technically, it tells you the degree to which a dependent variable's variation in returns (say a stock mutual fund), are explained by the variation of returns of an independent variable (say a benchmark such as the S&P). To now think of this statistic in a managerial context is the key. For example, If I have a fund with an R squared of 0.92, that tells me that 92% of the variation of the funds returns are due to systematic forces (nondiversifiable). More importantly, it tells me 8% of the variation of the funds returns are due to unsystematic or diversifiable risk. Beta is not an appropriate measure of risk in situations when the portfolio being analyzed has a R squared below .70. This also has ramifications for the appropriateness of performance indices that use beta (Treynor and Jensen).
The difference between correlation coefficient and covariance
The difference between correlation coefficient and covariance is that covariance is more of a refined statistic, designed to take to specific asset risk into account. Correlation coefficients are raw figures, which simply measure the degree of variation between two assets returns from one period to the next.
PRACTICE STANDARD 500-1 Agreeing on Implementation Responsibilities
The financial planning practitioner and the client shall mutually agree on the implementation responsibilities consistent with the scope of the engagement.
PRACTICE STANDARD 400-1 Identifying and Evaluating Financial Planning Alternative(s)
The financial planning practitioner shall consider sufficient and relevant alternatives to the client's current course of action in an effort to reasonably meet the client's goals, needs and priorities.
PRACTICE STANDARD 400-2 Developing the Financial Planning Recommendation(s)
The financial planning practitioner shall develop the recommendation(s) based on the selected alternative(s) and the current course of action in an effort to reasonably meet the client's goals, needs and priorities.
PRACTICE STANDARD 500-2 Selecting Products and Services for Implementation
The financial planning practitioner shall select appropriate products and services that are consistent with the client's goals, needs and priorities.
Bob, a high-risk investor, has come to you about a fund (Venture Fund, Inc.). The only data you can find is that it has a SD of 24%, Beta of 2, and R2 of 13%. How will this fund perform in relation to the S&P 500? The client should use Beta to evaluate the fund. The client should not use SD to evaluate the fund. The fund is quite independent of the S&P 500. The high R2 indicates the percentage of the portfolio returns that closely follows the S&P 500. The portfolio will perform like an index fund.
The fund is quite independent of the S&P 500. It's of no value to measure the risk of a portfolio by its Beta if the Beta has little value as a measure of portfolio risk (e.g., a gold fund). Use SD because with a low R2, the fund isn't diversified.
An alternative method for calculating the expected return
This procedure involves calculating the expected return on a portfolio as the weighted average of the expected returns on its component securities. The relative market values of the securities in the portfolio are used as weights. In symbols, the general rule for calculating the expected return on a portfolio consisting of N securities is:
To calculate the expected end-of-period value of the portfolio and use the formula:
To calculate the expected end-of-period value of the portfolio and use the formula for calculating the rate of return, recall the holding period equation: rp = (W1 - W0) / W0
Assume the following statistics are true of a Mutual Fund: Which of the three portfolio performance measures would you use to evaluate this fund? Treynor Jensen (alpha) Sharpe
To get the R2 (coefficient of determination), you must square the correlation coefficient. 0.75 x 0.75 = 0.5625 Based on a low R2 (less than 60), you would use Sharpe not Jensen/alpha or Treynor.
Which one of the following methods measures the reward-to-volatility trade-off by dividing the average portfolio excess return over the systematic risk of the market? Sharpe's measure Treynor's measure Jensen's measure Appraisal ratio
Treynor's measure The beta coefficient from a characteristic line is an index of an investment's nondiversifiable risk. Treynor suggested using a portfolio's risk premium relative to its beta. This is known as the Treynor's index of return-to-volatility portfolio performance. It measures the reward-to-volatility trade-off by dividing the average portfolio excess return over the beta of the asset's returns. TREYNOR = (Excess return/Index of nondiversifiable risk) = (rp - RFR/Beta).
Initial and Terminal Wealth
When investing in different securities, the percentage of change in an investor's wealth from the beginning to the end of the year can be calculated in terms of the rate of return as: HPR = ((P1 - P0 )+D)/P0, or Holding Period Return = ((End-of-Period Wealth - Beginning-of-Period Wealth) + Income)/Beginning-of-Period Wealth The above formula is used to calculate the one-period rate of return on a security, where beginning-of-period wealth is the purchase price of one unit of the security at t = 0. The end-of-period wealth is the market value of the unit at t = 1, along with the value of any cash (and cash equivalents) paid to the owner of the security between t = 0 and t = 1. One must also remember that in the calculation of the return on a security, it is assumed that a hypothetical investor purchased one unit of the security at the beginning of the period.
Modern Portfolio Theory
asserts that, in general, investors are risk-averse and they care about two outcomes of a portfolio: return and risk. Portfolio returns are determined by the combination of weighted returns of the securities within the portfolio. Portfolio risk is determined by the combination of standard deviation, beta, covariance and correlation of the securities within the portfolio.
With the Markowitz approach to investing, the focus of the investor is
on terminal (or end-of-period) wealth, W1. That is, in deciding which portfolio to purchase with his or her initial (or beginning-of-period) wealth (W0) the investor should focus on the effect of the various portfolios on W1. This effect can be measured by the expected return and standard deviation of each portfolio. Since a portfolio is a collection of securities, the expected return and standard deviation of a portfolio depends on the expected return and standard deviation of each security contained in the portfolio. Furthermore, the amount invested in each security is important.
After the periodic returns for a portfolio during a time interval (say, quarterly returns for four years) have been measured, next we need to determine the performance of these returns. This requires an estimate of the portfolio's risk level during the time interval. Two kinds of risk can be estimated:
the portfolios market (or systematic) risk, measured by its beta, and the portfolios total risk, measured by its standard deviation.
