Investment Planning: Portfolio Management & Measures (Module 9)
Dollar-weighted Return (Internal Rate of Return): Definition
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.
Which measure includes methods that are used when deposits or withdrawals occur sometime between the beginning and end of the investment interval? A. Time-weighted returns B. The geometric mean C. The arithmetic mean D. Dollar-weighted returns
Correct Answer: D. Dollar-weighted returns Explanation: 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.
Correlation Coefficient: Forumula
Correlation Coefficient = (Beta x SDM) / SDS
Which one of the following stock indexes is value weighted? a. Barclays Capital Aggregate b. Value Line c. Dow Jones Industrial Average d. Wilshire 5000
D The Dow Jones is price-weighted, Value Line is equally weighted and Barclays (formerly Lehman Brothers) is a bond index. The question asked for stock index.
Holding Period Return: Definition
(Terminal Value - Initial Value) / Initial Value. This method's major weakness is it fails to take the time value of money into account.
Dow Jones (DJIA)
30 of the largest U.S.-based companies
Who would not be interested in a corporation's profitability ratio? a. Creditors of the company b. Company owners c. Fund managers d. Consumers
D Consumers only care about the cost of the product
NASDAQ
Typically, a benchmark for technology companies and mid-size companies.
Alpha: Formula
r = Rf + beta * (Rm - Rf ) + alpha where: r = the security's or portfolio's return Rf = the risk-free rate of return beta = the security's or portfolio's price volatility relative to the overall market Rm = the market return
correlation coefficient: definition
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 negative correlation, and a value of +1.0 represents perfect positive correlation. In the real world, most financial assets have positive correlation coefficients ranging in value from .4 to .9. However, for purposes of diversification, combining assets with anything other than perfect positive (+1.0) correlation will have diversification benefits. The lower the coefficient (say .4 vs. .7) the better, and negative is much better than positive. If you could ever find perfect negatively correlated assets (in theory anyway), you could have zero risk with just two assets. Your return would be with complete certainty.
Of the four following funds, which will provide the optimum risk-adjusted return for an investor? Annual Return Beta Fund #1 24% 2.0 Fund #2 6% 0.5 Fund #3 12% 1.2 Fund #4 8% 0.8
1 & 2 On a risk-adjusted basis, Funds #1 and #2 (12%) do better than Funds #3 and #4 (10%).
The Sharpe index does which of the following? 1. Assumes the portfolio is well-diversified. 2. Assumes the portfolio is not diversified. 3. Compares the actual return to the expected return. 4. Standardizes performance by the portfolio's Beta coefficient.
2 Answers I, III and IV refer to the Jensen index.
Which two investments would not have low correlations? 1. Equity investments 2. Preferred stocks 3. Real estate 4. Bonds
2 & 4 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.
S&P 500
500 U.S.-based companies. Widely accepted as the standard index to benchmark against for large cap U.S. stocks. According to the S&P, 97% of money managers and pension funds are indexed against the S&P 500.
Assume the following statistics are true of a Mutual Fund: Beta 1.5 Standard Deviation 12% Mean 8% Correlation Coefficient 0.75 Which of the three portfolio performance measures would you use to evaluate this fund? a. Sharpe b. Treynor c. Jensen (alpha)
A 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.
Modern Portfolio Theory (MPT)
A method of choosing investments that focuses on the importance of the relationships among all of the investments in a portfolio rather than the individual merits of each investment. The method allows investors to quantify and control the amount of risk they accept and return they achieve.
Information Ratio: Definition & Formula
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. IR = (r-Rb) / SD r = average return Rb = benchmark return SD = standard deviation
According to the CAPM, which of the four is the most efficient? a. Asset A has a return of 14%; beta = 1.25; standard deviation = 18% b. Asset D has a return of 17%; beta = 1.25; standard deviation = 21% c. Asset A has a return of 19%; beta = 1.45; standard deviation = 24% d. Asset B has a return of 10%; beta = 1.15; standard deviation = 14%
B Divide standard deviation by return. The lowest result wins. This is calculating the Coefficient of Variance
Which portfolio is riskier when correlation is considered? a. 50% in the S&P 500 index and 50% in the EAFE index. b. 50% in the S&P 500 index and 50% in the Russell 2000 index.
B The S&P 500 and the EAFE index will have a lower correlation.
If you own both Stock A and Stock B equally, what is the risk if the correlation coefficient is 1.0? Expected Return Risk Stock A 10% 15% Stock B 35% 45% a. 45% b. 60% c. 30% d. 12.5% e. 15%
C (15% + 45%) / 2 = 30%
Which of the following is true about Dow Theory? a. Primary price movements are based on Modern Portfolio Theory. b. The theory uses EMH principles. c. It is a method that identifies the top of a bull market and the bottom of a bear market. d. The most important price movement is day-to-day fluctuations.
C Dow theory contradicts Modern Portfolio Theory and EMH. It is based on trends, not day to day fluctuations.
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.
Coefficient of Variation: definition & formula
Coefficient of Variation is a relative measure for determining if the return is worth the risk. Under the CAPM, it is an investment statistic that determines which investment is more efficient. The formula is standard deviation divided by the expected return.
Russell 2000
Commonly used as a benchmark for small company portfolios. The capitalization ranges from approximately $1.3 billion to $128 million.
Wishire 5000
Contains of 6,500 U.S.-based companies. Considered the broadest index for U.S. Stocks.
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: A. Risk-averse B. Risk-seeking C. Risk-neutral
Correct Answer: A. Risk-averse Explanation: 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.
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? A. 14% B. 8% C. 8.45% D. 9.11%
Correct Answer: B. 8% Explanation: 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%).
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? A. Sharpe's measure B. Treynor's measure C. Jensen's measure D. Appraisal ratio
Correct Answer: B. Treynor's measure Explanation: 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 ).
In selecting benchmark portfolios for comparison, the client should be certain that they represent ... A. The best possible portfolio construction available B. The best but not necessarily a feasible portfolio C. Alternative portfolios that could have been chosen instead of the one chosen D. Portfolios of varying degrees of risk
Correct Answer: C. Alternative portfolios that could have been chosen instead of the one chosen Explanation: 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.
Markowitz asserts that investors should base their portfolio decisions solely on two variables. A. Initial and terminal wealth B. Non-satiation and marginal utility C. Variance and covariance D. Expected returns and standard deviations
Correct Answer: D. Expected returns and standard deviations Explanation: 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.
Portfolio diversification is most effective when the correlation coefficient is A. Greater than zero B. Positive C. Less than one D. Less than zero
Correct Answer: D. Less than zero Explanation: 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? a. 100% in a short position on government bonds. b. 25% in Canadian bonds, 25% in a global fund, 50% in real estate LPs. c. 25% in equity REITs, 25% in an international fund, 50% in a gold fund. d. 50% in gold bullion, 25% in natural resources, 25% in cash.
D 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. Note: This question is typical of the nasty asset allocation questions on the CFP Exam.
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%? a. 0.625 b. 0.75 c. -0.6 d. -0.4
D 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
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.
Negatively correlated assets are "necessary" to reduce risk. True or false?
False Negatively correlated assets are NOT "necessary" to reduce risk (low positive are great).
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 what?
HPR = (P1 + D -- P0)/P0, or Holding Period Return = (End-of-Period Wealth + Income - Beginning-of-Period Wealth)/Beginning-of-Period Wealth
Dow Theory
It is a method that identifies the top of a bull market and the bottom of a bear market.
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.
You have a two security portfolio as follows: - Security A: expected return = 8%, standard deviation = 12% & portfolio weight is 40% - Security B: expected return = 14%, standard deviation = 30% & portfolio weight is 60% - correlation coef. = 0.22 What is the portfolio's standard deviation?
Since it is needed as input, calculate covariance between security A and security B first. 12 x 30 x .22 = 79.20 [(SDA2 x WA2) + (SDB2 x WB2) + 2(WA)(WB)(COVAB)]½ [(12 x 12 x .40 x .40) + (30 x 30 x .60 x .60) + (2 x .40 x .60 x 79.20)] ½ [ 23.04 + 324.00 + 38.02 ]½ [385.06]½ = 19.62 (This is a percent.)
coefficient of determination: definition
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)
You have a two security portfolio as follows: - Security A: expected return = 8%, standard deviation = 12% & portfolio weight is 40% - Security B: expected return = 14%, standard deviation = 30% & portfolio weight is 60% - correlation coef. = 0.22 What is the portfolio's return?
The portfolio weighted return is (40% x 8%) + (60% x 14%) = 11.60%
The portfolio return will always be a straight-forward function of relative asset return and asset weight, when is the only time you can do this for standard deviation?
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.
indifference curves
a line that shows the consumption bundles that yield the same amount of total utility
Given the following data on Fund X and assuming the risk-free rate is 6%, what is the alpha of the fund? Fund X Market Realized Return 17% 18% Beta 0.72 1.0 Standard Deviation 9% - R2 87% -
ap = rp - [rf + (rm - rf) B] ap = 17% - [6% + (18% - 6%) 0.72] ap = 2.36
investment approach of Harry Markowitz
as a method of solving that problem. With this approach, an investor should evaluate alternative portfolios on the basis of their expected returns and standard deviation. 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.
Terminal Wealth
can be determined by rearranging the one-period portfolio return equation: W0(1 + rp) = W1
Covariance: definition
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 portfolio's return (rp), whats the formula?
rp= (W1 -- W0)/W0 Here, W0 denotes the aggregate purchase price at t = 0 of the securities contained in the portfolio; W1 denotes the aggregate market value of these securities at t = 1 as well as the aggregate cash (and cash equivalents) received between t = 0 and t = 1 from owning these securities.