3. Investment Planning. 9. Portfolio Management and Measurements Flashcards
Stocks can provide high returns but are considered higher risk than other securities. Money market instruments are considered safe, but provide low yields. Is there an investment out there that has high returns and low risk? In 1952, Harry Markowitz published a landmark paper that is viewed as the origin of modern portfolio theory. Markowitz observes that investors seek to both maximize expected return and minimize uncertainty (that is, risk defined as a standard deviation of expected returns). He suggested that these two conflicting objectives must be balanced against each other when making a purchase decision. The Markowitz approach to attaining these dueling objectives states that investors should diversify by purchasing not just one security but several, thus creating a portfolio of securities. Thus Markowitz proposes to look at risk and return not at an individual security level but for an entire portfolio.
The Portfolio Management and Measurements module, which should take approximately four hours to complete, is designed to give an overview of various portfolio management topics and measurement concepts. First, you will be introduced to concepts of modern portfolio theory. Then, the module covers return measurements, benchmarks, performance measures, and probability forecasting.
Upon completion of this module you should be able to:
* Discuss modern portfolio theory, and
* Evaluate portfolio performance.
All investors wish to make fortunes from the market. However, the first thing one should understand before investing is that every investment has its own degree of risk associated with it. So, before committing a single dollar to a portfolio, individuals need to remember that there are unavoidable but manageable risks. To minimize risks and maximize returns when investing in a portfolio, the rule is to build a portfolio that includes securities from different asset classes. This calls for intelligent portfolio management.
An approach in this area is the Modern Portfolio Theory (MPT) developed by Harry Markowitz. The MPT has profoundly shaped how institutional portfolios are managed, and prompted the use of passive investment management techniques. The mathematics of MPT is used extensively in financial risk management.
To ensure that you have a solid understanding of portfolio management and measurements, the following lessons will be covered in this module:
* Modern Portfolio Theory
* Performance Measures
Section 1 - Modern Portfolio Theory
Most securities available for investment have uncertain outcomes and are thus risky. 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 Modern Portfolio Theory explores how risk-averse investors construct portfolios in order to optimize expected returns against market risk. In fact, MPT quantifies diversification.
To ensure that you have a solid understanding of modern portfolio theory, the following topics will be covered in this lesson:
* Initial and Terminal Wealth
* Non-satiation and Risk Aversion
* Expected Return and Standard Deviation
Upon completion of this lesson, you should be able to:
* Calculate the rate of return, and initial and terminal wealth,
* Identify risk-averse investors, and
* Calculate returns and standard deviation for portfolios.
Describe 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.
TEST TIP
Since the formulas on the distributed formula sheet for the CFP Certification Exam are not labeled, it is as important to recognize a formula by its components. Most questions that offer a beginning wealth (or price) and an ending wealth (or price) will have something to do with the Holding Period Return equation. The equation could also be manipulated where the return is given and you must solve for the ending or beginning wealth (price).
Calculate the above portfolio’s expected rate of return using the terminal versus the initial value.
* 22%
* 23%
* 16%
* 25%
22%
* Portfolio Expected Return =
* ($20,984 - $17,200) ÷ $17,200
* = 0.22, or 22%
How do you calculate Portfolio Expected Returns?
An alternative method for calculating the expected return on this portfolio is shown below. 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:
rp=∑Nj=1Xjr⎯⎯i=X1r⎯⎯1+X2r2+…+XNr⎯⎯N
where:
rp = the expected return of the portfolio
XI = the proportion of the portfolio’s initial value invested in security I
rI = the expected return of security I
N = the number of securities in the portfolio
TEST TIP
The formula sheet for the CFP examination has the following formula for determining the expected return of a portfolio, also know as the Capital Market Line. This equation assumes the existence of both systematic and nonsystematic risks:
Rp= Rf + SDP[(Rm – Rf)/SDm]
What is the portfolio’s expected rate of return?
* 8.22%
* 22%
* 3.77%
* 10.01%
22%
* Portfolio Expected Return = The sum of the contribution to portfolio expected returns =
* 3.77% + 10.01% + 8.22%
* = 22%
Describe Correlation
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.
In the real world, most financial assets have positive correlation coefficients ranging in value from 0.4 to 0.9. However, for purposes of diversification, combining assets with anything other than perfect positive (+1.0) correlation will have diversification benefits. The lower the coefficient (e.g., 0.4 vs. 0.7) 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.
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.
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.
TEST TIP
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).
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.
Section 1 - Modern Portfolio Theory Summary
What is the ideal investment? Something that has high returns and low risks! Unfortunately, in the investment world, higher returns usually come with higher risks (uncertainty of the ability to achieve the higher return). To solve this problem, Markowitz came up with the Modern Portfolio Theory. The theory proposes that investors consider not only the return of the investment, but also the amount of risk they are willing to take to attain it. It also suggests that a portfolio of securities can be built considering the combined effect of expected return while consisting of a combination of securities whose covariance and correlation will create a certain level of risk. A risk-averse investor has baskets of portfolios where they are indifferent due to the combination of risk and return. The optimal portfolio is the one that lies in the indifference basket that offers the investor the highest return with the lowest uncertainty.
In this lesson, we have covered the following:
- Initial and terminal wealth: Used to calculate the rate of return and help to decide the expected returns and standard deviations for portfolios.
- 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.
PRACTITIONER ADVICE
Computer programs are available to help determine portfolio return and risk data. It is more important to understand how they work and what they mean to an investor. A conversation about covariance may confuse a novice investor more than it helps. However, if your clients were directed to certain statistics such as R-squared on sales material or third party rating reports, it would be helpful for you to know what these statistics mean to a portfolio’s expected risk and return.
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.
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.
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%).
Portfolio diversification is most effective when the correlation coefficient is
* Greater than zero
* Positive
* Less than one
* Less than zero
Less than zero
* 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.
Section 2 – Performance Measures
An investor who has been paying someone to actively manage his or her portfolio has every right to insist on knowing what sort of performance was obtained. Such information can be used to alter the constraints placed on the manager, the investment objectives given to the manager, or the amount of money allocated to the manager. Perhaps even more important, by evaluating performance in specified ways, a client can forcefully communicate his or her interests to the investment manager and, in all likelihood, affect the way in which his or her portfolio is managed in the future. Portfolio performance evaluation and measures can be viewed as feedback and control mechanisms that can make the investment management process more effective.
To ensure that you have a solid understanding of performance measures, the following topics will be covered in this lesson:
* Investment policy statements
* Probability analysis
* Measures of return
* Risk adjusted performance measures
* Appropriate benchmarks
Upon completion of this lesson, you should be able to:
* Identify investment policies,
* List methods of probability analysis used in performance evaluation,
* Explain the various methods of measuring returns,
* Calculate the rate adjusted basis for evaluating performance, and
* Compare portfolios referred to as benchmark portfolios.
