Portfolio Theory Flashcards
What is Standard Deviation?
- A measure of risk and variability of returns
- The higher the SD, the higher the riskiness of the investment
- How much something “flip-flops” around an average
What can Standard Deviation be used to determine?
Total risk of an undiversified portfolio
What is the Exam Tip for Standard Deviation?
- 68, 95, 99% depending if the return is +/- 1, 2 or 3 standard deviations away from the average
Calculate the standard deviation for two stocks given the following returns over 5 years:
A: 10%, 13%, 8%, -2%, 14%
B: 6%, -3%, 4%, -5%, 7%
- Use the Σ+ key to enter each return, then [SHIFT] {SX, Sy] to solve
A: 6.3875%
B: 5.4498%
Stock A is more risky because it has a higher Standard Deviation
How could a CFP Exam question regarding Standard Deviation be phrased?
“Which of the following assets is most risky?”
They are really asking you to calculate the standard deviation and select the asset with the higher standard deviation.
Calculate the total expected return:
Expected Return__Probability of Return
10% 30%
15% 60%
18% 10%
The calculation is simply the sum of all expected returns multiplied by their respective probabilities:
Return = Σ (R X Probability)
Answer: 13.8%
What is Coefficient of Variation?
- Useful in determining which investment has more relative risk when investments have different average returns
- tells us the probability of actually experiencing a return close to the average return
- The higher the CV the more risky an investment per unit of return
Which investment has the highest risk per unit of return earned?
A: STD=12% and Avg Return=10%
B: STD=8% and Avg Return=5%
CV = Standard Deviation / Average Return
A: .12/.08=1.20
B: .08/.05=1.60
B has more risk per unit, don’t assume that just because A has higher standard deviation that it is more risky
When is it appropriate to consider a Normal Distribution?
If an investor is considering a range of investment returns.
When is it appropriate to consider a Lognormal Distribution?
- Not a normal distribution
- When considering a dollar amount or portfolio value at a point in time.
- looking for a trend line or ending dollar amount
Describe positive and negative skewness:
- Positive: tail stretches to the right (mode, median, mean)
- Negative: tail stretches to the left (mean, median, mode)
What is Kurtosis?
- Refers to the variation of returns
What is positive and negative Kurtosis?
- Positive: little variation of returns, high curve peak
- Negative: widely dispersed returns, low curve peak
What is Leptokurtic?
High peak and fat tails (higher chance of extreme events)
What is Platykurtic?
low peak and thin tails (lower chance of extreme events)
What is Mean Variance Optimization?
- Adding risky securities to a portfolio, but keeping the expected return the same
- Finding the balance of combining asset classes that provide the lowest variance as measured by standard deviation
What is Covariance?
- the measure of two securities combined and their interactive risk
- In other words, how price movements between two securities are related to each other
- A measure of relative risk
- If correlation coefficient is known, or a given, covariance is calculated as the deviation of investment “A” times the deviation of investment “B” times the correlation of investment “A” to investment “B”
- Provided on Formula sheet
- COVAB = (σA) (σB) (þAB)
- Where:
- (σA) = Standard deviation of Asset A
- (σB) = Standard deviation of Asset B
- (þAB) = Correlation coefficient of Assets A and B
What is Correlation/Correlation Coefficient?
- NOT A PROVIDED FORMULA; it is an algebraic equivalent of the Covariance formula (provided)
- Correlation and the covarianc measure movement of one security relative to that of another; both are relative measures
- þAB = COVAB / (σA) (σB)
Where:
(σA) = Standard deviation of Asset A
(σB) = Standard deviation of Asset B
(þAB) = Correlation coefficient of Assets A and B
Describe the correlation ranges +1 to -1:
- provides insight as to the strength and direction two assets move relative to each other
- A correlation of +1, two assets are perfectly positively correlated
- A correlation of 0; assets are completely uncorrelated
- A correlation of -1; perfectly negatively correlated
- Diversification benefits (risk is reduced) begin anytime correlation is less than 1
What is Beta coefficient?
- measure of an individual security’s volatility relative to that of the market
- Used to measure a diversified portfolio
- measures systematic risk dependent on the volatility of the security relative to that of the market
- Beta of the market is 1
- The greater the beta coefficient of a given security, the greater the systematic risk associated with that particular security
What is another method of calculating Beta?
Dividing the security risk premium by the market risk premium
Q1: What is the coefficient of determination or R2?
Q2:
- A1:
- A measure of what percentage of a security’s return is due to the market
- Provides insight into how well diversified portfolio is
- Higher = more return from market (systematic risk)
- Tells if Beta is appropriate measure for risk
- > 0.70 = appropriate
- < 0.70 then not apprpriate, used standard deviation
- A2: squaring the correlation coefficient
What does the Portfolio Deviation or Standard Deviation of a Two Asset Portfolio do?
- The risk of a portfolio
- Utilizes weight, deviations and correlation coefficient of both securities involved, Square root
- Provided on exam formula sheet, may not be necessary to use
- Can use weighted avg of the deviation, can be used to eliminate answers at least
What is the mnemonic for Systematic Risk?
PRIME
-
Purchasing Power Risk*
- Inflation will erode the amount of goods/services that can be purchased
- A dollar today can purchase the same amount tomorrow
-
Reinvestment Rate Risk*
- Will not be able to reinvest at the same rate of return currently being received
- Mostly impacts bonds
-
Interest Rate Risk*
- Changes in interest rates will impact both equities and bonds
- Inverse relationship between IR and equities/bonds
-
Market Risk
- Ups and downs for market, impacts all securities in short-term
-
Exchange Rate Risk
- change will impact price of international securities
What is the mnemonic for Unsystematic Risk?
ABCDEFG
-
Accounting Risk
- Audit firm too closely tied to company (Arthur Anderson/Enron)
-
Business Risk**
- inherent to operating in a particular industry
-
Country Risk**
- Doing business in a particular country
-
Default Risk**
- defaulting on debt payments
-
Executive Risk
- moral and ethical character of company management
-
Financial Risk**
- Financial leverage deployed by firm, ratio of debt vs. equity
-
Government/Regulation Risk**
- Tariffs/Restrictions placed on firm/industry affecting company’s ability to compete
**MOST LIKELY TO BE TESTED
Define Modern Portfolio Theory:
- The acceptance by an investor of a given level of risk while maximizing expected return objectives.
- Investors seek the highest return attainable at any level of risk
- Investors want the lowest level of risk at any level of return
- Assumption made tthat investors are risk averse
What is the Efficient Frontier?
- The curve which illustrate the best possible returns that could be expected from all possible portfolios
- To determine, compare portfolios based upon their risk-return relationship
- Represents the most “efficient” portfolios in terms of risk-reward relationship
- investor cannot achieve a portfolio that has a higher return for each level of risk
- Portfolios that lie BENEATH the EF are “INEFFICIENT” because there is a portfolio that provides more return for that level of risk
- The area ABOVE the EF is considered “UNATTAINABLE”.
What are the X and Y axis of Modern Portfolio Theory?
- X = RISK
- Y = RETURN
Explain Indifference Curves and how they look for an risk-averse and risk-seeking investor:
- Represents how much return an investor needs to take on risk
- Constructed using selections made based on the highest level of return given an acceptable level of risk
- Risk-averse: Steep; require more return to take on a little more risk
- Risk-seeking: Flat; don’t require more return to take on more risk
What is the Efficient Portfolio? Optimal?
- Efficient: Occurs when an investors indifference curve is tangent to the efficient fronter
- Optimal: the one selected from all the portfolios
What is the Capital Market Line (CML)?
- The macro aspect of the Capital Asset Pricing Model (CAPM)
- Specifies relationship between risk and return in all possible portfolios
- becomes the new efficient frontier, mixing in risk-free asset with a diversified portfolio
- A portfolio’s returns should be on the CML
- Inefficient portfolios are below the CML
- Not used to evaluate the performance of a single security
- EXAM TIP: Formula no longer on formula sheet, may be aske what measure of risk the CML uses (standard deviation)
- formula on page 35 of book
- required portfolio return = Risk Free ROR + Standard Deviation of Portfolio TIMES (return of the market - Risk Free ROR / Standard Deviation of the market)
What is the Capital Asset Pricing Model (CAPM)
- calculates the relationship of risk and return of an individual security using the Beta (b) as its measure of risk
- often referred to as Security Market Line (SML) equation because its inputs and results are used to construct the SML
- Equation:
- Required/Expected ROR = risk-free ROR PLUS (return of the market MINUS risk-free ROR) TIMES Beta
What is the equation for market risk premium?
- (rm - rf)
- rm = return of the market
- rf = risk-free rate of return
- EXAM TIP: you may be given market risk premium rather than return of the market
What is the Security Market Line?
- The relationship betwen risk and return as defined by the CAPM and graphically plotted results
- SML intersects y-axis at the risk-free rate of return
- Uses Beta as measure of risk (CML uses Standard Deviation)
- Returns above SML = undervalued/should be purchased
- Returns below SML = overvalued/should NOT be purchased
- May be used with individual securities
What is the Information Ratio?
- Measures the excess return and consistency provided by a fund manager, relative to a benchmark
- a relative risk-adjusted performance measure
- The higher the excess return (or Inofrmation Ratio) the better
- Can be positive or negative depending on fund’s performance relative to its benchmark
FORMULA:
IR = Portfolio’s actual return minus Return of the Benchmark divided by the Tracking Error of active return (standard deviation of the difference between portfolio returns and index returns) of the portfolio (p. 39)
What is the Treynor Ratio?
- A measure of how much return was achieved for each unit of risk
- the higher the better
- used for a diversified portfolio
- relative, risk-adjusted performance measure (must be compared to another Treynor)
- risk defined by Beta
- assumes that in a well-diversified portfolio, the unsystematic risk is already close to zero
- DOESN’T indicate if a portfolio manager has out/under performed the market
FORMULA:
Tp= (realized return on the portfolio) - (risk-free ROR) / Beta of the portfolio; p39
What is the Sharpe Index?
- A measure of how much return was achieved for each unit of risk
- the higher the better
- used for a non-diversified portfolio
- a relative risk-adjusted performance measure (must be compared to another)
- Measures risk premiums of the portfolio relative to the total amount of risk in the portfolio
- DOES NOT measure portfolio managers performance against that of the market
FORMULA:
Sp = (realized return of the porfolio) - (risk-free ROR) / standard deviation of the portfolio); p 40
What is the Jensen Model or Jensen’s Alpha?
- A measure of absolute performance on a risk-adjusted basis
- unlike Sharpe/Treynor, cabaple of distinguishing a manager’s performance relative to that of the market and determining differences between realized or actual returns and required returns as specified by CAPM
- positive = more return than expected for risk undertaken
- negative = less return for the risk undertaken
- zero = equal return for risk undertaken
- unlike Sharpe/Treynor, cabaple of distinguishing a manager’s performance relative to that of the market and determining differences between realized or actual returns and required returns as specified by CAPM
Formula:
ap = (realized portfolio return) - [risk-free ROR + (expected return of the market - risk-free ROR)*Beta]
What risk-adjusted performance measure is best to use with a diversified portfolio?
- Treynor and Alpha
- because they use Beta as measure of risk
When is a porfolio considered diversified?
- when r-squared is greater than or equal to 0.70
What risk-adjusted performance measure is best to use when a portfolio is not well diversified?
- Sharpe
- Uses Standard Deviation
- Q1: Which performance measures are relative?
- Which performance measures are absolute?
- What do you use to select the risk-adjusted performance measure?
- How do you calculated r-squared?
- A1:
- Sharpe & Treynor
- A2:
- Alpha
- A3:
- r-squared
- A4:
- correlation squared, e.g. .80 correlation = 0.86 R-quared
