Portfolio Theory (L2) Flashcards
Standard Deviation (total risk)
- A measure of risk and variability of returns
- HIGHER the SD = the HIGHER the riskiness of the investment
- Can be used to determine TOTAL RISK of an UNDIVERSIFIED portfolio
- Probability of Returns Graph (pg. 18)
Calculating Standard Deviation
- Will vary depending on your financial calculator. Use SAMPLE SD for the CFP Exam
- EXAMPLE:
○ Dan has 2 stock in his portfolio, calculate the SD
for both stocks, given the following returns of the
past 5 years…
§ Stock A - 10%, 13%, 8%, -2%, 14%
§ Stock B - 6%, -3%, 4%, -5%, 7%
○ Answers:
§ Stock A
□ 10[Sigma +], 13 [Sigma +], 8 [Sigma +].
-2[Sigma +], 14 [Sigma +]
□ [ORANGE] [Sx,Sy]
□ = 6.3875
§ Stock B □ 6 [Sigma +], -3 [Sigma +], 4 [Sigma +], -5 [Sigma \+], 7 [Sigma +] □ [ORANGE][Sx,Sy] □ = 5.4498
**Stock A is consider MORE RISKY
Coefficient of Variation
CV = SD / Average Return
- Useful in determining which investment has more RELATIVE RISK when investments have different average returns
- Tell us the probability of actually experiencing a return close to the average return
- The HIGHER the coefficient of variation = the MORE RISKY an investment per unit of return
Normal Distribution
Appropriate if an investor is considering a range of investment returns, as we covered above
Lognormal Distribution
○ NOT a Normal Distribution
○ Appropriate if an investor is considering a DOLLAR AMOUNT or PORTFOLIO VALUE at a point in time
For Example, if an investor invests $1 into the market 60 years ago, it would be worth $60 today. With a LOGNORMAL DISTRIBUTION you are looking for a trend line or ending dollar amount
Skewness
○ Refers to a normal distribution curve shifted to the left or right of the mean return.
○ Commodity returns tend to be skewed
○ Positive vs Negative Skewness Graph (pg. 22)
Kurtosis
○ Refers to variation of returns
○ POSTIVIE Kurtosis ==> LITTLE VARIATION of returns = distribution will have a HIGH PEAK (Treasuries)
○ NEGATIVE Kurtosis ==> LARGE VARIATION (widely dispersed) of returns = distribution will have a LOW PEAK
Leptokurtic
○ HIGH peak, FAT Tails
○ Higher chance of extreme events
Platykurtic
○ LOW peak, THIN Tails
○ Lower chance of extreme events
Mean Variance Optimization
○ The process of adding risky securities to a portfolio, but keeping the expected return the same
○ Its finding the balance of combining asset classes that provide the LOWEST VARIANCE as measured by SD.
Monte Carlo Simulation
A spreadsheet simulation that gives a probabilistic distribution of events occurring.
Covariance
(Provided on CFP formula sheet)
- The measure of 2 securities combined and their interactive risk. (how price movements between 2 securities are related to each other)
- Measure of RELATIVE RISK
- If the correlation coefficient is known, or 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” thus:
Correlation/Correlation Coefficient
- Correlation and the covariance measure movement of one security relative to that of another
- Covariance and correlation coefficient are BOTH RELATIVE MEASURES
- Correlation Coefficient is calculated as follows:
○ Correlation Coefficient = Covariance / (SDa)(SDb) - Correlation ranges from +1 to -1
○ Provides the investor with insight as to the
strength and direction two assets move relative
to each other
○ +1 = perfectly POSITIVE correlation
○ 0 = completely uncorrelated
○ -1 = perfectly NEGATIVE correlation - Diversification Benefits
○ Risk is reduced
○ BEGIN anytime correlation is LESS THAN 1
Beta (market risk)
- Beta coefficient is a measure of an individual security’s volatility TO THAT OF THE MARKET
- Best used to measure the volatility of a diversified portfolio
- Also, a measure of MARKET RISK (systematic risk)
- Measure SYSTAMTIC RISK dependent on the volatility of the security relative to that of the market
○ Market Beta = 1 - The GREATER the Beta Coefficient of a given security = the GREATEER THE SYSTEMATIC RISK associated with that security
- BETA may also be calculated = Security Risk Premium / Market Risk Premium
Coefficient of Determination of R-Squared
- Calculated by squaring the correlation coefficient (R)
- R-Squared is a measure of how return is due to the market OR what % of a security’s return is due to the market
- Also provides the investor insight into how well-diversified a portfolio is, because the HIGHER the r-squared, the HIGHER the % of return is from the market (systematic risk) and the less from unsystematic risk
- Tell the investor if Beta is an appropriate measure of risk
- If R^2 is GREATER THAN or EQUAL to 0.70
○ Beta is an appropriate measure of total risk - If R^2 is LESS THAN 0.70
○ SD is an appropriate measure of total risk
Portfolio Risk
(Provided in CFP formula sheet)
- The risk of a portfolio can be measure through determination of the interactivity of the SD and Covariance of securities in the portfolio
- The process also utilizes the weight of both securities involved, the deviations of the respective securities, and the correlation coefficient of the 2 securities.
- Formula = PORTFOLIO DEVIATION FORMULA or SD OF A 2 ASSET PORTFOLIO
Capital Market Line (CML)
- What Measure of Risk does CML use? Standard Deviation (SD)
- The MACRO aspect of the Capital Asset Pricing Model (CAPM). It specifies the relationship between risk and return in all possible portfolios
- CML becomes the new efficient frontier, mixing in the risk-free asset with a diversified portfolio
- Portfolio returns should be on the CML
- Inefficient portfolios are below the CML
- The CML is NOT USED to evaluate the performance of a single security
CML Graph
- The CML intersects the Y-axis at the RISK FREE RATE because an investor with 100% of his assets in the risk-free asset will yield a return but experience no variability (SD)
- CML runs tangent (touches only ONE SPOT) with the Efficient Frontier at the “optimal portfolio” or the “tangency portfolio”
- Before the CML touches the Efficient Frontier
○ Investor is said to have a security allocation made
up of the optimal portfolio mix and is LENDING a
portion on uninvested assets at the RISK FREE RATE - AT the optimal portfolio
○ Investor is fully invested in that portfolio
○ Does not lend anything at the risk free rate OR
borrow at that rate - AFTER (to the right) of the optimal portfolio
○ The investor is said to have BORROWED at the RISK
FREE RATE to fully invest all capital and borrowed
funds in that portfolio
Capital Asset Pricing Model (CAPM)
(Provided in CFP Formula Sheet)
- Calculates the relationship of risk and return of an individual security using the BETA as the measure of risk
- CAPM formula = Security Market Line (SML) equation
○ It inputs and results are used to construct the SML - Market Risk Premium = Market Return MINUS Risk Free Rate
Portfolio Performance Measures
Sharpe Ratio (SD)
Treynor Ration (BETA)
Jensen’s Alpha (BETA)
**If the CFP exam does not give you R^2, then use the Sharpe Ratio
***all formulas provided
Information Ratio
(Provided in CFP formula sheet)
○ A RELATIVE Risk-Adjusted performance measure
○ Measures that excess return and the consistency provided by a fund manager, RELATIVE to a benchmark
○ The HIGHER the excess return (or Information Ratio) = BETTER
○ Excess Return can be POSITIVE/NEGATIVE dependent on the funds’ performance relatives to its benchmark
Treynor Index
- Uses the BETA of a portfolio as its denominator, and the difference between the portfolio return and the Risk-Free Rate
- A risk adjusted performance measure
○ It’s also a RELATIVE risk adjusted performance
measure indicator, meaning one Treynor ratio needs
to be compared another to provide meaning - A measure of much return was achieved for each unit of risk
○ The HIGHER the Treynor ratio, the BETTER because
that means more return was provided for each unit
of risk - It measures the reward achieved relative to the level of SYSTEMATIC RISK (as defined by BETA)
- Accomplished by standardizing portfolio returns for volatility
- Treynor justifies use of the model on the assumption that in a well-diversified portfolio, the unsystematic risk is already close to ZERO
- Treynor Index DOES NOT indicate whether a portfolio manager has outperformed/underperformed the market
Sharpe Index
- Provides a measure of portfolio performance using a RISK ADJUSTED measure that standardizes returns for their variability. The model rewards the total variability, or TOTAL RISK.
- A risk adjusted performance measure
○ It’s also a RELATIVE risk adjusted performance
measure indicator, meaning one Shape ratio needs
to be compared another to provide meaning - A measure of much return was achieved for each unit of risk
○ The HIGHER the Sharpe ratio, the BETTER because
that means more return was provided for each unit
of risk - Sharpe Index measures risk premiums of the portfolio relative to the total amount of risk in the portfolio
- The formula DOES NOT measure a portfolio managers performance against that of the market
Jensen’s ALPHA (or Jensen Model)
- Significantly different from Sharpe or Treynor in that the Jensen’s ALPHA is capable of distinguishing a mangers performance relative to that of the market and determining differences between realized (or actual) returns and required returns as specified by CAPM
- Model attempts to construct a measure of ABSOLUTE PERFORMANCE on a risk adjusted basis (not relative)
- Absolute Performance Measure simply means that looking at Jensen’s ALPHA tells you something
○ Positive ALPHA ==> indicates that the fund
manager provided MORE return than was expected
for the risk undertaken
○ Negative ALPHA ==> indicates that the fund
manager provided LESS return than was expected
for the risk undertaken
○ ALPHA = 0 ==> indicates the fund manager
provided a return EQUAL to the return that was
expected for the risk that was undertaken
