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