Investments Lesson 2 Flashcards
Standard Deviation
Measure of risk & variability of returns
Total risk of undiversified portfolio (unsystematic)
1 standard deviation away will fall within __%
2 standard deviations away will fall within __?
3 standard deviations away will fall within __?
68%
95%
99%
Probability/Expected Return Formula
Sum of all (R x probability)
Coefficient of Variation
Which investment has more relative risk
Probability of experiencing return close to average return
CV = standard deviation / average return
Distribution of Returns:
Normal: considering range of investment returns
Lognormal: considering dollar amount of portfolio value at a point in time (looking for trend line or ending dollar amount)
Skewness: normal shifted left or right (commodities tend to be skewed)
Kurtosis
Variation of returns
Little variation: high peak/positive kurtosis
If returns high dispersed, low peak, negative kurtosis
Leptokurtic: high peak/fat tails (higher change of extreme events)
Platykurtic: low peak/thin tails (lower chance of extreme events)
Example Exam Question:
Noticed stock purchases tends to have very tight distribution around mean but seems to be high probability of outliers. This is most indicative of what type of curve?
A. Positive skewness
B. Leptokurtosis
C. Normal
D. Lognormal
B
Mean Variance Optimization
Process of adding risky securities to portfolio but keeping expected return the same. Balance of combining asset classes & provide lowest variance as measured by standard deviation
Monte Carlo Simulation
Gives a probabilistic distribution of events occurring
Adjusts assumptions & returns probability of an event occurring depending upon the assumption
Covariance
Measure of 2 securities & their interactive risk
“How price movements between 2 securities are related to each other”
Measure of relative risk
*formula provides
Correlation Coefficient
Measure movement of one security relative to that of another
Relative measure
Ranges from +1 to -1
1: perfectly positively correlated
0: completely uncorrelated
-1: perfectly negative correlation
Risk is reduced/diversification benefits are anytime correlation is less than 1
Example Exam Question:
When combining asset classes, investor receives diversification benefits when correlation is:
A. Equals -1 B. Less than 1 C. Less than 0 D. Less than or equal to 1 E. Equals 0
B
Beta
Measure of individual security’s volatility relative to that of the market
Volatility for diversified portfolio (systematic risk)
Beta of market is 1
Beta of 1 will mirror market
Beta of higher than 1: more risk
Beta of lower than 1: less risk
May also be calculated by dividing security risk premium by market risk premium
Example Exam Question:
When considering diversified portfolio, which is an appropriate measure of risk?
A. Standard deviation B. Beta C. Covariance D. Coefficient of determination E. Correlation coefficient
B
Coefficient of Determination (R-squared)
How much return is due to market
Calculate by squaring correlation coefficient
How well diversified a portfolio is - tells you if beta is appropriate
Example Exam Question:
Mutual fund has 5 year return of 12%, standard deviation of 15%. Beta of 1.4. Correlation of .90 to S&P 500. What percent of return from fund is due to S&P 500?
A. 90%
B. 81%
C. 19%
D. 10%
B
Example Exam Question:
Which mort appropriate benchmark for Sam to measure portfolio against?
Index 1: Beta .90, Std Dev 10%, r-squared .85%
Index 2: Beta 1.0, std dev 12% r-squared .89
Index 3: beta 1.5, std dev 15%, r-squared .95
A. 1 B. 2 C. 3 D. 1&2 E. 1&3
C
Portfolio Risk
Formula on exam
Systematic Risk
Lowest level of risk in fully diversified portfolio PRIME Purchasing Power Reinvestment Rare Interest Rate Market Exchange Rate
Unsystematic Risk
Risk that exists but could be eliminated through diversification ABCDEFG Accounting Business Country Default Executive Financial Government/Regulation
Example Exam Question:
Stock index funds & exchange traded fund that track market indices are subject to which risks?
A. Financial B. Business C. Systematic D. Unsystematic E. Diversifiable
C
Example Exam Question: Which are nondiversifiable risks? 1. Business 2. Management 3. Company or industry 4. Market 5. Interest rate 6. Purchasing power
A. 4,5,6 B. 1,2,3 C. 5,6,2 D. 1,3,4 E. 1,4,5
A
Modern Portfolio Theory:
Acceptance of given level of risk while maximizing expected return objectives
Efficient Frontier
Curve which illustrates best possible returns to be expected from all portfolios
Indifference Curves:
Highest level of return given acceptable level of risk
Efficient Portfolio:
When indifference curve is tangent to efficient frontier
Optimal Portfolio:
Selected from all efficient portfolios
Example Exam Question:
- Not many assets. Which on effjcient frontier?
1: expected return 4% risk 3%
2: er 6% risk 3%
3: er 8% risk 5%
4: er 8% risk 8%
5: er 10% risk 12%
A. 1,3
B. 2,3
C. 2,4
D. 4,5
B
Example Exam Question:
Modern asset allocation based upon model by Markowitz. Which is true in this model?
1. Risk, return, Covariance are important input variables in creating portfolios
2. Negatively correlated assets are necessary to reduce risk of portfolios
3. In creating portfolio, diversifying across asset types is less effective than diversifying within asset type
4. Efficient frontier is relatively insensitive to input variable
A. 1,2 B. 1,2,3 C. 1 D. 2,4 E. 1,2,4
C
Indifference Curves
Risk averse: steep
Risk seeking: flat
Optimal portfolio where indifference curve touches efficient frontier
Capital Market Line
Becomes new efficient frontier mixing risk free asset with diversified portfolio Portfolios returns should be on CML Inefficient portfolios below CML Not used to evaluate single securities Uses standard deviation Intersects y-axis at risk free rate
At optimal portfolio, investor is fully invested not lending anything at risk free rate or borrowing
To the right of optimal portfolio, investor is said to have borrowed at risk free rate to fully invest all capital & borrowed funds in that portfolio
Portfolio above efficient frontier/capital market line is __?
Below is __?
Unobtainable
Inefficient
Capital Asset Pricing Model (CAPM)
Uses Beta
Also Security Market Line Equation (SML)
Rm-Rf is market risk premium
May be used with individual securities
Example Exam Question:
Risk free rate is 3%. Beta is 1.5. Market risk premium is 9%. What is expected return?
A. 13.5% B. 12.5% C. 16.5% D. 12.0% E. 13.0%
C
Return above SML, considered __ & __ be purchased?
Return below SML, considered __ & __ be purchased?
Undervalued & should
Overvalued & should not
Example Exam Question:
What is intersection on y-axis of CML/SML?
A. Risk free rate B. Market portfolio C. Undervalued asset D. Overvalued asset E. Indeterminable
A
Information Ratio:
Relative risk adjusted performance measure
Measures excess return & consistency relative to benchmark
Higher is better
Can be positive or negative
IR = (Rp-Rb) / std dev A
Rp-Rb is excess return
Treynor Index:
Measures volatility using Beta Relative (must be compared to provide meaning) Systematic: well-diversified portfolio Doesn’t indicate performance Formula on sheet
Example Exam Question:
Considering 2 mutual funds. Growth has beta of 1.2. Risk free rate is 3%. Which do you recommend based on Treynor? Growth actual return: 12%. Index actual return: 9%.
A. Growth
B. Index
C. Growth & Index both have same risk-adjusted returns
D. None
A
Sharps Index
Measures variability using standard deviation
Relative
Example Exam Question:
Evaluating 2 mutual funds not well diversified. How do you recommend evaluating on risk-adjusted basis?
A. Calculate Treynor & select highest
B. Calculate Sharpe & select highest
C. Calculate Treynor & select lowest
D. Calculate Sharpe & select lowest
B
Jensen Model/Jensen’s Alpha
Measure of absolute performance on risk-adjusted basis \+: more return than expected -: less return than expected 0: equal to return expected Uses beta Judged relative to CAPM
Example Exam Question:
Which do you recommend?
Fund A: std dev 12%, r-squared .92, alpha 2.0, sharpe 1.2
Fund B: std dev 13, r-squared .90, alpha 1.8, sharpe 1.5
A. A because higher alpha
B. A because lower std dev
C. B because higher sharpe
D. B because higher std dev
A
Example Exam Question:
Returned 19% last year with beta of 2. Risk free rate was 3%. Market return was 8%. Std dev was 18%. What would you say regarding performance of fund?
A. Std dev too high, under compensated for risk
B. Sharpe is 1, earned adequate risk-adjusted return
C. Sharpe is 1, earned return less than required
D. Market outperformed mutual fund on risk adjusted basis
E. Alpha is 6%, which means fund manager returned higher rate of return than expected on risk-adjusted basis
E
Example Exam Question:
Fund beat market by 2%. Alpha of 2%. Under what circumstances is comment true?
A. Always, as it meets definition of alpha
B. Only if risk free rate is 0
C. Only if beta of fund is 1
D. Only if correlation is positive
C
Example Exam Question:
If mutual fund has correlation of .80 to S&P 500, which appropriate risk-adjusted performance measures?
A. Treynor B. Jensen C. Sharpe D. Treynor & Sharpe E. Treynor & Jensen
C
Lesson 2 Review:
Optimal portfolio occurs at the point of tangency between:
A. Utility curve & efficient frontier
B. Indifference curve & portfolio deviation
C. Efficient frontier & indifference curve
D. Optimal curve & utility function
C
Lesson 2 Review:
Asked you to speak of difference between variability of security & volatility of security. You explain by:
A. Variability is measured using deviation
B. Volatility measured using coefficient of variation
C. Variability measured using beta
D. Volatility measured using cov
A
Lesson 2 Review:
Two securities have perfect negative correlation. That means it A goes up 10, B goes down -0. Under these circumstances, how can a client ever hope to make any money?
A. If buy 2x as much A as B
B. Client should be striving for perfect positive correlation instead
C. The two will provide mean expected return & offset any risk
D. Client should sell rising stock & take profit to buy falling stock
C
Lesson 2 Review:
Portfolio made up of 2 assets. Info as follows:
US: return 12.2%, deviation 10.5%, weight 60%
Swaziland: return 18.4%, deviation 23.8%, weight 40%
Estimate risk. Correlation is .3.
Portfolio deviation is:
A. 20.6%
B. 12.9%
C. 8.5%
D. 18.9%
B
Lesson 2 Review:
Client purchasing stocks. Actual return as follows: 6,12,8,10. What is std dev?
A. 1.64
B. 2.58
C. 5.42
D. 10.72
B
Lesson 2 Review:
What does the term overvalued refer to with regards to the SML?
A. Alpha of security is above SML
B. Security is returning more value than expected
C. Security is selling at a low price compared to calculated value
D. Security is selling at a high price compared to calculated value
D
Lesson 2 Review:
Which formula Carrie’s out direct or absolute comparison between manager’s performance & performance of the market?
A. Treynor
B. Jensen
C. Sharpe
D. Belth
B
Lesson 2 Review:
Which of the performance models measures risk using a different variable than the others?
A. Treynor
B. Jensen
C. Sharpe
D. CAPM
C
Lesson 2 Review:
Which risk measure is appropriate to use when measuring risk of diversified portfolio?
A. Covariance
B. Standard deviation
C. Beta
D. Correlation
C
Lesson 2 Review:
Which risk measure is appropriate to use when measuring risk of nondiversified portfolio?
A. Covariance
B. Standard deviation
C. Beta
D. Correlation
B
Lesson 2 Review:
Assume fund has average return of 10% with standard deviation of 5%. What is probability of achieving return less than 0%?
A. 2.5%
B. 5%
C. 16%
D. 32%
A
Lesson 2 Review:
Mutual fund has correlation coefficient of .80. What percent of return is due to unsystematic risk?
A. 36%
B. 64%
C. 80%
D. 100%
A
Lesson 2 Review:
Which is a diversifiable risk?
A. Interest rate
B. Market
C. Purchasing power
D. Regulation
D
Lesson 2 Review:
All are unsystematic risks except:
A. Business
B. Default
C. Exchange rate
D. Financial
C
