Section I.A. Flashcards
Measures of Dispersion
*variance
*standard deviation
*semi variance
*semi deviation
*coefficient of variation
What is N vs. N 1?
If you are using all of the data available (i.e., a population) then use “N”;
if they are only using a sample then use “N 1” when calculating standard deviation.
- look for whether they actually tip you off by stating this is the entire data set or just a sampling.
- Start with N first and then go to N 1 on the exam
Variance
- Defined as the average squared difference between the mean and
each item in the population or in the sample. - Variance is always non negative.
Application
- A high variance means that data points are very spread out.
* Variance value of zero means that all values within the set are identical.
Steps for Calculating Variance
- Calculate the arithmetic mean rate of returns
- Subtract the mean rate of return from each year’s returns
- Square the differences
- Add the squares of the differences and find the arithmetic average of the sums = variance
Population
Sample
What is Standard Deviation?
Defined
* A measure of dispersion expressed as the square root of the variance.
- Measures the amount of variability around the average or mean.
- An advantage of using standard deviation (as compared to variance) is that it expresses dispersion in the same units as the original values in the sample or population.
Application:
* A low standard deviation indicates that data points gather close to the mean while a high standard deviation indicates that data points are spread far apart from the mean.
Standard Deviation is considered a measure of what?
“total risk”
Standard Deviation is used in what formulas?
Sharpe Ratio, M2, Information Ratio
What are the percentages for Standard Deviation?
What are the steps for Calculating Standard Deviation?
1.Calculate the arithmetic mean rate of returns
2.Subtract the mean rate of return from each year’s returns
3.Square the differences
4.Add the squares of the differences and find the arithmetic average of the sums = variance
5.Take the square root of variance = standard deviation
How do you Annualize Standard Deviation?
The quarterly standard deviation of a portfolio has been calculated to be 3.50.
Convert the quarterly standard deviation to annualized standard deviation.
Answer: a. 7.00
Solution: Multiply 3.50 by the square root of 4.
(3.50) x (2.00) = 7.00
What is Semi-Variance?
Defined
* Measures data that is below the mean or target value of a data set.
* Considered a better measurement of downside risk.
* Semi variance is the average of the squared deviations of all values less than the average or mean.
What is Coefficient of Variation (CV)?
- The ratio of the standard deviation to the mean.
- aka: relative standard deviation
- Formula: CV = standard deviation/mean.
- Result: it shows the extent of variability in relation to mean of
the population. - Assumptions: normal distribution.
Application:
* For comparison of data sets with different units or widely different means, one should use the CV instead of standard deviation.
What is Skewness? (Defined)
What is Skewness? (Applied)
What is Kurtosis?
What is Normal Distribution?
Investment management is easier when returns are normal.
– Standard deviation is a good measure of risk when returns are symmetric.
– If security returns are symmetric, portfolio returns will be, too.
– Future scenarios can be estimated using only the mean and the standard deviation.
Normal Distribution is considered foundational to what?
The development of Modern Portfolio Theory.
What if excess returns are not normally distributed?
– Standard deviation is no longer a complete measure of risk
– Sharpe ratio is not a complete measure of portfolio performance
– Need to consider skew and kurtosis
You expect there is a 68% probability of an investment returning 7% over the next 12 months and a 32% probability of a 0% return. What is the expected return on this investment?
Q: For a risky asset, you expect there is a 68% of an investment returning 7% over the next 12 months and a 32% probability of a 0% return. The risk-free money market fund should return 2% over the same period. Your portfolio mix is 80% risky asset and 20% risk-free asset. What is the expected return on this mixed investment?
Question: You are presented with an investment strategy with a mean return of 20% and a standard deviation of 10%. What is the approximate probability of a negative return if the returns are normally distributed?
What are the uses, advantages, and disadvantages of Monte Carlo Simulations?
What is Covariance?
Defined:
* indicates how two variables are related
* a measure of the degree to which the returns of two assets move together
* a positive covariance indicates that assets move together while a negative covariance indicates that assets move inversely
* assets possessing a high covariance with each other do not offer much diversification
Question: The correlation coefficient between investment A
and B is .63 and the standard deviations of investments A and B
are 13.65% and 17.44% respectively. What is the covariance of
investments A and B?
Answer
: [(.63) x (.1365 x .1744)] = 0.015
What is Correlation Coefficient?
- indicates the degree of relationship between two variables;
- always lies between (-1) and +1;
(-1) indicates perfect negative relationship between two variables, +1 indicates perfect positive linear relationship, and 0 indicates lack of any linear relationship
Question: The covariance between investment A and B is .015
and the standard deviations of investments A and B are 13.65%
and 17.44% respectively. What is the correlation coefficient of
investments A and B?
Answer:
[(.015)/(.1365 x .1744)] = 0.63
