Quantitative Investment Concepts

Question 1

Normal Probability Distribution

Answer 1

• characterized by a single peak in the center, which is the location of the arithmetic mean of the series of observations.
• also known as the bell curve
• assuming a normal distribution, an actual rate of return on investment will occur 68% of the time within one standard deviation of the arithmetic mean, 95% of the time within two standard deviations, and 99% of the time within three standard deviations of the mean.

Question 2

Lognormal Probability Distribution

Answer 2

• a probability distribution in which the series of observations is skewed to the left of the arithmetic mean.
• implies that there is a 50% chance that an observation selected at random will fall to the left of the mean.
• assumed whenever the investor is analyzing the ending or future value of a portfolio.

Question 3

Skewness

Answer 3

• measures how far the actual outcomes of a probability distribution deviate from the arithmetic mean.
• effectively, what is being measured in decimal terms is how far the median return is from the mean return.

Question 4

Positively Skewed

Answer 4

• the median return is less than the mean return
• exposes an investor to the possibility of a greater number of returns below the mean return than does an investment with positive skewness.

Question 5

Negatively Skewed

Answer 5

• the median return is greater than the mean return

- investor assumes more total (including downside) risk with a negatively skewed investment

Question 6

Kurtosis

Answer 6

• measures the degree of “fatness” in the tails of a probability distribution
• greater fatness or less peaked distribution, means that more returns with large deviations from the mean return have occurred than with a normal distribution i.e more total risk.

Question 7

Correlation Coefficient (R)

Answer 7

-measures how the returns of two assets are related and ranges in value from -1.0 to +1.0

Question 8

if R = +1

Answer 8

the two securities are perfectly positively correlated; the two securities move together exactly and there is no reduction of portfolio risk

Question 9

if R = -1

Answer 9

-the two securities are perfectly negatively correlated; the two securities move in exactly opposite of each other; risk is completely eliminated

Question 10

if R = 0

Answer 10

-there is no correlation between the price changes of these securities; that is, they move completely independent of one another; portfolio risk is unaffected.

Question 11

Coefficient of Determination (R squared)

Answer 11

• measures the proportion of the variation in one variable explained by the movement of other variables.
• can be used in comparing the movement of one stock to the market as a whole and the extent to which the portfolio is diversified.
• return is not measured, only risk

Question 12

Example of R Squared

Answer 12

• correlation is .81 between two securities
• .81x.81 = .656 or 65.6%
• this means that exactly 65.6% of the variation in the return of security A may be explained in the return of security B. The remaining 34.4% of the variation in Security A is due to other factors.

Question 13

Coefficient of Varitaion

Answer 13

• reflects the relative dispersion of one security to another on the basis of total risk per unit of expected return.
• CV = Standard Deviation/Expected or mean return
• choose the investment with the lower coefficient of variation (less total risk per unit of expected return).

Question 14

Standard Deviation

Answer 14

• an absolute measure of the variability of the actual investment returns around the average or mean of those returns.
• there is a direct relationship between standard deviation and risk; often standard deviation is used as a measurement of the risk that is assumed by an investor with respect to any asset (or portfolio), also known as total risk.
• assuming a normal probability distribution, it can be used to predict the expected return of an investment based on historical performance of the asset or portfolio.

Question 15

Beta

Answer 15

• relative measure of an asset’s or portfolio systemic risk.
• best used as a measure of risk for a diversified portfolio or a portfolio that has no unsystematic (or diversifiable) risk.
• it measures the volatility of a particular securities rate of return or price relative to the volatility of the market as a whole.
• beta of 1.2 is 20% more risky than the market.
• an asset with a negative Beta may assist greatly in protecting the investor from a significant decline in the value of their portfolio during a down market.

Question 16

Covariance

Answer 16

• measures the extent to which two variables move together (positively) or opposite of each other (negatively).
• best described as the relationship between or among stocks that includes not only the individual stock’s variability but also its impact on and interaction with other portfolio securities

Question 17

Semi-Variance

Answer 17

• measures only the series of risks of historical returns that are below the mean or average return.
• a better measure for a risk averse investor

Question 18

Indifference (utility) Curves

Answer 18

• measure the risk/reward preferences that an investor is willing to make along the efficient frontier.
• the steeper the curve, the greater the investors aversion to risk