Module 6: Types of Investment Risk and Quantitative Investment Concepts Flashcards
Investment Risk
The uncertainty that an investment’s actual, or realized, return will be different from its expected return.
How to eliminate Investment Risk?
Asset allocation and diversification
How to use diversification to minimize risk and maximize return?
- Structure a portfolio that contains assets with lw correlation to eachother
- have a longer investment time horizon or
- both
How much is enough for diversification?
Studies have shown that an investor needs only about 15-20 large-caps in different industries to fully diversify their portfolio
4-7 mutual funds in different asset classes optimize diversification benefits
25-30 mid or small cap securities in different industries
Different views of Risk
- loss of pricipal/variability of returns
- volatility of securities prices
- the possibility of not achieving an expected rate of return
- nonmatching cash flows
- uncertainty associated with future returns
Absolute Risk
Unsystematic, or diversifiable risk + systematic or nondivesrifiable risk
Measured by standard deviation
Systematic Risk Measure
Beta
Unsystematic Risk
Known as diversifiable risk, that affects only a particular company, country or sector and its securities. It’s not correlated with stock market returns
Types of Unsystematic Risk
- Business Risk
- Financial Risk
- Default Risk
- Political Risk
- Tax Risk
- Investment Manager Risk
- Liquidity Risk
- Marketability Risk
Systematic Risk
nondiversifiable risk, reflects the uncertainty of returns associated with an investment in any type of asset, inescapable because the risk of the overall investment market may not be completely avoided.
Types of Systematic Risk
- Purchasing Power Risk
- Reinvestment Rate Risk
- Interest Rate Risk
- Market Risk
- Exchange Rate Risk
Beta
A relative measure of systematic risk or volatility. Beta may be used as a measure for the risk associated with a particular security; however, it is better used as a measure of risk within a diversified portfolio or a portfolio that has little to no unsystematic risk.
Standard Deviation
An appropriate measure of risk for all assets, including nondiversified portfolios
Beta Formula
Beta = correlation coefficient between the investments and the market * Standard deviation of the investment / standard deviation of the market
Where Beta Can be misleading
Because of the way the formula is calculated the Beta of a specific stock does not make it less volatile than the overall market. Gold typically has a low beta, but is more volatile than the stock market, as correlation falls, so does the reliability of Beta
Negative Beta
According to CFP, a negative Beta can protect the investor from a significant decline in the value of the portfolio in a bear market.
Weighted Beta
This is the beta of a portfolio of securities, meaning that the portfolio beta is calculated by weighting the individual asset betas and adding the results.
Weighted Average Return
represents the return for a set of securities, such as a portfolio, where each return is weighted by the proportion of the security to the entire group or portfolio.
Standard Deviation
Also known as variance, is an absolute measure of the variability of the actual investment returns around the average or mean of those returns. Since most accepted measure of total, or absolute, risk in investment theory and tells an investor how far from the mean the investment’s actual return is likely to vary.
Calculating Sample Standard Deviation on Calculator
Put in each historical rate of return followed by the E+, then shift, 8 (Sx,Sy)
Calculating the Population Standard Deviation
The denominator is N, not N-1, in the real world, finding the standard deviation of an entire population is generally unrealistic. Although S (population standard deviation) tends to eliminate the statiscial bias associated with Sample standard deviation, it is likely that I will only be asked to compute Sample SD on the exam.
Normal Probability Distribution
Perfectly symmetrical, is characterized by a single peak in the center, which is the location of the arithmetic mean of the series of observations.
Mean
The best indicator of central tendency of distribution. It’s the average.
Median
The central value of observations arranged in order of lowest to highest.
Mode
The observation value with the greatest frequency.
Standard Deviation Return Interpretations with Bell Curve
A return will occur 68% of the time within one standard deviation of the mean, 95% of the time within two standard deviations of the mean, and 99% of the time within three standard deviations of the mean.
Z-Statisitic
Measure the number of standard deviations a data value is from the mean. Obtained by subtracting the mean from a given data value and dividing this result by the standard deviation.
Lognormal Probability Distribution
One in which the series of observations is skewed to the left of the arithmetic mean Implies that there is a greater than 50% chance than an observation selected at random will fall to the left of the mean (performance that is less than expected.)
Skewness
Measure how far the actual outcomes of a probability distribution deviate from the arithmetic mean or the asymmetry of the distribution.
Positively Skewed Distributions
The median is below the mean (long tail is on the positive side of the peak). There are more outliers to the right of the mean than to the left
Negatively Skewed Distributions
The median is above the mean (long tail is on the negative side of the peak). There are more outliers to the left of the mean than the right.
What Positive Skewness Means for an Investor
An investment with a positive skewness may have a larger-than-average number of positive price movements than an investment with a low positive skewness, but an investment with positive skewness subjects the investor to a greater number of returns below the mean.
Kurtosis
Kurtosis measures the degree of peak in a distribution of returns. In other words, it measures the degree to which exceptional values (those much higher or lower than average) Occur more frequently (high kurtosis) or less frequently (low kurtosis).
Platykurtic Distribution
A less peaked distribution that indicates that more returns with large deviations from the mean have occured, or are expected to occur, than with a normal distribution.
Leptokurtic Distribution
A more peaked distribution indicating that more returns are clustered around the mean than with normal distribution
Semivariance
In the real world, people who are risk-averse only are considered with the series of possible returns below the mean. So semivariance was developed to measure only those returns that are below the mean, with no consideration given to those above the mean. “Average square deviation below the mean”.
Coefficient of Variation
Computation of the relative measure of total risk per unit of expected return and is used tocompare investments with varying rates of return and standard deviations. Allows you to determine which security exhibited the least risk per unit of return.
Coefficient of Variation Formula
standard deviation / mean return of asset
Covariance
Measures the extent to which two variables (the return on investment assets) move together, either positively (together) or negatively (opposite).
Covariance Formula
Correlation Coefficient * Standard Deviation of Asset A * Standard Deviation of Asset B
What are Covariance and Correlation Coefficient Represented by in the text?
Covariance: lowercase r
Correlation Coefficient: uppercase R
Correlation Coefficient
Measures the strength of the straight-line or linear relationship between two variables. The overall range is between -1 and +1
Correlation Coefficient Formula
Covariance / (standard deviation of Asset A/standard deviation of Asset B)
Use of Correlation Coefficient
Investors want to know the Correlation Coefficient of one asset with the market. Therefore, the standard deviation of an individual asset and the standard deviation of the market are computered, then the covariance of the asset with the market is computed, and finally, the correlation coefficient between the asset and the market is computed.
Correlation Coefficient and the Market
The further away the correlation coefficient is from the market, the more diversification it provides to the portfolio.
Long-Term vs. Short-Term Correlations
- Correlations will be different depending upon the time frame used. This means that long-term correlations may be misleading if correlations have changed recently. Because correlations are not constant and change over time, investors and advisors need to be aware of the possibility of significant changes in correlation.
inconsistency of Correlations
Correlations are also inconsistent in rising and falling markets. Studies show that correlations tend to decrease in rising markets and increase inf alling markets, which is the opposite effect an investor would desire.
Standard Deviation of a Two Asset Portfolio Formula
SQRT(%of security A ^2 * Standard Deviation of SPortfolio ^2 + % of security B ^2 * Standard Deviation of Portfolio ^2 + 2%A%B(CovarianceAB))
Standard Deviation of Portfolio vs. the Weighted Standard Deviation of the two assets
- When the correlation coefficient is less than +1, you know that the standard deviation of the portfolio is going to be less than the weighted average standard deviation of the two assets.
Coefficient of Determination
R^2, which is the square of the correlation coefficient, describes the percentage of variability in one variable that is explained by the changes in a second variable or the strength of the relationship between the two variables. Could also be considered a measure of systematic risk with the balance being unsystematic risk.
Uses of R^2 or Coefficient of Determination
- The higher the R^2 of the stock or portfolio, the more the overall market is an appropriate benchmark for the measurement of investment risk. Reliability of R^2 declines as beta declines. For testing purposes, you are looking for an R^2 of 70% or greater - the threshold used by morningstar.
A reduction in risk also means a reduction in the possible return on the investment, True or False?
True
Is liquidity risk applicable to fixed income securities?
Yes
The best measure of risk in a well diversified portfolio?
Beta
What risk does beta measure?
It measures only systematic risk, standard deviation measures total risk.
