MIDTERM 2 Flashcards
Expected return
expected return = anticipated outcome
mean = average
median = middle number in series
mode = most common return
Expected Return (single asset)
sum of the individual weighted scenario returns
Mean
distance less-than-the-average and greater-than-the-average are the same. describes the point of “central tendency”; however, it does not describe the dispersion of results around that point
Variance
describes the dispersion around the mean
variance = sum of the squared individual dispersions around the mean times the probability
risk is defined as the chance that the expected return will not be realized, variance or dispersion of actual returns around the expected return is how risk is usually quantified
Standard Deviation
square root of variance, normalizes the dispersion of a normal distribution around the mean
allows for a direct comparison of the standard deviation with the mean because same “un-squared” units of observation
Measure of Dispersion
spread of data, reference to the measure of central tendency, variance of sample = sum squared differences / (N-1)
Semi-Variance (downside risk)
risk includes observations that deviate from mean; however, investors are not concerned about out-performance
-only measures dispersion for data points that fall below the mean (threshold)
- most relevant when distribution exhibits skewness
-semi-standard deviation is square root of semi-variance
Coefficient of Variation
relative risk-to-return statistic
- CV = standard deviation/mean return
- lower CV preferred
- used to compare to securities
Moments of a Probability Distributions
1st moment = mean
2nd moment = variance/stdev
3rd moment = skewness
4th moment = kurtosis
Normal Distribution
standard deviation normalized dispersion around mean
- 68.26% is +- 1 std dev
- 95.44% is +- 2 std dev
- 99.74% is +- 3 std dev
Skewness
cubed dispersions: distributions with different means, medians, and modes, one tail will be longer than the other
Kurtosis
raise dispersion to 4th power, answers how much of the distribution is in the tail
Expected Return (two-asset portfolio)
expected return = sum of the weighted returns of the assets
Variance (two-asset portfolio)
variance of a 2-asset portfolio is NOT simply the weighted average of the individual asset deviations because variance of a 2-asset portfolio depends on how the assets move relative to one another (covariance)
Covariance
describes how two assets move relative to each other, key to the power of diversification
Standard Deviation (two-asset portfolio)
creates a 2x2 matrix, can increase to any NxN size
Correlation Coefficient
adds clarity about the strength of the relationships by normalizing the co-movement between 1 and -1.
statistical relationship between returns, which describes the direction of the linear relationship and magnitude of move.
adding any two securities with correlation coefficient less than perfect +1 will dampen volatility
Coefficient of Determination
correlation coefficient squared, measures the proportion of asset a’s price movement that is explained by asset b
Practical Applications of R^2
-identifying appropriate benchmark
- benchmark tracking
- active management
- risk relative to benchmark
Asset Allocation
you could hold a risky-asset component and a risk-free component in your portfolio
Adding Risk-free Security
adding a risk-free security will bring down the standard-deviation and decreases portfolio volatility
Mean-variance Portfolio Theory
assuming mean variance is sufficient to describe the market minimization techniques (calculus) can be used to determine portfolio combinations that offer lowest level of risk for a given level of return
Efficient Frontier
describes highest return combinations for a given level of risk, any portfolio lying on the efficient frontier has the optimal return to variability payoff.
an efficient frontier can be generated for any set of assets and constraints given assets 1) expected return 2) standard deviation 3) correlation coefficients
Capital Allocation Line
adding a risk-free asset with a risky portfolio increases the risk-return profile in every case but one and that is the point of tangency
once a risk-free asset is introduced the slope represents the constant reward to variability profile. there can be numerous CALs (one for each risky asset) and the investor just decides what allocation to make between the portfolio and the risk-free rate