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
Slope = reward to variability ratio
slope (rise over run) describes the amount of extra return for each unit of additional risk
Sharpe Ratio
the reward-to-variability (slope of the CAL) is referred to as the Sharpe Ratio, additional units of return for additional units of risk
Risk Theory
Risk lover (A < 0)
Risk Neutral (A=0)
Risk Averse (A > 0)
risk averse investors demand a higher level of return to hold a higher level of risk, risk neutral investors focused just on expected return
Utility Theory
suggests that risk-averse investors compare risky assets based on their expected utility (welfare), not on nominal return
Indifference Curve
graphically depicts the unique preferences for individuals in terms of risk and reward. every point along the curve depicts the same risk/return ratio: therefore, the investor is indifferent about any combination (same level of utility)
Capital Market Line (CML)
CML is a special case of the capital allocation line. rather than unique portfolio, everyone holds the same risk portfolio = broad domestic stock market index, only decision is about allocation between risky asset (market index) and risk-free asset
Beta
measures systematic risk, describes the sensitivity of an asset’s return to the market, appropriate when considering a security for inclusion in a diversified portfolio
beta = (correlation of asset to market * risk of asset)/risk of market
quantifies an individual security’s price sensitivity to market’s price movement
Beta>1: greater sensitivity to market price changes
Beta=1: security exhibits the same volatility as the market
Beta<1: security has less sensitivity to market price changes
slope of the linear regression
scaling describes stock’s exposure to marker risk
Significance of beta
when adding a security to a portfolio, you are not concerned about the total risk, rather the amount of systematic risk that the asset will add to the portfolio. adding a security with a higher beta will increase overall portfolio
Security Market Line (SML)
Capital asset pricing model, beta replaces standard deviation as a measure of risk
Expected return = Rfree + [betasecurity*(Rmarket-Rfree)]
Rmarket-Rfree=market premium
slope of SML describes the proper theoretical pricing of financial assets
Significance of SML
slope represents the market risk premium, recognizes that with portfolios you are concerned about the amount of systematic risk that the asset will add to the portfolio, suggests that theoretical pricing of securities is linked to the beta
CAPM versus APT
capital asset pricing model: single factor model, pricing higher expected return required to hold higher expected risk
arbitrage pricing model, multi-factor model focused security’s sensitivity to various macroeconomic variables
Factor Models
build factor models fro projecting stock return
- macroeconomic data
- fundamental data
- statistical
realized return of asset = expected return + beta sensitivity to the different firm specific characteristics
Determinants of Portfolio Performance
asset allocation: 91% of portfolio performance is based on the asset allocation decision
other determinants: security selection, market timing, other factors
Impact of Individual Factors on Asset Allocation
variables influencing the asset allocation decision: tolerance for risk, financial need and return objective, time horizon, financial capacity, investment knowledge, investing experience, preferences and constraints
Assessing Risk Tolerance
risk tolerance cannot be measured with complete accuracy
- attitude
- financial capacity
- knowledge
- propensity
Challenges with Portfolio Optimization for Individuals
challenges include multiple life goals, several forms of individual taxes, liquidity needs, behavioral issues, income needs from investment portfolio
Life Cycle Investment Strategy
wealth = financial wealth + human capital wealth
- greater the human capital the greater focus on growth investments
- lower the human capital the more you focus on income-producing investments
equity allocation = 100 - age
Other Approaches: 60/40 & Risk-return
60/40 adjustment: start from 60% growth and 40% income mix.
risk-return bucket approach: categorize based on individual factors
- conservative investor (50/50)
- moderate (60/40)
- assertive (70/30)
- aggressive (80/20)
Strategic vs tactical allocation
strategic: establishing a long-term target strategic allocation, portfolio monitoring and periodic rebalancing to maintain target mix
tactical: overweighting of asset categories based on projected performance, minimum and maximum allocations might be established
Portfolio Rebalancing
- application of buying high and buying low
-rules: fixed-percentage threshold rule, percent variance from threshold, calendar, after major market event
Sector vs Industry
sector: broader economic groupings that include multiple industries (energy, real estate, utilities)
industry: group of companies with the same business activity (banking, defense)
Diversifying by Investment Style
value investing: invest in companies that are underpriced or under-recognized
growth investing: invest in companies that are growing at faster rates than overall market
Diversifying Concentrated Portfolios
concentrated portfolio positions occur when an individual or small number of securities represent a large percentage of the overall portfolio
- negative implications: lower risk-return profile, higher volatility impacts compounded growth, financial vulnerability
utility vs prospect theory
utility describes how decisions under uncertainty should be made
prospect theory describes how decisions are actually made
prospect theory
focus on loss or gain, change in wealth is reset to a reference point, more pain associated with losses
loss aversion
tendency for risk-averse investors to place greater value on avoiding losses than acquiring gains
Fast/slow brain
system 1 - fast, automatic unconscious thinking
system 2 - slow, conscious reasoning and thought
reptilian brain = caveman brain
anchoring
decision makers begin from a reference point and then adjust
representativeness
decision based on finding commonality between current situation and a prior experience, law of small numbers
availability
decision based on available data
affect
attitude impacts the decision
hyperbolic discounting
tendency to overvalue immediate rewards at the expense of long-term goals
mental accounting
assigning subjective value or emotional label to money based on its source
availability vs selective recall
availability bias: reliance on recent data
selective recall: tendency to overweight recent information and successful trading experiences
Cascading
make own assessment, observe actions of group, despite private contradictions, follow the group
regret avoidance
make decisions that allow them to avoid the pain of monetary loss and loss of self-esteem
inaction: refusing to admit that the investment was a mistake results in tendency to hold losers in hope they recover
indecision: fear of loss can cause investor to remaining in cash equivalents for too long a period
ambiguity aversion
make a decision that favors the familiar
