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Level 34

Securities & Portfolios – Risk & Return

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NPV Rule
What the managers use, their goal is to maximize NPV
Time Value
A dollar today is not the same value as a dollar two years from now
Opportunity Cost
the value of the best alternative foregone; crucial in world of scarce resources
agency problems
Arise when an agent acts in its own interest, rather than those of the principals (eg wolf of wall street)
Relationship between return and risk
The greater the risk, the greater the return; add various risks (rates) to discount rate
Quantify uncertainty
The expected and realized returns of a project are likely to be different
Probability distribution
used to develop a measure of risk
Stock Probability Distribution Procedure
Develop a PD of the Economy. For a specific economic activity level, estimate the stock price and return rate
expected return: level of benefits
2 features or characteristics of use on a PD
many formulas:
How to calculate risk and return of a single asset
Expected return
Return we expect to get from a project; also what we base our decisions on
Realized return
return we actually end up getting from the project; the risk in this realized return is the cause of variance
Holding period return
the total return received from holding an asset or portfolio of assets; not for different time frame and different investments.
Arithmetic Average Rate of Return
Return in an average year over a particular period;
Geometric Average Return
Average compound return per year over a particular period compounded; probably understates returns on short term investments
Uncertainty about outcomes that can be either negative or positive
variance calculation
Stock return - expected return numbers
Standard deviation calculation
square root of the variance
a collection or group of assets
Portfolio Expected return
summation of (weight of stock A)(expected return of A) + (weight of stock B)(expected return of B) +....
Portfolio Variance
Wealth weighed combination of risks of the assets comprising the portfolio
Returns of assets in a portfolio may be related; this relationship (measured by covariance) can affect variance of a portfolio ;
Correlation coefficient
Ranges from -1.00 (a perfect negative correlation) to 1.00 (a perfect positive correlation). This is a statistical index which shows the relationship between two sets of numbers. When a very strong correlation exists, if…
Correlation and causation relationship
correlation does not imply causation (think of drinking and grades)
Treasury Bill
No risk in nominal return, uncertain real return
Treasury Bonds
Interest-bearing obligations issued by the US Treasury with maturities that range from ten to thirty years from date of issue.
Corporate Bonds
Add default risk
Common Stock
Add market risk
interest or similar
Ex-Ante Return
The return we expect to get from a project, on which we base our decisions
Ex-Post Return
The return we actually end up getting from a project
The ex ante and the ex post returns of a project are likely to be different
the square of the standard deviation, i.e., SD(2)
Standard deviation
The square root of the variance
Statistical measure of how the returns on two assets are related
What does a correlation coefficient of .9949 tell you?
-closer we are to one, the closer the relationship
risk premium
the component of a return that compensates for risk (credit risk premium compensates for borrower's risk)
Normal Distribution (bell curve)
A symmetric, bell-shaped frequency distribution that is completely defined by its mean and standard deviation.
Arithmetic Average Return
The return earned in an average year over a multi-year period. Long-run projected wealth levels calculated using arithmetic average should be regarded as optimistic.
Efficient Capital Market
A market in which security prices reflect available information.
Efficient Market Hypothesis
The hypothesis that actual capital markets, such as the NYSE are efficient.
Portfolio Weight
The percentage of a portfolio's total value that is in a particular asset.
Systematic Risk
A risk that influences a large number of assets. Also known as market risk. For example, inflation.
Unsystematic Risk
The risk that effects at most a small number of assets; it is also called unique or asset-specific risk. For example, oil strike by a single company.
Principle of Diversification
That by spreading an investment across a number of assets you will eliminate some, but not all, of the risk. Unsystematic risk is essentially eliminated by diversification, so a portfolio with many assets as almost no unsystematic risk.
Systematic Risk Principle
States that the expected return on a risky asset depends on that asset's systematic risk.
Beta coefficient
The amount of systematic risk present in a particular risky asset relative to that in an average risky asset.
Security Market Line
The positively sloped straight line displaying the relations between expected return and beta.
Market Risk Premium
The slope of the SML. The difference between the expected return on a market portfolio and the risk-free rate.
Capital Asset Pricing Model (CAPM)
The equation of the SML showing the relationship between expected return and beta.
The Fama-French Results
A factor model that expands on the capital asset pricing model (CAPM) by adding size and value factors in addition to the market risk factor in CAPM. This model considers the fact that value…
Capital allocation line
a graph line that describes the combinations of expected return and standard deviation of return available to an investor from combining the optimal portfolio of risky assets with the risk-free asset
the extent to which variables are related
Indifference curve
a curve representing all the combinations of two goods or attributes such that the consumer is entirely indifferent among them
Homogeneity of expectations
the assumption that all investors have the same economic expectations and thus have the same expectations of prices, cash flows, and other investment characteristics
∑ CFt / (1+rt)^t
Price of an asset =
Capital market line (CML)
the line with an intercept point equal to the risk-free rate that is tangent to the efficient frontier of risky assets; represents the efficient frontier when a risk-free asset is available for investment
Capital market line; E(Rp) =
Rf + [(Rm - Rf)/σ(m)]σ(p)
Rf + [(Rm - Rb)/σ(m)]σ(p)
Capital market line; E(Rp) (if debt at different price is used) =
Informationally efficient market
a market in which asset prices reflect new information quickly and rationally
Passive investment
a buy and hold approach in which an investor does not make portfolio changes based on short-term expectations of changing market or security performance
Active investment
an approach to investing in which the investor seeks to outperform a given benchmark
Nonsystematic risk
risk that is local or limited to a particular asset or industry that need not affect assets outside of that asset class; investors should not be compensated for nonsystematic risk because it can be diversified away
Examples of systematic risk
interest rates, inflation, economic cycles, political uncertainty, and widespread natural disasters
Examples of nonsystematic risk
the failure of a drug trial, major oil discoveries, or an airliner crash
Total variance =
systematic variance + nonsystematic variance
Return-generating model
a model that can provide an estimate of the expected return of a security given certain parameters and estimates of the values of the independent variables in the model
Multi-factor model
a form of a return-generating model that explains a variable in terms of the values of a set of factors
Three-Factor and Four-Factor models
a return-generating model for stock returns that also includes size of the company and relative book-to-market value of the company in addition to beta
Single-Index Model (or single-factor linear model)
the simplest form of a return-generating model in which only one factor is considered
Total variance (formula)
σ²i = β²iσ²m + σ²e
Systematic variance (formula)
β²iσ²m = σ²i - σ²e
Nonsystematic variance (formula)
σ²e = σ²i - β²iσ²m
Total risk =
√(β²iσ²m + σ²e)
Market model
a regression equation that specifies a linear relationship between the return on a security (or portfolio) and the return on a broad market index
Market model (formula)
Ri = αi + βiRm + ei,
a measure of how sensitive an asset's return is to the market as a whole and is calculated as the covariance of the return on i and the return on the market divided by…
Beta (formula)
βi = Cov(Ri,Rm)/σ²m = Ρi,mσiσm/σ²m = Ρi,mσi/σm
Capital asset pricing model (CAPM) (formula)
E(Ri) = Rf + βi[E(Rm) - Rf]
Assumptions of the CAPM
investors are risk-averse, utility maximising, rational individuals
Security market line (SML)
a graphical representation of the CAPM with beta on the x-axis and expected return on the y-axis; slope of the line is the market risk premium (Rm - Rf)
Portfolio beta =
w₁β₁ + w₂β₂
CAPM (portfolio) (formula)
E(Ri) = Rf + (w₁β₁ + w₂β₂)[E(Rm) - Rf]
Applications of the CAPM
as an estimate of expected return
Performance evaluation
the measurement and assessment of the outcomes of investment management decisions
Sharpe ratio =
Rp - Rf / σp
Treynor ratio =
Rp - Rf / βp
M-Squared (M²) =
(Rp - Rf)σm/σp - (Rm - Rf)
Jensen's Alpha: αp =
Rp - [Rf + βp(Rm - Rf)]
Security characteristic line (SCL)
a plot of the excess return of a security on the excess return of the market, where Jensen's Alpha is the y-intercept and β is the slope
Information ratio (alpha / nonsystematic risk)
α(i) / σ(ei), determines the relative weight of a security to be added to a portfolio
a model that simplifies a complex investment environment and which allows investors to understand the relationship between risk and return
Theoretical limitations of the CAPM
is a single-factor model, i.e. only systematic risk or beta risk is priced
nearsightedness; lack of imagination, foresight, or intellectual insight
Practical limitations of the CAPM
market portfolio; the true market portfolio according to the CAPM includes all assets, financial and nonfinancial, and therefore includes many assets that are not investable, such as human capital and assets in closed economies
Ex ante
based on forecasts rather than actual results
Ex post
based on actual results rather than forecasts