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Rotman Commerce

RSM332H1

Jennifer So

Fall

Description

Risk and Return
Risk is defined as the "possibility of incurring harm."
Ex post returns: returns past or historical returns
Ex ante returns: returns future or expected returns
Return on investment compromises of income yield and capital gain (or loss) yield
Income yield: the return earned by investors as a periodic cash flow (interest, dividends)
CF1/P0
Capital gain (or loss): appreciation (or deprecation) in the price of the asset from some
starting price
(P1 - P0) / P0
Paper losses: capital losses that people do not accept as losses until they actually sell and
realize them
Mark to market: carrying securities at the current market value regardless of whether they
are sold
Measuring average returns
Arithmetic mean or average: sum of all returns divided by the total number of observations
Appropriate when trying to estimate typical return for a given period
Geometric mean: the average or compound growth rate over multiple periods
Determining "true" average rate of return over multiple periods
Standard deviation: a measure of risk over all the observations; the square root of the
variance
Expected returns is the sum of the probabilities of most likely returns under various scenarios
Measuring risk
Standard deviation formula
Expressed as a percentage
Ex ante standard deviation sum of Prob * (return - expected)^2
Variance: the standard deviation squared
Risk premium is the additional return above the risk-free rate resulting from bearing risk
Compensation for additional risk
Sometimes called excess return
Expected return and risk for portfolios
Portfolio: a collection of securities, such as stocks and bonds, that are combined and considered a
single asset
Modern portfolio theory (MPT): the theory that securities should be managed within a portfolio
rather than individually, to create risk-reduction gains; also stipulates that investors should
diversify their investments so as not to be unnecessary exposed to a single negative event
Expected return of portfolio is the weighted average of the expected returns on each individual
securities
Standard deviation of portfolio
covariance: statistical measure of the correlation of the fluctuations of the annual rates of
return of different investments
Strength or magnitude
Correlation coefficient: a statistical measure that identifies how security returns move in
relation to one another +1 = 1 perfect positive correlation, -1 = -1 perfect negative correlation
Lower correlation, lower the standard deviation
Diversification: process of investing funds across several securities, which results in reduced risk
Random or naïve diversification: the act of randomly buying securities without regard to
relevant investment characteristics, such as company size, industry classification, and so on
Benefit does not continue indefinitely, marginal risk reduction decrease
Total risk = market + unique
Unique (non-systematic) or diversifiable risk: the company-specific part of total risk that is
eliminated by diversification
Market (systematic) or non-diversifiable risk: the systematic part of total risk, directly
influenced by overall movements in the general market or economy that cannot be
eliminated by diversification
Portfolio theory
Efficient frontier
3 security portfolio variance (page 317)
Modern portfolio theory
Assumptions
Investors are rational decision-makers
Investors are risk averse, which means they like expected returns and dislike risk and
therefore require compensation to assume additional risk
Investor preferences are based on a portfolio's expected return and risk
Minimum variance frontier: the curve produced when determining the expected return-risk
combinations available to investors from a given set of securities by allowing portfolio
weights to vary
Attainable portfolios: portfolios that may be constructed by combining the underlying
securities
Dominated portfolio: inefficient, lower expected rate of return for same risk as others
Efficient frontier: set of efficient portfolios
Efficient portfolios: those portfolios that offer the highest expected return for a
given level of risk, or offer the lowest risk for a given expected return
Minimum variance portfolio (MVP): a portfolio that lies on the efficient frontier and
has the minimum amount of portfolio risk available from any possible combination of
available securities
Portfolio with lowest possible risk and therefore defines the lowest expected
return we should be willing to accept
Alternate way to find weight in 8A and find efficient frontier
Introduction of risk-free borrowing and lending
Insurance premium: payment to get out of a risk situation
Tangent portfolio: the risky portfolio on the efficient frontier whose tangent line cuts the
vertical axis at the risk-free rate
The tangent line from Rf to this portfolio is known as the Capital Market Line (CML)
With RF and risky assets, we would never invest in any portfolio that is NOT on
the CML
New (or super) efficient frontier: portfolios composed of the risk-free rate and the tangent
portfolio that offer the highest expected rate of return for any given level of risk
Borrow RF and invest everything in M Short position: a negative position in an asset; the investor achieves a short position
by borrowing part of the asset's purchase price from the stockbroker
Separation theorem: the theory that investment decision (how to construct the portfolio of
risky assets) is separate from the financing decision (how much should be invested or
borrowed at the risk-free rate)
Market portfolio: a portfolio that contains all risk securities in the market
Everyone will choose to invest in the same risky market portfolio
CAPM
Capital asset pricing model: a pricing model that uses one factor, beta, to relate expected returns
to risk
Assumptions
All investors have identical expectations
No transaction costs and can borrow/end at risk free RoR
Same one period time horizon
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