9.1 Portfolio Risk and Return: Part 1 Flashcards
Historical returns
document past performance
expected returns
reflect anticipated future performance
An asset’s expected return is a function of the real risk-free rate, expected inflation, and any risk premiums that investors require as compensation
Using a mean and variance approach assumes that
assumes that returns are normally distributed and that markets are informationally and operationally efficient.
However, these assumptions do not necessarily hold.
A normal distributions has three characteristics:
- Its mean and median are equal.
- It is completely defined by its mean and variance
- It is symmetric around its mean.
Utility
measures the relative satisfaction gained from a particular portfolio
The utility that investors derive from an asset or portfolio is a function of their degree of risk aversion, which is the marginal reward that they require as compensation for taking an additional unit of risk
The key conclusions from utility functions are:
- Utility has no maximum or minimum
- A higher return contributes to higher utility
- Higher variance reduces utility (for risk-averse investors)
- Utility is only useful in ranking investment options
Indifference curves
plot the risk-return pairs that have the same utility.
For risk-averse investors, the slope will be positive.
All the points on a particular indifference curve have the same utility.
Greater utility is present on higher indifference curves, as shown in the diagram below.
Indifference curves are steeper for investors that are
more risk-averse
The capital allocation line (CAL)
represents the investment options for this portfolio of two securities.
It is the plot of different risk-return combinations derived by changing the weights of the two securities.
The CAL represents all the investment options. An investor must be somewhere on the line
what does the slope of the capital allocation line (CAL) represent?
the additional return required for every increment in risk, which is the market price of risk
The slope is equivalent to the Sharpe ratio.
The covariance between the returns on two assets is calculated as:
the product of their correlation and the individual standard deviations
The minimum-variance frontier
the left edge of the possibilities in the graph below
It represents the least portfolio risk that can be obtained for a given expected return
The global minimum-variance portfolio
located on the far left of the curve, is the least risky of the minimum variance portfolios.
the Markowitz efficient frontier
The section of the minimum-variance frontier that lies above the global minimum-variance portfolio
Risk-averse investors will not consider portfolios on the lower half of the minimum-variance frontier because, for any portfolio that plots in this section, there is a Markowitz efficient frontier that offers a higher expected return for the same level of risk.
According to the two-fund separation theorem
all investors will use the risky portfolio P to a greater or lesser extent depending on their level of risk aversion
Investors will have different allocations to the risk-free asset, but they will all create portfolios that use the optimal portfolio, P, and plot on the CAL according to their risk tolerance
Optimal Investor Portfolio
The location of an investor’s optimal portfolio on the CAL will be at its point of tangency with their indifference curve
With respect to the mean–variance portfolio theory, the capital allocation line, CAL, is the combination of the risk-free asset and a portfolio of all:
a) risky assets.
b) equity securities.
c) feasible investments.
a) risky assets.
Which of the following statements is least accurate? The efficient frontier is the set of all attainable risky assets with the:
a) highest expected return for a given level of risk.
b) lowest amount of risk for a given level of return.
c) highest expected return relative to the risk-free rate.
c) highest expected return relative to the risk-free rate.
Compared to the efficient frontier of risky assets, the dominant capital allocation line has higher rates of return for levels of risk greater than the optimal risky portfolio because of the investor’s ability to:
a) lend at the risk-free rate.
b) borrow at the risk-free rate.
c) purchase the risk-free asset.
b) borrow at the risk-free rate.
The CAL dominates the efficient frontier at all points except for the optimal risky portfolio. The ability of the investor to purchase additional amounts of the optimal risky portfolio by borrowing (i.e., buying on margin) at the risk-free rate makes higher rates of return for levels of risk greater than the optimal risky asset possible.
Which of the following is least likely an assumption underlying the capital asset pricing model (CAPM)?
a) Investors analyze securities according to their own future cash flow estimates and probability distributions.
b) There are no restrictions on short selling assets.
c) The amount invested in an asset can be as much or as little as the investor wants.
a) Investors analyze securities according to their own future cash flow estimates and probability distributions.
When constructing the optimal portfolios for investors with different risk preferences, the investor with the higher risk aversion is most likely to have a:
a) lower expected return.
b) steeper capital allocation line.
c) flatter indifference curve.
a) lower expected return.
