3. Managing Portfolios: Theory Flashcards
For each pair of portfolios, identify which one dominates the other or if neither dominates the other.
a. X (E(R) = 4%, s = 8%); Y (E(R) = 4%, s = 10%)
b. X (E(R) = 8%, s = 12%); Y (E(R) = 10%, s = 12%)
c. X (E(R) = 6%, s = 10%); Y (E(R) = 8%, s = 14%)
a. X (same expected return, less risk)
b. Y (same risk, greater expected return)
c. neither (Y has a greater expected return, but also has more risk)
After running the statistics for two companies, you conclude that the
covariance of returns is .0020, and that the standard deviations of returns are
.06 and .08. What is the correlation coefficient?
a. Correlation coefficient = ovariance/product of the standard deviations =.0020/(.06 x .08) = .4167
The correlation coefficient between two securities is -.5, and the standard
deviations are .06 and .08. What is the covariance between them?
Covariance = product of the standard deviations x correlation coefficient
= (.06x .08) x (–.5) = –.0024
If the standard deviations for two securities are .06 and .08, what are the
minimum and maximum values of the covariance?
c. The maximum value of correlation = +1, so if 1 = COV/(.06 x .08), then COV = .0048.
The minimum value of correlation = –1, so if –1 = COV/(.06 x .08), then COV =–.0048.
You want to create a two-security portfolio. One of the holdings will be company A. The other will be B, C, or D.
All three of these companies have identical expected returns and standard deviations. However, they differ in terms of their correlation coefficient with company A.
The three correlation coefficients are .2, .6, and –.2. Which company should you choose and why?
You should choose company D because it has the lowest correlation coefficient. This
means that the efficient frontier will allow one to move to the highest possible indifference
curve.
Explain why the SML differs from the CML.
The security market line shows the expected return for any holding, be it a single security,
an inefficient portfolio, or an efficient portfolio (that is, one that lies on the capital market
line). The capital market line is defined in terms of the risk-free asset and the market
portfolio. Only the most efficient portfolios plot on the CML.
Define the efficient frontier, first without borrowing or lending allowed and
then with both allowed at the risk-free rate.
If there is no borrowing or lending, then the efficient frontier consists of the portfolio
providing the highest expected return for a given level of risk or the least risk for a
given expected return. Each portfolio on the frontier consists of different assets
and different weights. When a risk-free asset is introduced, the efficient frontier
becomes a straight line emanating from the risk-free asset and going through
the market portfolio (which consists of all assets in their exact value-weighted
proportions). To hold a portfolio along this line is to hold both the risk-free asset
and the market portfolio in varying proportions (points to the right of the market
portfolio involve borrowing to purchase more of the market portfolio).
What does the efficient frontier look like with risk-free lending only (no
borrowing)?
If only lending is possible, the efficient frontier consists of the line connecting the
risk-free asset and the market portfolio. To the right, the frontier is once again the
efficient frontier without the risk asset.
Describe what is meant by market risk and nonmarket risk.
The total risk of a security can be broken down into two components: market risk,
which is the product of the square of a security’s beta and the variance of the
returns on the market portfolio, and the nonmarket risk, which is the variance of
its unique returns.
What determines the effect of market risk for an individual security?
The beta coefficient determines the effect of market risk on an individual security.
What is the difference between a “prudent man” investment objective and a
“prudent investor” investment objective?
The prudent man investment objective says that each investment individually must be
evaluated in light of what a prudent man who wanted to preserve his estate would do.
A prudent investor is allowed to focus on the performance of the portfolio, rather than
each security or holding separately.
The riskiness of a portfolio is greater than the riskiness of the securities it contains.
False. A portfolio of securities is less risky than its component securities. This is why diversification is an important investment strategy.
A correlation coefficient of 0 does not necessarily mean there is no relationship between two sets of returns, only that there is no obvious linear relationship.
True
A portfolio’s return is the arithmetic average of the returns of the assets included therein.
False. A portfolio’s return is the weighted average of the returns of its assets. The average assumes that each asset has an equal weight in the portfolio. As relative prices change, the relative impact of each asset on the portfolio return also changes. Therefore, using an unweighted average would result in an inaccurate measure of portfolio return.
A correlation coefficient of -1 between two assets provides the least opportunities to reduce the variability of the portfolio’s return.
False. A perfectly negative correlation (-1) of the returns between two assets would provide the maximum opportunity to reduce the variability of the portfolio’s return.
