BA 472 Investments Final
7-15 Should investors generally expect positive correlations between stocks and bonds? Bonds and bills? Stocks and real estate? Stocks and gold?
7-15. Investors should typically expect stock and bond returns to be positively related, as well as bond and bill returns. Note, however, that correlations can change depending upon the time period used to measure the correlation. Stocks and gold have been negatively related, and stocks and real estate are typically negatively related. NOTE: It is important to remember that these correlations can change depending upon the time periods examined, and the indexes used (for example, DJIA, Nasdaq, etc.).
7-17 Evaluate this statement: For any two-stock portfolio, a correlation coefficient of -1.0 guarantees a portfolio risk of zero.
A correlation of -1.0 does not guarantee a risk of zero for a portfolio of two securities. Optimal weights also must be chosen for each security for this to occur.
7-13 When, if ever, would a stock with a large risk (standard deviation) be desirable in building a portfolio?
A stock with a large risk (standard deviation) could be desirable if it has high negative correlation with other stocks. This will lead to large negative covariances which help to reduce the portfolio risk.
12-1 What is meant by an efficient market?
An efficient market is defined as one in which the prices of securities fully reflect all known information quickly and accurately.
7-5 What does it mean to say that portfolio weights sum to 1.0 or 100 percent?
Each security in a portfolio, in terms of dollar amounts invested, is a percentage of the total dollar amount invested in the portfolio. This percentage is a weight, and the general assumption is that these weights sum to 1.0, accounting for all of the portfolio funds.
7-11 How many covariance terms would exist for a portfolio of 10 securities using the Markowitz analysis? How many unique covariances?
For 10 securities, there would be n (n-1) covariances, or 90. Divide by 2 to obtain unique covariances; that is, [n(n-1)] / 2, or in this case, 45.
8-16 Can gold be used as part of an asset allocation plan? If so, how can this be accomplished?
Gold can be used as part of an asset allocation plan. This can be accomplished using ETFs, mutual funds, gold mining stocks, and the ownership of gold bullion.
12-12 If all investors believe that the market is efficient, could that eventually lead to less efficiency in the market?
If all investors believed that the market is efficient, and numerous participants ceased the pursuit and study of information about stocks, the result could be less market efficiency. Obviously, this statement would depend upon who is left to do the analysis, and how much they do. The point of this question is to stimulate thinking about what is going on in the market in the way of information gathering and processing.
8-18 Can a single asset portfolio be efficient?
If the single asset is an ETF or mutual fund holding a broad market index, on a practical `basis it might be considered efficient.
7-9 How many, and which, factors determine portfolio risk?
In the Markowitz model, three factors determine portfolio risk: individual variances, the covariances between securities, and the weights (percentage of investable funds) given to each security.
9-4 What is the market portfolio?
In theory, the market portfolio (portfolio M) is the portfolio of all risky assets, both financial and real, in their proper proportions. Such a portfolio would be completely diversified; however, it is a risky portfolio. In equilibrium, all risky assets must be in portfolio M because all investors are assumed to hold the same risky portfolio. If they do, in equilibrium this portfolio must be the market portfolio consisting of all risky assets.
9-1 How do lending possibilities change the Markowitz model? borrowing possibilities?
Lending possibilities change part of the Markowitz efficient frontier from an arc to a straight line. The straight line extends from RF, the risk-free rate of return, to M, the market portfolio. This new opportunity set, which dominates the old Markowitz efficient frontier, provides investors with various combinations of the risky asset portfolio M and the riskless asset. Borrowing possibilities complete the transformation of the Markowitz efficient frontier into a straight line extending from RF through M and beyond. Investors can use borrowed funds to lever their portfolio position beyond point M, increasing the expected return and risk beyond that available at point M.
12-11 What are market anomalies? Describe four.
Market anomalies are research findings that do not support market efficiency; that is, they are evidence that inefficiencies do exist. These results are in contrast to what would be expected in a totally efficient market. Well known anomalies include: (a)the SUE effect, or the proposition that the adjustment of stock prices to quarterly earnings announcements occurs with a lag (b)the P/E effect, or the proposition that low P/E stocks will, on average, outperform high P/E stocks (c)the size effect, or the proposition that small capitalization stocks have earned higher risk-adjusted returns than have large capitalization stocks (d)the seasonal effect, or the proposition that stocks have exhibited higher returns than expected in January. This could also include the monthly effect, the weekend effect, and so forth. (e)the Value Line results, which seem to indicate that this investment advisory service has classified stocks into five groups that have performed in a monotonic fashion, with very impressive results for the top (expected best performers) two groups
7-7 Many investors have known for years that they should not "put all of their eggs in one basket." How does the Markowitz analysis shed light on this old principle?
Markowitz was the first to formally develop the concept of portfolio diversification. He showed quantitatively why, and how, portfolio diversification works to reduce the risk of a portfolio to an investor. In effect, he showed that diversification involves the relationships among securities.
8-14 Assume that you inherit $25,000 and decide to invest this amount in bonds also, adding the new bonds to your existing bond portfolio. Is such a decision consistent with the lessons of modern portfolio theory?
No. Modern portfolio theory argues for diversification among asset classes.
8-13 Assume that you have an investment portfolio worth $100,000 invested in bonds because you are a conservative investor. Based on the discussion in this chapter, is this a sound decision?
No. The evidence suggests an investor can improve his/her position by holding some percentage of the portfolio's assets in stocks.
8-3 Why do rational investors seek efficient portfolios?
Rational investors seek efficient portfolios because these portfolios promise maximum expected return for a specified level of risk, or minimum risk for a specified expected return.
12-4 Why is a market that is weak-form efficient in direct opposition to technical analysis?
Technical analysis relies heavily on known price and volume data to predict future price changes. The weak form of the EMH states that such data should already be reflected in current prices and therefore is of no value in predicting future price changes.
9-6 Why does the CML contain only efficient portfolios?
The CML extends from RF, the risk-free asset, through M, the market portfolio of all risky securities (weighted by their respective market values). This portfolio is efficient, and the CML consists of combinations of this portfolio and the risk-free asset. All asset combinations on the CML are efficient portfolios consisting of M and the risk-free asset.
7-3 The Markowitz approach is often referred to as a mean-variance approach. Why?
The Markowitz model is based on the calculations for the expected return and risk of a portfolio. Another name associated with expected return is simply "mean," and another name associated with the risk of a portfolio is the "variance." Hence, the model is sometimes referred to as the mean-variance approach.
9-7 How can we measure a security's contribution to the risk of the market portfolio?
The contribution of each security to the standard deviation of the market portfolio depends on the size of its covariance with the market portfolio. Therefore, investors consider the relevant measure of risk for a security to be its covariance with the market portfolio.
7-10 What is the relationship between the correlation coefficient and the covariance, both qualitatively and quantitatively?
The correlation coefficient is a relative measure of risk ranging from -1 to +1. The covariance is an absolute measure of risk. Since COVAB = ρAB*σA σB, COVAB ρAB = ───── σA σB
7-2 How is expected return for one security determined? For a portfolio?
The expected return for one security is determined from a probability distribution consisting of the likely outcomes, and their associated probabilities, for the security. The expected return for a portfolio is calculated as a weighted average of the individual securities' expected returns. The weights used are the percentages of total investable funds invested in each security.
10-5 What problems are encountered in using the dividend discount model?
The problems encountered in the dividend discount model stated as Equation 10-2 in the text, and shown above in answer number 10-4, include: (a) The last term indicates we are dealing with infinity. (b) The dividend stream is uncertain. (c) The required rate of return has to be determined. PVcs= D1/ (1+K)+D2/(1+k)^2+ D3/(+k)^3
8-15 What is the difference between traditional beliefs (starting in the 1960s) as to the number of securities needed to properly diversify, and the very recent evidence that has been presented by Malkiel and others?
The traditional beliefs about diversification, popularized by Evans and Archer in the 1960s, was that something like 8-16 securities provided most of the diversification benefits that could be obtained. In round numbers, call it 20 stocks. Malkiel's evidence suggests that many more securities are required to achieve adequate diversification. In round numbers, call it 50 stocks.
8-1 Consider a diagram of the efficient frontier. The vertical axis is __________. The horizontal axis is __________, as measured by the __________.
The vertical axis of the Efficient Frontier is expected return. The horizontal axis is risk, as measured by standard deviation.
8-17 Suppose you are considering a stock fund and a bond fund and determine that the covariance between the two is -179. Does this indicate a strong negative relationship?
There is no way to know for sure because there is no reference point for this situation. This is why the correlation coefficient is used in these situations.
7-14 Evaluate the following statement: As the number of securities held in a portfolio increases, the importance of each individual security's risk decreases.
This statement is CORRECT. As the number of securities in a portfolio increases, the importance of the covariance relationships increases while the importance of each individual security's risk decreases.
10-16 List two advantages of using the Price/Sales ratio as a valuation technique. How is this ratio calculated without using per share numbers?
Two advantages of using the Price/Sales ratio are: 1. It can be used to value a company with no earnings. 2. Sales are much less likely to be "managed" as compared to earnings. Without using per share numbers, it can be calculated as total market value (price times number of shares) divided by annual sales.
9-2 Why, under the CAPM, do all investors hold identical risky portfolios?
Under the CAPM, all investors hold the market portfolio because it is the optimal risky portfolio. Because it produces the highest attainable return for any given risk level, all rational investors will seek to be on the straight line tangent to the efficient set at the steepest point, which is the market portfolio.
8-4 Using the Markowitz analysis, how does an investor select an optimal portfolio?
Using the Markowitz analysis, an investor would choose the portfolio on the efficient frontier that is tangent to his/her highest indifference curve. This would be the optimal portfolio for him/her.
7-12 How many total terms (variances and covariances) would exist in the variance-covariance matrix for a portfolio of 30 securities using the Markowitz analysis? How many of these are variances, and how many covariances?
With 30 securities, there would be 900 terms in the variance-covariance matrix. Of these 900 terms, 30 would be variances, and n (n - 1), or 870, would be covariances. Of the 870 covariances, 435 are unique.
7-8 Evaluate this statement: With regard to portfolio risk, the whole is not equal to the sum of the parts.
With regard to risk, the whole is not equal to the sum of the parts. We cannot simply add up the individual (weighted) standard deviations of the securities in the portfolio, and obtain portfolio risk. If we could, the whole would be equal to the sum of the parts.
8-19 Can the original Markowitz efficient frontier ever be a straight line?
Without borrowing and lending, which is not included in the original Markowitz analysis, the Markowitz efficient frontier cannot be a straight line.
7-28 Select the INCORRECT statement from among the following: a. Under the Markowitz formulation, a portfolio of 30 securities would have 870 covariances. b. Under the Markowitz formulation, a portfolio of 30 securities would have 30 variances in the variance-covariance matrix. c. Under the Markowitz formulation, a portfolio of 30 securities would have 870 terms in the variance-covariance matrix. d. Under the Markowitz formulation, a portfolio of 30 securities would require 435 unique covariances to calculate portfolio risk.
c (30 securities would have 30 x 30 = 900 terms)
12-3 Describe the three forms of market efficiency.
he three (cumulative) forms of market efficiency are: (a)The weak form, which states that market data (price and volume information) are reflected in current prices and should be of no value in predicting future price changes. (b)The semistrong form, which states that all publicly known and publicly available data are incorporated into stock prices. (c)The strong form, which states that prices fully reflect all information, public and nonpublic (i.e., information that can be restricted to certain groups)
