Questions and Answers of Fundamentals Investments Valuation

If CAPM beta does not explain stock returns, what does? In this regard, Fama and French (1992) found that stock returns were related to two firm characteristics. What are these characteristics and
Fama and French (1993) used the size and BM variables to construct zero investment factors. Define these factors and write the equation for their resultant three-factor model. What are the
Fama and French (1993) conducted tests of their proposed three-factor model.What were the test asset portfolios? What did they find? Discuss the results for estimated beta coefficients and
How did Fama and French (1993) cross-sectionally test the three-factor model? What did they find in test results?
Fama and French (1993) specified and tested a bond model. What did their results show?
If the CAPM is dead, and asset prices are better explained by multiple factors, what theoretical support for multifactor models exists?
Fama and French (1996) argued that size and value factors are linked to economic fundamentals such as earnings within the firm. What were their arguments in this regard?
Did Fama and French (1996) find evidence to support a link between earnings and the size and value factors? Review their findings. What are the underlying state variables that produce variation in
Controversy surrounded the three-factor model due to skepticism by researchers. Black (1993, 1995) said that the model had two problems. Discuss these two potential problems.
Kothari, Shanken, and Sloan (1995) found evidence to support the CAPM.Also, they criticized the Fama and French studies. Review these issues in their study.
What is a possible endogeneity problem in the Fama and French asset pricing tests of the three-factor model? How can we reduce this problem in asset pricing tests?
How did Fama and French (1996) counter criticisms of their three-factor model? Do you think that multifactor models are needed to more fully price assets or are investors irrational leading to
Assume that stocks are sorted into a 2×3 matrix of size and value (BM). How did Fama and French (1993) use this matrix to create their size and value factors?
Draw a diagram that depicts Fama and French’s three-factor model. How many dimensions are there in your drawing?
What is momentum in asset returns? Can it be used to construct a long/short factor? How did Carhart (1997) modify the three-factor model to take into account momentum?
In Carhart’s (1997) empirical tests, did momentum affect stock returns of mutual funds? What practical advice to investors in mutual funds did his research reveal?
Fama and French (2015) built upon their three-factor model to develop a fivefactor model. What motivated them to add two more factors to their model?Write their five-factor model.
Fama and French (2015) tested their five-factor model in the sample period 1963–2013. What test asset portfolios did they use? Was the five-factor model supported?
Hou et al. (2015) developed a model that is very close to the Fama and French four-factor model. Write the equation for their model. What is the theoretical foundation for their model? What did they
Stambaugh and Yuan (2017) developed a four-factor model. They added two new factors to the market and size factors. How did they construct these new factors? In empirical tests of over 80 anomalies,
Write the Fama and French (2018) six-factor model. They expanded this model to include different variations of these factors for a total of 48 factors.Which model worked the best?
More recently, Fama and French (2020) proposed a modified version of their five-factor model in which the multifactors are replaced by long/short mimicking portfolios estimated from a cross-sectional
Fama and French (2020) proposed two additional models that allow for timevarying risk parameters. Write the equations for these two conditional models.In empirical tests, which model was the best
Normally, joint tests that the intercepts (αi s) equal zero are in-sample tests.What is a criticism of this testing approach?
Lettau and Pelger (2020) proposed the use of Principal Component Analysis (PCA) to identify latent asset pricing factors. How does PCA find factors in stock returns? How many latent factors did they
Distinguish between theoretical methods, discretionary methods, and machine learning methods of developing asset pricing models. What are examples of each of these methods?
Draw a diagram of returns on the Y-axis and time in months over the past year on the X-axis. Using this diagram, illustrate how momentum portfolios are formed.
Draw a diagram comparing the machine learning methods of Fama and French’s(2020) cross-section factors and Lettau and Pilger’s (2020) latent factors.
Draw a picture of Markowitz’s mean-variance investment parabola. Label the Y-axis as E(RP) for expected returns and X-axis as σ2P for the variance of returns. Where is the minimum variance
In their picture of the mean-variance investment parabola, Kolari, Liu, and Huang (KLH) (2021) argued that commonly used general stock market indexes (e.g., the value-weighted CRSP index or S &P 500
Assuming a riskless asset exists, write the equation for the theoretical ZCAPM. What do beta risk and zeta risk measure in this model? Does the ZCAPM have an empirical advantage in terms of testing
According to Kolari, Liu, and Huang (KLH) (2021), zeta risk (denoted by Z∗i ,a) in the ZCAPM can be positive or negative in sign. Illustrate this two sided zeta risk in a diagram with the ith
Show how two-sided return dispersion effects impact expected stock returns. Assume there are two time periods t = 1 and 2 in addition to two assets B and C. Return dispersion in the market increases
Kolari, Liu, and Huang (KLH) (2021) argued that the mean-variance parabola is shaped by the dual systematic risk effects of beta risk and zeta risk. How is the architecture of the parabola affected
Kolari, Liu, and Zhang (KLH) (2021) conducted out-of-sample (or one month-ahead), cross-sectional Fama and MacBeth (1973) tests of a number of different test asset portfolios. The final form of the
Following standard practices, Kolari, Liu, and Zhang (KLH) (2021) implemented Fama–MacBeth cross-sectional regression tests. The analyses were rolled forward one month at a time to generate a
Kolari, Liu, and Zhang (KLH) (2021) repeated the question above by comparing other multifactor models to the empirical ZCAPM. For the six-factor model of Fama and French (2018) compared to the
In empirical tests of the ZCAPM, is there an explanation for why multifactor models were dominated by the ZCAPM? Fama and French (1993, 1995, 2015, 2018) link that multifactor models to Merton’s
Given their new geometry of the parabola, how did Kolari, Liu, and Huang (KLH) (2021) define the expected returns for the special case of orthogonal portfolios I∗ and ZI∗ on the parabola?
If we substitute the definitions of E(RI∗ ) and E(RZI∗ ) into the zero-beta CAPM Eq. 10. 1, we can derive a theoretical ZCAPM without a riskless rate. Show how to get the theoretical ZCAPM in
Kolari, Liu, and Zhang (KLH) (2021) proposed a novel empirical ZCAPM to capture positive and negative sensitivity to return dispersion (i.e., zeta risk). Write their empirical model. What is Dit in
How did Kolari, Liu, and Zhang (KLH) (2021) compute mean market returns as well as the return dispersion for U.S. stocks? Are equal-weighted or value weighted return used in their computations of
Kolari, Liu, and Zhang (KLH) (2021) conducted out-of-sample Fama and Mac- Beth (1973) cross-sectional regression tests for the empirical ZCAPM and a number of other models, including the market model
Explain the concepts of event date, event time, event window, and estimation window.
Explain normal return, abnormal return, and cumulative abnormal return.
Discuss pros and cons of standardized event study tests with relation to Non standardized tests.
Suppose that you want to test the null hypothesis of no mean effect when event days are completely clustered. The sample size is n = 100 firms and the test statistic applied is BMP due to its good
In the text it was noted that the BHAR approach in long-run event studies is vulnerable to cross-sectional correlation. Is it vulnerable to autocorrelation or heteroskedasticity of the returns too?
Consider a long-run event study of SEO events with abnormal returns defined as the difference between the returns of the event firm and its matched control firm. What would you consider to be a major
Discuss some of the major pros and cons of nonparametric rank tests in event studies.
A key requirement for efficient capital markets is that prices fully and instantaneously reflect all available relevant information. Consider the event of an earnings announcement. Suppose that the
The table below reports event day abnormal returns, standard deviations of the estimation window abnormal returns (i.e., OLS residuals of the market model), and rank number of the event day abnormal
It is proved that OLS estimation of the market model is the empirical counterpart of the CAPM under classical Gauss–Markov assumptions. Show that: (i) E(ui t ) = 0, (ii) Var (uit ) = σ2i (1 −
What is the two-step investment process proposed by Markowitz?
Write the general present value formula used to maximize the discounted value of future investment returns. What are the two components of the discount rate?
Assume that there are s states of nature. Write the formulas for the expected return of security j and the variance of security j returns. Next assume that there are two securities 1 and 2 in a
What is the difference between ex ante and ex post returns?
Write the formulas for ex post computation of mean or average returns for security j for time t = 1, . . . , T periods and the sample variance of returns.
According to Markowitz, what is wrong with maximizing returns of a portfolio as an investment goal? How can investors use ex post data to evaluate an investment?
How does the correlation between different assets in a portfolio affect the risk of the portfolio?
Figure 1. 2 in the text plots the mean-variance parabola of Markowitz. Why is the parabola curved in shape? What is the minimum variance portfolio? What is the efficient frontier? Are some portfolios
In the real world, there are millions of assets. Why have investors had difficulty implementing Markowitz’s optimization methods to find the optimal weights of assets to hold and therefore hold
Table 1. 1 contains some computations of the expected rate of return and variance of returns for an asset. Assume that the probability ps are changed to 0. 30, 0. 40, and 0. 30 in states 1, 2, and 3,
Table 1. 2 computes the average return and variance of returns for two securities.For security 1, change the returns for years 1 through 5 to the return series 5, 10, 6, 12, and 15. For security 2,
Table 1. 3 computes the portfolio return and risk (in percent) using the data in Table 1. 2. Use the data in your new Table 1. 2 from problem 2 to create a new Table 1. 3.Table 1.2Table 1.3 Table 1.2
In a perfect capital market, rational behavior dictates that investors prefer more to less wealth. Give some examples of irrational market behavior. Why might investors act irrationally?
Give three characteristics of a perfect capital market and briefly discuss them.
Under the efficient markets hypothesis (EMH), what are the three types of market efficiency? Briefly describe them.
What is the Random Walk Hypothesis (RWH)? Is there any evidence against this hypothesis?
What is a certainty equivalent return of a risky investment?
What is a risk premium on an investment?
Figure 2. 2 gives an example of a utility curve for a risky investment. For this risky investment, expected utility is on the Y-axis, and expected returns are on the X-axis. What is the main concept
When risk-averse investors evaluate multiple investments in a portfolio context, what do investors use to evaluate investments? Also, what is an indifference curve in this respect? Is this curve
Write the simple return for a stock. Also, write the continuously compounded rate of return. How are these two returns related to one another?
Assume that investment A offers the portfolio combination of investment return I1 with probability α (0 < α < 1) and investment return I2 with probability(1 - α). What is the expected utility of
Suppose that there is some certain return I∗ with the same utility as A, i.e.,¯U(A) = U(I∗). Also, assume that this certainty equivalent return I∗ is less than the actuarial value of A. What
Draw a graph of the utility curve showing risk-averse investor behavior with respect to the risky investment opportunity in problem 1 above. How would this graph change for risk loving investors?
How would you compute the k-period gross return 1+ Rt (k) for an investment from t −k +1 to t? Assume no dividends are paid. Write the general formulas using gross return 1 + Rt = Pt /Pt−1. Also,
How can we compute the mean return for an investment over some time period k? Show the formulas for the arithmetic mean and geometric mean. Utilizing the gross returns in problem 4, i.e, (1+ R1) = 1.
How would we compute the gross return 1 + Rt (k) over some time period k using log returns? In this case, what is the simple arithmetic mean of these gross returns? Is the average of this multiperiod
Consider the monthly returns of a stock. Assume that the returns are normally distributed with mean μ = 1% and standard deviation σ = 9% (per month).How often would you expect to see a monthly
Download Microsoft stock prices in addition to S &P 500 and German DAX index values for the sample period from January 1, 2010 until December 31,
Write the present value formula for future cash flows. Re-write this present value formula using m-talk. Redefine the m-talk equation in terms of expected returns.
Draw the Capital Market Line (CML) of Sharpe (1964). What does this line show?
Assuming Markowitz’s efficient frontier and Tobin’s mean-variance indifference curves, what portfolio should the investor select? Illustrate this portfolio with a graph with mean returns on the
Write the expected return of the portfolio combination of the riskless asset in proportion a and risky efficient portfolio P in proportion (1 − a). What is the standard deviation of returns for
Given the results for question 4 above, which portfolio will an investor optimally select to maximize their expected returns per unit risk as measured by the standard deviation of returns σ(R)? Draw
Do you think that professional investors can buy a risky portfolio that “beats the market” in the sense of outperforming portfolio M?
Draw the Security Market Line (SML). Is this line an equilibrium relation between risk and return? Is systematic risk part of total risk?
A certainty equivalent form of the CAPM is as follows:Why does the equation use the riskless rate to discount the cash flows in the numerator? Po E (P) - [Cov(P, RM)/0 (RM)][E(RM) R] 1+ Rf
Give a definition of the market portfolio M. Are some assets in the market not contained in M?
The CAPM has a number of implications for the theory and practice of finance. Discuss five implications.
Assume that investors hold a portfolio of an individual risky asset and riskless asset f . Starting with the expected return of this combination and its standard deviation, derive the slope of the
Using data in the following table, compute the expected returns for different assets using the CAPM. E(R) Rf (%) 2.00 2.00 2.00 2.00 2.00 2.00 2.00 Beta, Bi -0.25 0.00 0.25 0.75 1.00 1.50 2.00 E(RM)
Write the equation for the market model form of the CAPM. What is the intercept term in this model? Can the intercept be used to test the CAPM?
Why put a random error term in the market model? How would you estimate the market model with regression analysis?
Black, Jensen, and Scholes (BJS) (1972) tested the CAPM using the market model. Why did they use portfolios rather than individual stocks in their tests?How were the portfolios formed for their
Fama and MacBeth (FM) (1973) tested the CAPM using cross-sectional regression analysis. What is the cross-sectional regression model that they tested?
What did Fama and MacBeth (1973) find in their cross-sectional tests of the CAPM?
Write a simple regression model with one explanatory variable. Also, write a multiple regression model with k explanatory variables x1, . . . , xk . How would you test for a non-linear relationship

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