Exam questions Flashcards
Q1: Portfolio theory:
Portfolio theory addresses the question how to form an optimal portfolio given the beliefs about future risks and returns of teh relevant assets. Specifically, it studies the risk-return profile of combinations of assets.
a) Explain the difference between calculating portfolio returns versus portfolio risks.
Portfolio return is the weighted average of the returns of the individual assets in the portfolio.
Portfolio risk is the weighted average of the risk of the individual assets PLUS the covariance between the assets.
Q1: Portfolio theory:
Portfolio theory addresses the question how to form an optimal portfolio given the beliefs about future risks and returns of teh relevant assets. Specifically, it studies the risk-return profile of combinations of assets.
b) Why is it reasonable to use volatility instead of epected volatility of the horizontal axis of the figure?
It is reasonable to use volatility instead of expected volatility in portfolio theory because the assumption is that volatility is constant over time. This is not true in reality, because there is volatility clustering. Volatility is still, however, highly persistent.
Q1: Portfolio theory:
Portfolio theory addresses the question how to form an optimal portfolio given the beliefs about future risks and returns of teh relevant assets. Specifically, it studies the risk-return profile of combinations of assets.
c)Given a world with two assets, explain in which situation the Capital Market Line (CML) and Efficient Fronteir coincide.
The Capital Market Line and Efficent Frontier coincide (=are the same), when the correlation between the assets is minus one (-1). In this case, the minimum risk point lies on the y-axis, which represent the risk-free asset.
Or: when there is no risk free rate, the CML and the Efficient Fronteir are the same.
The Capital Asset Pricing Model (CAPM) appears relatively straightforward, but testing it is a challenge. Among things, authors go through great lengths in estimating β in the equation given by 𝑟𝑡=𝛼+𝛽𝑟𝑚+𝜀, in which 𝑟𝑡 is the return of the asset and 𝑟𝑚 the market return.
In many papers, the first analysis researchers apply is to sort stocks into portfolios (for example, group stocks with similar β’s into portfolios) and check how expected returns vary over the portfolios. The second analysis is typically a regression analysis.
a. (6 points) Give one advantage and one disadvantage of using portfolio sorts over the technically more advanced regression analysis.
Advantages:
- Do not assume a linear relation between return and the variable of interest
- It is a non-parametric test
- Do not assume a constant relation over time
Disadvantages:
- Hard to do multivariate analysis
- Exclusive focus on top-bottom deciles (extremes)
- Not possible to do statistical inference
Q2 - Empirically testing the CAPM
Typically, authors first estimate the β of individual assets, then group assets into decile portfolios by their estimated β, and finally re-estimate β on the decile portfolio returns.
b. (5 points) Intuitively explain why researchers, such as Fama and McBeth, apply this two-step procedure in estimating β.
The two-step procedure is applied in order to reduce the noise in the beta estimate. First of all, the nise is less when estimating a portfolio beta. Second, the stocks in the top (bottom) decile from the first estimate have a high probability to have a postive (negatve) bias.
Another issue in testing the CAPM, is the choice of market portfolio 𝑟𝑚. Theoretically, the market portfolio includes all possible investment objects, such as equity, bonds, real estate, etc. In practice, researchers tend to choose some form of equity market index.
c. (6 points) Assume that the investment universe not only consists of equity, but also of bonds (so other markets are assumed nonexistent) that are all less risky than equity. Imagine a researcher trying to test the CAPM using an equity index only. How are the results affected?
When estimating betas on the market index that excludes bonds, there are two effects (note that beta = cov(m,i) / var(m)). First, the covariance between the individual asset and the market will be higher, which pushes the market beta up. However, the variance of the market will also be higher, which pushes the beta down. Net effect is not directly clear, but first will probably be stronger. This, however, does not necessarily change the ordering of stocks (i.e., high beta stocks will remain high beta stocks, low beta stocks will remain low beta stocks). Therefore, in the cross-sectional analysis there should be no effect! (6 points).
Question 4: Limits to Arbitrage
The concept of Limits to Arbitrage states that textbook arbitrage might be limited due to three factors: 1) noise trader risk; 2) implementation costs; 3) fundamental risks.
a. (5 points) Explain how the three factors contribute to limiting arbitrage forces. Also, indicate which of the three factors is the most ‘behavioral’ in nature.
Noise trader risk: noise traders in the market that caused the mispricing in the first place could make the mispricing worse in the short run (1 point).
Implementation costs: trading costs, bid-ask spread (1 point).
Fundamental risk: The market could move against the arbitrageur in the short run. This risk cannot be completely hedged because there is never a perfect hedge (1 point).
Noise trader risk is the most behavioral in nature because it captures the irrational behavior of investors (2 points).
The noise trader risk was formalized in the model of DeLong, Shleifer, Summer, and Waldman (DSSW). The main result is that ‘noise traders’, i.e., investors that are not fully rational, do not necessarily go bankrupt and can survive in the long run. Their results are centered around four effects: make space effect, price pressure effect, hold more effect, and Frydman effect.
b. (5 points) Explain how the ‘make space effect’ contributes to the survival of noise traders in the model of DSSW.
Noise traders increase the risk in the risky asset because their misperception is stochastic (i.e., changes over time). Because arbitrageurs are risk averse, they will take smaller positions against the noise traders to eliminate the mispricing. As a result, noise traders create their own space, the risk they introduce assures their survival (5 points).
Market liquidity can also be seen as a limit to arbitrage. Pastor and Stambaugh (2003) study
whether a stock’s liquidity beta (i.e., a stock’s exposure to a common liquidity factor) is a priced
factor in the cross-section of stock returns. The table below presents part of the main results of
Pastor and Stambaugh (2003). The decile portfolios are portfolios of stocks sorted on their
liquidity betas with the number 1 portfolio containing stocks with low liquidity betas and the
number 10 portfolio containing stocks with high liquidity betas.
Some people argue that the size premium, small stocks outperforming large stocks, is driven by
the limited liquidity of small stocks.
c.
(7 points) Explain whether the table above confirms or rejects the hypothesis that the size
premium is driven by the limited liquidity of small stocks relative to large stocks.
Looking at the SMB loadings, the Table shows that stocks with a LOW liquidity beta have a relatively high SMB beta and vice versa. This implies that stocks that are relatively insensitive to the liquidity factor load positive on SMB, implying that these portfolios contain many small cap stocks. Hence, the table REJECTS the hypothesis, even stronger, it suggests the opposite relation (7 points).
2 points when looking at SMB but drawing opposite conclusion.
Question 5: Alternative Preferences and Beliefs
Baker and Wurgler (2007) study the effect of investor sentiment on the cross-section of stock returns. Their hypotheses build on the following figure:
a. (5 points) Explain why high (low) sentiment causes the valuation level of difficult to arbitrage stocks to increase (decrease) and why high (low) sentiment causes the valuation level of easy to arbitrage stocks to decrease (increase).
Difficult to value stocks / difficult to arbitrage stocks are more sensitive to sentiment because the limits to arbitrage are stronger for these stocks. Also, these valuations are more driven by expectations. Therefore, positive (negative) sentiment causes overvaluation (undervaluation) of these types of stocks. The opposite holds for safe easy to value / arbitrage stocks due to flight to quality in case of low sentiment (5 points).
Prospect theory offers an alternative to the standard mean-variance or quadratic utility functions that are typically used in financial economics. It states, among things, that people consider changes in wealth rather than the level of wealth, people are risk averse over gains but risk seeking over losses, and suffer from loss aversion.
The frequency with which pension funds publish their performance (in terms of coverage ratio) has increased substantially over the past years. The general public can now read in the newspapers on a monthly basis how their fund is doing, whereas previously they were only confronted with the performance of their pension savings once per year.
b. (6 points) Explain, using the components of prospect theory, what this increase in reporting frequency might to the level of utility of pension participants.
Loss aversion causes losses to hurt more than gains yield. When observing investment returns more often, pension fund participants are more often confronted with negative returns (remember: daily basis, 50% negative returns, 50% positive returns. Annual bias: 70 – 30%). More negative returns more experienced losses, so lower utility (6 points).
3 points for higher utility due to increased transparency
Harvey and Siddique (2000) consider the skewness preferences of investors. That is, they study whether with stocks with a high skewness perform differently than stocks with a low skewness. The figure below is taken from their paper and presents the distribution of returns of the smallest size decile portfolio (fixed line) compared to the normal distribution (dotted line).
c)(6 points) Explain how this figure gives a possible explanation for the size premium.
The figure shows that small cap stocks are left skewed (negative skew). Harvey and Siddique show that stocks with a lower skewness earn a higher expected return because investors prefer positive skewness. Hence, the negative skewness of small stocks could potentially explain the small cap premium (6 points).
Question 6: Delegated asset management
Carhart (1997) shows that the average mutual fund has a negative four-factor alpha.
a. (5 points) Explain economically what this implies regarding the performance of the average mutual fund.
The risk adjusted returns are negative (not: returns are negative) (5 points).
Question 6: Delegated asset management
Berk (2005) argues that a negative alpha is not necessarily a negative sign regarding the skill of mutual fund managers.
b. (5 points) Explain intuitively what a negative (or, non-positive) implies in the world of Jonathan Berk.
A fund with a positive alpha attracts capital inflow because investors look at past performance. Because of decreasing returns to scale, the increased capital inflow lowers the expected returns of the fund, so lowers the alpha. Because there is a perfectly competitive market for skill, alpha’s are equalized (5 points).
Question 6: Delegated asset management
The huge size of the mutual fund industry has major implications for the way we think of markets and market efficiency, and of investors and investor rationality.
c. (6 points) Why is it that the size of the mutual fund industry must imply market inefficiency and/or bounded rationality of investors?
From the market perspective: IF the mutual industry is so large, there MUST be inefficiencies that funds can benefit from (3 points)
From the individual perspective: IF mutual funds underperform, it MUST be that investors are boundedly rational because they keep on investing in mutual funds (3 points).
Question 1: The Basics
Financial markets bring together the supply of and demand for capital. As such, it provides an intermediary function between borrowers and lenders. Banks effectively serve the same purpose.
a. Discuss the advantages and disadvantages (at least 1 advantage and 1 disadvantage) of financial markets relative to banks as intermediaries (6 points).
Pro Banks: Lower costs, closer monitoring, interest deductibility
Pro Markets: Larger pool of capital, risk sharing, equity
In his guest lecture, Dennis Karstanje (Robeco) distinguished between momentum from underreaction and momentum from overreaction. We also know that the results in the momentum study by Jegadeesh and Titman (1993) are mainly driven by the past winners, and the results in the mean-reversion study by DeBondt and Thaler (1985) are mainly driven by the past losers.
c. What can we conclude from the results of Jegadeesh and Titman
Jegadeesh and Titman show that momentum results are mainly driven by winner portfolio. This suggests that the momentum effect in J&T is driven by underreaction,
