Reading:

The recommended textbook for this class is:

• Elton, E.J., Gruber, M.J., Brown, S.J., and W.N. Goetzmann, 2014, Modern Portfolio Theory and Investment Management, 9th Edition.

Any Investments textbook is also suitable for this class.

A more advanced text is:

• Ferson, W.E., 2019, Empirical Asset Pricing: Models and Methods, MIT Press.

This is an excellent reference book if you wish to dig deeper into some of the topics in the class.

The material for the first part of the class on Markowitz and Michaud optimization draws heavily on:

• Michaud, R.O. and R.O. Michaud, 2008, Efficient Asset Management, Oxford University Press.
• Michaud, R.O., 2023, Finance’s Wrong Turns: A New Foundation for Financial Markets, Asset Management, and Social Science, Palgrave MacMillan.

A couple of useful additional books are by Haim Levy:

• 2011, The Capital Asset Pricing Model in the 21st Century: Analytical, Empirical, and Behavioral Perspectives, Cambridge University Press.
• 2022, Stocks, Bonds, and the Investment Horizon: Decision Making for the Long Run, World Scientific Publishing.

Links to individual papers are on the My Place website.

Assessment

This class is a 20 credit class and should involve 200 notional student effort hours.
The assessment for this class consists of a coursework element that accounts for 40% of the final mark and a three-hour final examination that accounts for 60%.
The coursework is the completion of questions in the problem set. The coursework should be submitted online by Thursday of week 8 in semester 2.

The aim of the problem set is to develop the following skills:

• Undertaking empirical research
• Evaluating and interpreting evidence

The coursework will be an optional group-based submission where you can work in groups of up to 6 people. All members in the group will be allocated the same mark as this is an option to work in the group. You are responsible for finding a group if you wish to work in a group.

The written part of the report should be a maximum of 5 pages (Times New Roman font size 12, double spaced). After the report should go all the tables and graphs. All of the answers to calculations must go either in Tables or graphs. Put each graph and table on a separate page. The tables and graphs should be presented in a similar fashion to research papers i.e. have a number, a title, and a short explanation of what is in the table. The references go at the end of the report. The references should be double spaced and presented in the same way as a research paper. The references should match the studies cited in the report. You are required to include at least two references in the reference section.

When doing the questions in the problem set, the material will be assessed on how well the questions in each set have been addressed as well as the overall presentation. Answer the questions specifically. Do not include literature reviews or extensive discussion of research methods or Matlab code unless the question asks you for that.

Feedback will be provided through the use of an evaluation form on how well these criteria have been met.

The final exam will consist of two essays out of a choice of 5 essays. The main criteria for essay-based questions will primarily focus on the level of understanding of the material covered in the class.

You are welcome to come and see me to get additional feedback for any part of your assessment.

Problem Set Questions

All questions about the relevant Matlab commands should be directed to Martin and Donald who will provide support in the Matlab commands. During the computing lab sessions, you can work through the Matlab workbook and do the problem set questions and also receive feedback on your answers. It is important that you use this opportunity to receive informal feedback on your initial attempt at the problem set and how you can incorporate that feedback in improving your performance.

We are going to use the data based on the recent study by Jensen, Kelly, and Pedersen (2023), which provides data on a large number of anomaly portfolios for 93 countries in U.S. dollar terms. Your group is free to select any country and time period. You should download monthly data on 15 anomaly portfolios (do not download the themes) for the country of choice. You are free to select any 15 portfolios. You should also download the Market factor for your country of choice. Keep the weighting at Capped Value Weighted.

https://jkpfactors.com/factor-returns is the data link.

1. For each of your portfolios, and the market index, calculate the average excess returns, standard deviation, and the t-statistic of the null hypothesis that the average excess market return equals zero across the whole sample period. In addition, calculate the 95% confidence interval of the average excess market return for each portfolio.What can we learn from these results?
2. Using the market index as the market portfolio, run the time-series regressions of your test asset excess returns to examine the CAPM. Report your statistical results in a Table, and discuss whether the zero alpha null hypothesis of the CAPM is rejected or not in your set of test assets.
3. Looking at the magnitude of the individual alphas of your set of portfolios, how well does the CAPM price the anomaly portfolios?

Matlab Workshops

Workshop 1 Questions

Using the U.K. excess market returns:

1. Calculate summary statistics of the excess market returns across the whole sample period.
2. Conduct a t-statistic of the null hypothesis that the average excess market return is equal to zero and estimate the 95% confidence interval. Do stocks outperform bonds over this sample period?

Workshop 2 Questions

This workshop will focus on testing the CAPM. We will use all the size/BM portfolios as the test assets (columns 1 to 16). Columns 1 to 4 are Small companies, and Columns 13 to 16 are Big companies. In each batch of four, we go from Growth to Value.

1. Calculate excess returns of the size/BM portfolios using the Treasury Bill return (Rf). Calculate the mean and standard deviation of the size/BM portfolios. Are there any patterns in the summary statistics of the size/BM portfolios?
2. Using the excess returns of the U.K. market index, run the time-series regressions of the size/BM portfolios on the market index. Report the results in a Table, and discuss the results.
3. How well does the CAPM perform in terms of the zero alpha null hypothesis?

Workshop 3 Questions

1. Calculate the average returns and covariance matrix of the 16 size/BM portfolios.
2. Calculate the optimal portfolio weights when t=0.2 for the unconstrained mean-variance frontier with a risk-free asset. Also, calculate how much is invested in Rf.
3. Calculate the risk tolerance of the tangency portfolio and the corresponding optimal portfolio weights from the unconstrained mean-variance frontier.
4. Using the Portfolio Matlab function, estimate the constrained mean-variance frontier using the 16 size/BM portfolio returns and impose the restriction of no short selling constraints.

Workshop 4 Questions

This workshop will focus on testing multifactor models. We will look at the Fama and French (1993) three-factor model (Market, SMB, and HML) (FF3).

1. Run the time-series regressions of the size/BM portfolio excess returns on the FF3 model.
2. Report the results in a Table, and discuss how well the FF3 model performs using the zero alpha null hypothesis.
3. Estimate the average excess returns of each factor and use the t-statistic to examine if the mean excess factor excess returns are equal to zero or not.
4. Compare the results between the FF3 model and the CAPM in Workshop 2.

Workshop 5 Questions

1. Run an individual regression of the excess returns of the five factors on a constant and the lagged one-month excess return of the factor. Report the relevant statistics.  This test looks at whether the past excess factor returns predict the future excess factor returns.
2. Run an individual regression of the excess returns of the five factors on a constant and the lagged one-month Treasury Bill return. Report the relevant results.  This test looks at whether a lagged information variable predicts the excess factor returns.
3. Using the four smallest size/BM portfolios (columns 1 to 4), run the regression of the excess portfolio returns on a constant and a January dummy variable.Report the relevant results.

Workshop 6 Questions

The examplefund.xlsx file contains the monthly returns on two U.K. funds (Trust 1 and Trust 2), the excess returns on the three factors in the Fama and French(1993) model (Market, SMB, and HML), and the return on the one- onth U.K. Treasury Bill.

1. Calculate the excess returns of the two funds and estimate the Sharpe (1966) performance of the two funds and the market index.
2. Calculate the Jensen performance of the two funds using the CAPM and Fama and French (1993) models and conduct statistical tests if the Jensen performance equals zero or not
3. Calculate the Information Ratio and Appraisal Ratio for both funds using both models.

Provisional Timetable

Week 1 Types of financial securities, managed funds, use of benchmarks and market indexes, introduction to statistics and regression analysis.

Week 2 Calculating expected return and risk of a 2-asset and N-asset portfolio, naïve portfolio diversification, mean-variance analysis with N risky assets.

Week 3 Mean-variance analysis with N risky assets and risk-free asset, Applications, and criticisms of mean-variance analysis.

Week 4 CAPM, theory of CAPM, predictions of the model, testing the CAPM.

Week 5 Estimation risk problem, Constrained Mean-Variance Optimization, Resampled Portfolio Efficiency.

Week 6 Arbitrage Pricing Theory (APT) and Multifactor Models.

Week 7 APT, Market efficiency.

Week 8 Market Efficiency and Empirical Tests.

Week 9 Evaluating Managed Fund Performance.

Week 10 Bond Valuation and Bond Portfolio Management.

Week 11 Revision.

Sample Outlines of the 2021 Main and Resit Exams

Main Diet

Answer any two questions.

1. Discuss the estimation risk problem of sample mean-variance portfolios and the resampled portfolio efficiency approach of Michaud(1998) and Michaud and Michaud(2008).
2. Are stock returns predictable over time? Discuss the implication that this predictability has for market efficiency.
3. Critically examine the Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Theory (APT) as alternative linear factor models.
4. Examine the main factors that affect the valuation of bonds.
5. Critically examine the main performance measures used to evaluate fund performance.

Resit Diet

Answer any two questions.

1. Critically examine the challenges that stock return predictability has for the Efficient Markets Hypothesis.
2. Critically examine the resampled portfolio efficiency approach of Michaud and Michaud(2008).
3. Does naïve diversification pay? Explain why diversification can reduce portfolio risk.
4. Discuss the main approaches to bond portfolio management.
5. Do mutual funds add value to investors? Discuss the empirical evidence on mutual fund performance to see whether or not mutual funds add value to investors.

Main Diet:

1. Discuss the estimation risk problem of sample mean-variance portfolios and the resampled portfolio efficiency approach of Michaud(1998) and Michaud and Michaud(2008).

This answer should draw heavily on the material in the Michaud and Michaud(2008) book, especially chapters 4 to 6. The paper by Michaud and Michaud in 2008 also covers much of the same material.

The answer can begin with an overview of mean-variance analysis of Markowitz.  There can then be some discussion as to the uses of mean-variance analysis and some of the criticisms.  The main point of Michaud and Michaud is that estimation risk problem is the main issue and not the criticisms in chapter 3 of their book.

The answer should explain what the estimation risk problem is and why it is a serious issue in mean-variance analysis.  The main problem is very unstable and extreme portfolio weights and poor out-of-sample performance (Jobson and Korkie(1981), DeMiguel, Garlappi and Uppal(2009)).

This leads to a discussion as to what resampled portfolio efficiency is and how it address the estimation risk problem in mean-variance analysis.  The answer can conclude with some discussion as to how well resampled portfolio efficiency performs relative to Markowitz optimization.

2. Are stock returns predictable over time? Discuss the implication that this predictability has for market efficiency.

The focus of this essay is on the empirical evidence of time-series predictability and the implications for market efficiency.  Chapter 17 in Elton et al(2014) provides a good coverage to answer the question as does the review paper by Schwert(2003).

The answer should begin with an over of the EMH and the different forms.  There should be a discussion of the joint hypothesis problem of Fama(1970), and the implications of EMH.  There then should a review of the relevant empirical evidence of both short run and long run predictability using past returns and other lagged information variables.  The answer can finish with a discussion of the implications this evidence has for market efficiency.

3. Critically examine the Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Theory (APT) as alternative linear factor models.

The answer to this question should provide a review of the CAPM and APT factor models.  Chapters 13, 15 and 16 of Elton et al(2014) provides a good base for this answer.  See also the review paper by Fama and French(2004).

The answer should begin with an overview of the CAPM and the CML and SML relations.  The answer should mention the main testable predictions of the model.  Practical uses can also be discussed.  A similar outline can be followed with the APT.  There should be a discussion of the differences between the two models.  The answer can also discuss the time-series regression approach of testing these models, and a brief overview of the empirical evidence of the models.

4. Examine the main factors that affect the valuation of bonds.

This answer draws heavily on chap 21 of Elton et al(2014).  The answer can begin with a short discussion of different types of bonds.  The answer can then proceed to discuss the main factors that affect the valuation of bonds.  This includes the impact of interest rates and the different models of the term structure.  This is followed by default risk, which can include a discussion of the role of rating agencies.  The final two factors include the role of tax and the option characteristics that some bonds can have.

5. Critically examine the main performance measures used to evaluate fund performance.

The answer should draw heavily on chaps 25 and 26 of Elton et al(2014), as well as the review papers by Aragon and Ferson(2008), and Elton and Gruber(2013,2020).

The answer should begin with a discussion of performance ability and value added from Aragon and Ferson(2008).  The answer can then go through the main performance measures from Sharpe(1966), to Jensen(1968), to using portfolio weights and conditional performance measurement.  When discussing the measures, you can include how these measures are estimated in practice.  For multifactor models, there should be a discussion of the different factor models that have been used (see Elton and Gruber(2013,2020).  The answer can conclude with a brief overview of the empirical evidence of fund performance.

Resit Diet:

1. Critically examine the challenges that stock return predictability has for the Efficient Markets Hypothesis.

The focus of this essay is on the empirical evidence of both time-series and cross-sectional predictability.  Chapter 17 in Elton et al(2014) provides a good coverage to answer the question as does the review paper by Schwert(2003).

The answer should begin with an over of the EMH and the different forms.  There should be a discussion of the joint hypothesis problem of Fama(1970), and the implications of EMH.  There then should a review of the relevant empirical evidence of both short run and long run time-series predictability using past returns and other lagged information variables.  There can then be a review of cross-sectional predictability, focusing on the relation between stock characteristics and average returns.  The answer can finish with a discussion of the implications this evidence has for market efficiency.

2. Critically examine the resampled portfolio efficiency approach of Michaud and Michaud(2008).

This answer should draw heavily on the material in the Michaud and Michaud(2008) book, especially chaps 4 to 6.  The paper by Michaud and Michaud in 2008 also covers much of the same material.

The answer can begin with an overview of mean-variance analysis of Markowitz.  There can then be some discussion as to the uses of mean-variance analysis and some of the criticisms.  The main point of Michaud and Michaud is that estimation risk problem is the main issue and not the criticisms in chapter 3 of their book.

There can then follow a discussion of the estimation risk problem in mean-variance analysis and how resampled portfolio efficiency of Michaud and Michaud addresses this problem.  The answer can then focus on the benefits of Michaud optimization and some of the challenges can face.

3. Does naïve diversification pay? Explain why diversification can reduce portfolio risk.

This answer draws heavily on chaps 4 and 12 of Elton et al(2014).  The answer should start with 2 asset case and show the link between correlation and portfolio risk reduction.  The answer can then proceed to the N-asset case and show the relation between the number of assets and level of portfolio risk reduction.  The answer should explain which type of risk is diversified away.  The answer could then be extended to look at the benefits of international diversification (Solnik(1974)), followed by emerging markets.

4. Discuss the main approaches to bond portfolio management.

This answer draws heavily on chap 22 of Elton et al(2014).  The answer can begin with a short discussion of different types of bonds and the main factors that affect bond valuation.  The answer can then proceed to discuss the role of interest rate risk and how it can be measured using Duration and Convexity measures.  There can be a discussion of the different approach to manage interest rate risk such as cash flow matching or immunisation strategies.  The answer can conclude with passive and active strategies in bond portfolio management.

5. Do mutual funds add value to investors? Discuss the empirical evidence on mutual fund performance to see whether or not mutual funds add value to investors.

The answer should draw heavily on chaps 25 and 26 of Elton et al(2014), as well as the review papers by Aragon and Ferson(2008), and Elton and Gruber(2013,2020).  The answer should begin with a discussion of performance ability and value added from Aragon and Ferson(2008).

There can then be a brief discussion of the main performance measures used by academic studies and then a discussion of the empirical evidence.  Elton and Gruber(2013,2020) provide a good discussion of empirical evidence.  The answer can conclude with a brief summary of whether managed funds add value to investors.

Exam Diet 2023

Main Diet

Answer any two questions.

1) “The pioneering studies of Jobson and Korkie demonstrate that unbounded MV optimization has essentially no practical investment value” (Michaud and Michaud(2008)). Critically examine the impact of the estimation risk problem on optimal portfolio choice.

The material for the answer should draw heavily on Michaud and Michaud(2008). The main focus of the question is a discussion of the estimation risk problem in mean-variance analysis, and why it has such a negative impact on the performance of mean-variance portfolios.

The answer may then explore possible solutions such as imposing portfolio constraints, and the resampled portfolio efficiency approach of Michaud and Michaud and how it attempts to address the estimation risk problem.

2) “Factors War” (Zhang(2016)). Discuss the main multifactor models based on the APT, and ICAPM, and review any relevant empirical evidence.

This answer should begin with an overview of the main multifactor models based on the APT and the ICAPM. Included here can be a discussion of the different ways factors have been formed such as statistical factors, economic factors, and empirical factor models along the lines of Fama and French(1993,2015). There can also be a discussion of how these models differ from the CAPM.

The answer can then explore how multifactor models can be tested using time-series regression, and then with a discussion of the performance of multifactor models.

3) “Market efficiency survives the challenge from the literature on long-term return anomalies” (Fama(1998)). Discuss the Efficient Markets Hypothesis and provide a review of the empirical evidence that examine issues related to market efficiency.

The focus of this question is on the Efficient Markets Hypothesis of Fama(1970,1991,1998). The answer should explain what market efficiency is, the different forms, and the implications for investors. The answer should point out the joint hypothesis problem of testing market efficiency.

As well as the review papers of Schwert(2003), Ball(2009), the paper by Asness and Liew(2014) is of use. The answer should also include a discussion of the relevant empirical evidence including time-series predictability, and cross-sectional predictability. Other empirical evidence can be considered here as well such as market crashes.

4) “On a practical level, our results on long-term performance is that … alpha in net returns for investors is negative for most if not all active funds” (Fama and French(2010)). Discuss the main performance measures that have been used to evaluate mutual fund performance.

The answer can draw heavily on the review papers by Aragon and Ferson(2008), and Elton and Gruber(2013,2020). The answer should begin with an explanation of performance ability and value added as defined by Aragon and Ferson. The answer can then provide an overview of the performance measures used to evaluate managed funds, such as the Sharpe(1966) measure, and then the Jensen(1968) measure using both the CAPM and multifactor models. Additional measures can then include the Treynor and Black appraisal ratio, measures of market timing, and conditional performance measures of Ferson and Schadt(1996). The answer can finish with a discussion of empirical evidence on managed fund performance.

5) Critically examine the main factors that affect the valuation of bonds.

The answer for this question should draw on the relevant chapters in the Elton et al(2014) textbook. The answer should focus on the term structure of interest rates (with the alternative explanations, and the impact of default risk and the role played by bond rating agencies. The answer should also mention the effect of taxes and option characteristics on bonds.

Resit Diet

Answer any two questions.

1. “The Markowitz optimization enigma” (Michaud(1989)). Discuss the resampled portfolio efficiency approach of Michaud and Michaud(2008) to address the estimation risk problem of optimal portfolio choice.The material for the answer should draw heavily on Michaud and Michaud(2008).  The answer should begin with an explanation of the estimation risk problem in mean-variance analysis and then discuss the results of Jobson and Korkie(1981).  The answer can then explain the resampled portfolio efficiency approach of Michaud and Michaud and how it deals with the estimation risk problem.  A discussion of possible extensions can be included here such as alternative inputs of expected returns, and the covariance matrix.

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2. “The CAPM is wanted: Dead or Alive” (Fama and French(1996)). Critically examine the main predictions of the CAPM, and discuss how the CAPM can be tested using the time-series regression approach.The answer can draw heavily from the Fama and French(2004) review paper.  The answer should begin with an overview of the CAPM, and a discussion of the CML and SML.  The answer can then explore the main predictions of the CAPM and the challenge of the Roll(1977) critique.  The answer should then address as how the CAPM can be tested using time-series regression, and finish with a short discussion on the relevant empirical evidence.
3. “How many good or bad funds are there really? (Ferson and Chen(2021)). Do mutual funds add value? Discuss whether managed funds are able to provide superior performance to investors.This question draws heavily on the review papers by Aragon and Ferson(2008), and Elton and Gruber(2013,2020).  The answer should begin with a discussion of what the terms value added and performance ability mean.  The main performance measures can then be discussed, especially the Jensen(1968) measure relative to the CAPM and multifactor models.  The answer could address the different factor models that have been used to evaluate performance.  The answer can then discuss the relevant empirical evidence.
4. “Hundreds of papers and factors attempt to explain the cross-section of expected returns” (Harvey, Liu and Zhu(2016)). Critically review the empirical evidence of cross-sectional return predictability, and whether this is consistent with market efficiency or not.The focus of this question is of the Efficient Markets Hypothesis of Fama(1970,1991), and a discussion of the cross-sectional predictability evidence.  As well as the review papers of Schwert(2003), Ball(2009), the paper by Asness and Liew(2014) is of use.  The answer can begin with a discussion of EMH, and the different forms of EMH.  The joint hypothesis problem can then be discussed.  The relevant empirical evidence of cross-sectional predictability can then be discussed, focusing on the role of stock characteristics such as size, book-to-market ratio, and momentum among others.  Within this discussion, the implications for market efficiency can be addressed.
5. Discuss the main approaches that are used in bond portfolio management.

The answer should draw heavily on the relevant chapters in Elton et al.  The answer should begin by an explanation of duration and convexity measures of the impact of interest rates on bond prices.  The answer should then proceed to look at the different ways portfolio managers can manage interest rate risk in their bond portfolios, along with alternative bond portfolio strategies such as sector selection, sector rotation, and identifying undervalued bonds.

May 2024

Answer any two questions.

1. “The Markowitz optimization enigma: Is optimized optimal? (Michaud(1989)). Discuss the estimation risk problem in mean-variance analysis and consider the usefulness of resampled portfolio efficiency developed by Michaud and Michaud(2008) to address the estimation risk problem.
2. “The CAPM is wanted: Dead or Alive” (Fama and French(1996)). Critically examine the empirical performance of the CAPM. Include in your answer a discussion of how the CAPM can be tested.
3. “The recent evidence on the predictability of returns from other variables seems to give a more reliable picture of the variation through time of expected returns” (Fama(1991)). Discuss the Efficient Markets Hypothesis and provide a review of the empirical evidence of stock return predictability over time and across stocks.
4. “On a practical level, our results on long-term performance is that … alpha in net returns for investors is negative for most if not all active funds” (Fama and French(2010)). Discuss the main methods that have been used to evaluate managed fund performance. Include in your answer a review of the empirical evidence on whether managed funds add value to investors.
5. Discuss the duration and convexity measures of capturing the impact of interest rate changes on bond prices. Evaluate the alternative approaches that portfolio managers can follow to manage interest rate risk.

Resit

Answer any two questions.

1. “Finance Wrong Turns (Michaud(2023)). Critically explain the estimation risk problem in mean-variance analysis, and explore the usefulness of resampled portfolio efficiency developed by Michaud and Michaud(2008) as a possible solution.
2. “A Five-Factor Asset Pricing Model” (Fama and French(2015)). Discuss the main multifactor models that have been proposed as alternatives to the Capital Asset Pricing Model. Include in your discussion how these models might be tested in practical applications.
3. “How many good and bad funds are there really?” (Ferson and Chen(2021)). Critically review the alternative methods to evaluate fund performance, and discuss whether managed funds add value to investors.
4. “The recent evidence on the predictability of returns from other variables seems to give a more reliable picture of the variation through time of expected returns” (Fama(1991)). Are stock returns predictable over time? Discuss. Include in your answer a discussion of whether any predictability is consistent with market efficiency.
5. Discuss the main factors that affect the valuation of bonds.

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