MF825 – Spring 2021
Exam 1 study guide
Final Version
Further practice questions added at the end on 3/15
The exam
• The exam is on Tuesday March 16th from 8:15am to 10:15am. Use the 8:00am section zoom link to log in. Read these instructions now so you will not be surprised. The extra 15 minutes is to give you time to scan your answers and upload your solved exam.
• You will log in on Gradescope (not Questrom Tools) to download the exam. It will be available at 8:15am. You will upload your completed exam on Gradescope. Uploading must be over at 10:30am with no recourse. Make sure to upload each question separately in the allocated space on the template.
• You may consult anything posted on Questrom Tools or the recommended readings. You are encouraged to use R for computations. You should not use the “internet”: anything not in line with the notation or the assumptions of the course will be considered wrong with no recourse. If your answer appears to have been copied from an internet web site, you will get a zero and be referred to the Graduate Office for violation of the academic integrity rules.
The exam is zoom proctored: You must never leave zoom and must have your video on at all times otherwise points will be taken off your total grade. In brief, if we don’t see you, you lose points.
• You cannot communicate with anybody by any means during the exam. So if you are at home, make it clear that you cannot be disturbed or talked to during the exam. So you can not use any device to call, email, text, chat, zoom, etc.. with anybody. Put your phone in Do Not Disturb mode during the duration of the exam.
• You can not be in the same room as another student taking the exam.
• The exam is zoom proctored: You must never leave zoom and must have your video on at all times otherwise points will be taken off your total grade. In brief, if we don’t see you, you lose points.
• You cannot communicate with anybody by any means during the exam. So if you are at home, make it clear that you cannot be disturbed or talked to during the exam. So you can not use any device to call, email, text, chat, zoom, etc.. with anybody. Put your phone in Do Not Disturb mode during the duration of the exam.
• You can not be in the same room as another student taking the exam.
• The exam has a number of independent questions: algebraic or number calculations as in class or homework, or a bit different, discussion questions involving a concise but complete justification of the answer to check that you understood the discussions in class.
• Discussion questions may have a True / False feature: If part of a statement is correct and part is False, you must label the statement as False. Then in your discussion, write clearly what is correct, what is false. and why. If you say True, explain why the entire statement is true. Saying True with no explanation gets zero point even if it is correct.
• The topics to review include what we did in class, the two articles, and the two problem sets. If you make sure that you understand, can do the proofs, and can use all the material in the lecture notes and homework, you are in very good shape.
• Correct numerical answers without justification or starting theoretical formula get zero point.
General Guidelines
Use the lecture notes as the time line of topics. Re-read the book as a support, concept checks, numerical examples, back of the chapter problems.
• The lecture notes include numerical examples solved in class. You should make sure you can solve and understand every one of them.
• The notes also include tables which were the source of discussion in class. You should be able to answer questions based upon the information supplied in the table, as we discussed in class.
• The class discussions can also be the basis for qualitative questions testing your understanding of the concepts. Make sure to review the discussions we had. Make sure you can explain and discuss in words every concept we defined and discussed.
• The exercises solved in the homework are obvious candidates for inclusion in the midterm. If you did not get it right when you first did it, you should make sure to understand the solutions, and that can now solve them.
• You can go back to your connect homework as practice with new (randomly generated) numbers.
• The back of the chapters problems are additional exercises which you should practice, see below for guideline.
• The JKM article and my chapter on portfolio theory in the Filbeck book are crucial to support the lectures but only read what we did in class for the exam. The two Kritzman articles are important.
• Notation warning: BKM has the following notation in mean variance chapters, uppercase R for excess returns, lower case r for total returns. We (and many others!) do not have this notation in the notes, we just write R-Rf if needed. Whenever you read different material, do not expect everybody to use the same notation.
Crucial topics and concepts not to forget
Everything we did in class can come up at the exam.
Below is a selection, which does not meant that concepts not outlined below could not come at the exam: Go methodically through the notes and the additional exercises we did in class.
Unless specified otherwise, you are responsible for knowing the proofs we have done so far.
Obvious candidates for questions in the lectures notes (LN) include:
Since the exam is open notes, you will not be asked to do proofs which are spelled out in the notes.
Very important see highlighted comment below
• Indices and Trading LN:
• Taxable vs Non-taxable Muni bond yields
• Properties of different market indices and their weighting schemes.
• Cost of Trading: Limit-order book and the specialist
• Buying on margin, margins for short sales. IMR, MMR, margin calls.
• Mutual Funds:
• Impact of costs on Investment, could you explain Table 4.2?
• Power of compounding – computing future value with and without fees, see the R file. You should be able to do a basic computation with the annuity formulas
• Historical Record LN:
• Real vs nominal interest rate, expected inflation
• Arithmetic vs. geometric average: which one to use for what?
• Unbiased estimate and minimum MSE estimate (proof p 16 not asked)
• Basic use of standard deviation: shortfall probability, VaR
• Normality: Why?
• Normality vs Log-normality: when does it matter? multiperiod VaR
• Long Term Mean LN:
• Unbiased estimate and minimum MSE estimate (proof p 16 not asked)
• Know how to use and motivation.
• LNs on Utility: St Petersburg – Building Utility, Utility to Mean Variance
• Constructing utility function,
• Computing EU, CE, RP, IP for classic log or power utility.
• Solve insurance problems for the insured and for the insurer, partial insurance
• Risk Pooling vs Sharing, Risk Transfer (rich to poor) with constant RRA.
• Proving approximate (Pratt-Arrow) risk premium, $ and relative terms
• Power vs Exponential Utility
• Proving CE and risk premium with Power Utility and Log-Normal returns
• Comparing portfolios in mean-variance
• Mean-Variance Efficient Sets LN 7
• Prove and use 1 risky – 1 risk-free allocation
• The CAL and the Sharpe Ratio
• Optimal choice on the CAL: prove and use Merton, understand the effects of the inputs (mean, variance, RRA)
• Effect of TCs in the Tbill market: Impact on allocation, impact on fund ranking
• Optimal market timing asset allocation
• Computing implied average investor’s RRA from market data.
• 2 risky assets: prove minimum variance, maximum expected utility
• Impact of on frontier
• Prove that Beta is sole measure of risk using the two-asset case
• Merton’s General Asset Allocation
• Be able to do the proofs Ito’s lemma for dS vs dLogS, dLogP.
• Be able to prove the final result, take expectation of [4], differentiate [5]
• Efficient Sets LN 8
• Diversification and portfolio size: given average stock variance, average correlation across stocks, what is the variance of an (equal-weighted) portfolio of n stocks? How many stocks are needed for the portfolio standard-deviation to be below a certain value? What is the lowest standard deviation achievable?
• Portfolio variance and ip as sole measure of risk, proof
• Frontier with many assets, key features of the frontier
• Introducing a Tbill: Maximizing the Sharpe Ratio
• “Qualitative” facts about the mean-variance frontier: effect of short-sales restrictions, why is the MVP interesting, where are investors on the frontier, what happens when a risk-free rate is available. What happens to M when borrowing and lending rates differ.
• Frontier Results LN 9
• Be able to do similar proofs! You are a quant, you can design and solve frontier problems.
• I will give you A, B, C, Delta, if needed no need to learn them.
• Proofs: Min , Min ST E(R) constraint, Frontier equation, Max CE, Max CE with Rf.
• Special attention to the reasoning for getting the Tangency portfolio weights with Rf
• Black’s argument: MV Efficiency of the market portfolio even without Rf.
• You should be ready to compute optimal portfolios and plot a frontier using R and the formulas in LN9. The data you will have to use are in your Data folders. You have daily returns from 1991 for 16 industries and the Fama French file. To prepare for your exam, create your excess returns data now and practice making the optimal portfolios using data from 1996 to 2000.
Homework and R and XL files
Review the homework solution as soon.
The shorter problems (insurance, asset allocation, market model regression, alpha, etc..) are typical of what you can get. Consider them as review problems
Don’t neglect the solutions given on R and XL files.
The R file Compounding, the XL files Insurance, have important computations you should know how to do. Vary the inputs to see the effects
Make sure you understand the dynamics of some of the allocation, the effect of RRA, variance, expected returns, correlations, Transaction costs on the geometry of the opportunity sets
Additional Exercises and Problems
You have data in the data folder.
Any of your connect problems can be used for practice. In addition to the notes and the homework, consider the following numerical examples. They will help you make sure you understand and can use the material:
BKM 3: Examples 3.1, 3.2, 3.3. Problems 9, 10, 12
BKM 5: Examples 5.7
BKM 6: Examples 6.3, 6.4, Problems 1-5, 8, 13-15, 20-22, 27-28, CFA 1-5
BKM 7: Examples 7.1-7.3, Table 7.4, Concept 7.5, CFA 4-10
Problems: 3, 4-16 are a bit too long for an exam but they test your understanding.
FURTHER PRACTICE QUESTIONS: CFA style questions, NO explanation will be given
• The Benchmark has expected return 0.08 and standard deviation 0.18. The one-year TBill rate is 0.02. What is the Benchmark Sharpe ratio? What is the optimal allocation of a log utility investor? What investor invests optimally 100% in the Benchmark?
• Same numbers as in 1. BUT: Borrowers borrow at 3% and lenders only get 1%. Characterize the three types of investors 1) who borrow, 2) who lend, 3) who invest 100% in the benchmark without borrowing or lending
• An efficient passive portfolio manager has a 8.5% return and charges a 25 bp fee, and has a 15% standard deviation. The Tbill. rate is 2%. You manage a portfolio with an expected return of 12.4%, and 25% standard deviation. How high a fee can you charge and still be competitive with the efficient portfolio manager?
• Many risky assets, borrowing and lending rates are 5% and 2%. The portfolio with the highest lending Sharpe ratio TL has mean return 0.13 and standard deviation 0.25. The portfolio with the highest borrowing Sharpe Ratio TB has mean 0.19 and standard deviation 0.35. Draw by hand the investment opportunity set clearly indicating RB, RL, TB TL. Which class of investors (give risk aversion ranges) invest 1) in risky assets only via TL , 2) only via TB , 3) in a combination of TL and TB? Does this third category borrow or lend at the risk free rate?
Be able to draw the picture.
Be able to say what happens if investors can (or can’t) short-sell without transaction costs.