EXERCISESFORExercises for Efficiently Inefficient© Lasse Heje Pedersen 2ContentsPreface to the ExercisesPART I: ACTIVE INVESTMENT1 Understanding Hedge Funds and Other Smart Money2 Evaluating Trading Strategies: Performance Measures3 Finding and Backtesting Strategies: Profiting in Efficiently Inefficient Markets4 Portfolio Construction and Risk Management5 Trading and Financing a Strategy: Market and Funding LiquidityPART II: EQUITY STRATEGIES6 Introduction to Equity Valuation and Investing7 Discretionary Equity Investing8 Dedicated Short Bias9 Quantitative Equity InvestingPART III: ASSET ALLOCATION AND MACRO STRATEGIES10 Introduction to Asset Allocation: The Returns to the Major Asset Classes11 Global Macro Investing12 Managed Futures: Trend-Following InvestingPART IV: ARBITRAGE STRATEGIES13 Introduction to Arbitrage Pricing and Trading14 Fixed-Income Arbitrage15 Convertible Bond Arbitrage16 Event-Driven InvestmentsExercises for Efficiently Inefficient© Lasse Heje Pedersen 3Preface to the ExercisesThis compendium of exercises is meant to be used with the book on Efficiently Inefficient: How SmartMoney Invests and Market Prices Are Determined, by Lasse Heje Pedersen, Princeton University Press,2015. The compendium contains exercises for each chapter in the book, except the introductory chapters(i.e., chapters 6, 10, 13). I am grateful for feedback from students and colleagues at New York UniversityStern School of Business and Copenhagen Business School and especially to Niklas Kohl for taking the leadon developing several of the exercises (7.1‐7.6, 9.8‐9.12, 16.1‐16.8).Several of the exercises require additional material, which is distributed separately. For example, severalproblems rely on data to be processed in a spreadsheet such as Excel, while other problems rely onfinancial statements such as merger offers. Professors who use the book can contact me for this material.Exercises for Efficiently Inefficient© Lasse Heje Pedersen 41. Exercises for Understanding Hedge Funds and Other Smart Money1.1. Selection vs. Timing. Explain the meanings of market timing and security selection, highlighting theirsimilarities and differences.1.2. Biases. You work as an analyst at a discretionary equity hedge fund. You have the investment thesisthat it pays to buy the “best in breed”, that is, stocks that are the industry leaders. You find thecompanies that are currently the largest in each industry and track their performance the last 5years. This portfolio significantly outperforms the market over the time period.Are there any issues with this analysis? Should the hedge fund buy this portfolio and, if so, what arethe risks?1.3. Hedge funds vs. mutual funds. Consider a passive mutual fund, an active mutual fund, and a hedgefund. The mutual funds claim to deliver the following gross returns:ݎ௧passive fund before feesݎ ൌ௧stock indexݎ௧active fund before fees ൌ 2.20% ݎ௧stock index ߝ௧The passive fund charges an annual fee of 0.10%. The active mutual fund charges a fee of 1.20% andseeks to beat the same stock market index by about 1% per year after fees. The active mutual fundhas a beta of 1 and has a tracking error volatility of ටvar൫ߝ௧ ൯ ൌ 3.5%.The hedge fund uses the same strategy as the active mutual fund to identify “good” and “bad” stocks,but implements the strategy as a long‐short hedge fund, applying 4 times leverage. The risk‐freeinterest rate is ݎൌ 1% and the financing spread is zero (meaning that borrowing and lending ratesare equal). Therefore, the hedge fund’s return before fees isݎ௧hedge fund before fees ൌ 1% 4 ൈ ൫ݎ௧active fund before fees െ ݎ௧stock index൯a. What is the hedge fund’s volatility?b. What is the hedge fund’s beta?c. What is the hedge fund’s alpha before fees (based on the mutual fund’s alpha estimate)?d. Suppose that an investor has $40 invested in the active fund and $60 in cash (measured inthousands, say). What investments in the passive fund, the hedge fund, and cash (i.e., the risk‐free asset) would yield the same market exposure, same alpha, same volatility, and sameexposure to ߝ௧ ? As a result, what is the fair management fee for the hedge fund in the sensethat it would make the investor indifferent between the two allocations (assume that the hedgefund charges a zero performance fee)?Exercises for Efficiently Inefficient© Lasse Heje Pedersen 5e. If the hedge fund charges a management fee of 2%, what performance fee makes the expectedfee the same as above? Ignore high water marks and ignore the fact that returns can be negative,but recall that performance fees are charged as a percentage of the (excess) return aftermanagement fees. Specifically, assume the performance fee is a fraction of the hedge fund’soutperformance above the risk‐free interest rate.f. Comment on whether it is clear that hedge funds that charge 2‐and‐20 fees are “expensive”relative to typical mutual funds. More broadly, what should determine fees for activemanagement?1.4. Styles and Strategiesa. Fill out the answers for each HF style in the table below. (While most problem set questions willtest that you can apply what you learned in class, some of the information in the table was notcovered in class. The idea is that you should start thinking carefully about each style, discussing itwith your classmates, friends in the industry, and answer to the best of your knowledge.)
LongshortequityShortbiasedQuantequityGlobalmacroMan.futuresFixedincomearbConvertbondarbEventdrivenarb
Name the securities most commonly used
Invests in liquid securities (1=highly illiquid, 5=highly liquid)
Has a large turnover (1=very low turnover, 5=high turnover)
Uses a lot of leverage (1=unlevered, 5=super high leverage)
Discretionary/heuristic or quantitative/systematic (1=gut driven, 5=model driven)
Left tail (1=often positive return, but sometimes blows up, 5=positive skewness)
Name one or more hedge funds in this style
b. Explain the main idea behind the three equity strategies and how they are different. Also, discusswhy these strategies might profit over the long term and why they might not.Exercises for Efficiently Inefficient© Lasse Heje Pedersen 6c. Discuss how global macro investors and managed futures traders trade and the potential driversof their returns. Explain the distinction between top‐down vs. bottom‐up investing.d. Discuss the common idea behind arbitrage strategies. What are the potential risks of trading onan apparent arbitrage opportunity? What are the differences across the three types of arbitragestrategies?Exercises for Efficiently Inefficient© Lasse Heje Pedersen 72. Exercises for Evaluating Trading Strategies: Performance MeasuresFor each of the following exercises, consider the hedge fund index data provided and evaluate theperformance (abstracting here from the potential biases in the data).2.1. Performance measures. For each hedge fund style, calculate and interpret the followingperformance measuresa. Annualized arithmetic average returnb. Annualized geometric average returnc. Annualized volatilityd. Annualized Sharpe ratioe. Market betaf. Annualized alpha to the marketg. Annualized Information ratioh. Maximum drawdowni. Skewnessj. Excess kurtosis2.2. Cumulative return and drawdown. Make the following plots for Global Macro Hedge Fund indexa. The cumulative returnb. The drawdown2.3. Factor models. For Equity Long/Short, run two regressions: (i) a univariate regression of the hedgefund index’s excess return on market excess return; and (ii) a multivariate regression on the market,size, value, and momentum factors.a. Interpret the loadings on the different factors. What do we learn of the investment style?b. Compare the multivariate alpha with the alpha from the univariate market regression. Discussthe difference in interpretation between the univariate vs. multivariate alphas.2.4. Illiquidity and stale prices. For Convertible Bond Arbitrage, compare:a. The beta in a monthly univariate regression on the marketb. The beta in a univariate regression on the market using 3‐month returns. (The regressioncoefficients can still be estimated by running the regression monthly, i.e., with overlapping data,but, in this case, t‐statistics need to be adjusted if you were to consider these)c. The sum of betas in a monthly regression on the market, the 1‐month lagged market, and the 2‐month lagged marketExercises for Efficiently Inefficient© Lasse Heje Pedersen 83. Exercises for Finding and Backtesting Strategies: Profiting in EfficientlyInefficient MarketsExamples of backtests of trading strategies are contained in many of the exercises in the chapters to come(e.g., 9.1‐9.12, 11.1‐11.7, 12.1‐12.4, 16.11‐16.13). Hence, exercises with techniques for backtests are notincluded here, but instead we consider some conceptual exercises.3.1. Information collection. Discuss how active investors can be compensated for their informationcollection. Give examples of how you could try to collect information about specific firms and howyou could trade on this.3.2. Adverse selection and IPOs. Some initial public offerings (IPOs) are oversubscribed, meaning thatmore investors want to be allocated shares than what is for sale. Other IPOs are undersubscribed,meaning that the firm and its underwriter struggle to sell the shares.
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In which case do you expect that the return after the IPO is the highest?Suppose that you bid for an allocation for IPO shares without knowing whether the offering isoversubscribed or undersubscribed. In which case are you more likely to be allocated the numberof shares that you ask for and how does this affect your expected return?Historically first‐day IPO returns have been positive on average, i.e., an investor who put an equal
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amount in all IPOs and sold at close on the first trading day made abnormal profits. Does thisimply abnormal profits from participating in IPOs?3.3. Market and funding liquidity. Suppose that you are considering buying a home, which you expect tolive in for about 5 years, and, given the mobile workforce in the region, you also expect future buyersof the property to move relatively frequently. You find a house and an apartment which are equallyattractive and consider which one to buy. (The house and apartment are equally attractive in thesense, for instance, that something similar could be rented at the same rates.)a. Market liquidity. Suppose that the house is much more expensive to trade in terms of fees to thereal estate agent, a longer expected waiting time when the property is on the market (and youmay already have moved), and other costs. What would you pay more for, the house or theapartment? Explain your answer.b. Funding liquidity. Suppose that the house and apartment are equally easy and costly to trade(have equal market liquidity), but the bank will give you (and future potential buyers) a largerloan for the apartment. Would that lead you to be willing to pay more for the apartment thanthe house? What would Modigliani‐Miller say and why? Why might your answer be different?c. Liquidity spirals and liquidity risk.
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If the house can be expected to be more difficult to trade than the apartment, whichproperty do you think the bank will be more willing to provide a large loan for?
Exercises for Efficiently Inefficient© Lasse Heje Pedersen 9
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If the apartment is more easy to borrow against, which property do you think will be moreeasy to sell?If suddenly there are many more properties for sale in this area than available buyers, howcould the market and funding liquidity evolve? Might the market for houses evolvedifferently than the market for apartments?How does this liquidity risk affect the price you want to pay for the house vs. the apartment?How does the answer change if you expect to live in the property for 40 years?
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3.4. Demand pressure. Suppose that a significant fraction of the population of investors needs to buy asecurity, say a stock ABC, for reasons unrelated to the stock’s fundamentals (its expected futureearnings and dividends). For instance, suppose that an important stock market index suddenly gives alarge weight to stock ABC.a. What will happen to the stock price in a perfectly efficient market?b. What is likely to happen to the stock price in a market with limited arbitrage?c. In an efficiently inefficient market, where the stock price moves (as discussed in 3.4), what islikely to happen to the price of another stock that is highly correlated to stock ABC (but notdirectly affected by the demand pressure)?Exercises for Efficiently Inefficient© Lasse Heje Pedersen 104. Exercises for Portfolio Construction and Risk ManagementThe following exercises are based on the hedge fund index data provided. The underlying data is the sameas that used in the exercises for Chapter 2 and these exercises complement each other.4.1. Portfolio optimization. Suppose that you were running a fund of hedge funds in 2003 and needed toallocate your capital between the various hedge fund styles. (Alternatively, you could be running amulti‐strategy hedge fund and allocating capital across the various trading groups or running apension fund allocating capital to various hedge funds.) Compute the excess return of each of thehedge fund indices.a. Define portfolio weights above each column for each of the first 9 hedge fund styles (notincluding the overall index called “DJCS Hedge Fund USD”) and choose these portfolio weights tobe equal (i.e., 1/9). Compute the excess return of the corresponding portfolio (as theSUMPRODUCT of portfolio weights and excess returns of hedge funds). Finally, compute theSharpe ratio over the early sample 1994‐2003 (that you would have been aware of in 2003), thelate sample 2004‐2012 (the period over which your returns would be realized), and the fullsample.b. Compute another weighted average of these 9 hedge fund styles, where the weights are chosento maximize the Sharpe ratio over the early sample (e.g., use the “solver” in Excel). What is theSR of this portfolio over the late sample? How does the answer compare to a.? Discuss the issueswith portfolio optimization and what you might do about it.4.2. Risk management and drawdown control.a. For each hedge fund style and each month, compute the annualized volatility as the realizedstandard of excess returns over the past 12 months. For the first year 1993, use the value fromJanuary 1994 (which is cheating, but it does not matter here). Plot the volatility over time forfixed income arbitrage.b. For each hedge fund style, compute the return of the risk‐managed strategy. Specifically, choosean investment x such thatx 3 σt ≤ MADD – DDtwhere σt is the current annualized volatility, MADD=30% is the maximum acceptable drawdown,and DDt is the current drawdown of the risk‐managed strategy. Specifically, if 3 σt ≤ MADD – DDtthen you are not in “drawdown control mode” and you continue with a full investment of x=1.Otherwise, you enter drawdown control model is set x= ( MADD – DDt ) / ( 3 σt ).Exercises for Efficiently Inefficient© Lasse Heje Pedersen 11In one plot, show the drawdowns of emerging markets hedge funds with and without drawdowncontrol. In another plot, show the cumulative return of these two strategies.c. Compute the SR, average return, and maximum drawdown for the strategy without drawdowncontrol (as in the exercises for Chapter 2, where x is always 1) and the corresponding numbersfor the risk‐managed strategies. Comment on the differences.Exercises for Efficiently Inefficient© Lasse Heje Pedersen 125. Exercises for Trading and Financing a Strategy: Market and FundingLiquidityThe following sections contain exercises related to how trading is funded (e.g., 8.1, 15.4, 16.13) and howtransaction costs affect the performance of trading strategies (e.g., 11.4). The following questions regardingtrade execution should be answered independently of each other and relate to the following limit orderbook:5.1. Bid‐ask spread. What is
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