## FIN 421

FIN 421

INSTRUCTIONS

HOMEWORK 1

• Form groups of 2 or 3 students. Answer 9 of the 15 questions below. Questions 1, 14 and 15 are mandatory.

• To make sure you get full credit for your homework:

o All your answers must demonstrate sufficient effort.

o Include all your answers in one Excel file or one Word file.

o Show your work. Numerical answers without accompanying calculations will not be considered.

o Make sure your Excel/Word file is well organized, so the grader can clearly read all your answers.

QUESTIONS

1) Listen to Barry Ritholtz’s recent interview with James O’Shaughnessy, quantitative portfolio manager and author of What Works on Wall Street, a book in our syllabus. The link is below (at least one of them will work!). Choose two topics from the interview to discuss. Choose whatever interview ideas you find interesting or useful or illuminating. I expect one long paragraph per topic or more. Connecting interview ideas with classroom material is encouraged. http://www.ritholtz.com/blog/2014/08/mib-james-oshaugnessy/ http://thereformedbroker.com/2014/08/31/barry-ritholtz-interviews-james-oshaughnessy/ http://lmgtfy.com/?q=Barry+Ritholtz+interviews+James+O%27Shaughnessy

2) Your friend wants to backtest a particular investment idea, for example, stocks that share attributes X, Y, and Z tend to beat the market. To do that, your friend will first classify all stocks that are currently part of the Russell3000 index into two groups: stocks having attributes X, Y, and Z, and stocks not having attributes X,Y, and Z. Then he will calculate an equally-weighted average return for each of the two groups over the previous 5 years. If the average stock return of the X,Y, and Z group is considerably higher than average stock return of the other group, your friend will conclude that his investment idea “works”. Do you see any problems with this approach?

3) What are OTC stocks? There are two reasons why backtests of Quantitative Investing ideas typically exclude OTC stocks. What are they?

4) Why do Quantitative Investors hold portfolios with many stocks (40 or more) as opposed to concentrated portfolios? Why do Quantitative Investors do not engage in deep analyses of the individual stocks they hold?

5) In principle, stock mispricing is likely to be more severe on the overpricing than on the underpricing side. Why?

6) Large quantitative investors typically hope to beat their benchmarks (think of the Market Portfolio or a broad stock market index) by 2 to 3% per year, after transaction costs and before management fees. Is this setting the bar too low? Why? Why not?

7) What is wrong with the following statement? “Because the average investor is human, hence affected by cognitive biases that distort decision making, it is obvious that stock markets cannot possibly be efficient in processing information”.

8) What kind of society-wide benefit, if any, could quantitative equity managers (a type of “shark”/arbitrageur) provide? In other words, could quantitative equity managers fulfill a broader social role?

9) Describe, in your own words, two situations in which stock prices were clearly wrong.

10) Explain why, as a matter of pure logic, stock markets cannot be fully efficient.

11) This exercise shows that market cap-weighted (aka value-weighted) portfolios incur in lower transaction costs by cutting out rebalancing. You have $10,000 to invest in stocks A and B. Both stocks have 1,000,000 shares

outstanding and a market price of $20 per share. Consider portfolios of stocks A and B: i) a market-cap or value- weighted portfolio; ii) an equally-weighted portfolio. These portfolios are to be rebalanced quarterly. After one quarter, at the first rebalancing date, the price of stock A is $15 per share while the price of stock B is $25 per share.

a. How many shares of stock A and B do you need to buy at the beginning for each of the portfolios?

b. What trades (buys/sells) do you have to do at the first rebalancing date for each of the portfolios?

12) Most wealth allocated to the stock market as a whole is long term in nature, as people invest for retirement or other similarly long-term endeavors. Despite this, however, most professional equity managers have fairly short investment horizons (i.e., one year). Explain why. Is there an easy fix to this problem?

13) Consider two car owners who seek to reduce their costs.

a. Adam switches from a gas-guzzler of 12 mpg to a slightly less voracious guzzler than runs at 14 mpg.

b. The environmentally virtuous Beth switches from a 30 mpg car to one that runs at 40 mpg. Suppose both car owners travel equal distances over a year. Who will save more gas by switching? Compare your quick, System 1 answer to your slow, System 2 answer.

14) In Portfolio123, create a custom universe of Russell 3000 stocks (Prussell3000 NEW) with non-missing PE ratios (PEExclXorTTM: Diluted, Excluding Extraordinary Items, TTM basis) and a rating system based solely on such PE ratios (*just like the slides*)

a) As of January 15 2015, how many stocks are there in the custom Universe? And how many stocks are there in the Prussell3000 NEW Universe? What are the two potential reasons why a stock has a missing PE ratio in P123?

Hint: Screen-> Main Settings -> Choose Universe = Prussell3000 (NEW) and click Run Screen.

Then click Rule->Add Free Form Rule-> Write the rule: PEExclXorTTM!=NA and click Run Screen

b) Check the performance of the ranking in the Custom Universe using 10 buckets, MAX time period, rebalancing every three months, minimum price equal to 3, All Sectors, Long, 0.0 Slippage, and Russell 3000 with dividends benchmark. (*just like the slides*). Copy-paste the graph with Annualized Returns.

c) How is it possible that all the 10 buckets have returns above the Russell 3000 index?

d) Suppose your boss know nothing about Quantitative Investing or Portfolio123. Explain to him why the graph in b shows that, on average in the 1999-2014 period, P/E ratios could forecast relative stock returns.

e) Now repeat the analysis breaking down the sample period in two halves: 1/2/1999 to 12/31/2006 and 1/1/2007 to today (January 2015). Copy paste the graph of Annualized Return in both cases. Answer: Is the strength of P/E ratio as a predictor of future returns the same in two subperiods?

15) A more consistent PE ratio

In Portfolio123, create a new stock ranking system based on the following stock formula:

0.5*(1/ProjPECurFY)+0.5*(1/ProjPENextFY)

Rather than historical PE ratios based on financial statement data (as in PEExclXorTTM), this formula uses PE ratios calculated using corporate earnings as forecasted by sell-side stock analysts. The formula simply averages (the inverse) of two PE ratios calculated using analysts’ data. Essentially, instead of using trailing 12 month earnings, the formula uses the average of earnings forecasted by sell-side analysts for the current fiscal year and for the next fiscal year. (Question: if you want “cheap” stocks to be on the right-hand side of the Annualized Returns graph, should you choose “Lower Values” or “Higher Values” in P123’s Node Properties?)

Create a custom universe of Russell 3000 stocks (Prussell3000) with non-missing ProjPECurFY and non-missing ProjPENextFY.

a) What are sell-side stock analysts? Do ProjPECurFY and ProjPENextFY use average or median earnings forecasts across sell-side analysts?

Hint: Google + P123 factor definitions for second question (choose factor and click on Full Description).

b) Check the performance of the ranking in the Custom Universe using 10 buckets, MAX time period, rebalancing every three months, minimum price equal to 3, All Sectors, Long, 0.0 Slippage, and Russell 3000 with dividends benchmark. (*just like the slides*). Copy-paste the graph with Annualized Returns and

answer: Does PE ratio computed from analysts’ earnings forecasts forecast relative stock returns from 1999 to 2014?

c) Now repeat the analysis breaking down the sample period in two halves: 1/2/1999 to 12/31/2006 and 1/1/2007 to today (January 2015). Copy paste the graph of Annualized Return in both cases. Answer: Compared to PE ratio from historical earnings, is PE ratio computed from analysts’ earnings forecasts a more consistent predictor of relative stock returns?

d) Copy-paste a P123 graph with the median number of sell-side analysts for Russell 3000 over time, based on next fiscal year earnings forecasts).

Hint: See Lecture 1 slide with Median P/E ratio plot on how to create such graph. By searching stock factors within Rank or Screen, you can find that the relevant stock factor mnemonic is #AnalystsNextFY

FIN 421 DUE BY: Wednesday Feb 11 at midnight (FIRM DEADLINE)

Spring 2015

INSTRUCTIONS

HOMEWORK 2

• Form groups of 2 or 3 students. Answer questions 1, 2, and 3 below. Answer either question 4 or question 5.

• To make sure you get full credit for your homework:

o All your answers must demonstrate sufficient effort.

o Include all your answers in one Excel file or one Word file.

o Show your work. Numerical answers without accompanying calculations will not be considered.

o Make sure your Excel/Word file is well organized, so the grader can clearly read all your answers.

QUESTIONS

1) The purpose of this exercise is to train you to do performance measurement and evaluation from raw data. The spreadsheet HW2_Q1 has monthly (end of month) data for an investment fund. The fund invests in two stocks, Sears and AIG. The first four columns have the date, the cashflows from clients, and the number of shares purchased/sold by the fund. Assume that client flows and stock purchases/sales are at the end of each month, and dividend payments reflect the number of stocks held at the end of the previous month). The other columns have the prices and dividends per share of Sears and AIG, and a Total Return Index for the Russell 3000.

a) Calculate how much the fund has at each point in time.

Hint: Start with the number of Sears and AIG shares owned at each point in time. Then calculate the amount of cash held at each point in time, taking into account client flows, stocks purchases/sales, and dividend receipts. Then add the value of stock positions to the amount of cash held.

b) What is the dollar-weighted average return of the fund? (monthly and annualized)

c) What is the time-weighted average return of the fund? (monthly and annualized)

d) What is the Sharpe Ratio of fund (monthly and annualized)? What is the CAPM alpha of the fund (monthly and annualized). Assume the risk-free rate is equal to zero throughout the entire period, and that the Russell 3000 index is the Market Portfolio.

Hint: compute monthly returns, making sure they are unaffected by clients’ flows.

e) What is the Information Ratio of the fund? (monthly and annualized). Assume the Russell 3000 is the benchmark.

f) What is the Maximum Draw Down of the fund?

g) Are fund managers doing a good job?

2) The purpose of this exercise is to train risk-adjusting returns using real world data. In portfolio123, create a custom universe of Russell 3000 stocks (Prussell3000) with non-missing PE ratios (Diluted, Excluding Extraordinary Items, TTM basis) and a rating system based solely on such PE ratios.

Check the performance of the ranking in the custom Universe using 10 buckets, MAX time period, rebalancing every 3 months, minimum price equal to 3, All Sectors, Long, 0.0 Slippage, and Russell 3000 with dividends benchmark.

a) Check the performance of this ranking system in the MAX time period using OUTPUT=Annualized Returns. Download results to an Excel spreadsheet. Copy-paste the graph.

b) Same as item a) but using OUTPUT=Performance Graph. Download results to an Excel spreadsheet. Copy-paste the graph.

c) Calculate period-by-period returns for each of the 10 buckets and the benchmark using the item b) results you downloaded. Note each period (but the last) has 91 days. Calculate both the arithmetic average return and the geometric average return. Annualize both averages, considering that a year has 365 days. Using this calculations, answer: Does portfolio123 use geometric averages or arithmetic averages when you choose OUTPUT=Annualized Returns?

d) Evaluate the performance of the top bucket portfolio (lowest PE ratios). You will need the risk-free rate each period. Use the time series of risk-free rate 91-day returns from the HW2_risk-free Excel spreadsheet on Blackboard.

i) Calculate the Sharpe Ratio of the top bucket and the Sharpe Ratio of the Russell 3000 with dividends (91-day and annualized).

ii) Calculate the CAPM alpha of the top bucket, using the Russell 3000 with dividends as the Market Portfolio. (91-day and annualized)

iii) Calculate the 91-day Information Ratio of the top bucket, using the Russell 3000 with dividends as the benchmark. (91-day and annualized)

iv) Find the maximum drawdown of the top bucket and maximum drawdown of the Russell 3000 with dividends. Calculate the volatility of the top bucket and the Russell 3000 (91-day and annualized). Calculate the CAPM beta of the top bucket.

Given the risk calculations above, discuss whether the top bucket appears to be a good investment portfolio.

e) This exercise shows that even a small position in the top bucket portfolio leads to performance improvement relative to holding a portfolio with the risk-free asset and the Market Portfolio. Calculate the 91-day Sharpe Ratio of a portfolio that has 20% in the risk-free asset (earning the risk-free rate), 70% in the Russell 3000 with dividends, and 10% in the top bucket portfolio. The portfolio is rebalanced to keep these proportion throughout. How does this Sharpe Ratio of this portfolio compare to the Sharpe Ratio of the Russell 300 with dividends? Hint: create a new column with the returns of the 70%-10%-20% portfolio

3) The purpose of this exercise is to train you to subject claims about stock market returns to rigorous data testing. Your friend is a big fan of megacap stocks (the top 100 or so stocks in terms of market cap). He claims that megacaps have outperformed other stocks over the last 15 years or so. Use portfolio123 to test this claim. Make sure to test the claim both on a risk-unadjusted basis and on a risk-adjusted basis (using Sharpe Ratios). Use the risk-free returns from the HW2_risk-free spreadsheet.

4) Mr. Smith is a busy entrepreneur. A financial advisor decides where to invest Mr. Smith’s stock portfolio worth several million dollars. After a few years, Mr. Smith hires two consultants to independently evaluate the performance of his stock portfolio. These consultants were given daily data on the total dollar value of portfolio, as well as the data on the episodic infusions of cash from Mr. Smith. “I can’t trust these guys”, says Mr. Smith. “It is true they found the same return, but the risk-adjustment calculations don’t match.” Consultant 1 reports that Mr. Smith’s stock portfolio had an annual Sharpe Ratio of 0.43, and while “a broad stock market index” had an annual Sharpe Ratio of 0.39. He also found an annual CAPM alpha of 1.54% per year. In contrast, Consultant 2 reports annual Sharpe Ratios of 0.41 and 0.40 for Mr. Smith’s portfolio and for a market index, respectively, and an annual CAPM alpha of 0.12%. Can both consultants have correct calculations? Explain in detail.

5) Mr. Newton Burt claims risk-adjustment is easy because “Once you have all the data in a spreadsheet, it is very easy to calculate Sharpe Ratios, CAPM alphas, Information Ratios, and Max DD.” Is it possible that Mr. New B. is both right and wrong at the same time? Discuss.

INSTRUCTIONS

HOMEWORK 3

• Form groups of 2 or 3 students. Answer questions 1 t 3 below, and 3 additional questions among questions 4 to 9.

• To make sure you get full credit for your homework:

o All your answers must demonstrate sufficient effort.

o Include all your answers in one Excel file or one Word file.

o Show your work. Numerical answers without accompanying calculations will not be considered.

o Make sure your Excel/Word file is well organized, so the grader can clearly read all your answers.

• You can access the Value Combo ranking system of Lecture 4 by copy-pasting the following web address: http://www.portfolio123.com/app/ranking-system/250832

QUESTIONS

1) The purpose of this exercise is to study the effectiveness of Value signals within economic sectors.

We know that, on average, valuation ratios forecast relative stock returns. This does not necessarily imply, however, that valuation ratios forecast returns within sectors. It is possible that Value signals work because they work across sectors, even though they do not work within sectors. That is, it could be that value signals identify sectors that are relatively cheap and sectors that are relatively expensive, although it cannot discriminate cheap vs. expensive stocks within each sector.

Knowing whether Value signals work within sectors is useful. If it does work, one can create sector-neutral value investing strategies. In these strategies, each sector receives the same weight as in the benchmark index. However, stock weights within each sector differ from benchmark weights: stocks with low valuation ratios are overweighted and stocks with high valuation ratios are underweighted.

In Portfolio123, create the Value Combo ranking system of Lecture 4 (see Slides). Check the performance of such ranking in the PRussell 3000 (NEW) Universe using the following parameters: MAX time period, rebalancing every 4 weeks, 5 buckets, minimum price=3, Slippage = 0.0, Long, and the Russell 3000 with dividends as a benchmark.

a) Use Sector=ALL. Copy-paste the graph of average annualized returns across buckets.

b) Instead of Sector=ALL as in item a), use each of the 10 USA S&P GICS sectors at a time (Consumer Discretionary, Consumer Staples, Energy, Financials, Health Care, Industrials, Information Technology, Materials, Telecommunication Services, Utilities). Copy-paste the graph of average annualized returns across buckets for each of the 10 sectors.

c) Do Value signals work within sectors? Discuss.

Note 1: The way the Sector=????? Restriction works in the Rank->Performance engine is as follows. Portfolio123 first ranks all stocks in the Universe into buckets, and only then applies sectoral restrictions to the buckets. As a result, the number of stocks within each bucket is not necessarily the same across buckets. A perhaps superior (but more time consuming) alternative is to first create Custom Universes for each of the 10 USA S&P GICS sectors, and then apply the ranking system to each of the Custom Universes at a time. This equalizes the number of stocks in each bucket. To create a Custom Universe for each of the sectors use the rule GICS(FINANCIAL), for example. For the other 9 mnemonics, within Add Free Form Rule click on Classification->Sector and then Full Description.

Note 2: IF you want to find out how many Russell 3000 stocks are there in each of the 10 USA S&P GICS sectors at each point in time, do: Screen->New->Stock Screen->Add Free Form Rule->Classification. Add two rules at a time: Universe(Prussell3000) and Sector=FINANCIAL, for example. Then hit Run Screen to see the results.

2) The purpose of this exercise is to further study the Value Combo system using Portfolio123’s Screen Engine. Backtest the performance of an equally-weighted portfolio containing the top 100 stocks in the Russell 3000 according to the Value Combo system. The portfolio will be rebalanced every three months.

To do that, first click on Click on Screen-> New Stock Screen. Then click on Main Settings and choose the following:

Universe=PRussell3000 (NEW) Benchmark=Russell3000 w/div Method = Long

Ranking = Ranking System -> Choose the Value Combo system from Lecture 4 (same from Question 1) Max No. Stocks =100

Then click on Backtest and choose: Price=Next Open

Rank Tolerance = 0 Max Pos = 0 Carry Cost=0 Slippage = 0 Long Weight =100

Start Date – End Date= MAX Rebalance Frequency = 3 months

Save this screen as Value Combo Top 100, for example.

a) Click on Run Backtest to obtain the results of the backtest. Copy-paste the resulting graphs and answer:

i) What is the annualized return of the Top 100 portfolio and of the Russell 3000?

ii) What is the average 3-month return of the Top 100 and of the Russell 3000 portfolio in up markets? And in down markets?

iii) How many (consecutive, non-overlapping) 3-month periods are there from Jan 1999 to now? What is the 3-month Hit Rate of the Top 100 portfolio? That is, in how many 3-month periods does the Top100 beat the Russell 3000 Index (positive Excess% column)?

Hint: Download to Excel and use the function COUNTIF

iv) What is the average Turnover of the Top 100 portfolio (3-month and annual)?

Note that Portfolio123 only counts stocks entering or exiting the portfolio, and ignores rebalances back to equal weights. Thus, Portfolio123’s turnover calculation underestimates the true turnover. However, the turnover coming from rebalances back to equal weights is of second order compared to the turnover coming from stocks entering or exiting the portfolio, so turnover is not underestimated by too much.

b) The results in a) do not incorporate transaction costs. A quick and dirty way to do so is to fix a Slippage parameter in Portfolio123. This incorporates transaction costs by assuming that stocks purchases and sales are done at worse prices than the historical record: buy at higher price, sell at lower price. Repeat the backtest choosing Slippage=0.45%, which is the average all-in transaction cost per trade for institutional investors. This is a quick and dirty approach because true slippage depends on how much money one is actually trading. Bigger trades move prices against you more. And, as mentioned above, Portfolio123’s Slippage only accounts for stocks entering or exiting the portfolio, and ignores rebalances back to equal weights. Run Backtest again and answer:

What is the annualized return of the Top 100 portfolio incorporating transaction costs?

c) The results in a) assume trades occur at the Next Open price. Now investigate what happens when trading is delayed by a little bit. Set Slippage=0 again and choose Price=Next Close instead of Next Open.

What is the annualized return of the Top 100 portfolio when trading is delayed?

d) The backtests in a), b), and c) are done under the assumption that one starts sorting stocks and investing on 01/02/1999. This, and the choice of Rebalance Frequency, determines the dates of all future stock trades.

What if one starts the analysis at some other date? To investigate, do a Rolling Backtest. Set Price=Next Open and Slippage=0 again and click on Rolling Backtest. Choose frequency=every week, holding period=3 months, and Start Date – End Date=MAX. Then click on Run Rolling Backtest and answer:

i) How many overlapping 3-month periods are you considering now?

ii) What is the 3-month Hit Rate of the Top 100 portfolio? That is, in how many 3-month periods does the Top100 beat the Russell 3000 Index?

iii) What is the average 3-month return of the Top 100 Value Combo portfolio and of the Russell 3000 across these 3 month periods?

3) The purpose of this question is to solidify your understanding of backtest calculations that Portfolio123 does. The spreadsheet HW3_Q3 has a hypothetical Universe of 10 stocks, labeled from A to J. You are given information on stock returns, EV/EBITDA, and market cap. Consider a ranking system based only on EV/EBITDA. Backtest the ranking system using the given Universe of stocks, a sample period of one year (two semesters), 6-month rebalancing, 5 buckets, and choose a Universe cap-weighted Index as a benchmark. Report the outcome as a bar graph with annualized returns just like Portfolio123’s Annualized Returns plot.

4) For this question, assume taxes, depreciation and amortization are always equal to zero. Consider an all-equity firm with market capitalization equal to $10,000, earnings equal $500 per year, and with zero cash.

a. What are the P/E and EV/EBITDA of the firm?

The firm then decides to change its capital structure. It takes on $5000 of debt and use all debt proceeds to buy back its own stock. The new debt is a perpetuity with interest rate equal to 4% per year.

b. What are the P/E and EV/EBITDA of the firm after the capital structure change?

c. Based on your answers to a) and b), explain why, compared to P/E ratios, EV/EBITDA is a conceptually superior valuation ratio.

5) If EV/EBITDA is the best valuation ratio in principle, can you see reasons why quantitative investors typically combine EV/EBITDA with other valuation ratios such as P/E, P/Cashflow, Shareholder Yield, and P/Book?

6) Explain why, ignoring transaction costs, the Russell 3000 Value Index is a “slow rabbit” benchmark (i.e., relatively easy to beat) for quantitative investors focusing on Value signals?

7) When looking at the stocks that get classified as Value/Glamour according to valuation ratios, certain patterns emerge. What kind of stocks tend to be Value stocks? What kind of stocks tend to be Glamour stocks?

8) It is not a secret that, on average, valuation ratios forecasted relative stock returns in the past, not only in the US stock market but also in other markets. Nonetheless, why does it still make sense, going forward, to take into account Value signals when investing?

9) On average over time, valuation ratios are powerful quantitative signals to forecast relative stock returns.

a. Could there be circumstances under which quantitative strategies should not rely on valuation ratios too much?

b. In practice, how would you figure out whether we are currently facing one of such circumstances?

INSTRUCTIONS

HOMEWORK 4

• Form groups of 2 or 3 students. Choose 2 questions among questions 1,2, and 3, and 3 additional questions among questions 4 to 14.

• To make sure you get full credit for your homework:

o All your answers must demonstrate sufficient effort.

o Include all your answers in one Excel file or one Word file.

o Show your work. Numerical answers without accompanying calculations will not be considered.

o Make sure your Excel/Word file is well organized, so the grader can clearly read all your answers.

You can access the UM Super Combo ranking system of Lecture 4 using the following link: https://www.portfolio123.com/app/ranking-system/250759

•

QUESTIONS

1) The purpose of this exercise is to study additional features of the UM Super Combo system using Portfolio123’s Screen Engine. Backtest the performance of an equally-weighted portfolio containing the top 100 stocks in the Russell 3000 according to the UM Super Combo system. The portfolio will be rebalanced every four months. To do that: Click on Screen-> New Stock Screen.

Then click on Main Settings and choose the following: Universe=PRussell3000 (NEW) Benchmark=Russell3000 w/div

Method = Long

Ranking = Ranking System -> Choose the UM Super Combo system from Lecture 4. Max No. Stocks =100

Then click on Backtest and choose: Price=Next Open

Rank Tolerance = 0 Max Pos = 0 Carry Cost=0 Slippage = 0 Long Weight =100

Start Date – End Date= MAX Rebalance Frequency = 3 months

Save this screen as UM Super Combo Top 100, for example.

a) Click on Run Backtest to obtain the results of the backtest. Copy-paste the resulting graphs and answer:

i) What is the annualized return of the Top 100 portfolio and of the Russell 3000?

ii) How many (consecutive, non-overlapping) 3-month periods are there from Jan 1999 to now? What is the 3-month Hit Rate of the Top 100 portfolio? That is, in how many 3-month periods does the Top100 beat the Russell 3000 Index (positive Excess% column)?

Hint: Download to Excel and use the function COUNTIF

iii) What is the average Turnover of the Top 100 portfolio (3-month and annual)?

Note that Portfolio123 only counts stocks entering or exiting the portfolio, and ignores rebalances back to equal weights. Thus, Portfolio123’s turnover calculation underestimates the true turnover. However, the turnover coming from rebalances back to equal weights is of second order compared to the turnover coming from stocks entering or exiting the portfolio, so turnover is not underestimated by too much.

b) The results in a) do not incorporate transaction costs. A quick and dirty way to do so is to fix a Slippage parameter in Portfolio123. This incorporates transaction costs by assuming that stocks purchases and sales are done at worse prices than the historical record: buy at higher price, sell at lower price. Repeat the backtest choosing Slippage=0.45%, which is the average all-in transaction cost per trade for institutional investors. This is a quick and dirty approach because true slippage depends on how much money one is actually trading. Bigger trades move prices against you more. And, and before, Portfolio123’s Slippage only accounts for stocks entering or exiting the portfolio, and ignores rebalances back to equal weights. Run Backtest again and answer:

What is the annualized return of the Top 100 portfolio incorporating transaction costs?

c) The backtest in a) is done using Russell 3000 stocks. Repeat item a (sub-items i, ii, and iii) using large caps only, that is using the Russell 1000 as Universe (and Russell 1000 with dividends as benchmark).

d) The backtest in a) is done using Russell 3000 stocks. Repeat item a (sub-items i, ii, and iii) using small caps only, that is using the Russell 2000 as Universe (and Russell 2000 with dividends as benchmark).

e) Based on your findings above, answer: Do the quantitative signals in UM Super Combo work better for large cap or small cap stocks?

2) The purpose of this exercise is to examine different ways to combine signals.

Consider the Value and Quality Combos in Lecture 4 Slides.

a) Usual Ranking combo seen in class. Create a Value and Quality combo with weights 50% in Value and 50% in Quality. Test the performance of the ranking in the PRussell 3000 (NEW) universe, with 10 buckets, 3-month rebalancing, MAX time period, minimum price=3, All Sectors. Answer: what is the average return (CAGR/geometric average) of the top 10% bucket?

Note: Save the time series of top 10% portfolio returns for use in item e.

b) Separate portfolios combo. Repeat a) for two separate combos, one at a time: Value Combo and Quality Combo. Create a portfolio that is invests 50% in the top 10% bucket of the Value Combo and invests 50% in the top 10% bucket of the Quality Combo. The combined portfolio is rebalanced back to these weights every 91 days. Answer: what is the average return (CAGR/geometric average) of the combined portfolio?

Note: Save the time series of top 10% portfolio returns for use in item e.

c) Sequential Screening I. Now you will first screen for the stocks in the bottom 50% using Quality, and then choose the top 20% of these stocks according to the Value Combo. To do this you must save the Value and Quality combos separately with names you will remember, such as Value Combo and Quality Combo. Now go to Screen->New Screen-> . In Main Settings, choose the PRussell3000 (NEW) as your Universe, Method=Long, and Ranking=No Ranking. Then click on Rules and add the following rules (the order matters!):

i) Rating(“Quality Combo”)>50

ii) Rating(“Value Combo”)>80

Then click on Backtest, and choose Slippage=0 and Carry cost=0, and MAX time period, and 3 month rebalancing. Answer: what is the average return (CAGR/geometric average) of the screened portfolio? Note: Save the time series of top 10% portfolio returns for use in item e.

d) Sequential Screening II: Repeat c) but change the order of the rules:

i) Rating(“Value Combo”)>50

ii) Rating(“Quality Combo”)>80

Note: Save the time series of top 10% portfolio returns for use in item e.

e) What are the correlations between the returns of the 4 Value/Quality portfolios in a), b), c), and d)?

f) Will the 4 Value/Quality portfolios in a), b), c), and d) necessarily have the same (or at least very similar)