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Homework 1: MFIN 7037

In this assignment, we’ll learn the basics of portfolio management, performance measurement, and performance attribution.

What to submit

1. You may work in groups of 3 (no working in groups of 4, sorry). Keep in mind slight benefit of working in team sizes of 1 or 2.

2. Due date: February 21, 2024 morning (e.g. Yuxiao will start grading on Feb 21)

3. What to submit: A writeup and code. The writeup may be an .ipynb file with embedded output + writeup.

4. You must use code. Python, R, Julia are acceptable. NO VBA, Excel etc.

5. How to submit: Moodle

6. At the top, please write

· Each group member’s name

· Each group member’s HKU email

· Each group member’s HKU Student ID

· What percentage each group member did

7. The assignment is out of 100. There are a few conceptually difficult questions that you get 1 point for, for a total of about 105 points possible. The point of making the reward so small is that nobody feels pressure to do all of them – from a grade perspective they’re only really worth it if the material is already easy for you or if you find it fun.

Questions

1. Based on US data (from Aswath Damodaran), what have equity returns been the last 100 years? How does that compare to (1) the risk free rate, (2) government bonds, (3) corporate bonds, (4) housing?

File: hw1_histretSP.xls

· Assuming full and costless reinvestment, show a table where the each row is one of the following (in this order): annualized compound return, annualized volatility (arithmetic), Sharpe ratio, skewness, total cumulative nominal return, total real (i.e. inflation adjusted) return.

· Plot a cumulative wealth curve over time of those 5 (Equity, risk free rate, govt bonds, corporate bonds, housing) asset classes on one plot.

· What is the most performant asset class? According to the efficient market hypothesis, why would this asset class perform the best? Does this asset class have the highest risk?

· Should I pick the asset class with the highest Sharpe ratio and only invest in that? Give me an example of a portfolio with a superior risk to reward ratio, and show me that the risk-to-reward is higher. Is the outperformance of your portfolio relative to the highest Sharpe ratio asset statistically significant? Note: you don’t need the optimal portfolio. Any reasonable portfolio will do. Regarding outperformance, to clarify, all I was hoping for here is that you either show that the t-test of the simple difference in returns is statistically positive and significant or that the regression of the new portfolio on the old portfolio is significant. If you wanted to test for differences, you’d have to do something like the Gibbons Shaken and Ross test but that’s too esoteric.

· On a Sharpe ratio basis, is housing better than stocks? Is the last 30 years different than the overall 100? There is no right answer, but what do you think happened? Do you think this will last forever or that this period was special? (Just say something reasonable)

2. I have a strategy named the monthly dice roll which randomly selects a stock from the S&P 500 and holds for one month.

This is a conceptual question, there is no coding.

· Relative to a passive equal-weighted selection from the S&P 500 (where I re-balance monthly), what is the expected return of this strategy? Is the Sharpe ratio of this strategy higher or lower than simply holding that index? Assume no transaction costs or taxes.

· Relax the assumptions about transaction costs and taxes, and assume I care nothing about volatility but just about total return, why is this trading strategy a terrible idea?

3. Let’s understand factor regressions and products in the real world.

data: mfin7037_2024_hw1_data.parquet

I have provided returns to various ETFs. ETFs are advertised as low-cost products one can buy on an exchange as opposed to a mutual fund. Generally ETFs are advertised as lower-cost and you get a real-time market price, whereas mutual funds pool trades at EOD typically.

Most of you who asked this question clearly understood, but I may have made a slight mistake in the answer key last year – oops – but generally please try to subtract rf for an ETF. No need to do that for QMJ, MKT_RF,MOM, etc since its already long/short. Makes nearly no difference in the low interest rate era of the last thirty years but.

· SPY is the most popular ETF in the world, just tracks the S&P 500.

· Mystery ETF #1 you don’t have to guess the specific ticker (you can) but I just want to know what type of product it is

· MTUM, per its product description, is a momentum product based on Jegadeesh an Titman (1993). QMOM / JMOM are tickers of ETFs from other famous asset managers.

Tasks:

OP

· For the mystery ETF, tell me the Sharpe ratio annualized, annualized return, and plot the cumulative return graph.

o If you started off with 1 million dollars at the same time as ret_mystery, how much would it be by the end of the sample period? What about, over the same sample period, SPY?

o Using a factor regression, can you tell me what the mystery product is? What is the annualized alpha and beta with respect to SPY?

o According to the regression, what would be more profitable, βSPY x (SPY - rf) or the mystery ETF? Assume borrowing is free and easy like in textbooks.

o The alpha as you discovered is not positive. In practice, is levering up SPY free?

· Extra credit: Answer the following questions. (1 point each out of 100)

o What are some other ways I can implement a similar trade as the mystery ETF? Are those methods cheaper? You’ll have to search online and read. There is no real right answer, but it would be great if you cited sources to justify your assumptions.

o Why does the ETF exist? What are some advantages of trading this way over those other methods (which involve margin)?

o Do you think it’s a good investment? What types of investors with what types of trading horizon and preferences might think it’s a good idea? Or is there an implementation that is strictly better?

· Run the following regressions: (1) MTUM, JMOM, QMOM against just the Fama-French MOM factor, (2) MKT_MINUS_RF, (3) MOM + MKT_MINUS_RF. Display them in a single regression table, 9 regressions in total.

- What is the covariance between these supposed momentum ETFs and the MOM factor?

- By itself, why are MTUM/JMOM/QMOM so bad at providing momentum exposure? What are the differences between how they’re constructed and the long-short implementation of the MOM factor by Fama-French (hint, look at regression set (2) ), and why does this result in the covariance between MTUM/JMOM/QMOM not being close to 1?

- Extra credit (1 point): Take one of the ETFs. What are some other implementation differences, how might this change the overall momentum exposure? What are likely the reasons that the ETF creators designed the ETF this way?

- Extra credit (1 point): Can you find me a financial product that more closely approximates the FF implementation of a market neutral momentum product?

- If it were free to short, borrow, etc. what trades would I make using MTUM and MKT_MINUS_RF (assuming it was a hypothetical security, it’s actually an index) and construct a market-neutral portfolio with a MOM exposure of 1?