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MFIN 7037 2025: HW1
In this course, we work backwards: we start from a known set of working quan8ta8ve trading strategies, we understand how to evaluate them, then how to construct them and intuit them. In the first step, we solidify our understanding of what we mean by a “working” quant trading strategy”. In this assignment, we examine the basics of evalua8ng quan8ta8ve trading strategies. While they might sound in8mida8ng at first, in reality, the tools we have to evaluate investor performance are incredibly powerful rela8ve to have simple they are to use.
Rules:
1. Due Friday Feb 7 6pm HKT
2. Max 4 people (+1 point for groups of 1-2), all groups must submit a peer evalua8on form if you work in groups of 3 or 4. Both submission link/group form link will be submiUed later.
3. Total is out of 100, so extra credit points are meant to provide those with interest or background room to go further but without overburdening those with less background or interest in the material.
4. Please submit a Python notebook with clear comments. Use markdown to point out what ques8on is being answered. Jupyter is the preference of the TA for assignments 1 and 2.
5. The data you need are in our Dropbox folder / FTP, but not in SQL. quant_2025_public/data/bitcoin_historical_data.parquet, as well as hw1_factors.parquet
Crypto
1. Assume that Bitcoin’s return is a price return. Calculate the returns of the cryptocurrency I have provided on a daily basis. What is the average arithme8c return (annualized), average geometric return (annualized), and vola8lity (annualized)? What is the Sharpe ra8o? What is the 10th, 50th and 90th percen8le daily returns?
Report three rows (full sample, 2017 onward, pre-2017). Do the same for the US market using the Fama French factors file. Make sure when comparing, you are comparing excess returns to excess returns and non-excess returns to non-excess returns. (jargon: an excess return is in excess of risk-free rate). In total, the table should be six rows.
Which asset carries higher risk, US equi8es or Bitcoin? In terms of Sharpe, and then in terms of drawdown.
2. Extra credit (1 point): Explain, with no more than 3 sentences, why price-based returns in crypto are incomplete? (e.g: any other way to make money?) Give me a rough es8mate of the incremental return to these sources.
3. What is the market beta of bitcoin? If you ran this regression pre-2017 and post-2016, how would this differ? How 8ghtly does bitcoin track the stock market in the data? What reasons do you have for why this beta is different between the two periods? My friend who is a macro strategist called bitcoin a “levered bet on the equity market”, do the post 2016 numbers support my friends’ asser8on?
4. Since 2017, if you were a BTC investor, would a BTC alloca8on be addi8ve to an investor who otherwise is inves8ng in Fama-French factors? How does this result compare from the Risk and Returns of Cryptocurrency, published in the RFS?(note, for ques8ons #2 and #4, to be nice to the TA, please report the three required regressions in a single regression table)
5. A bet on the SP500 is essen8ally a bet on discounted future dividends of the firm, the risks associated with that growth, and the risks of holding those cashflows when discount rate are high and thus prices are low. Explain the ra8onale for long-term inves8ng in cryptocurrency. Is there a reason why you should expect high returns? Do you believe there are mispricing-related or non-fundamental reasons that best explain cryptocurrency’s returns? There’s no right answer, and you certainly do not have to be pro-crypto, but form an opinion for yourself.
- Here’s a paper I reviewed at an academic journal
- https://academic.oup.com/rfs/ar8cle-abstract/32/5/1798/5427781?redirectedFrom=fulltext
- You can also look at rosier views from outspoken pundits like Arthur Hayes
For BTC to hit $1,000,000, what would be true under your view?
6. How would you place the monthly bet that bitcoin outperforms the SP500? What instruments would you trade and how? What adjustments do you have to make every month? What are the profits of this strategy?
7. Take the beta from the single factor model. How would you place the market-neutral bet on bitcoin? Using the post-2016 numbers, roughly much BTC would you have to buy/sell and how much SPY would you have to buy/sell?
• Extra credit (1 point): What could go wrong with using these numbers? describe an approach to fix it. There’s no right answer. Just think out loud here. One hint is consider if the 2016-2025 beta is knowable in 2018? But there are other issues.
8. Extra credit (2 points): The above strategies are basically long-term buy and hold strategies.
Backtest some sort of strategy. Here are some ideas. I have not tried this myself actually.
- What about a strategy that buys the dip, selling the next day? Assume you cannot short before 2017 anyway. Does this strategy outperform bitcoin itself?
- You need to define a no8on of a “dip” that is knowable up un8l 8me t-1, then decide what to do.
- What is the win-loss ra8o?
- What are the sta8s8cal proper8es (sharpe, drawdown, annualized return) of the trading strategy? Plot a profit and loss curve.
- Would this survive transac8on costs?
- What would its factor loadings to FF5+momentum be?
- A convergence trade between MSTR and BTC? ETH and BTC? You probably need to pull the ETH data yourself. MSTR/BTC can be pulled from CRSP although we don’t have updated recent data this past year.
9. Extra credit (2 points): what is the op8mal asset alloca8on of cryptocurrency, bonds (TLT as an ETF proxy), stocks (SPY as an ETF proxy) with a target of 15% vola8lity? You may compute expected returns and covariances in any reasonable way you like but explain your assump8ons. You may use historical assump8ons, but of course looking forward may be beUer. If you want the data, please extract them from crsp.dsenames and crsp.dsf