Discipline of Finance FINC3017 Investments and Portfolio Management S1-2025 Assignment 2 Assignment Overview This assignment guides you through the key procedures of portfolio management, including choos- ing an investment style, implementing smart beta strategies, timing the market, and portfolio hedging. This is a group assignment and you must work in teams of four to five students. What to Submit (on the due date to be announced): • A report that includes all results, tables, figures, and detailed interpretations; • List each member’s name and student ID; • An Excel file containing raw data, calculations, regressions, and all other relevant work; • You will be provided with a report template to help structure your responses and ensure clarity and consistency. However, you are welcome to deviate from the template if needed to include additional information that supports your conclusions. Part 1: Testing Factors with Fama-MacBeth Regression In this section, you will perform Fama-MacBeth regressions to identify priced factors. A rational investor seeks to build a portfolio with exposure to the factor offering the highest price of risk. 1. Download the following datasets (monthly frequency) from the Ken French Data Library: • 48 Industry Portfolios. Replace missing values with 0 Note: Missing data are indicated by -99.99. Use the Excel formula =IF(input=-99.99, 0, input) to replace missing values with zero. • 100 Portfolios Formed on Size and Book-to-Market (10 x 10). • Fama-French three factors (Market, Size, Value), the Momentum factor, and the risk- free rate. • Sample period: July 1963 to December 2024. 2. Run a Fama-MacBeth regression using the 48 Industry Portfolios: 1 • Use the four factors as independent variables. • Estimate the mean of risk prices (λ) and their t-statistics. • Evaluate statistical significance using a threshold of |t| > 2. 3. Repeat the same regression using the 100 Size-B/M portfolios instead of the industry portfolios. • Report the estimated risk prices and their t-statistics. • Discuss whether the same factors are statistically significant or not. 4. Compare the results of the two regressions. Explain why there may be differences. Reference Fama and MacBeth (1973) for insights into factor testing and asset pricing models. Part 2: Smart Beta Strategy Based on the results of question 3, you have identified the factor with the highest price of risk (note that we need to pay attention to the magnitude of the coefficient, instead of the t-stat). Based on the selected factor, construct a smart beta portfolio that deviates from the S&P 500 index and outperforms the S&P 500 index. In this question, you are given daily returns of top 163 largest stocks included in S&P 500 index and daily returns of S&P 500 index. 5. Factor selection: Identify the factor with the highest price of risk from question 3. Explain the implication of a high price of risk for expected returns. 6. Beta estimation: With the daily stock returns for the in-sample period: Jan 4, 2021 – Dec 29, 2023, run a time-series regression for each stock (download daily factor returns from Ken French Data Library): Rit −Rft = αi + βi,MKTMKTt + βi,SMBSMBt + βi,HMLHMLt + βi,MOMMOMt + ϵit 7. Define investment universe: Sort stocks based on their beta with respect to the factor identified in Question 5 (e.g., if the MOM factor has the highest price of risk, use βMOM). Report mean, standard deviation, median, minimum value, and maximum value of the selected factor beta. Select the 40 stocks with the highest betas to define your investment universe. 8. Calculate factor-based weights: The weight for stock i is: wi = βselected factori∑40 j=1 β selected factor j 9. Equal-weighted portfolio: Construct an equally weighted portfolio using the same 40 stocks (each stock weight = 2.5%). Many practitioners support equal-weighted smart beta portfolios because they often generate positive alpha and reduce concentration risk compared to value-weighted or factor-weighted portfolios. 10. In-sample performance: Compute daily returns of both portfolios (factor-weighted and equal-weighted) for Jan 4, 2021 – Dec 29, 2023. Report the following (all annualized): 2 • Mean return, standard deviation, and Sharpe ratio. Compare them with those of S&P 500 index. (Note: Use the risk-free on Dec 29 2023 from Ken French Data Library, translate daily risk-free into annual one by multiplying 252). • Alpha and Beta relative to S&P 500 index: Rp,t −Rf,t = α + β(S&P500t −Rf,t) + ϵt • Tracking error (standard deviation of ϵt from the above regerssion) • Information ratio 11. Out-of-sample performance: Use 2024 as the out-of-sample period. Keep the stock selection and weights fixed, and calculate the same performance metrics as question 10. (Use the risk-free rate on Dec 31 2024 for shape ratio calculation) Part 3: Betting Against Beta (BAB) Strategy If you wish to avoid exposure to systematic risk, constructing a beta-neutral portfolio is a viable option—especially if it can deliver a positive alpha. In this section, you will build a market-neutral portfolio that exploits the low-beta anomaly. Use the same stock return data and estimation period as in Part 2. 12. Market beta estimation: Estimate market beta for all stocks using daily returns (Jan 4, 2021 – Dec 29, 2023) and S&P 500 index returns by running the following time series regression: Ri,t −Rf,t = αi + βi(S&P500t −Rf,t) + ϵi,t Report mean, standard deviation, median, minimum value, and maximum value of the betas. 13. Define investment universe: Select 30 stocks with the highest beta (short leg) and 30 stocks with the lowest beta (long leg). 14. Weight allocation: Compute average beta for each leg: β¯high = ∑ βhighi 30 , β¯low = ∑ βlowi 30 Set: wlong = 1 β¯low , wshort = − 1 β¯high Allocate weight of wlong/30 and wshort/30 to each stock in long and short positions. Assign the remaining capital 1− (wlong + wshort) to the risk-free asset to ensure the total weight is 1. 15. In-sample performance: Using in-sample data, calculate portfolio return. Report: • Mean return, standard deviation, and Sharpe ratio (using the risk-free rate from the last trading day of 2023 for the Sharpe ratio calculation) 3 • Alpha and Beta relative to S&P 500 index: Rp,t −Rf,t = α + β(S&P500t −Rf,t) + ϵt • Tracking error (standard deviation of ϵt from the above regerssion) • Information ratio • Treynor ratio 16. Out-of-sample performance: Repeat the analysis using 2024 out-of-sample data. (Use the risk-free rate from the last trading day of 2024 when calculating the Sharpe ratio.) Part 4: Volatility-Managed Portfolios (ETF-based) If you are not confident with your stock picking skills, as an alternative, you may consider using ETFs that track your selected factor and implement a market timing strategy. 17. Correlation check: Assume momentum is the factor with the highest price of risk. Use the following ETFs as proxies (daily return data is provided): • iShares MSCI USA Momentum Factor ETF (Ticker: MTUM) • Invesco DWA Momentum ETF (Ticker: PDP) • Alpha Architect U.S. Quantitative Momentum ETF (Ticker: QMOM) Construct a correlation matrix between each ETF and SPY (where SPY return is provided). 18. Build volatility-managed portfolios: For each ETF: (a) Compute the monthly return and monthly volatility of the ETF using daily returns within each month. (b) Set the scaling constant c = 1. For each month t: • Calculate the portfolio position: positiont = c σt−1 , where σt−1 is the volatility estimated from the previous month. • Calculate the volatility-managed return: returnt = positiont × rt, where rt is the raw return of the ETF in month t. (c) Compute the volatility (standard deviation of monthly returns) of: • The original momentum portfolio: σ • The volatility-managed portfolio: σvm (d) Use Excel’s Solver to find the value of c such that σ = σvm. (e) For each ETF volatility managed portfolio, summarize performance (annualized): 4 • Constant c • Largest position (take the maximum value of positiont) • Mean and standard deviation • Sharpe ratio • Sortino ratio • Alpha and tracking error • Information ratio • Use the original, unmanaged momentum ETF as the benchmark (e.g., use MTUM as the benchmark for the volatility-managed MTUM). Download the monthly risk- free rate from the Ken French Data Library to compute the excess returns of both the ETFs and the volatility-managed ETFs for your regressions. For the Sharpe ratio calculation, use the last available monthly risk-free rate in 2024 and convert it into an annualized risk-free rate. Part 5: Portfolio Hedging with Volatility Assets A more common approach to portfolio hedging is to allocate a small portion to volatility assets. In this section, you will explore the effectiveness of adding VIX exposure as a means of protecting against downside risk. 19. Correlation check: Using the provided data for VXX (iPath Series B S&P 500 VIX Short- Term Futures ETN), calculate its daily return, and construct a correlation matrix with the three momentum ETFs: MTUM, PDP, and QMOM. 20. Hedging portfolio: For each ETF, build a hedged portfolio by investing w (where w = 0%, 5%, 10%, 15%) in VXX, and the remaining 1− w in the ETF. 21. Performance analysis: For each hedged portfolio, compute and report (annulized): • Mean and standard deviation • Sharpe ratio and Sortino ratio (use the risk-free rate from the last trading day of 2024 when calculating the Sharpe ratio). • Comment on whether adding VXX improves the Sharpe ratio, and how it varies with w allocated to VXX. Part 6: Summary You have explored various trading and hedging strategies. Summarize and compare their perfor- mance (in 500 words or less, organize your answers in bullet points): • Figures: Calculate cumulative returns of each trading strategy and their comparison with benchmarks. Benchmark for different strategies: – S&P 500 index is the benchmark for smart beta, betting against beta 5 – Corresponding MOM ETFs are benchmarks for volatility-managed portfolios and hedg- ing portfolios. For example, MTUM is the benchmark for the volatility-managed version of MTUM • Evaluation of strategies: Discuss the pros and cons of each strategy • Portfolio strategy selection and justification: Choose your preferred strategy (or a combo of two, e.g., long position plus hedging position) as a portfolio manager and justify your choice based on your results 6 References Fama, E. F. and MacBeth, J. D. (1973)
