FINM7403 Semester 1 2020
Assignment 2: Predictive Models, Term Structure of Interest
Rates, and Performance Evaluation
UQ Business School, University of Queensland
May 7, 2020
Assignment Overview
• Overview: This is an individual assignment total of 100 marks counting towards 25% of your final
grade.
• Assignment due: 2pm 4th June 2020. Submit electronically on Blackboard.
1 Task 1: Building Predictive Models
1.1 Overview
In this task, you are required to build time-series predictive models (full-sample and real-time) to predict
future equity premium i.e. equity return in excess of the risk-free rate. You will use term structure of
interest rates and default yield spreads as your predictors.
1.2 Data
1. Download Predictor2018.csv from Blackboard.
2. The file contains various aggregate economic variables from Jan 1871 to Dec 2018. More details
about the variable definition can be found in Welch and Goyal (2008).
3. You want to build predictive models on monthly frequency data. Your sample period is from Jan
1926 to Dec 2018.
4. You are interested in the following variables:
• Rfree: Risk-free rate,
• tbl: Treasury-bill rate,
• lty: Long-term government bond yield,
• AAA: AAA-rate coporate bond yield,
• BAA: BAA-rated corporate bond yield,
• CRSP_SPvw: S/P 500 stock market returns including dividends.
1.3 The Variables
| A. Construct the term structure of interest rates (tms) and default yield spreads (dfy) variables. marks) |
(5 |
1
1.4 Model
• You attempt to build a linear regression model as below:
| Yt+1 = α + β × Xt + ϵt where Y is one-month ahead stock market excess returns, X is a predictor observed at time t. • Your forecast for T + 1 is formed at time T as: ^YT +1 = ^ α + β^ × XT |
(1) |
| (2) |
where Y^T +1 is the predicted stock excess return at time T+1, α^ is the estimated intercept, and β^ is
the estimated coefficient from model (1).
• You decide to build your model in two ways:
1. Full-sample: For each predictor (tms or dfy), run model (1) using the entire sample from Jan
1926 to Dec 2018.
A. Report α^, β^, and R2. (5 marks)
B. Explain and discuss the regression results. (5 marks)
2. Real-time: You also want to build the predictive models using 5-year rolling windows.1
A. Report the forecasts for each model. (5 marks)
B. You also calculate naive forecasts as the simple averages of historical excess returns using
5-year rolling windows. Report the naive forecasts. (5 marks)
C. Calculate the out-of-sample R2. (5 marks)
D. Explain and discuss the forecast results. (5 marks)
2 Task 2: Bond Yields
2.1 Overview
Let’s suppose today is 1/4/2020 and you observe the information from various coupon bonds issued by
the Australian Government. The information can be downloaded from bond_data_raw.csv, available on
Blackboard site. Using the bond information, please complete the following tasks:
2.2 Yield Curve
A. Construct the on-the-run-yield curve. (5 marks)
B. Construct the pure yield curve.2 (10 marks)
C. Suppose that there is a risk-free investment which pays $100,000, $200,000, $300,000, $400,000,
and $500,000 at the beginning of April each year for the next 5 years. How much will you pay for
the investment? Your answer should rely on the above constructed yield curves. (5 marks)
2.3 Duration and Convexity
A. Calculate Macaulay Duration, Modified Duration, and Convexity for each bond. (10 marks)
B. Approximate the change in price for each bond using duration-convexity rule if there is 1% increase
in yield to maturity. (5 marks)
1 For example, to form a forecast for Jan 2016 in Dec 2015, you run model (1) using data from Jan 2011 to Nov 2015 to estimate
α^ and β^. You then form the forecast for Jan 2016 based on variable X in December 2015 and α^ and β^ as in (2). Forecast for Feb
2016 is formed by in Jan 2016 and α^ and β^ estimated by running model (1) from Feb 2011 to Dec 2015.
2You need to use Excel Solver for this task.
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3 Task 3: Performance Evaluation
3.1 Overview
In this task, you are asked to evaluate Fidelity Magellan Fund (FMAGX) performance for the period from
Jan 1964 to Dec 2019.
3.2 Data
To analyse the fund, you need to download the following datasets from Blackboard:
• fmagx.csv: The dataset contains FMAGX monthly prices from Dec 1963 to Dec 2019.
• factorret.csv: The dataset contains monthly returns (in %) for Fama-French-Cahart four factors i.e.
MktRf, SMB, HML, MOM, along with the risk-free rate (RF).
• qmj.csv: The dataset contains Quality factor returns (for factor construction detail, see Asness et al.
(2018)) .
• bab.csv: The dataset contains Low Beta Bias factor returns (for factor construction detail„ see Frazzini and Pedersen (2014)).
3.3 Performance Metrics
Please complete the following task using the data from Jan 1964 to Dec 2019:
A. Calculate the fund’s cumulative return. (2 marks)
B. Calculate the fund’s Sharpe Ratio and M2. (5 marks)
C. Calculate the fund’s Treynor Ratio and T2. (5 marks)
D. Calculate the fund’s Jensen α using the CAPM as the benchmark. (5 marks)
E. Calculate the fund’s Information Ratio using regression analysis and the CAPM as the benchmark.
(5 marks)
F. Using style analysis to evaluate the fund’s investment characteristics e.g. Do they invest in small-
/large, value/growth, quality/junk etc.? Discuss the regression results. Hint: You should use all of
the provided factor returns. (5 marks)
G. Which factors can/can not explain the fund’s Jensen α in Section 3.3.D? Hint: Identify the set of
factors that can/cannot drive away the Jensen’s alpha? (8 marks)
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Info:
Notes:
• Excel: Your Excel files should include all workings and calculations. Formulas for the calculations should have cell references wherever possible. If you have computed a number incorrectly
and just typed that number into the spreadsheet (or typed a formula using numbers when cell
references could have been used), you will not receive partial credit for any portion of your
computation that is correct.
• All of your answers should be contained in the Excel files. There is no word limits.
Submission:
• Students should submit the entire assignment by uploading THREE Excel files on Blackboard.
– Task 1 Excel: Please name the file Task 1_Lastname_StudentNumber.xlsx.
– Task 2 Excel: Please name the file Task 2_Lastname_StudentNumber.xlsx.
– Task 3 Excel on BLACKBOARD TEAM ASSIGNMENT: Please name the file
Task 3_Lastname_StudentNumber.xlsx.
• You may re-submit as many as you like, but only your last submission will be graded.
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References
Asness, C. S., Frazzini, A., and Pedersen, L. H. (2018). Quality minus junk. Review of Accounting Studies.
Frazzini, A. and Pedersen, L. H. (2014). Betting against beta. Journal of Financial Economics, 111(1):1–25.
Welch, I. and Goyal, A. (2008). A comprehensive look at the empirical performance of equity premium
prediction. Review of Financial Studies, 21(4):1455–1508.
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