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# ECO1500H1F Financial Economics I - Empirical Projects: Equity Premium Predictability

ECO1500H1F Financial Economics I

Description of Empirical Projects

Estimate predictive regressions for forecasting the equity premium by taking the following steps:

1. Collect monthly data for the US equity premium, defined as the S&P 500 return that includes dividends net of the treasury bill rate. Also collect monthly data on 14 monthly economic fundamentals used as predictors in the literature. The data are available on Amit Goyal’s website, a Professor at the University of Lausanne. The predictors include:

1. dividend yield

2. dividend-price ratio

3. earnings-price ratio

4. payout ratio

5. book-to-market ratio

6. net equity expansion

7. stock variance

8. treasury bill rate

9. long-term yield

11. long-term rate of return

14. inflation

2. Report summary statistics on the data: the equity premium and the 14 predictors. For the equity premium only, also present annualized summary statistics.

3. Estimate 14 predictive regressions for the one-month ahead equity premium, each conditioning on one of the predictors for the full sample. Also estimate a kitchen-sink regression that conditions on all of the predictors in a single regression. All regressions will be estimated with OLS. See Welch and Goyal (2008) for more details.

1

1. Report the betas, t-statistics and R2 of each in-sample regression. Compute the in-sample forecasts of the equity premium and report the mean squared error (MSE) of each regression.

2. Compute the in-sample forecasts of the equity premium and report the MSE for a simple forecast combination: the mean forecast across the 14 models. See Rapach, Strauss and Zhou (2010) for more details.

3. Repeat the analysis imposing the positive forecast constraint of Campbell and Thompson (2008), which truncates forecasts at zero: if a predictive regression provides a negative equity premium forecast at time t, replace the forecast with zero.

4. Repeat the analysis using out-of-sample estimates for a 20-year rolling window. Note that this is computationally intensive. Report the out-of-sample R2 for each of the models you estimate.

5. In your out-of-sample analysis, report results for the full sample, expansions and recessions. Expansions and recessions are determined by the NBER. See their website for these dates.

Project 2: Asset Allocation

Design an asset allocation investment strategy across a large set of assets by taking the following steps:

1. Collect monthly data for at least 12 assets (e.g., stocks, bonds, currencies or commodities) for a sample period that begins the month and year that the eldest member of your group was born and ends as recently as possible. If you hold foreign assets, your perspective must be that of a Canadian investor and hence you must account for exchange rate fluctuations.

2. Report summary statistics on the data.

3. Design three mean-variance strategies for allocating wealth across these assets: maximum return, minimum variance and maximum utility strategies. In doing so, choose a reasonable degree of risk aversion, target portfolio volatility and target portfolio expected return.

4. Report the weights and performance of the strategies: mean, standard deviation and Sharpe ratio for the portfolio returns. Performance must be reported in monthly and annualized terms.

2

1. Discuss the role of transaction costs. Try to find a way to explicitly account for transaction costs (even a simple way is fine).

2. Compare the results to a simple 1/N strategy.

3. All strategies require estimates of means, variances and covariances. You must estimate these both in sample and out of sample, where in the latter case you can use a 10-year rolling window. Out-of-sample estimation must be realistic and avoid the forward looking bias, i.e., in forming the weights at time t, you can only use information available at time t.

Instructions

The main text of the empirical project must be about 10 pages long, excluding tables, figures and references. Please ensure that the main text is no longer than 12 pages long. The main text should include the following sections:

• A title page, which will include an abstract of no more than 150 words (1 page).

• An introduction that summarizes the main ideas, objectives and contribution of the

project (2-3 pages).

• Description of the data (1-2 pages).

• Discussion of the results (2-3 pages).

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