For this exercise you would need to use the spreadsheet mini-case.xls posted on Blackboard The file contains information about monthly returns of ten momentum portfolios.

The portfolios are formed as follows. Each month all NYSE-listed stocks are ranked according to their past 12-month cumulative returns. Then, ten groups of equal number of stocks are formed. Each group of stocks is combined into an equal-weighted portfolio, which is held for one month. The file also contains the Fama- French three factors as well as the risk-free rate. The sample period begins January 1983 and ends June 2013.

NOTE: Each time before using Solver to calculate portfolio weights, please assign a weight of 1 in cell B373 and zero weight in cells C373 through K373.

1. Calculate the Fama-French risk-adjusted return of each momentum portfolio by running a regression of the monthly returns of the portfolio (excess of the risk-free rate) on the monthly returns of the three factors MKT-RF, SMB, and HML. The risk-adjusted return is the intercept of this regression. You can choose different portfolios by changing the values in cells B373 through K373. For example, to choose Portfolio 1 just plug 1 into cell B373 and zero into cells C373 through K373. This would immediately provide you with the excess returns of this portfolio in Column P, which you can then use for the regression. Graph the average returns (excess of risk-free rate) and risk-adjusted returns for each portfolio (on the same graph).

2. Looking at the graph in (1) you decide to consider an investment strategy using these ten portfolios. You therefore decide to find the tangency portfolio using the ten portfolios as basis assets. Find the portfolio weights and the maximum attainable Sharpe ratio. You can use the Solver to maximize cell P372 while holding cell P373 at a value of 1. Compare the Sharpe ratio of the tangency portfolio to that of the market portfolio (Cell L372).

3. Since the portfolios are rebalanced each month, you are worried that short sales would involve high transaction costs. You therefore decide to prohibit short sales. Calculate the portfolio weights and the maximum attainable Sharpe ratio without allowing for short sales. This could be achieved by using Solver as in (2) with the addition of holding cell P374 at 10. (Cells B374 through K374 indicate whether each momentum portfolio is held with a non-negative weight in the tangency portfolio.)

4. Suppose you further worry about transactions costs, and you estimate that the cost of trading a portfolio is proportionate to its weight wp in the tangency portfolio multiplied by the standard deviation of its returns p. Specifically, after considering transactions costs the expected net return of each portfolio can be calculated as:

E [Rp]Net = E [Rp]Raw - wpp

where E[Rp]Raw is the average monthly returns of a portfolio (provided by the data) and is the price- impact coefficient. In the Excel file, cell K378 contains the value of and cells B376 through K376 contain the expected net returns of the momentum portfolios. The goal now is to study how the tangency portfolio weights and Sharpe ratio change with the magnitude of transactions costs. Re-calculate portfolio weights

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and Sharpe ratio of the tangency portfolio for the following values of : 0.2, 0.8, and 1.0. This could be easily achieved by changing the value in cell K378 and using Solver to maximize cell P378 while holding cell P373 at 1 and cell P374 at 10. Graph the weights of the ten momentum portfolios as a function of transactions costs: one line for the case of no short sales calculated in part (3); and three more lines corresponding to the different values of .

5. a) What can you conclude about the impact of transactions costs on the weights of the momentum portfolios in the tangency portfolio?

b) What implications do transactions costs have with respect to market efficiency? Is the market portfolio efficient in the presence of transactions costs? (Notice the Sharpe ratio of the tangency portfolio relative to that of the market portfolio when equals 0.8.)

Instruction:

• This mini-case is optional and is worth 10 extra points toward the exams (mid-terms and final), wherever you need it.
• The mini-case is due 12/20/2017. I wish I could give you more time but the grades are due on 12/22 and I need some time to look at your work.
• I prefer to collect them on the exam day. If not, you can always slide it under my office door. My office is Sargent Hall 5629.
• Hand in a hard copy, document format. No electronic version, no direct print outs from Excel. Copy and paste the required tables/graphs from your Excel worksheets to your report.
• The main outputs of your work are two graphs, bunch of Sharp rations (along with portfolio weights), and some analysis of what happened. Try to be brief and right to the point in your analysis. Your report should not be longer than 3 pages. (You don't have to include all regression outputs.)