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# Page 1 of 2 Principal of Investments FIN-315 Professor Saeid Hoseinzade Extra-credit mini-case For this exercise you would need to use the...

Page 1 of 2

Principal of Investments

FIN-315

Extra-credit mini-case

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

σp. Specifically, after considering transactions costs the expected net return of each portfolio can be

calculated as:

E [Rp]Net = E [Rp]Raw - φwpσp

where E[Rp]Raw is the average monthly returns of a portfolio (provided by the data) and φ is the priceimpact

coefficient. In the Excel file, cell K378 contains the value of φ 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 φ: 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 φ.

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 φ equals 0.8.)

Instruction:

 This mini-case is optional and is worth 10 extra points toward your second mid-term.

 The mini-case is due 04/26/2018.

 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.)

 Work on this mini-case individually.