The spreadsheet entitled performance modeling homework assignment.xlsx contains monthly return data for the period 1995-2013 one hedge fund, Fund #61, called SC Fundamental Value LP. It is a long-short equity fund.

The spreadsheet also contains monthly return data for the risk free rate and the stock market (which is a value-weighted index of all NYSE, NASDAQ, and AMEX stocks and is called mkt), as well as a number of other index returns. The descriptions of the index returns are in the tab called Descriptions.

Univariate measures

The tab entitled performance measures has a space for you to calculate all the performance measures we have covered. Please calculate these measures as follows for the fund. See spreadsheet

1. Average return in excess of risk free rate.
2. Standard deviation (function in Excel: stdev.s)
3. Semi-Variance (function in excel for variance is VAR. Note that semi-variance is the variance of all negative returns in the year)
4. Semi-standard deviation (standard deviation of semi-variance)
5. Tracking error (Figure this out using the formulas in the slides and the Excel functions)
6. Sharpe ratio
7. Beta (using formula)
8. Treynor
9. Sortino
10. Information ratio

For the entire period:

11. Maximum monthly drawdown for the entire period
12. Standard deviation, whole period (function in Excel: stdev.s)

Multivariate measures

1. Regressions to complete for the fund.

The first regression is a single-factor model, where the factor is the market risk free rate (mktrf).

The second regression is the Fama-French three factor model, where the factors are mktrf, smb, and hml.

The third regression is the Carhart four factor model, where the factors are the three factors from Fama-French plus momentum: umd.

2. Write out the regression equations for all four regressions.

Single factor:

3 factor:

4 factor

3a. What is the R-squared for each equation?

3b.How do you interpret the R-squared? Be specific to your R-squared in interpreting its value.

3c. Also, refer to the individual factors that appear to be contributing to the level of the R-squared, whether these factors are individually statistically significant, and what the coefficients on these factors indicate in terms of the managers style.

Single factor:

3 factor:

4 factor:

4. What is the alpha for each equation? Do these alphas indicate that the manager has skill? *use a p-value of 0.10 for this determination. Also be sure to consider the R-squared value when making this assessment.

Single factor:

3 factor:

4 factor:

5. The fund is a long-short equity fund. Is the coefficient on the market factor consistent with this fund calling itself a long-short equity fund?

Single factor:

3 factor:

4 factor:

\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|} \hline A & B & C & D & E & F & G & H & 1 & J & K \\ \hline 1 Date & 61_SC Fundan & & smb & hml & umd & if & mkt & 61_excess & 61 less S\&P & market less risk fr \\ \hline 12/31/11 & 0.3% & 0.7% & 0.6% & 1.6% & 1.9% & 0.0% & 0.7% & 0.3% & 1.0% & 0.7% \\ \hline 1/31/12 & 2.7% & 5.1% & 2.5% & 2.1% & 8.0% & 0.0% & 5.1% & 2.7% & 2.4% & 5.1% \\ \hline 2/29/12 & 1.2% & 4.4% & 1.7% & 0.0% & 0.3% & 0.0% & 4.4% & 1.2% & 3.2% & 4.4% \\ \hline 3/31/12 & 2.8% & 3.1% & 0.3% & 0.1% & 1.5% & 0.0% & 3.1% & 2.8% & 0.3% & 3.1% \\ \hline 4/30/12 & 1.3% & 0.9% & 0.6% & 0.2% & 3.8% & 0.0% & 0.9% & 1.3% & 0.5% & 0.9% \\ \hline 5/31/12 & 3.1% & 6.2% & 0.1% & 0.1% & 6.6% & 0.0% & 6.2% & 3.1% & 3.1% & 6.2% \\ \hline 6/30/12 & 1.1% & 3.9% & 0.8% & 0.5% & 1.1% & 0.0% & 3.9% & 1.1% & 2.8% & 3.9% \\ \hline 7/31/12 & 3.4% & 0.8% & 2.6% & 0.0% & 3.1% & 0.0% & 0.8% & 3.4% & 2.6% & 0.8% \\ \hline 8/31/12 & 1.2% & 2.6% & 0.7% & 0.6% & 2.4% & 0.0% & 2.6% & 1.2% & 3.8% & 2.6% \\ \hline 9/30/12 & 1.7% & 2.7% & 0.5% & 1.6% & 1.0% & 0.0% & 2.7% & 1.7% & 1.0% & 2.7% \\ \hline 10/31/12 & 2.6% & 1.8% & 1.1% & 4.2% & 0.1% & 0.0% & 1.8% & 2.6% & 4.4% & 1.8% \\ \hline 11/30/12 & 1.7% & 0.8% & 0.7% & 1.1% & 0.4% & 0.0% & 0.8% & 1.7% & 0.9% & 0.8% \\ \hline 12/31/12 & 0.5% & 1.2% & 1.6% & 3.3% & 2.9% & 0.0% & 1.2% & 0.5% & 1.7% & 1.2% \\ \hline 1/31/13 & 4.9% & 5.6% & 0.5% & 1.3% & 1.9% & 0.0% & 5.6% & 4.9% & =0.7% & 5.6% \\ \hline 2/28/13 & 0.1% & 1.3% & 0.4% & 0.3% & 1.4% & 0.0% & 1.3% & 0.1% & 1.2% & 1.3% \\ \hline 3/31/13 & 0.9% & 4.0% & 0.9% & =0.1% & 2.0% & 0.0% & 4.0% & 0.9% & 3.1% & 4.0% \\ \hline 4/30/13 & 2.1% & 1.6% & 2.4% & 0.4% & 0.3% & 0.0% & 1.6% & 2.1% & 0.5% & 1.6% \\ \hline 5/31/13 & 6.5% & 2.8% & 2.0% & 1.3% & 1.9% & 0.0% & 2.8% & 6.5% & 3.7% & 2.8% \\ \hline 6/30/13 & 0.3% & 1.2% & 1.2% & 0.4% & 0.6% & 0.0% & 1.2% & 0.3% & 0.9% & 1.2% \\ \hline 7/31/13 & 0.1% & 5.7% & 1.9% & 0.7% & 1.8% & 0.0% & 5.7% & 0.1% & 5.6% & 5.7% \\ \hline 8/31/13 & 3.4% & 2.7% & 0.2% & 2.5% & 0.1% & 0.0% & 2.7% & 3.4% & 0.7% & 2.7% \\ \hline 9/30/13 & 2.4% & 3.8% & 2.9% & 1.6% & 3.0% & 0.0% & 3.8% & 2.4% & 1.4% & 3.8% \\ \hline 10/31/13 & 1.8% & 4.2% & 1.6% & 1.4% & 0.1% & 0.0% & 4.2% & 1.8% & 2.4% & 4.2% \\ \hline 11/30/13 & 1.7% & 3.1% & 1.3% & 0.4% & 0.5% & 0.0% & 3.1% & 1.7% & 1.4% & 3.1% \\ \hline 12/31/13 & 1.5% & 2.8% & 0.4% & 0.2% & 0.1% & 0.0% & 2.8% & 1.5% & 1.3% & 2.8% \\ \hline & & & & & & & & & & \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline & A & B & C & D & E & F & G & H & 1 & J & K \\ \hline 1 & mktrf & \multicolumn{4}{|c|}{ Market (value-weighted CRSP) less risk free rate } & & & & & & \\ \hline 2 & smb & \multicolumn{2}{|c|}{ small minus big } & & & & & & & & \\ \hline 3 & hml & \multicolumn{2}{|c|}{ high minus low } & & & & & & & & \\ \hline 4 & rf & risk free & & & & & & & & & \\ \hline 5 & umd & \multicolumn{3}{|c|}{ up minus down (Momentum) } & & & & & & & \\ \hline \multicolumn{12}{|l|}{6} \\ \hline \multicolumn{12}{|l|}{7} \\ \hline \multicolumn{12}{|l|}{8} \\ \hline \multicolumn{12}{|l|}{9} \\ \hline \multicolumn{12}{|l|}{10} \\ \hline \multicolumn{12}{|l|}{11} \\ \hline \multicolumn{12}{|l|}{12} \\ \hline \multicolumn{12}{|l|}{13} \\ \hline \multicolumn{12}{|l|}{14} \\ \hline \multicolumn{12}{|l|}{15} \\ \hline \multicolumn{12}{|l|}{16} \\ \hline \multicolumn{12}{|l|}{17} \\ \hline \multicolumn{12}{|l|}{18} \\ \hline \multicolumn{12}{|l|}{19} \\ \hline \multicolumn{12}{|l|}{20} \\ \hline \multicolumn{12}{|l|}{21} \\ \hline \multicolumn{12}{|l|}{22} \\ \hline \multicolumn{12}{|l|}{23} \\ \hline \multicolumn{12}{|l|}{24} \\ \hline \multicolumn{12}{|l|}{25} \\ \hline \multicolumn{12}{|l|}{26} \\ \hline 27 & & & & & & & & & & & \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|} \hline A & B & C & D & E & F & G & H & 1 & J & K \\ \hline 1 Date & 61_SC Fundan & & smb & hml & umd & if & mkt & 61_excess & 61 less S\&P & market less risk fr \\ \hline 12/31/11 & 0.3% & 0.7% & 0.6% & 1.6% & 1.9% & 0.0% & 0.7% & 0.3% & 1.0% & 0.7% \\ \hline 1/31/12 & 2.7% & 5.1% & 2.5% & 2.1% & 8.0% & 0.0% & 5.1% & 2.7% & 2.4% & 5.1% \\ \hline 2/29/12 & 1.2% & 4.4% & 1.7% & 0.0% & 0.3% & 0.0% & 4.4% & 1.2% & 3.2% & 4.4% \\ \hline 3/31/12 & 2.8% & 3.1% & 0.3% & 0.1% & 1.5% & 0.0% & 3.1% & 2.8% & 0.3% & 3.1% \\ \hline 4/30/12 & 1.3% & 0.9% & 0.6% & 0.2% & 3.8% & 0.0% & 0.9% & 1.3% & 0.5% & 0.9% \\ \hline 5/31/12 & 3.1% & 6.2% & 0.1% & 0.1% & 6.6% & 0.0% & 6.2% & 3.1% & 3.1% & 6.2% \\ \hline 6/30/12 & 1.1% & 3.9% & 0.8% & 0.5% & 1.1% & 0.0% & 3.9% & 1.1% & 2.8% & 3.9% \\ \hline 7/31/12 & 3.4% & 0.8% & 2.6% & 0.0% & 3.1% & 0.0% & 0.8% & 3.4% & 2.6% & 0.8% \\ \hline 8/31/12 & 1.2% & 2.6% & 0.7% & 0.6% & 2.4% & 0.0% & 2.6% & 1.2% & 3.8% & 2.6% \\ \hline 9/30/12 & 1.7% & 2.7% & 0.5% & 1.6% & 1.0% & 0.0% & 2.7% & 1.7% & 1.0% & 2.7% \\ \hline 10/31/12 & 2.6% & 1.8% & 1.1% & 4.2% & 0.1% & 0.0% & 1.8% & 2.6% & 4.4% & 1.8% \\ \hline 11/30/12 & 1.7% & 0.8% & 0.7% & 1.1% & 0.4% & 0.0% & 0.8% & 1.7% & 0.9% & 0.8% \\ \hline 12/31/12 & 0.5% & 1.2% & 1.6% & 3.3% & 2.9% & 0.0% & 1.2% & 0.5% & 1.7% & 1.2% \\ \hline 1/31/13 & 4.9% & 5.6% & 0.5% & 1.3% & 1.9% & 0.0% & 5.6% & 4.9% & =0.7% & 5.6% \\ \hline 2/28/13 & 0.1% & 1.3% & 0.4% & 0.3% & 1.4% & 0.0% & 1.3% & 0.1% & 1.2% & 1.3% \\ \hline 3/31/13 & 0.9% & 4.0% & 0.9% & =0.1% & 2.0% & 0.0% & 4.0% & 0.9% & 3.1% & 4.0% \\ \hline 4/30/13 & 2.1% & 1.6% & 2.4% & 0.4% & 0.3% & 0.0% & 1.6% & 2.1% & 0.5% & 1.6% \\ \hline 5/31/13 & 6.5% & 2.8% & 2.0% & 1.3% & 1.9% & 0.0% & 2.8% & 6.5% & 3.7% & 2.8% \\ \hline 6/30/13 & 0.3% & 1.2% & 1.2% & 0.4% & 0.6% & 0.0% & 1.2% & 0.3% & 0.9% & 1.2% \\ \hline 7/31/13 & 0.1% & 5.7% & 1.9% & 0.7% & 1.8% & 0.0% & 5.7% & 0.1% & 5.6% & 5.7% \\ \hline 8/31/13 & 3.4% & 2.7% & 0.2% & 2.5% & 0.1% & 0.0% & 2.7% & 3.4% & 0.7% & 2.7% \\ \hline 9/30/13 & 2.4% & 3.8% & 2.9% & 1.6% & 3.0% & 0.0% & 3.8% & 2.4% & 1.4% & 3.8% \\ \hline 10/31/13 & 1.8% & 4.2% & 1.6% & 1.4% & 0.1% & 0.0% & 4.2% & 1.8% & 2.4% & 4.2% \\ \hline 11/30/13 & 1.7% & 3.1% & 1.3% & 0.4% & 0.5% & 0.0% & 3.1% & 1.7% & 1.4% & 3.1% \\ \hline 12/31/13 & 1.5% & 2.8% & 0.4% & 0.2% & 0.1% & 0.0% & 2.8% & 1.5% & 1.3% & 2.8% \\ \hline & & & & & & & & & & \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline & A & B & C & D & E & F & G & H & 1 & J & K \\ \hline 1 & mktrf & \multicolumn{4}{|c|}{ Market (value-weighted CRSP) less risk free rate } & & & & & & \\ \hline 2 & smb & \multicolumn{2}{|c|}{ small minus big } & & & & & & & & \\ \hline 3 & hml & \multicolumn{2}{|c|}{ high minus low } & & & & & & & & \\ \hline 4 & rf & risk free & & & & & & & & & \\ \hline 5 & umd & \multicolumn{3}{|c|}{ up minus down (Momentum) } & & & & & & & \\ \hline \multicolumn{12}{|l|}{6} \\ \hline \multicolumn{12}{|l|}{7} \\ \hline \multicolumn{12}{|l|}{8} \\ \hline \multicolumn{12}{|l|}{9} \\ \hline \multicolumn{12}{|l|}{10} \\ \hline \multicolumn{12}{|l|}{11} \\ \hline \multicolumn{12}{|l|}{12} \\ \hline \multicolumn{12}{|l|}{13} \\ \hline \multicolumn{12}{|l|}{14} \\ \hline \multicolumn{12}{|l|}{15} \\ \hline \multicolumn{12}{|l|}{16} \\ \hline \multicolumn{12}{|l|}{17} \\ \hline \multicolumn{12}{|l|}{18} \\ \hline \multicolumn{12}{|l|}{19} \\ \hline \multicolumn{12}{|l|}{20} \\ \hline \multicolumn{12}{|l|}{21} \\ \hline \multicolumn{12}{|l|}{22} \\ \hline \multicolumn{12}{|l|}{23} \\ \hline \multicolumn{12}{|l|}{24} \\ \hline \multicolumn{12}{|l|}{25} \\ \hline \multicolumn{12}{|l|}{26} \\ \hline 27 & & & & & & & & & & & \\ \hline \end{tabular}