Econometrics of Mutual Funds

Topics: Mutual fund, Stock market, Stock market index Pages: 7 (1921 words) Published: May 29, 2013
Econometrics II
Homework assignment 3
Ultimate due date: Tuesday, April 23 at 18:55

Part 1: Mutual Funds
1. Posted to my.nes.ru are monthly returns for 9 mutual funds. Accidentally, I have forgotten to match the fund names to the correct return data for 7 of these 9 mutual funds. Please run regressions of each of the 9 funds on the Fama-French three-factor model and make an educated guess regarding which fund goes with which data. Explain the reasoning behind your guess. In the list “HW_FundsAndReturns.csv” of the Excel book “HW3_FundsAndReturns” were used additional columns to the right from last occupied column “X”. In columns “Y:AB” for the parameters α; β3; βs; βv corresponding to the model Mretf=α1+Rf+β3Rm-Rf+βsSMB+βvHML+ε

Columns “AC” and “AD” were used for presentation of error and error squared. After this for each fund (time series of 60 values taken monthly from 31/01/2006 to 31/12/2010). In this case intrinsic function of Excel for the regression was used (despite usage of built in functions with formula like ИНДЕКС(ЛИНЕЙН(ExchangeRates!B4:B170;'Oil Prices'!B4:B170;ИСТИНА;ИСТИНА);3;1)) is also clear, but probably not very comfortable for limited amount of funds =9). After that for each fund two plots, like on figure 1 and figure 2 were drawn.

Figure 1

Figure 2
Also estimations of model parameters, dispersion, R2 values etc. were calculated for each fund individually. After all the whole set of results was collected in the list “Summary” of the same book. Part of the results (respecting to question 1) are presented in the table 1.

#| Fund label| β| β small| <rp>| σ| σ/<rp>| TI| SI| SI/50| R2| 1| 8292| 0,9728| 0,1911| 2,45 E-03| 5,62E-02| 22,95| 6,30E-04| 1,09E-02| 2,18E-04| 0,9863| 2| A| 0,9636| 0,8230| 3,53E-03| 7,47E-02| 21,19| 1,74E-03| 2,26E-02| 4,52E-04| 0,8302| 3| B| 0,0661| -0,1050| 2,01E-03| 9,13E-03| 4,53| 1,83E-04| 1,95E-02| 3,89E-04| 0,0181| 4| C| 0,9410| -0,1256| -8,68E-04| 5,11E-02| -58,88| -2,78E-03| -5,29E-02| -1,06E-03| 0,9868| 5| D| 0,9986| 0,9206| 3,94E-03| 6,86E-02| 17,43| 2,16E-03| 3,06E-02| 6,12E-04| 0,8937| 6| E| 1,0819| 0,7713| 2,35E-03| 6,66E-02| 28,39| 5,23E-04| 7,64E-03| 1,53E-04| 0,8848| 7| F| 0,9647| 0,0167| 2,01E-03| 5,32E-02| 26,40| 1,83E-04| 3,35E-03| 6,70E-05| 0,9953| 8| 32022| 1,0658| 0,0449| 4,89E-04| 5,78E-02| 118,31| -1,39E-03| -2,33E-02| -4,66E-04| 0,9891| 9| G| 0,0036| -0,0324| 1,10E-03| 3,28E-03| 2,99| -7,61E-04| -2,26E-01| -4,51E-03| 0,0005| Table 1

2. For each of the 9 series mutual fund returns, please calculate measures of mutual fund performance: a. Sharpe Ratio
b. Treyner measure
c. Morning Star Risk Adjusted Return (MRAR)
d. Jensen’s alpha
Sharpe and Treynor’s indexes were readily calculated for each fund and are also presented in the previous table.

Morning Star Risk Adjusted Returns (MRAR) were calculated in the columns “AI:AL” on the list “HW_FundsAndReturns.csv” of the Excel book “HW3_FundsAndReturns” separately for each fund and for each year/ After that date were collected in the “Summary” and averaged among all years. Jensen’s alpha is presented in each plot , similar to Figure 2, but also summarized in the table.

#| Fund label| σ| TI| SI| Jensen's α| <MRAR>| MRAR 2006| MRAR 2007| MRAR 2008| MRAR 2009| MRAR 2010| 1| 8292| 5,62E-02| 6,30 E-04| 1,09 E-02| 3,00E-04| 4090,58| 4200,7| 3962,1| 3195,7| 4630,2| 4464,0| 2| A| 7,47E-02| 1,74 E-03| 2,26 E-02| 3,00E-04| 4077,57| 4203,5| 3605,5| 3299,4| 4673,2| 4606,0| 3| B| 9,13E-03| 1,83 E-04| 1,95 E-02| 1,00E-03| 4099,26| 4043,7| 4065,7| 4016,9| 4295,8| 4073,9| 4| C| 5,11E-02| -2,78 E-03| -5,29 E-02| 3,60E-03| 4016,28| 4150,8| 3959,7| 3156,1| 4510,4| 4304,2| 5| D| 6,86E-02| 2,16 E-03| 3,06 E-02| 3,00E-04| 4105,17| 4178,1| 3845,0| 3195,5| 4678,2| 4628,8| 6| E| 6,66E-02|...