Question: In the tab labeled Fund X Return Data Data since 1977 of the monthly return to investors that have invested their money in fund X,

  1. In the tab labeled Fund X Return Data
    • Data since 1977 of the monthly return to investors that have invested their money in fund X, labeled variable RX.
    • Size of the fund, that is the amount of capital that investors have jointly put in the fund, expressed in millions of USD, also called the Assets-Under-Management or AUM.
  2. In the tab labeled Fund X Expense Ratio
    • Annual expense ratio that the fund has charged to investors expressed as an annual percentage.
    • The return to investors (or net performance) has already taken into account the fact that the expense ratio is taken out. So, to evaluate the gross performance of the fund you need to add back the expense ratio to the returns.
  3. In the tab labeled Benchmark Data Vanguard SP500
    • Information about the benchmark, which in this case is the S&P500 index fund of Vanguard, which is labeled RVG.
    • Information about the risk-free interest rate, which is labeled Rf
  • questions

Question 1 1pts

In your spreadsheet, start by computing the monthly returns of both Fund X as well as the Vanguard S&P 500 index in excess of the risk-free interest rate. These returns are called 'excess returns'.

a) What is the Excess return of Fund X for November 1978?

Enter value to 4 decimal places.

Question 2 1pts

In your spreadsheet, start by computing the monthly returns of both Fund X as well as the Vanguard S&P 500 index in excess of the risk-free interest rate. These returns are called 'excess returns'.

b) What is the Excess return of the S&P 500 for November 1978?

Enter value to 4 decimal places.

Question 3 1pts

Compute the so-called (which is a measure of risk exposure) of Fund X by regressing the excess returns of Fund X on the excess returns of the Vanguard index fund. You can this in Excel by using the "slope" function, where the first input of that function is the column of excess returns on Fund X and the second input is the column of excess returns on the index.

Enter value to 4 decimal places.

Question 4 1pts

Use the from step b) to compute the monthly excess outperformance (or underperformance in case the number is negative) of Fund X. The formula is: RX - RVG (as a reminder Rx and Rvg are excess returns and not absolute returns). What is the average excess outperformance (or net alpha) for this fund over this time period?

Enter value to 5 decimal places.

Question 5 1pts

Compute the gross outperformance in each month by adding 1/12 of the annual expense ratio to each monthly outperformance number. Note that the expense ratio changes.

What is the average gross outperformance over this time period?

Enter value to 4 decimal places.

Question 6 1pts

Compute the monthly value added by multiplying the gross alpha in each month by the AUM from the previous month. What is the average value added of this fund?

Enter value to 2 decimal places.

Question 7 1pts

Does the data demonstrate "skill" on the part of the manager?

Group of answer choices

Yes

No

FUND X RETURN DATE Benchmark Data Vanguard SP500 Expense Ratio
Date AUM Monthly Return to Investors Date Vanguard S&P 500 Index Fund Return to Investors Risk free Rate R_f 1977-2000 1.00%
19770131 63.20 -0.036 19770131 -0.049559 0.0036 2001-2017 0.75%
19770228 60.31 -0.026 19770228 -0.014286 0.0035
19770331 60.76 0.009 19770331 -0.013161 0.0038
19770429 57.87 0.007 19770429 0 0.0038
19770531 57.07 0.007 19770531 -0.014826 0.0037
19770630 60.45 0.065 19770630 0.045182 0.004
19770729 60.69 0.006 19770729 -0.015262 0.0042
19770831 57.83 0.001 19770831 -0.014022 0.0044
19770930 57.94 0.018 19770930 0.000074 0.0043
19771031 55.99 -0.019 19771031 -0.041572 0.0049
19771130 62.73 0.113 19771130 0.0347 0.005
19771230 63.21 0.026 19771230 0.005335 0.0049
19780131 56.02 -0.059 19780131 -0.059954 0.0049
19780228 55.41 0.007 19780228 -0.017171 0.0046
19780331 59.17 0.071 19780331 0.025762 0.0053
19780428 66.38 0.104 19780428 0.085316 0.0054
19780531 72.58 0.067 19780531 0.01285 0.0051
19780630 71.58 0.012 19780630 -0.01568 0.0054
19780731 77.84 0.091 19780731 0.056705 0.0056
19780831 86.21 0.076 19780831 0.034083 0.0056
19780929 82.03 -0.017 19780929 -0.005554 0.0062
19781031 60.81 -0.192 19781031 -0.089031 0.0068
19781130 65.55 0.084 19781130 0.025801 0.007
19781229 70.84 0.015 19781229 0.016742 0.0078
19790131 76.42 0.092 19790131 0.04119 0.0077
19790228 73.36 -0.017 19790228 -0.028571 0.0073
19790330 81.24 0.092 19790330 0.057258 0.0081
19790430 87.72 0.021 19790430 0.003605 0.008
19790531 78.24 -0.034 19790531 -0.016523 0.0082
19790629 81.57 0.042 19790629 0.040191 0.0081
19790731 84.14 0.029 19790731 0.011356 0.0077
19790831 95.18 0.118 19790831 0.061053 0.0077
19790928 99.78 0.039 19790928 0.001984 0.0083
19791031 89.34 -0.065 19791031 -0.065333 0.0087
19791130 103.59 0.107 19791130 0.051355 0.0099
19791231 121.86 0.063 19791231 0.017622 0.0095
19800131 130.91 0.041 19800131 0.059426 0.008
19800229 124.09 -0.001 19800229 0.003868 0.0089
19800331 110.07 -0.127 19800331 -0.098123 0.0121
19800430 123.21 0.057 19800430 0.043228 0.0126
19800530 137.19 0.053 19800530 0.055249 0.0081
19800630 145.68 0.028 19800630 0.027982 0.0061
19800731 167.67 0.100 19800731 0.066238 0.0053
19800829 190.60 0.031 19800829 0.012666 0.0064
19800930 209.45 0.035 19800930 0.026802 0.0075
19801031 203.02 0.021 19801031 0.019906 0.0095
19801128 227.26 0.068 19801128 0.109644 0.0096
19801231 230.96 -0.012 19801231 -0.033488 0.0131
19810130 220.48 -0.034 19810130 -0.044283 0.0104
19810227 219.52 0.010 19810227 0.021114 0.0107
19810331 246.91 0.061 19810331 0.03744 0.0121
19810430 269.89 0.020 19810430 -0.021812 0.0108
19810529 280.28 0.020 19810529 0.006289 0.0115
19810630 279.09 -0.014 19810630 -0.008523 0.0135
19810731 264.74 -0.023 19810731 0 0.0124
19810831 393.16 -0.045 19810831 -0.05443 0.0128
19810930 381.69 -0.022 19810930 -0.050214 0.0124
19811030 416.31 0.053 19811030 0.052185 0.0121
19811130 442.11 0.040 19811130 0.044017 0.0107
19811231 423.28 0.001 19811231 -0.027549 0.0087
19820129 414.97 -0.010 19820129 -0.01482 0.008
19820226 419.45 -0.022 19820226 -0.051014 0.0092
19820331 426.11 -0.008 19820331 -0.006927 0.0098
19820430 464.19 0.057 19820430 0.041462 0.0113
19820528 441.47 -0.023 19820528 -0.02834 0.0106
19820630 433.22 -0.010 19820630 -0.016738 0.0096
19820730 444.73 -0.013 19820730 -0.021459 0.0105
19820831 505.34 0.116 19820831 0.124269 0.0076
19820930 512.50 0.019 19820930 0.010135 0.0051
19821029 593.42 0.116 19821029 0.110677 0.0059
19821130 637.77 0.067 19821130 0.043376 0.0063
19821231 658.22 0.017 19821231 0.016819 0.0067
19830131 716.94 0.036 19830131 0.034169 0.0069
19830228 783.36 0.047 19830228 0.02478 0.0062
19830331 831.97 0.016 19830331 0.03502 0.0063
19830429 918.66 0.044 19830429 0.075996 0.0071
19830531 954.21 0.021 19830531 -0.008768 0.0069
19830630 997.97 0.036 19830630 0.037475 0.0067
19830729 981.89 -0.026 19830729 -0.032489 0.0074
19830831 949.11 -0.004 19830831 0.018272 0.0076
19830930 1010.12 0.028 19830930 0.012513 0.0076
19831031 1000.62 -0.026 19831031 -0.01401 0.0076
19831130 1072.77 0.042 19831130 0.022538 0.007
19831230 1061.72 -0.016 19831230 -0.006229 0.0073
19840131 1054.01 -0.049 19840131 -0.005076 0.0076
19840229 988.16 -0.047 19840229 -0.033163 0.0071
19840330 998.22 0.005 19840330 0.016314 0.0073
19840430 1016.32 0.002 19840430 0.007338 0.0081
19840531 955.86 -0.053 19840531 -0.05359 0.0078
19840629 1016.73 0.048 19840629 0.021467 0.0075
19840731 1002.86 -0.016 19840731 -0.014674 0.0082
19840831 1162.99 0.135 19840831 0.111969 0.0083
19840928 1115.38 -0.039 19840928 0 0.0086
19841031 1113.00 0.002 19841031 0.003003 0.01
19841130 1088.78 -0.023 19841130 -0.00998 0.0073
19841231 1131.72 0.041 19841231 0.025436 0.0064
19850131 1242.13 0.088 19850131 0.07582 0.0065
19850228 1239.18 -0.008 19850228 0.01381 0.0058
19850329 1215.92 -0.031 19850329 0.000052 0.0062
19850430 1205.64 -0.022 19850430 -0.002842 0.0072
19850531 1307.84 0.055 19850531 0.060333 0.0066
19850628 1330.26 0.029 19850628 0.014333 0.0055
19850731 1350.41 0.013 19850731 -0.002226 0.0062
19850830 1319.27 -0.016 19850830 -0.006693 0.0055
19850930 1244.74 -0.045 19850930 -0.031447 0.006
19851031 1296.08 0.037 19851031 0.043966 0.0065
19851129 1388.30 0.084 19851129 0.069444 0.0061
19851231 1444.30 0.048 19851231 0.046738 0.0065
19860131 1453.13 0.013 19860131 0.00435 0.0056
19860228 1560.98 0.072 19860228 0.07579 0.0053
19860331 1620.60 0.042 19860331 0.05475 0.006
19860430 1645.51 0.013 19860430 -0.013451 0.0052
19860530 1693.36 0.053 19860530 0.054538 0.0049
19860630 1656.82 -0.015 19860630 0.016658 0.0052
19860731 1569.45 -0.044 19860731 -0.057425 0.0052
19860829 1675.20 0.064 19860829 0.074505 0.0046
19860930 1523.28 -0.077 19860930 -0.083062 0.0045
19861031 1618.29 0.058 19861031 0.056327 0.0046
19861128 1632.50 0.012 19861128 0.025535 0.0039
19861231 1567.76 -0.014 19861231 -0.026413 0.0049
19870130 1814.84 0.149 19870130 0.132674 0.0042
19870227 1970.77 0.077 19870227 0.039651 0.0043
19870331 1949.16 0.000 19870331 0.028598 0.0047
19870430 1983.54 0.006 19870430 -0.009925 0.0044
19870529 2011.90 0.003 19870529 0.01037 0.0038
19870630 2082.94 0.030 19870630 0.050213 0.0048
19870731 2171.53 0.042 19870731 0.049148 0.0046
19870831 2278.25 0.052 19870831 0.038413 0.0047
19870930 2264.80 -0.007 19870930 -0.022855 0.0045
19871030 1774.84 -0.211 19871030 -0.21727 0.006
19871130 1612.38 -0.093 19871130 -0.081851 0.0035
19871231 1774.17 0.113 19871231 0.075507 0.0039
19880129 1781.49 0.003 19880129 0.041746 0.0029
19880229 1859.80 0.058 19880229 0.0459 0.0046
19880331 1808.17 -0.025 19880331 -0.030411 0.0044
19880429 1810.97 0.005 19880429 0.010129 0.0046
19880531 1787.13 -0.009 19880531 0.008099 0.0051
19880630 1898.75 0.068 19880630 0.045555 0.0049
19880729 1828.99 -0.032 19880729 -0.003683 0.0051
19880831 1756.05 -0.032 19880831 -0.034011 0.0059
19880930 1824.71 0.045 19880930 0.042555 0.0062
19881031 1815.43 -0.001 19881031 0.027347 0.0061
19881130 1746.72 -0.021 19881130 -0.014029 0.0057
19881230 1806.40 0.043 19881230 0.016635 0.0063
19890131 1936.79 0.085 19890131 0.073216 0.0055
19890228 1894.14 -0.012 19890228 -0.024683 0.0061
19890331 1913.84 0.017 19890331 0.022599 0.0067
19890428 2034.56 0.063 19890428 0.051844 0.0067
19890531 2125.91 0.051 19890531 0.040357 0.0079
19890630 2092.09 -0.016 19890630 -0.00586 0.0071
19890731 2214.25 0.063 19890731 0.090061 0.007
19890831 2276.04 0.033 19890831 0.01859 0.0074
19890929 2302.17 0.015 19890929 -0.004046 0.0065
19891031 2245.53 -0.024 19891031 -0.023392 0.0068
19891130 2256.30 0.003 19891130 0.020359 0.0069
19891229 2242.18 0.001 19891229 0.023758 0.0061
19900131 2093.15 -0.061 19900131 -0.067182 0.0057
19900228 2120.94 0.011 19900228 0.012747 0.0057
19900330 2193.60 0.032 19900330 0.026073 0.0064
19900430 2150.26 -0.017 19900430 -0.025015 0.0069
19900531 2390.86 0.115 19900531 0.096927 0.0068
19900629 2378.86 -0.002 19900629 -0.006888 0.0063
19900731 2245.41 -0.052 19900731 -0.003215 0.0068
19900831 2002.42 -0.112 19900831 -0.090323 0.0066
19900928 1846.59 -0.080 19900928 -0.048904 0.006
19901031 1817.33 -0.017 19901031 -0.004093 0.0068
19901130 2009.71 0.116 19901130 0.064384 0.0057
19901231 2087.11 0.049 19901231 0.027154 0.006
19910131 2250.31 0.089 19910131 0.043214 0.0052
19910228 2424.71 0.081 19910228 0.071494 0.0048
19910328 2497.33 0.031 19910328 0.024053 0.0044
19910430 2501.59 0.004 19910430 0.001971 0.0053
19910531 2625.56 0.046 19910531 0.042721 0.0047
19910628 2421.65 -0.077 19910628 -0.045592 0.0042
19910731 2588.82 0.063 19910731 0.046267 0.0049
19910830 2706.92 0.028 19910830 0.023332 0.0046
19910930 2666.13 -0.009 19910930 -0.016684 0.0046
19911031 2702.61 0.017 19911031 0.013276 0.0042
19911129 2610.14 -0.037 19911129 -0.040107 0.0039
19911231 3007.88 0.134 19911231 0.114134 0.0038
19920131 2985.83 0.004 19920131 -0.01882 0.0034
19920228 3076.08 0.018 19920228 0.012442 0.0028
19920331 2923.02 -0.044 19920331 -0.019257 0.0034
19920430 2938.74 -0.004 19920430 0.029142 0.0032
19920529 2970.54 0.011 19920529 0.004847 0.0028
19920630 2946.09 -0.018 19920630 -0.014915 0.0032
19920731 2997.80 0.027 19920731 0.040435 0.0031
19920831 2941.90 -0.024 19920831 -0.020678 0.0026
19920930 2998.96 0.025 19920930 0.011695 0.0026
19921030 3023.29 0.007 19921030 0.003287 0.0023
19921130 3184.43 0.061 19921130 0.034022 0.0023
19921231 3233.71 0.019 19921231 0.012117 0.0028
19930129 3300.01 0.014 19930129 0.008055 0.0023
19930226 3317.16 -0.005 19930226 0.013559 0.0022
19930331 3346.97 0.016 19930331 0.021075 0.0025
19930430 3192.56 -0.047 19930430 -0.024241 0.0024
19930528 3339.38 0.052 19930528 0.026532 0.0022
19930630 3311.64 -0.007 19930630 0.002674 0.0025
19930730 3256.90 -0.009 19930730 -0.00424 0.0024
19930831 3369.83 0.055 19930831 0.037852 0.0025
19930930 3371.52 0.018 19930930 -0.007944 0.0026
19931029 3414.70 0.028 19931029 0.020785 0.0022
19931130 3328.82 -0.019 19931130 -0.009955 0.0025
19931231 3386.70 0.023 19931231 0.012248 0.0023
19940131 3434.63 0.026 19940131 0.033767 0.0025
19940228 3369.49 -0.013 19940228 -0.027146 0.0021
19940331 3189.89 -0.044 19940331 -0.043884 0.0027
19940429 3143.12 -0.013 19940429 0.0129 0.0027
19940531 3225.89 0.031 19940531 0.016038 0.0031
19940630 3096.08 -0.036 19940630 -0.024468 0.0031
19940729 3186.89 0.034 19940729 0.032767 0.0028
19940831 3350.63 0.054 19940831 0.04076 0.0037
19940930 3227.72 -0.035 19940930 -0.02446 0.0037
19941031 3276.17 0.020 19941031 0.022467 0.0038
19941130 3139.36 -0.034 19941130 -0.036547 0.0037
19941230 3164.86 0.012 19941230 0.014614 0.0044
19950131 3161.95 0.015 19950131 0.025832 0.0042
19950228 3267.18 0.040 19950228 0.038793 0.004
19950331 3295.14 0.013 19950331 0.029534 0.0046
19950428 3334.01 0.015 19950428 0.029412 0.0044
19950531 3453.68 0.047 19950531 0.039545 0.0054
19950630 3568.19 0.043 19950630 0.023112 0.0047
19950731 3732.37 0.049 19950731 0.03304 0.0045
19950831 3749.55 0.010 19950831 0.00265 0.0047
19950929 3808.67 0.023 19950929 0.042115 0.0043
19951031 3753.96 -0.008 19951031 -0.003637 0.0047
19951130 3888.30 0.038 19951130 0.043804 0.0042
19951229 3886.19 0.003 19951229 0.019323 0.0049
19960131 3984.02 0.033 19960131 0.033854 0.0043
19960229 4061.99 0.026 19960229 0.009404 0.0039
19960329 3968.17 -0.024 19960329 0.009768 0.0039
19960430 4041.43 0.022 19960430 0.01456 0.0046
19960531 4059.51 0.014 19960531 0.025277 0.0042
19960628 3964.69 -0.021 19960628 0.003829 0.004
19960731 3681.32 -0.072 19960731 -0.044204 0.0045
19960830 3752.86 0.031 19960830 0.020962 0.0041
19960930 4049.38 0.091 19960930 0.056062 0.0044
19961031 4014.75 0.001 19961031 0.027558 0.0042
19961129 4289.86 0.086 19961129 0.075486 0.0041
19961231 4167.82 -0.026 19961231 -0.019732 0.0046
19970131 4270.03 0.042 19970131 0.062328 0.0045
19970228 4187.58 -0.010 19970228 0.008032 0.0039
19970331 3973.75 -0.048 19970331 -0.041357 0.0043
19970430 4094.95 0.042 19970430 0.059556 0.0043
19970530 4359.62 0.081 19970530 0.060881 0.0049
19970630 4452.88 0.031 19970630 0.044536 0.0037
19970731 4776.74 0.088 19970731 0.079657 0.0043
19970829 4646.11 -0.020 19970829 -0.05609 0.0041
19970930 4863.87 0.050 19970930 0.05469 0.0044
19971031 4757.65 -0.016 19971031 -0.033503 0.0042
19971128 4809.85 0.022 19971128 0.045868 0.0039
19971231 4990.23 0.044 19971231 0.017251 0.0048
19980130 4982.14 0.003 19980130 0.011215 0.0043
19980227 5379.14 0.088 19980227 0.071923 0.0039
19980331 5612.21 0.047 19980331 0.051037 0.0039
19980430 5682.57 0.016 19980430 0.010077 0.0043
19980529 5488.55 -0.038 19980529 -0.017435 0.004
19980630 5769.82 0.055 19980630 0.040716 0.0041
19980731 5783.35 -0.002 19980731 -0.010541 0.004
19980831 4912.01 -0.159 19980831 -0.144736 0.0043
19980930 5250.98 0.074 19980930 0.064111 0.0046
19981030 5598.08 0.071 19981030 0.081641 0.0032
19981130 5947.46 0.064 19981130 0.060716 0.0031
19981231 6412.78 0.092 19981231 0.058052 0.0038
19990129 6739.16 0.050 19990129 0.042036 0.0035
19990226 6532.76 -0.042 19990226 -0.031245 0.0035
19990331 6573.94 0.002 19990331 0.039965 0.0043
19990430 6767.62 0.027 19990430 0.03852 0.0037
19990528 6817.67 0.009 19990528 -0.023891 0.0034
19990630 7278.90 0.076 19990630 0.05556 0.004
19990730 7038.41 -0.037 19990730 -0.031302 0.0038
19990831 6937.68 -0.015 19990831 -0.004965 0.0039
19990930 6906.35 -0.006 19990930 -0.02739 0.0039
19991029 7083.66 0.030 19991029 0.063264 0.0039
19991130 7393.11 0.048 19991130 0.02023 0.0036
19991231 7906.43 0.084 19991231 0.059776 0.0044
20000131 7813.55 -0.013 20000131 -0.050321 0.0041
20000229 7996.84 0.025 20000229 -0.019063 0.0043
20000331 8463.90 0.067 20000331 0.09752 0.0047
20000428 8323.34 -0.020 20000428 -0.029985 0.0046
20000531 8148.63 -0.021 20000531 -0.020384 0.005
20000630 8315.95 0.026 20000630 0.024946 0.004
20000731 8252.04 -0.010 20000731 -0.014982 0.0048
20000831 8565.35 0.058 20000831 0.061899 0.005
20000929 8276.20 -0.036 20000929 -0.052894 0.0051
20001031 8531.16 0.032 20001031 -0.004299 0.0056
20001130 8067.04 -0.063 20001130 -0.078852 0.0051
20001229 8419.87 0.038 20001229 0.005132 0.005
20010131 8717.99 0.040 20010131 0.035451 0.0054
20010228 8158.03 -0.071 20010228 -0.091377 0.0038
20010330 7713.81 -0.062 20010330 -0.063563 0.0042
20010430 8311.17 0.082 20010430 0.077706 0.0039
20010531 8473.86 0.017 20010531 0.0065 0.0032
20010629 8456.40 -0.007 20010629 -0.024455 0.0028
20010731 8441.46 -0.006 20010731 -0.009998 0.003
20010831 8047.63 -0.055 20010831 -0.06274 0.0031
20010928 7191.60 -0.112 20010928 -0.08091 0.0028
20011031 7437.48 0.030 20011031 0.01895 0.0022
20011130 8180.10 0.098 20011130 0.076538 0.0017
20011231 8355.02 0.010 20011231 0.00874 0.0015
20020131 8264.50 -0.023 20020131 -0.014732 0.0014
20020228 8091.69 -0.033 20020228 -0.019362 0.0013
20020328 8660.60 0.058 20020328 0.037432 0.0013
20020430 8405.21 -0.046 20020430 -0.060746 0.0015
20020531 8469.62 -0.002 20020531 -0.007544 0.0014
20020628 7866.30 -0.080 20020628 -0.071345 0.0013
20020731 7227.15 -0.078 20020731 -0.077193 0.0015
20020830 7309.61 0.005 20020830 0.006526 0.0014
20020930 6710.32 -0.092 20020930 -0.108748 0.0014
20021031 7186.03 0.076 20021031 0.087829 0.0014
20021129 7784.45 0.079 20021129 0.058752 0.0012
20021231 7351.50 -0.068 20021231 -0.058927 0.0011
20030131 7349.24 -0.010 20030131 -0.026248 0.001
20030228 7304.30 -0.009 20030228 -0.015186 0.0009
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