Question

In: Finance

Using the CAPM, calculate the 2016 expected return on Facebook’s shares. Assumptions: Risk-free rate, Rf =...

Using the CAPM, calculate the 2016 expected return on Facebook’s shares.

Assumptions:

Risk-free rate, Rf = 2.5%

E(Rm) = 7.5%

Use the SP500 index to proxy for the market portfolio.

Hints to calculate beta:

- Use daily stock returns during 2016 (start date 01-Jan-2016, end date 31-Dec-2016).

- Download stock prices for Facebook and the SP500 with ticker name FB and ^GSPC, respectively, from www.finance.yahoo.com.

- Use adjusted prices to calculate returns.

Solutions

Expert Solution

We know beta = Covariance of security wit benchmark/Variance of security

We have downloaded the yearly data for 2016 and provided returns:

FB S&P FB return S&P return
104.66 2043.939941
102.22 2012.660034 -0.02331361 -0.01530373
102.73 2016.709961 0.004989258 0.002012226
102.97 1990.26001 0.002336202 -0.0131154
97.92 1943.089966 -0.04904344 -0.02370044
97.33 1922.030029 -0.00602529 -0.01083837
97.51 1923.670044 0.001849378 0.000853272
99.37 1938.680054 0.019074977 0.007802799
95.44 1890.280029 -0.03954917 -0.02496545
98.37 1921.839966 0.030699926 0.016695906
94.97 1880.329956 -0.0345634 -0.0215991
95.26 1881.329956 0.003053606 0.000531822
94.35 1859.329956 -0.00955284 -0.01169386
94.16 1868.98999 -0.00201371 0.005195438
97.94 1906.900024 0.040144412 0.020283701
97.01 1877.079956 -0.00949561 -0.01563798
97.34 1903.630005 0.003401649 0.014144336
94.45 1882.949951 -0.02968974 -0.01086348
109.11 1893.359985 0.155214446 0.005528577
112.21 1940.23999 0.028411676 0.024760217
115.09 1939.380005 0.025666135 -0.00044324
114.61 1903.030029 -0.00417061 -0.01874309
112.69 1912.530029 -0.01675246 0.004992039
110.49 1915.449951 -0.01952262 0.001526733
104.07 1880.050049 -0.05810479 -0.01848125
99.75 1853.439941 -0.04151052 -0.01415394
99.54 1852.209961 -0.00210525 -0.00066362
101 1851.859985 0.01466746 -0.00018895
101.91 1829.079956 0.009009941 -0.01230116
102.01 1864.780029 0.000981238 0.019518049
101.61 1895.579956 -0.00392119 0.016516654
105.2 1926.819946 0.035331128 0.016480439
103.47 1917.829956 -0.01644483 -0.00466571
104.57 1917.780029 0.010631091 -2.6033E-05
107.16 1945.5 0.024768136 0.014454197
105.46 1921.27002 -0.01586417 -0.01245437
106.88 1929.800049 0.013464802 0.004439787
108.07 1951.699951 0.01113401 0.011348275
107.92 1948.050049 -0.00138801 -0.00187011
106.92 1932.22998 -0.00926612 -0.00812098
109.82 1978.349976 0.027123102 0.023868792
109.95 1986.449951 0.001183728 0.004094308
109.58 1993.400024 -0.00336512 0.003498741
108.39 1999.98999 -0.01085967 0.003305892
105.73 2001.76001 -0.02454097 0.000885014
105.93 1979.26001 0.001891582 -0.01124011
107.51 1989.26001 0.014915529 0.005052393
107.32 1989.569946 -0.0017673 0.000155805
109.41 2022.189941 0.019474506 0.0163955
109.89 2019.640015 0.004387122 -0.00126097
110.67 2015.930054 0.007097998 -0.00183694
112.18 2027.219971 0.013644186 0.005600352
111.02 2040.589966 -0.01034055 0.006595236
111.45 2049.580078 0.003873176 0.004405644
111.85 2051.600098 0.003589062 0.000985577
112.25 2049.800049 0.003576236 -0.00087739
112.54 2036.709961 0.002583528 -0.00638603
113.05 2035.939941 0.00453174 -0.00037807
113.69 2037.050049 0.005661203 0.000545256
116.14 2055.01001 0.021549802 0.008816652
114.7 2063.949951 -0.01239885 0.004350315
114.1 2059.73999 -0.00523103 -0.00203976
116.06 2072.780029 0.017177914 0.006330915
112.55 2066.129883 -0.03024294 -0.00320832
112.22 2045.170044 -0.00293205 -0.01014449
113.71 2066.659912 0.013277473 0.010507619
113.64 2041.910034 -0.0006156 -0.01197579
110.63 2047.599976 -0.02648717 0.002786578
108.99 2041.98999 -0.01482418 -0.00273979
110.61 2061.719971 0.014863777 0.009662134
110.51 2082.419922 -0.00090407 0.010040137
110.84 2082.780029 0.002986101 0.000172927
109.64 2080.72998 -0.01082639 -0.00098428
110.45 2094.340088 0.007387796 0.006541026
112.29 2100.800049 0.016659158 0.003084485
112.42 2102.399902 0.00115769 0.000761545
113.44 2091.47998 0.009073154 -0.00519403
110.56 2091.580078 -0.02538791 4.78599E-05
110.1 2087.790039 -0.00416064 -0.00181205
108.76 2091.699951 -0.01217072 0.001872752
108.89 2095.149902 0.001195265 0.001649353
116.73 2075.810059 0.071999303 -0.00923077
117.58 2065.300049 0.007281753 -0.00506309
118.57 2081.429932 0.008419782 0.007809947
117.43 2063.370117 -0.00961457 -0.00867664
118.06 2051.120117 0.005364881 -0.00593689
117.81 2050.629883 -0.00211757 -0.00023901
119.49 2057.139893 0.01426025 0.003174639
119.24 2058.689941 -0.00209223 0.000753497
120.5 2084.389893 0.010566941 0.012483644
119.52 2064.459961 -0.0081328 -0.00956152
120.28 2064.110107 0.006358785 -0.00016947
119.81 2046.609985 -0.00390756 -0.00847829
118.67 2066.659912 -0.00951507 0.009796653
117.35 2047.209961 -0.01112328 -0.0094113
117.65 2047.630005 0.002556489 0.000205179
116.81 2040.040039 -0.00713986 -0.00370671
117.35 2052.320068 0.004622892 0.006019504
115.97 2048.040039 -0.01175967 -0.00208546
117.7 2076.060059 0.014917616 0.013681383
117.89 2090.540039 0.001614291 0.00697474
119.47 2090.100098 0.013402341 -0.00021044
119.38 2099.060059 -0.00075336 0.004286857
118.81 2096.949951 -0.00477466 -0.00100526
118.78 2099.330078 -0.0002525 0.001135042
118.93 2105.26001 0.001262847 0.002824678
118.47 2099.129883 -0.00386781 -0.00291181
118.79 2109.409912 0.002701106 0.004897281
117.76 2112.129883 -0.00867076 0.001289446
118.39 2119.120117 0.005349839 0.003309566
118.56 2115.47998 0.001435924 -0.00171776
116.62 2096.070068 -0.01636298 -0.00917518
113.95 2079.060059 -0.02289492 -0.00811519
114.94 2075.320068 0.008688065 -0.00179889
114.6 2071.5 -0.0029581 -0.00184071
114.39 2077.98999 -0.00183245 0.003132991
113.02 2071.219971 -0.01197659 -0.00325797
113.37 2083.25 0.00309685 0.005808185
114.38 2088.899902 0.008908829 0.002712061
113.91 2085.449951 -0.00410905 -0.00165156
115.08 2113.320068 0.010271249 0.013364079
112.08 2037.410034 -0.02606882 -0.0359198
108.97 2000.540039 -0.02774805 -0.0180965
112.7 2036.089966 0.034229567 0.017770165
114.16 2070.77002 0.01295481 0.017032673
114.28 2098.860107 0.001051112 0.013565044
114.19 2102.949951 -0.00078751 0.001948602
114.2 2088.550049 8.75296E-05 -0.00684748
116.7 2099.72998 0.021891419 0.005352963
115.85 2097.899902 -0.00728362 -0.00087158
117.24 2129.899902 0.011998274 0.015253349
117.87 2137.159912 0.005373635 0.003408616
117.93 2152.139893 0.00050901 0.007009293
116.78 2152.429932 -0.00975156 0.000134768
117.29 2163.75 0.004367203 0.005259204
116.86 2161.73999 -0.00366613 -0.00092895
119.37 2166.889893 0.021478709 0.002382295
120.61 2163.780029 0.010387853 -0.00143517
121.92 2173.02002 0.010861429 0.004270301
120.61 2165.169922 -0.01074473 -0.00361253
121 2175.030029 0.003233554 0.004553965
121.63 2168.47998 0.005206587 -0.00301148
121.22 2169.179932 -0.00337085 0.000322785
123.34 2166.580078 0.017488822 -0.00119854
125 2170.060059 0.013458765 0.001606209
123.94 2173.600098 -0.00847998 0.001631309
124.31 2170.840088 0.002985283 -0.00126979
123.09 2157.030029 -0.00981419 -0.00636162
122.51 2163.790039 -0.00471195 0.003133943
124.36 2164.25 0.0151008 0.000212572
125.15 2182.870117 0.006352533 0.008603496
125.26 2180.889893 0.000878945 -0.00090717
125.06 2181.73999 -0.00159671 0.000389794
124.88 2175.48999 -0.00143932 -0.00286469
124.9 2185.790039 0.000160194 0.004734588
124.88 2184.050049 -0.00016017 -0.00079605
123.9 2190.149902 -0.00784749 0.002792909
123.3 2178.149902 -0.00484261 -0.00547908
124.37 2182.219971 0.008678021 0.00186859
123.91 2187.02002 -0.00369863 0.002199617
123.56 2183.870117 -0.00282468 -0.00144027
124.15 2182.639893 0.004775041 -0.00056332
124.37 2186.899902 0.001772058 0.001951769
123.48 2175.439941 -0.00715607 -0.00524028
123.89 2172.469971 0.003320343 -0.00136523
124.96 2169.040039 0.008636694 -0.00157882
126.54 2180.379883 0.012644062 0.005228047
125.84 2176.120117 -0.00553189 -0.00195368
126.12 2170.949951 0.002225103 -0.00237586
126.17 2170.860107 0.000396408 -4.1385E-05
126.51 2179.97998 0.002694809 0.004201041
129.73 2186.47998 0.025452486 0.002981679
131.05 2186.159912 0.010175033 -0.00014639
130.27 2181.300049 -0.00595192 -0.00222301
127.1 2127.810059 -0.02433412 -0.02452207
128.69 2159.040039 0.012509866 0.014677053
127.21 2127.02002 -0.01150053 -0.01483067
127.77 2125.77002 0.004402154 -0.00058768
128.35 2147.26001 0.004539477 0.010109273
129.07 2139.159912 0.005609669 -0.00377229
128.65 2139.120117 -0.00325415 -1.8603E-05
128.64 2139.76001 -7.7691E-05 0.000299138
129.94 2163.120117 0.010105745 0.010917162
130.08 2177.179932 0.00107742 0.006499785
127.96 2164.689941 -0.01629769 -0.00573677
127.31 2146.100098 -0.00507972 -0.00858776
128.69 2159.929932 0.010839714 0.00644417
129.23 2171.370117 0.004196084 0.005296554
128.09 2151.129883 -0.00882148 -0.00932141
128.27 2168.27002 0.001405324 0.007967969
128.77 2161.199951 0.003898027 -0.0032607
128.19 2150.48999 -0.00450417 -0.00495556
128.47 2159.72998 0.00218425 0.004296691
128.74 2160.77002 0.002101689 0.00048156
128.99 2153.73999 0.001941898 -0.00325348
130.24 2163.659912 0.009690673 0.004605905
128.88 2136.72998 -0.01044226 -0.01244647
129.05 2139.179932 0.001319041 0.001146589
127.82 2132.550049 -0.00953121 -0.00309926
127.88 2132.97998 0.000469387 0.000201604
127.54 2126.5 -0.00265871 -0.00303799
128.57 2139.600098 0.008075945 0.006160403
130.11 2144.290039 0.011977864 0.002191971
130 2141.340088 -0.00084545 -0.00137572
132.07 2141.159912 0.015923131 -8.4142E-05
133.28 2151.330078 0.009161747 0.00474984
132.29 2143.159912 -0.00742802 -0.00379773
131.04 2139.429932 -0.00944894 -0.00174041
129.69 2133.040039 -0.01030213 -0.00298673
131.29 2126.409912 0.012337042 -0.0031083
130.99 2126.149902 -0.00228493 -0.00012228
129.5 2111.719971 -0.01137495 -0.00678688
127.17 2097.939941 -0.01799229 -0.0065255
120 2088.659912 -0.05638121 -0.0044234
120.75 2085.179932 0.00625 -0.00166613
122.15 2131.52002 0.011594219 0.022223544
124.22 2139.560059 0.016946369 0.003771974
123.18 2163.26001 -0.00837225 0.011077021
120.8 2167.47998 -0.01932129 0.001950746
119.02 2164.449951 -0.01473515 -0.00139795
115.08 2164.199951 -0.03310364 -0.0001155
117.2 2180.389893 0.018421924 0.007480798
116.34 2176.939941 -0.00733789 -0.00158226
117.79 2187.120117 0.012463513 0.00467637
117.02 2181.899902 -0.00653709 -0.0023868
121.77 2198.179932 0.040591353 0.007461401
121.47 2202.939941 -0.00246363 0.002165432
120.84 2204.719971 -0.00518651 0.000808025
120.38 2213.350098 -0.00380668 0.003914387
120.41 2201.719971 0.000249269 -0.00525454
120.87 2204.659912 0.003820272 0.001335293
118.42 2198.810059 -0.02026975 -0.0026534
115.1 2191.080078 -0.02803581 -0.00351553
115.4 2191.949951 0.002606464 0.000397006
117.43 2204.709961 0.01759097 0.005821305
117.31 2212.22998 -0.0010219 0.003410888
117.95 2241.350098 0.005455622 0.013163242
118.91 2246.189941 0.008139102 0.002159343
119.68 2259.530029 0.006475452 0.005938985
117.77 2256.959961 -0.01595925 -0.00113743
120.31 2271.719971 0.021567471 0.006539775
120.21 2253.280029 -0.00083118 -0.00811717
120.57 2262.030029 0.002994768 0.003883228
119.87 2258.070068 -0.00580573 -0.00175062
119.24 2262.530029 -0.00525574 0.001975121
119.09 2270.76001 -0.00125798 0.003637512
119.04 2265.179932 -0.00041981 -0.00245736
117.4 2260.959961 -0.01377687 -0.00186297
117.27 2263.790039 -0.00110737 0.001251715
118.01 2268.879883 0.006310267 0.002248373
116.92 2249.919922 -0.00923654 -0.00835653
116.35 2249.26001 -0.00487513 -0.0002933
115.05 2238.830078 -0.01117314 -0.00463705
Variance FB 0.00031801 7.45243E-05
Covariance 7.45243E-05
Beta 0.234345857

variance formula in excel: =VAR.P(H3:H254) where h3 to h 254 are daily returns of facebook
Covariance formula excel: =COVARIANCE.P(H3:H254,I3:I254) where h3 to h 254 and i3 to i254 are daily returns of facebook and S&P 500 respectively

Now beta = 0.2343
Rf= 2.5
E(Rm)=7.5

As per CAPM: E(r) of facebook = Risk free rate (Rf)+Beta[E(Rm)-Rf
=2.5+0.2343*(7.5-2.5)=3.67%

jeff jeffy answered 4 months ago
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