Today is June 4, 2020. Stock X is selling at $150 per share. The stock has a dividend yield of 5% per year. There is a call option with an August 18, 2020 expiration date and an exercise price of $145, with an implied volatility of 20%. The annual risk-free rate is 1%, compounded continuously. Shares and options can only be bought and sold in whole numbers. Requires use of normal probability table - see image See image for June 5th data Calculate the value of the delta-dedged portfolio on June 5, 2020 before rebalancing.

Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
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S3 Q13

Today is June 4, 2020. Stock X is selling at $150 per share. The stock has a dividend yield of 5% per year. There is a call option with an August 18, 2020 expiration date and an exercise price of $145, with an implied volatility of 20%. The annual risk-free rate is 1%, compounded continuously. Shares and options can only be bought and sold in whole numbers.

Requires use of normal probability table - see image

See image for June 5th data

Calculate the value of the delta-dedged portfolio on June 5, 2020 before rebalancing. 

Call Option delta=0.564
Change in Option value with respect to change in stock price represent delta.
Value of Option=0.564 x $152=$85.728
Transcribed Image Text:Call Option delta=0.564 Change in Option value with respect to change in stock price represent delta. Value of Option=0.564 x $152=$85.728
Normal Probability Table
IZ
0.02
0.04
0.00
0.0 0.5000 0.5040 0.5080 0.5120 0.5160
0.1 0.5398 0.5438 0.5478 0.5517 0.5557
0.2 0.5793 0.5832 0.5871 0.5910 0.5948
0.3 0.6179 0.6217 0.6255 0.6293 0.6331
0.4 0.6554 0.6591 0.6628 0.6664 0.6700
0.5 0.6915 0.6950 0.6985 o.7019 0.7054
0.6 0.7257 0.7291 0.7324 0.7357 0.7389
0.7 0.7580 0.7611 0.7642 0.7673 0.7704
0.8 0.7881 0.7910 0.7939 0.7967 0.7995
0.9 0.8159 0.8186 0.8212 0.8238 0.8264
0.8413 0.8438 0.8461 0.8485 0.8508
1.1 0.8643 0.8665 0.8686 0.8708 0.8729
1.2 0.8849 0.8869 0.8888 0.8907 0.8925
1.3 0.9032 0.9049 0.9066 0.9082 0.9099
1.4 0.9192 0.9207 0.9222 0.9236 0.9251
1.5 0.9332 0.9345 0.9357 0.9370 0.9382
1.6 0.9452
0.01
0.03
0.05
0.5199
0.06
0.5239
0.5596 0.5636
0.6026
0.07
0.5279
0.5675 0.5714 0.5753
0.6064 0.6103 0.6141
0.6443 0.6480 0.6517
0.6808 0.6844 0.6879
0.7157 0.7190 0.7224
0.7486 0.7517 0.7549
0.7794 0.7823 0.7852
0.8078 0.8106 0.8133
0.8340 0.8365 0.8389
0.8577 0.8599 0.8621
0.8790 0.8810
0.8980 0.8997 0.9015
0.9147 0.9162 0.9177
0.9292 0.9306 0.9319
0.9418 0.9429 0.9441
0.9525 0.9535
0.9616 0.9625
0.9693 0.9699 0.9706
0.9756 0.9761
0.9808 0.9812 0.9817
0.08
0.09
0.5319 0.5359
0.5987
0.6368
0.6736
0.6406
0.6772
0.7088 0.7123
0.7422 0.7454
0.7734 0.7764
0.8051
0.8315
0.8554
0.8770
0.8944 0.8962
0.9131
0.9265 0.9279
0.9406
0.9515
0.9608
0.9686
0.9744 0.9750
0.9798 0.9803
0.8023
0.8289
0.8531
0.8749
0.8830
0.9115
0.9394
0.9505
0.9599
0.9678
l0.9463
0.9474 0.9484 0.9495
0.9545
1.7 0.9554 0.9564 0.9573 o.9582 0.9591
1.8 0.9641 0.9649 0.9656 0.9664 0.9671
1.9 0.9713 0.9719 0.9726 0.9732 0.9738
0.9772 0.9778 0.9783 0.9788 0.9793
2.1 0.9821 0.9826 0.9830 0.9834 0.9838
2.2 0.9861 0.9864
2.3 0.9893
2.4 0.9918 0.9920 0.9922 0.9925 0.9927
2.5 0.9938 0.9940 0.9941 0.9943 0.9945
2.6 0.9953 0.9955 0.9956 0.9957 0.9959
2.7 0.9965 0.9966 0.9967 0.9968
2.8 0.9974 0.9975 0.9976 0.9977 0.9977
2.9 0.9981 0.9982 0.9982 o.9983 0.9984
0.9987 0.9987 0.9987 0.9988 0.9988
0.9633
0.9767
12
0.9842
0.9846 0.9850 0.9854 0.9857
0.9868 0.9871 0.9875
0.9896 0.9898 0.9901 0.9904
0.9878 0.9881
0.9909
0.9931
0.9946 0.9948
0.9961
0.9970 0.9971
0.9979
10.9985
0.9989
0.9992
10.9994
0.9884 0.9887 0.9890
0.9911
0.9932 0.9934
0.9949
0.9962
0.9972 0.9973 0.9974
0.9979
0.9985
0.9989
0.9992
0.9995
0.9916
0.9936
0.9951 0.9952
0.9963 0.9964
0.9906
0.9929
0.9913
0.9960
l0.9969
0.9978
0.9984
0.9989
0.9992
0.9980
0.9986
0.9990
0.9993
0.9995
0.9996 0.9996 0.9996
0.9997
0.9981
0.9986
3
3.1 0.9990 0.9991 0.9991
3.2 0.9993 0.9993 0.9994 0.9994 0.9994
3.3 0.9995 0.9995 0.9995
3.4 0.9997 0.9997 0.9997
3.5 0.9998
3.6 0.9998 0.9998 0.9999 0.9999 0.9999
3.7 0.9999 0.9999 0.9999 0.9999 0.9999
3.8 0.9999
3.9 1.0000
4
0.9990
0.9991 0.9992
0.9993
0.9995
0.9997
0.9998
0.9994
0.9996
0.9997
0.9998
0.9999
0.9999
0.9999
1.0000
1.0000
0.9996 0.9996
0.9997 0.9997
0.9998 0.9998
0.9997
0.9998
0.9999
0.9999
0.9999
1.0000
1.0000
0.9997
0.9998 0.9998 0.9998
0.9999 0.9999 0.9999
0.9999
0.9999 0.9999
0.9998 0.9998
0.9999
0.9999
1.0000
1.0000
0.9999
0.9999
1.0000
l0.9999
1.0000
1.0000
0.9999
1.0000
1.0000
0.9999
1.0000
1.0000
1.0000
1.0000 1.0000
1.0000
1.0000
1.0000
Transcribed Image Text:Normal Probability Table IZ 0.02 0.04 0.00 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.5 0.6915 0.6950 0.6985 o.7019 0.7054 0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8413 0.8438 0.8461 0.8485 0.8508 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 1.2 0.8849 0.8869 0.8888 0.8907 0.8925 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 1.5 0.9332 0.9345 0.9357 0.9370 0.9382 1.6 0.9452 0.01 0.03 0.05 0.5199 0.06 0.5239 0.5596 0.5636 0.6026 0.07 0.5279 0.5675 0.5714 0.5753 0.6064 0.6103 0.6141 0.6443 0.6480 0.6517 0.6808 0.6844 0.6879 0.7157 0.7190 0.7224 0.7486 0.7517 0.7549 0.7794 0.7823 0.7852 0.8078 0.8106 0.8133 0.8340 0.8365 0.8389 0.8577 0.8599 0.8621 0.8790 0.8810 0.8980 0.8997 0.9015 0.9147 0.9162 0.9177 0.9292 0.9306 0.9319 0.9418 0.9429 0.9441 0.9525 0.9535 0.9616 0.9625 0.9693 0.9699 0.9706 0.9756 0.9761 0.9808 0.9812 0.9817 0.08 0.09 0.5319 0.5359 0.5987 0.6368 0.6736 0.6406 0.6772 0.7088 0.7123 0.7422 0.7454 0.7734 0.7764 0.8051 0.8315 0.8554 0.8770 0.8944 0.8962 0.9131 0.9265 0.9279 0.9406 0.9515 0.9608 0.9686 0.9744 0.9750 0.9798 0.9803 0.8023 0.8289 0.8531 0.8749 0.8830 0.9115 0.9394 0.9505 0.9599 0.9678 l0.9463 0.9474 0.9484 0.9495 0.9545 1.7 0.9554 0.9564 0.9573 o.9582 0.9591 1.8 0.9641 0.9649 0.9656 0.9664 0.9671 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9772 0.9778 0.9783 0.9788 0.9793 2.1 0.9821 0.9826 0.9830 0.9834 0.9838 2.2 0.9861 0.9864 2.3 0.9893 2.4 0.9918 0.9920 0.9922 0.9925 0.9927 2.5 0.9938 0.9940 0.9941 0.9943 0.9945 2.6 0.9953 0.9955 0.9956 0.9957 0.9959 2.7 0.9965 0.9966 0.9967 0.9968 2.8 0.9974 0.9975 0.9976 0.9977 0.9977 2.9 0.9981 0.9982 0.9982 o.9983 0.9984 0.9987 0.9987 0.9987 0.9988 0.9988 0.9633 0.9767 12 0.9842 0.9846 0.9850 0.9854 0.9857 0.9868 0.9871 0.9875 0.9896 0.9898 0.9901 0.9904 0.9878 0.9881 0.9909 0.9931 0.9946 0.9948 0.9961 0.9970 0.9971 0.9979 10.9985 0.9989 0.9992 10.9994 0.9884 0.9887 0.9890 0.9911 0.9932 0.9934 0.9949 0.9962 0.9972 0.9973 0.9974 0.9979 0.9985 0.9989 0.9992 0.9995 0.9916 0.9936 0.9951 0.9952 0.9963 0.9964 0.9906 0.9929 0.9913 0.9960 l0.9969 0.9978 0.9984 0.9989 0.9992 0.9980 0.9986 0.9990 0.9993 0.9995 0.9996 0.9996 0.9996 0.9997 0.9981 0.9986 3 3.1 0.9990 0.9991 0.9991 3.2 0.9993 0.9993 0.9994 0.9994 0.9994 3.3 0.9995 0.9995 0.9995 3.4 0.9997 0.9997 0.9997 3.5 0.9998 3.6 0.9998 0.9998 0.9999 0.9999 0.9999 3.7 0.9999 0.9999 0.9999 0.9999 0.9999 3.8 0.9999 3.9 1.0000 4 0.9990 0.9991 0.9992 0.9993 0.9995 0.9997 0.9998 0.9994 0.9996 0.9997 0.9998 0.9999 0.9999 0.9999 1.0000 1.0000 0.9996 0.9996 0.9997 0.9997 0.9998 0.9998 0.9997 0.9998 0.9999 0.9999 0.9999 1.0000 1.0000 0.9997 0.9998 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9999 0.9999 1.0000 1.0000 0.9999 0.9999 1.0000 l0.9999 1.0000 1.0000 0.9999 1.0000 1.0000 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
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