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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 Normal Probability Table see image june 5th data see image Rebalance the delta-hedged portfolio on June 5, 2020. What are the positions on shares, call options, and risk free asset in this rebalanced portfolio?

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 Normal Probability Table see image june 5th data see image Rebalance the delta-hedged portfolio on June 5, 2020. What are the positions on shares, call options, and risk free asset in this rebalanced portfolio?

Survey of Accounting (Accounting I)
Survey of Accounting (Accounting I)
8th Edition
ISBN:9781305961883
Author:Carl Warren
Publisher:Carl Warren
Chapter11: Cost-volume-profit Analysis
Section: Chapter Questions
Problem 11.18E
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S3 Q15

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 Normal Probability Table see image

june 5th data see image

Rebalance the delta-hedged portfolio on June 5, 2020. What are the positions on shares, call options, and risk free asset in this rebalanced portfolio?

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
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
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