In Table 5.2 the fifth line gives the gain expectation for $5 OTM 30 day covered calls as 0.242 with probability of a gain as 54 %. Since the gain could be anywhere between 0 and 5.36, assume it is the mid-point, 2.68. Further assume that the trade loses $1 36 % of the time. How much does it lose the remaining 10 % of the time? Under these conditions, what is the Kelly fraction of ones portfolio to be allocated to this investment?

Data given in table 5.2

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Table 5.2 Gain expectation for covered call trades So $80.00, r= 1%, μ =4%, d= 20% = Trade Time Price Amt to at expir. risk 82.50 call 82.50 call 82.50 call 85 call 15 0+ 30 0+ 45 1.27 78.73 0+ 15 0.10 79.90 0+ 0.43 79.57 0.89 79.11 85 call 30 85 call 45 Total Gain Ex- loss prob pected prob(%) (%) gain 0.36 79.64 0.64 0+ 79.36 0+ 56 0.110 59 0.200 0.295 0.121 0.242 0.337 61 52 54 56 Gain rate (%) 4 3 تت تت م م شت 3 3