Answer:
$274.95
Step-by-step explanation:
The mean return for the option is:
[tex]\mu=100*0.70-500*(1-0.70)\\\mu=-\$80[/tex]
The variance and standard deviation are given by:
[tex]V=x_1^2p_1+x_2^2p_2-\mu^2\\SD=\sqrt V[/tex]
Where "x" represents the possible returns ($100 and -$500), and "p" represents their respective likelihoods (70% and 30%). The standard deviation is:
[tex]V=100^2*0.7+(-500)^2*0.30-(-80)^2\\V=75,600\\SD=\sqrt 75,600\\SD=\$274.95[/tex]
The standard deviation of the day trader's option value is $274.95.
