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Expected value, Variance, Covariance

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Expected value, Variance, Covariance.Need help answering the below questions / please provide steps taken to get to answer ASAP! Thanks

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Stock A is sold for $1.

Each day, it increases by 80% (to a value of $1.8) with probability 0.5, or decreases by 20% (to

a value of $0.8) with probability 0.5. The movement each day is independent of other days.

(2) If you buy stock A today for $1, what is its expected value tomorrow?

 

(2) If you buy stock A today, what is the standard deviation of its value tomorrow?

 

(3) If you buy stock A today, what is its expected value and standard deviation in

two days?

 

Another stock, stock B, is traded in the market and has the following behavior. If stock A goes

up by 80% (which occurs with probability 0.5) then stock B goes down by 80%, and if stock A

goes down by 20% (which occurs with probability 0.5), then stock B goes up by 20%.

 

(4) If you take $1 and split it equally into the two stocks (i.e., 50 cents in each),

what is the expected value of the portfolio value in $'s after one day?

 

(5) What is the correlation coefficient between stocks A and B? Note: no need for a

rigorous derivation and calculations just state the answer and explain your reasoning...