Investment A has an expected return of $25 million and investment B has an expec

Question

Investment A has an expected return of $25 million and investment B has an expected retun of $ 5 million. Market risk analysts believe that standard deviation of the return from A is $10 million and for B is $30 milion (negative returns are possible here)

A) If you assume returns follow a normal distribution, which investment would give a better chance of getting at least a $40 million return?

B) How could your answer in part A change if you knew returns followed a skewed distribution instead of a normal distribution?

Explanation / Answer

Solution:-

a)Return A: Probablity that the expected return will be greater than or equal to $40 is given by,Let X be the returns.
P ( X 40) = 1 P(X<40)
We standardize it and get
1 - P(Z<1.5) = 1 - 0.933 = 0.067
Return B: Probablity that the expected retirn will be greater than or equal to $40 is given by:
P ( X 40) = 1 P(X<40)
= 1 - P(Z<1.16667)
= 1 - 0.8781
= 0.1219

b) if there would have been a skewed distribution then the probablities will remain the same ,they will depend on if the distribution is positively skewed or negatively skewed

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