Question

Let's observe three distinct styles of investing $1000. The profits are evaluated in the following three ways:

Style No. 1:

$10 000 profit with probability 0.15 and $1000 loss with probability 0.85.

Style No. 2.

$1000 profit with probability 0.50 $500 profit with probability 0.30 and $500 loss with probability 0.20.

Style No. 3:

Guaranteed $400 profit.

a) Which investment style has the best expected value?

b) Which investment style has the greatest risk?

c) Which metod would you prefer?

Thank you for your input!

Answer 1

I'll take a crack at it. Just letting you know that i'm starting it (i saw your chat)

Answer 2

Thanks mate!

Answer 3

Expected value is a term for over the long run (as trials approaches infinity) what should the value end up being. The formula is:
Expected value = Summation of: Gains(Probability) + Losses(Probability)
Style 1 Expected Value: 10,000*.15 + (-1000)*.85 = 1500-850 = $650 net expected gain
Style 2 EV = 1,000*.50 + 500*.3 + (-500)*.2 = $550 net expected gain
Style 3 EV = $400 guaranteed profit
A.) Style 1 has the highest (best) expected value
B.) Look to the potential losses in the worse case scenario for each style of investment. Style 3 has 0 loss, so ignore it. Style 2 has a potential of $500 loss and Style1 has a potential of $1000 loss.
So Style 1 has the greatest risk.
C.) This is your own preference depending on your fiscal leanings. Some people are risky (Style 1), some people don't like risk at all (Style 3), and some are in between (Style 2)
Pick whatever you want.
I'd personally pick Style 3 and invest tons of money - > guaranteed profits. Can't lose. 40% investment return is huge. normally it's around 8%.

Answer 4

Thanks a ton for the thorough answer!

Answer 5

You're welcome. I'm procrastinating my calc homework :p

Answer 6

Lol I do that too :D