A bank account is guaranteed to earn a fixed rate of 6% on a $10,000 deposit over the next year.?

Question:

A speculative investment offers the possibility of 15% earnings on the $10,000 if the investment succeeds and a loss of 5% of the $10,000 if the investment fails. Using what you know about probability and expectation, find the necessary probility of success for the speculative investment to be the better choice.

Answer:
The value of $10,000 at 6% is $600.

That determines the expected value of the speculative investement must be greater than $600 for it to be the better choice.

(10,000 * 0.15) (x) + (10,000 * -0.05) (1-x) = 600
1500x + (-500+500x) = 600
2000x = 1100
x = 1100/2000 = 0.55 or 55%

So if you knew the probability of the 15% earnings outcome occurs 55% of the time, then it would be equivalent to the bank account with the 6% interest.

However, it would be prudent to add a margin of safety to the probability. Something like 25%, so if the positive outcome of 15% return occured 55% * 1.25 = 68.75% it would be a good decision.

You may want to read up on: expected value and modern portfolio theory.

A bank account is guaranteed to earn a fixed rate of 6% on a $10,000 deposit over the next year.?

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