You have two functions. The first returns an integer between zero and ten, while the second returns any real value between zero and ten. If you get paid based on whatever value is returned, which payoff function would you rather have?

I am looking at this question that trading companies sometimes ask, and I understand the expected value for both is 5, but the variance for the 1st is 27/2> 25/3 which is the variance for the 2nd.

Is there any other consideration. If not I presume investors pick investments that have the same expected value with lower variance, so would be inclined for the uniformly distributed returns.

I am actually interested generally, as from my primitive understanding, the proposed variance and expected value, and other moments, are surely the main thing that drives an investment decision.

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    The larger the variance, the further the data points are away from the mean and the higher the risk. Low variance is suitable for conservative investors with a lower risk tolerance. Higher variance is good for aggressive traders who are less risk averse. My guess is that if this question is posed by a trading company, they want the answer to be high variance. – Bob Baerker Jun 22 '18 at 16:04

Based on This question, volatility and variance are fairly well related in that variance represents (sigma squared) where volatility is an observed measure of (sigma). This means that variance can give you an idea of how volatile the asset can be, where volatility is a measured or observed metric describing how much the asset fluctuated in value over a specified time period.

That being said, if you're only given variance, the smaller variance leads to smaller potential volatility leads to a less risky investment, given the same Expected Value. Beyond that, it's entirely dependent on the opinion and risk-adversity of the individual/firm in question.

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  • I don't see how this answers the question. OP asks whether variance is or is not beneficial to the value of an investment; this answer claims but does not give evidence that smaller variance = less risk, and does not say whether risk is good or bad. – dg99 Jun 22 '18 at 22:20
  • @dg99 The second paragraph of my answer says "it's entirely dependent on the opinion and risk-adversity of the individual/firm in question", I can bold that line if it's not clear that the answer stems from that. – GOATNine Jun 25 '18 at 11:08

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