Suppose that Susan has $100 to invest in two alternative assets.

Asset A offers a return of 10% with probability .5 and a loss of 8% with probability .5.

Asset B can gain 16% with probability .5 and lose 10% with probability .5. Gains and losses of the two assets are completely unrelated and Susan cannot purchase a portfolio of the two assets.

Basically she has to choose between two actions:

Action 1: Invest the $100 in asset A.

Action 2: Invest the $100 in asset B.

If Susan is risk averse,

Question

Suppose that Susan has $100 to invest in two alternative assets.

Asset A offers a return of 10% with probability .5 and a loss of 8% with probability .5.

Asset B can gain 16% with probability .5 and lose 10% with probability .5. Gains and losses of the two assets are completely unrelated and Susan cannot purchase a portfolio of the two assets.

Basically she has to choose between two actions:

Action 1: Invest the $100 in asset A.

Action 2: Invest the $100 in asset B.

If Susan is risk averse,

BlackTom AI · Accepted Answer

Here we restate the scenario and the single answer option to ground the analysis.
Question: Susan has $100 to invest in one of two assets. Asset A yields +10% with probability 0.5 and -8% with probability 0.5. Asset B yields +16% with probability 0.5 and -10% with probability 0.5. The two assets are unrelated and she cannot mix them. If Susan is risk averse, which action should she take? 
Option presented: "it is impossible to say which actions she chooses without knowing he utility function"

Now we evaluate the reasoning for this option and the surrounding considerations.
First, note that the choice under risk depends on Susan's utility function, not only on expected returns. Risk-averse behavior is captured by how Susan values certain outcomes versus uncertain ones, which is encoded in her utility function. Therefore, without specifying or at least assuming a utility function, we cannot determine which asset she would prefer.
Consider the two assets: Asset A has an expected return of 1% (0.5×10% + 0.5×(-8%)) and Asset B has an expected return of 3% (0.5×16% + 0.5×(-10%)). If Susan were choosing purely on expected return without regard to risk, Asset B would be preferred. However, risk aversion highlights the trade-off between higher potential gains and larger potential losses; it is possible for a risk-averse person to prefer the asset with the smaller variance if the utility of losses is weighted more heavily than the utility of gains.
Next, consider what happens if we try to evaluate this using familiar risk measures. The variance (or standard deviation) of outcomes differs between the two assets, and the introduction of a concave utility function (as in risk aversion) will generally tilt preferences toward less volatile options, all else equal. But whether Asset A or Asset B is preferred hinges on how steeply Susan discounts risk in her utility, which is not specified here.
Therefore, without knowing Susan’s utility function (or at least a qualitative description of her risk preferences), we cannot definitively declare which action she would take. The statement that it is impossible to say without the utility function accurately captures this core point and avoids making an unfounded assumption about her risk attitude.
In summary, the key source of ambiguity is the missing information about Susan’s utility function. The two assets offer different expected returns and different risk profiles, and risk aversion alone does not fix the choice without specifying how Susan values outcomes in both gain and loss regions.

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