Select the right statement(s).

A coherent measure of risk is:

Sub-additive
Possibly Homogeneous
Translation Invariant
Concave
Monotone

To select the right statement(s) regarding a coherent measure of risk, let's understand what each of these terms means in the context of risk measurement:

- Sub-additivity: A coherent measure of risk is sub-additive if the risk of the combined portfolio is never greater than the sum of the risks of its individual components. In other words, when combining two or more risks, the total risk should not exceed the sum of their individual risks.

- Homogeneity: Homogeneity refers to the property where the measure of risk remains the same when the scale of the investment is changed. A coherent measure of risk is possibly homogeneous, meaning that it may exhibit homogeneity but not necessarily for all scales.

- Translation Invariance: A coherent measure of risk is translation invariant if adding or subtracting a constant from every outcome does not change the risk measure. In other words, the measure of risk should not be affected by a change in the location or the mean of the distribution.

- Concavity: A risk measure is concave if it satisfies the property that increasing the amount invested in a specific asset reduces the overall risk of the portfolio. Essentially, larger investments in less risky assets should decrease the risk of the portfolio.

- Monotonicity: A coherent measure of risk is said to be monotone if it reflects the basic idea that increasing the amount invested in an asset with higher risk should increase the overall risk of the portfolio.

Based on these definitions, the correct statements regarding a coherent measure of risk are:

- Sub-additive (a coherent measure of risk should be sub-additive)
- Possibly Homogeneous (a coherent measure of risk may exhibit homogeneity)
- Translation Invariant (a coherent measure of risk should be translation invariant)
- Concave (a coherent measure of risk should be concave)

Monotone is not necessarily a required property of a coherent measure of risk.