A deviating, but more natural definition of risk

In Modern Portfolio Theory, Risk is defined as a quantified return uncertainty. Every deviation, up or down, from the expected return is considered a risk and thus bad. Typically, returns are assumed to be normally distributed around a mean. Consequently, the risk measure is symmetric.

Our definition is different:

• First, the risk definition we use here refers to values and not returns (returns are the first difference of value over time).
• Second, we consider value increases as good and value decreases as bad.
• Third, we use an asymmetric risk definition: the shape of up and down value risks do not need to match.

Technically, we use lognormal distribution of values in our calculations.