A short sale has a limited gain potential, but an unlimited loss. If we short a stock at $50, it can only go down to $0, but it could rise to $500. Without a hedge or predefined exit strategy that limits the risk, the risk of $500 vs. a potential gain of $50 is an asymmetric risk.
Symmetric risk is when the risk and reward payoff are equal. An example of a symmetric risk could be an option collar. A collar constructed with options typically starts out with a gain and loss that are the same. The collar is a protection position constructed by buying an out of the money put option and selling an out of the money call option.
The out-of-the money put option is limits the loss in the underlying position and locks in a profit.
The price paid for the puts is offset by the premium collect by selling the out of the money call. The call puts a collar on the upside similar to the downside, giving the strategy a limited risk and limited reward: a symmetric risk. However, the position is structured to allow the underlying position to continue to gain some before the short call caps the gain.
Keywords: Symmetric Risk, Symmetrical Risk Reward, Symmetrical Payoff, Symmetry