Symmetrical risk implies that the movement of a particular contract or an asset in either direction leading to a corresponding impact – be it positive or negative – on the net position value.
In an Unsymmetrical risk; the similar impact is unequal.
Example: If a Mutual Fund is holding 1000 shares of a particular company; say RIL. An increase of decrease in the price of the instrument (shares of RIL in this example) will lead to change in the value of the portfolio in either direction by equal value (value of prince change multiplied by number of shares on both direction: positive or negative)
On the other hand, assuming if the same Mutual Fund has an Option contract – say Put Options to be precise – on the same shares; an increase in the price of the shares of RIL in the cash market beyond the strike price would result in a decline in the value of the option contract held. However any further price movement on the higher side would not result in an equal fall in the value of the option contract. And after certain value of the same shares in the cash market, the value of the Option contract may be worthless (taking strike price and premium into account)