If income strategies do well in calm markets, it stands to reason that they will do poorly if markets make a big move, either up or down.
If markets are trending strongly upwards, a covered call strategy could see a good portion of its market gains disappear. If a call is written, say, 2% out of the money and the market goes up 6%, the strategy will not enjoy the full upward move in the market. The gains to the strategy will be capped. The strategy essentially sold off the unknown potential for gains for the known gain of the option premium. This should be viewed as an opportunity cost.
Inability to Hedge Large Drawdowns
But the bigger risk to most income strategies happens when markets sell off. A covered call strategy consists of two parts: a traditional long position and some short calls. If markets sell off significantly, the premium collection from the short calls might offset a bit of the downward move in the long portfolio. However, in the face of a significant sell off the long portfolio is unhedged and premium from selling calls is unlikely to fully offset losses.
A put-write strategy has a similar risk-return profile. The cash position will help insulate against a market sell-off, but the short puts expose the strategy to losses the more the market goes down.
Finally, one of the biggest risks to any strategy that writes options is leverage. If a strategy opts to write two, three, four, or more options against their collateral positions, the potential for losses can accelerate quickly. Many of the well-publicized blow-ups in derivative strategies can be blamed on leverage more than anything else.