Short term price volatility? nope
market meltdown? sounds plausible, actually it is the market risk, not risk tied to the specific stock(s) you are holding.
Geographical/political risk? for example, if Hugo Chavez is areally a maniac guy, HNR is a very risky investment. If military conflicts outbreak in taiwan straight, I will dump OVTI immediately.
However those are things we cannot control, let's just focus on what we can control. When I claimed that ASPV, SIGA are low risk holders, people may not agree with me. However the truth is the shares you are holding are the certificates of partial ownership of the company. If the company's business has very low downside risk, then your partial ownership has very little downside. Also your price paid to get that partial ownership really matters, leave enough margin of safety to yourself.
When I am trying to find such buy-holders, the downside risk of the business is really all I care about.