Volatility exposure in the Conditional Factor Model for Hedge Fund Strategies

I am being thrown off by the volatility exposure factor in the conditional factor model in hedge fund strategies.
Can someone pls confirm if the 2 points listed are correct?

  1. Positive exposure means we are long volatility. We can be long volatility with either a long call or a long put or long VIX futures
  2. Negative exposure means we are shorting the volatility which means we sold either calls or puts

Now trying to understand the conditional factor model.
Let’s assume that in a normal situation, we are long the equity and long volatility. The reason we took long vol was to have protection in case markets were expected to be volatile and we know that equity and volatility have a negative correlation. So if equity goes up, it means markets are not so volatile. Can we say we win from both positions?

What if we have short equity and long vol. Equities are down which means we are in a volatile market. Is my understanding correct?

Lastly, during a crisis, let’s assume, we have negative exposure to both equities and volatility. Ok I understand we are shorting equities because markets are in stress times, but why does the exposure of vol is turn negative, like why we are selling vol? Don’t we need more protection during bad times? From fixed-income chapters, I thought we sell volatility when markets are calm so we can collect the premium

No.

Think of your volatility position as a hedge on your equity position: when equities are up, volatility is likely down, and vice versa. Equity position first, volatility position second, as a hedge. That should answer all of your questions.

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ok so I think I got half of it

  1. Long equity and long vol - equity markets are up, but as a hedge, I will also buy volatility to protect myself from higher volatility ( during normal times)
  2. Short equity and short vol - equity markets are down, but in case markets go up, then I should also have volatility exposure so I sell it?
    I think I just confused myself even more because when I read the table during normal and crisis, I cant make a sense of it and I feel I cant make the connection with the actual strategy, the inherent correlation between equity and volatility, and also if we are long or calls/puts/futures based on the signs of the coefficient. I went over the reading and I felt it made sense, but in front of a problem it literally throws me off