This is what happens when people discourage you from studying FRM and justify the all pervasive nature of CFA. Don’t get me wrong. In no way, am I being sarcastic. I also underwent this sort of confusion.
The core to this problem lies in NOT understanding the real purpose of Derivatives , which are mainly two: 1. To speculate ( Even with Jim Simmons, Peter Lynch, Bill Gross,CFA or Mark Howard,CFA) and if you do it enough number of times over an elongated period especially with uncovered naked position - you would lose. I can underwrite a bond on this.
The second (and the most apt) purpose is to HEDGE. Hedging is essentially a SHORT TERM tool.
So the real purpose of doing the above exercise of borrowing, investing, re investing, shorting is to hedge the underlying for a LIMITED time frame.
Discard the notation and the formulas presented and apply your logic to it. You would see the risk manager has perfectly hedged his position irrespective of the underlying’ movement over the horizon. Earning rf for a LIMITED time frame on your investment asset is much better than selling (and thus incurring brokerages, t.c., taxes) and re investing (incurring brokerage, t.c., taxes) ESPECIALLY when your short term prospect of the asset is not encouraging. So you don’t wanna sell yet you wanna hedge.
Another aspect to consider is even if you seek today and buy after the bleak period is over your anticipation might have been wrong and the stock appreciates . So you end selling cheap today just to recapture the same at a higher price. Loss, is not it.
I hope you like the above explanation and your doubts are rested to peace.
Do consider studying FRM. Having done both , I can perhaps say wit some degree of confidence, FRM is in its limited scope ( It is not all pervasive) is a much better if not advanced course than any other financial certification or charter.