bk 4 pg. 193 "assume management has entered a fix 4 float swap to offset cf risk of floating rate liability; a transaction that increases the net duration of the liabilities w/o affecting the net duration of their assets. *If int. rates increase, the mkt val of the firm (i.e. equity value) falls less than if they had not entered the swap, cuz the relative changes in values if its assets and liabilities.* . . “Since the fix for floating swap has increased liability duration w/o changing the duration of assets, the duration of firms equity has fallen… *This means the mkt value of the firm’s equity is less sensitive to changes in interst rates, so it will not benefit as much from falling rates”… * My question is if the firm entered into fix for floating, say swap rate @ 1%, and then LIBOR went up to 20%… HOW DOES THE EQUITY VALUE OF A FIRM “FALL”, let alone “LESS” than if it “DIDN’T ENTER SWAP”… they would have been paying 20% on their loans now, (even though duration of liabilities would have been lower), so MKT VALUE of equity would have went DOWN if no swap right? but wouldn’t mkt value go UP if they did enter swap, since there is less interest expense, thus higher Net Income, thus higher equity value? Am I missing something? Also, the “mkt value of firm’s equity is LESS sensitive to changes in interest rates”… after entering into swap? The duration of liabilities go UP, thus MORE sensitive to interest changes after entering swap right? SO… if Liabilities more sensitive to interest changes, wouldn’t the equity value ALSO be MORE sensitive to interest changes, hence larger duration?.. if I had a duration of 99 (from say 1 pre swap) and my liabilities are going up/down like crazy to interest changes, wouldn’t my equity value ALSO BE GOING CRAZY (more sensitive) TO INTEREST CHANGES? (I.E. HIGHER duration) Please help… I’ve spent too much time on this one page… I think I’m officially crazy…
This is a complete guess – I don’t have the books in front of me and, scary as this is, I have absolutely zero recollection of the section you’re talking about. But here goes: Before the swap, if rates increased, PV of the firm’s assets would decrease due to lower present value/higher discount rate. With floating rate liabilities, the duration of liabilities would be close to zero, so the value of the firm’s liabilities wouldn’t change. Since equity value = assets - liabilities, if assets decline in value and liabilities stay roughly the same, equity value decreases. Now we swap fixed 4 float. Duration of liabilities is now positive. If rates go up, asset value still decreases, but with positive duration, the value of liabilities also decreases. So although equity value may go down, liabilities have gone down as well, dampening the effect of the decline in asset PV, making equity value less sensitive to the change in rates. Does any of this sound at all plausible? I dunno, I think I 'm gonna give up for the night and go watch some tv like I’d been planning to. Yeah, I think that’s best… Enough is enough…
A = L + E DA = DL + DE Hence when DL goes up, DE must come down to keep the balance.