Balanced Option Hedge published to Wall Street pre-1973

The company Arnold Bernhard & Co. Inc. distributed to Wall Street firms in the late 1960 sheets with Balanced Hedge Ratios on a series of warrants and convertible bonds, what we today would call delta neutral hedge. Personally I like the term "balanced hedge" better than market neutral delta hedge. We do not know the standard deviation of the lifetime of the option (and even less about the future tails), and as the delta often is sensitive to the volatility used in modern delta calculations (watch your DDeltaDVol as described in my Know Your Weapon) we simply do not know the market neutral delta hedge. And even if you knew the standard deviation of the future, delta hedging would still fail dramatically as an argument for risk neutral valuation due to discreteness and in particular due to price-jumps in practice.

Arnold Bernhard & Co in 1970 also published a booklet describing how one could run a very low risk often good upside portfolio by going long warrants or convertible bonds and putting on a balanced hedge using the underlying asset. Such a portfolio was in many ways immune for the errors in delta hedging (delta replication risk is not symmetrical). Any big jump and you made profit. This was not enough to give you an edge, you could simply not buy options and put on balanced hedge (except as pure insurance policy), it was also important to try to distinguish between what likely was over or undervalued options (easier said than done), but if successful at it this was a rather robust strategy, at least you could not blow up.

It is also a myth that knowledgeable traders fully aware of the large replication error in the BSM delta hedging argument simply are buying options and hoping for a Black-Swan-Event. All we say is to truncate your tails. When options according to your analysis are extremely overpriced there exist several ways to take in option premium and still truncate your tail.

Arnold Bernhard & Co. 1970: More Profit and Less Risk --- Convertible Securities and Warrants.