A commenter on another site asked whether it would be simpler to calculate Black-Scholes or another options pricing model in an Excel spreadsheet than to spend three seconds entering a position into Portfolio Armor. My academic finance consultant, the all-but-dissertation Ph.D. candidate in finance who developed Portfolio Armor’s algorithm, offered this response:
Seems like the person who left that comment doesn’t really understand what Portfolio Armor is supposed to be doing (or option pricing models for that matter). The Black-Scholes formula is used to compute prices and hedge ratios for options. It will not tell you which contracts provide the optimal level of protection to preserve your wealth in a stock or ETF holding, given the market prices. An investor would use an option pricing formula (such as Black-Scholes) if he/she does not think the market quotes represent the “true” price of the option… so you put in the strike, the expiration, the stock price, the risk-free rate, and the volatility; then the model will spit out a price for the option assuming the model is “right” (if you believe markets are efficient then the model just serves as a check on the validity of the underlying assumptions).
Breaking up a block of text with the Porfolio Armor logo
Most option pricing models will also give you a “hedge ratio” which says how many shares of stock you would have to buy (sell short) for every 1 call option sold (or bought) so that the P&L on the option is canceled out by the P&L on the stock position. The problem with model-implied hedge ratios is that they will change every time the underlying asset price (stock or ETF price) changes; so in order to maintain a perfect hedge- where every $1 loss on the option is offset by a $1 gain in the stock- the investor/trader must “dynamically hedge” meaning he/she has to continuously buy and sell the stock and options to modify the ever-changing hedge ratio… while in theory this should work perfectly, the existence of transaction costs completely eats away at the benefits of attempting such dynamic hedge strategies.
Recall that Portfolio Armor, on the other hand, maintains a static hedge ratio of close to 1 giving them a more conservative position and the potential to make more money than they loose should the stock fall in price (remember the concept of “positive hedge error”… I think that’s what we called it? [We called it "positive hedging error"]).
So basically, the points are:
* Portfolio Armor gives you the optimal protection strategy (number of options and specific choice of contract) at the lowest possible cost, given current market prices
* Option pricing models say nothing about which contract is the optimal choice for a particular investor’s objective (i.e. cap losses at 20%, etc.)
* Option pricing models seek to find the “true” price conditional on the model assumptions
* Portfolio Armor is non-parametric and is not vulnerable to model error (resulting from flawed model assumptions)
* Option pricing models can give you a hedge ratio so that P&L gains in one position perfectly offset P&L losses in the other position, but they require continuous and dynamic re-balancing of the hedge portfolio
* Portfolio Armor maintains a static and conservative hedge ratio, and by taking the cost of the options into account, does so in the most economical (“cheapest”) way for the investor
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