A typical device used in designing company strategy when financial outcomes depend strongly on a market price is a so-called “hedge report” or “sensitivity report” that shows the change in profits or market value associated with a positive or negative change in the underlying market price (which is sometimes called a “risk factor”).    When portrayed on a graph, with the risk factor change on the horizontal or “x” axis and the profit change on the vertical or “y” axis, the relationship between profit and risk factor can take on a variety of shapes.  If the shape is a line with a positive slope, we say that the company is “long” the risk factor.  For example, the profit profile of a gold miner would generally increase as the price of gold rises.  If the shape is a line with a negative slope, we can say the company is “short” the risk factor.  An example of this might be an airline company where profits decline sharply as the price of a major input, like oil, rises.

Sometime the relationship between profit and risk factor is non-linear, like a parabola facing upwards or downwards.  If the parabola faces upwards, this means that the profit increases when the risk factor rises or falls, and we call this profile a “smile.”  Generally, smiles occur when a company owns valuable options that can be profitably deployed as market conditions change.  If the parabola faces downwards, so that profit declines when the risk factor rises or falls, we call this a “frown.”  Frowns occur when a company has sold options.  Financial intermediaries often “sell” valuable options to their customers, and therefore have risk profiles that are frown-like.  A typical example would be a mortgage lender that provides loans with the ability to refinance with no penalty (this is called a prepayment option).  Another example would be a bank that offers deposit customers the option to withdraw funds before maturity at no charge.

Naturally, there can be combinations like a long or short exposure to a risk factor along with owning options – a “smirk” – or a long or short exposure to a risk factor along with selling options – a “grimace.”

It seems clear that it would be better to have a smile than a frown (or a smirk over a grimace).   This way, profits tend to rise when conditions change (or, rise more in good times than they decline in bad times).  However, the business model of many financial intermediaries is intentionally to run a frown or a grimace and to rely on risk management expertise to prevent a major debacle.

Why run a frown?  One reason that a financial institution might run a frown is that competition forces the company to offer attractive options to customers. A cynic might argue that financial institutions offer complex options to customers comfortable with the notion that the customer won’t have the financial sophistication to exercise them optimally.  While that may be cynical, it certainly is reasonable to assume that the vast majority of retail customers do not have options sophistication.  Consider again the case of a mortgage refinance. The typical decision rule promoted by mortgage lenders is that the borrower should refinance whenever the present value of future loan payments will decline due to the refinance, or worse, simply if the monthly mortgage payment drops after the refinance.  The effect of these rules is to exercise sub-optimally; to refinance much more frequently (in a falling interest rate environment) than is optimal. This is because these strategies ignore the potential economic benefit of waiting for a further interest rate drop.  Every refinance means substantial profit for the lender, but may involve giving up a potential benefit for the borrower.

Sub-optimal exercise of the options customers own is a major factor reducing the risk to a financial institution of running a frown. Another way to mitigate the risk is to adopt a hedging strategy that consists of going long options.  In general, this can be done in two ways; either by buying options outright in the options market or by attempting to replicate an option by engaging in a dynamic trading strategy in the underlying futures or cash market.  Sometimes this dynamic trading strategy is referred to as “delta hedging.”  Every institution determines the optimal hedge for itself (which could be no hedge), both in terms of magnitude and approach.  The totality of such company-level decisions has a major bearing on financial stability.

In theory, it doesn’t matter if you buy an option outright or synthetically create one through delta hedging.  In practice it does.  The strategy of buying options outright (assuming markets exist for the appropriate options) is generally considered, in “sophisticated” circles, to be an expensive way to run a hedge.  This is because the cost of the options is crucially dependent on the volatility of the underlying risk factor that is embedded in the market price of the option.  Empirical research has shown that it is generally the case that the implied volatility is an upwardly biased estimate of future realized or “actual” risk factor volatility.  Therefore, it is advisable to run the synthetic hedge rather than the outright option purchase.

A problem with the sophisticated approach is that it can be de-stabilizing for the entire market.  The essence of the delta hedging strategy is to “buy when the price rises and sell when the price falls.”  This is sometimes called “positive feedback trading” and tends to create more volatile swings in asset prices – bigger booms and bigger busts.  This may be an instance in which a strategy is “smart” in a micro sense, but not from a macro perspective.

How do you tell if you have a frown or smile or some other feature?  The most straightforward way is to conduct scenario analysis, where you shock important risk factors up or down and trace through the implications on profit or market value.   There is an art to scenario analysis, which we’ll address in a future essay.