Adding a Hedging Choice

by Jay Pestrichelli on December 14th, 2012

When hedging, there are a few main concerns to consider. What is the max loss you’re willing to take and what is the cost of that protection. Of course when investing time horizon and targets for growth are also a consideration, but for the protection part, let’s focus on the first two points.
Step 1: Define CaR (Capital at Risk):
This is the amount you’re willing to endure to the down side. Typically we hear that range from 10-20% Of course no one wants any losses, but the reality is enduring market fluctuations is part of investing.  For this article, we’ll use 15% as the most client John Smith is willing to lose.

That exposure can be constructed in many ways. The first and most common way we discuss is to buy a put that is 15% below the market for all shares Mr. Smith owns. In this case if the market drops by significantly the max loss would limited 15% (excluding hedging costs, which we’ll get to).

However you can also consider buying protection on only 90% of the portfolio with puts that are 5% below the market.  In that scenario 90% of the assets will stop losing after a 5% decline and the other 10% has exposure to a full 100% loss. That works out to a 14.5% weighted exposure.
The question that arises is if it is really sensible to expect a 100% decline in the market. That leads us to the next step.
Step 2: Set Market Max Loss by Time
In our book: Buy and Hedge, we talk about hedging in many ways, sometimes absolute and other times as partial hedges. For this post we’re going to consider how making some assumptions about what isn’t going to happen can impact expenses and prevent over hedging.  For example, let’s assume that the market isn’t going to decline more than 50% in say, 6 months. By the way, even in the worst 6 month of the credit crisis between Sep 2008 and Feb 2009, the market didn’t decline more than 50%, so that’s probably a pretty safe assumption.  If we want to make this assumption, then there’s no need to insure against it or buy protection for it.   This would allow us to re-weight how many puts to buy.
In the example above, if we want to limit our downside to 15%, we can still buy 100% protection at the 15% downside limit. Or we can buy 90% protection at 11% below the market and leave 10% unhedged Both work out to a 15% risk IF you assume the market won’t decline more that 50%.
On a side note, using indexes or index based ETFs reduce the chance of a large decline vs single stocks. There are plenty of stocks that have declined 50% in one month, so we recommend careful consideration if using this approach with individual names.  
Step 3: Calculating the Costs
The costs of these scenarios is very different and for good reason…probabilities. Option prices reflect probabilities of it expiring in-the-money (ITM). For put protection, going ITM means the stock or index is not lower than our protection level and the hedge is paying off in the form of offsetting gains.

The higher the probability that the option goes in the money, the more expensive it is as reflected by its premium. These probabilities are not linear though. The probability of a stock going down 7.5% compared to that same stock or index going down 15% is not half. The probability of a 7.5% move is more than double the probability of a 15% move (think bell curves from statistical distributions). Hence the price of a put 7.5% away from the market is more than double the price of a put 15% away.

Here’s an example. With the SPX trading at 1416 right now, the chance of a 7.5% decline to 1310 by say February expiration is about 18.5%. The chance of the SPX declining 15% to 1205 is 6.2%. This information can be found right in your option chain in case you want to look at it on your own.  And since the probability is different, so is the pricing. A Feb2013 1310 put will cost $10.75 and a Feb2013 1210 put has a premium of $3.50.

Let’s take a look at the John Smith example again where the downside estimate is a max 50%. As a reminder we are comparing 100% protection at 15% down vs. 90% protection at 11% below the market. We need a few more data points though to do the cost comparison. First off, let’s use the SPY (S&P 500 ETF) as the underlying symbol and for simplicity purposes, assume he is buying 1000 shares. Also our time frame will be 6 months and that means out to June expiration.

Here’s a chart that compares protection levels and cost.
You will notice that the cost of hedging is more for the 9 contract solution at 11.5% lower vs. the full coverage at 15%. So why even bring this tactic up of not fully hedging at the desired downside protection? The answer is that at times this will change, so it is worth always considering as an alternative. This data also changes as you adjust yoru max market loss assumption.  If your max loss assumption was 30% the 9 contracts would use a lower strike to create the same CaR and the costs would be the same.
You may also want to employ a partial hedge when looking to tighten up hedges. This will keep the CaR the same, but the puts may actually pay off. So when there is fear of a sell off, this tactic has a better chance of keeping the hedges from expiring worthless.  In our example, above if the market did actually decline by 15% in the next 6 months the full hedge would be worthless at expiration but the 9 contracts would now be in the money. This gives investors a chance to generate some cash in a down market vs. letting the hedge expire worthless and endure the max loss.

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