An ITA Platinum Member recently asked me to comment on a long term “Collar” Hedge that used SPY (the S&P 500 Index ETF) as the hedging instrument. To keep things simple we will start by assuming that our investment portfolio behaves like SPY i.e. is highly correlated with SPY and has a beta weighting of 1. Thus, in this example, the “portfolio” is represented by shares in SPY.

The suggested collar was to purchase a ~6 month Put Option ~15% below current market prices for insurance and to sell a Call Option (expiring in the same month) ~ 10% above current prices to help finance/pay for the Put Option/insurance. The Profit/Loss graph for this position (for ~$100,000 “portfolio”) is shown below:

In this example, with SPY trading at 188.16, the September 2014 160 Strike Put Options (~15% below current $188 SPY price) are purchased for $2.11 each or $1,055 (500 x $2.11) to insure the “portfolio” valued at ~$94,000 (500 x 188.16). To offset this cost, September 2014 Call Options at the 205 Strike price (~10% above current $188 SPY price) are sold for $0.93 each or $465 (500 x 0.93). Thus, the net cost of “insurance” on this position is $590 ($1,055 – $465).

Is this an attractive position? The answer to this question really depends on your objectives. If you are not (for whatever reason) going to be looking at your portfolio for the next 6 months and want to sleep well knowing that your maximum loss cannot be greater than $15,000 (15%) then this position achieves that objective and the cost of the insurance ($590) is small.

However, let’s consider some of the probabilities. The maximum loss occurs if SPY drops below $160 (black line in above figure). $160 also happens to be 2 Standard Deviations from the current ($188) price – so the probability of SPY dropping below $160 is only ~2.3%. So, is it worth insuring against this low probability? Maybe? It depends on how worried you are about a significant “crash” (>15% in 6 months) and how important it is to preserve capital.

To the upside we are are selling Options at $205, which happens to be 1 Standard Deviation above current prices. Again, looking at probabilities there is ~16% chance that prices will go higher than $205 and you will have “Opportunity Losses”. Is this acceptable? Maybe.

Finally let’s take a look at maximum reward : maximum risk – this is ~ $8,000 : $14,500 (~ 1:2) – not too impressive, but may be acceptable to some investors.

How might we be able to improve this hedge? The first thing we might consider is to buy a Put Spread rather than a simple Put Option. This might look as shown below:

In this case I have purchased a Put Option at the $180 Strike Price and Sold a Put Option at the $160 Strike. This will cost me (500 x (5.73-2.11)) $1,810 ($755 more than buying the $160 Put Option in the first example) and will reduce my maximum upside profit by $755 assuming I still sell the $205 Strike Call Option.

However, if the price drops to between $180 and $160 (4 -15%) my loss will only be ~$5,250 (~5%). Since $180 is well within the 1 Standard Deviation range, there is a reasonably high probability (~40%) that it will get there – so this looks like a better hedge (even if a little more expensive).

The reward/risk profile also looks better at ~ $7,250 : $5,250 (> 1:1).

The only caveat on this position is that risk is not totally limited. Below $160 we begin to lose money again – but we only reach our original 15% limit ($15,000) with SPY at ~ $140 (25% below current prices). This is over 3 Standard Deviations away from current prices with a probability of ~0.1% of being reached (but, remember, this is a statistical probability, so still a “black swan” possibility).

The Profit/Loss on the above positions is shown in the position overlays below:

Compare the black and grey lines (values at September expiration) to decide which position you prefer. (Sorry the figure may be confusing – I couldn’t figure out how to eliminate the colored lines (intermediate time values)).

As regular readers may know, my personal preference is to move the strike price of the closest Put Option purchased to the current price (the At-The-Money, ATM Option) and to purchase a butterfly spread:

In the above example I might buy the 190/160/130 Put Butterfly for $2,930. If I sell the 205 Call Option as in the other examples above, my maximum profit is limited to $6,000. However, my maximum loss down to $160 (15% price drop) is now only ~$1,500 (1.5%) – a 4 : 1 reward/risk ratio. As noted above, the probability of the price dropping below $160 is ~2.3%, after which losses will increase. A $15,000 loss is reached with price at ~$145 – about 3 SD from current prices.

The figure below shows an overlay comparison of the Butterfly Hedge with the standard “Collar” hedge described in the first example above:

The above are only a few examples of how different Option positions might be used to hedge a portfolio. Any decision as to which strategy to use will depend on an individual investors objectives and preference with respect to reward and risk.

In the above examples I have assumed that the 6 month Call Option is sold for $0.93 for consistency, however, Calls could be sold monthly (6 times). Assuming these are sold at the same distance from current prices (in relation to standard deviations) this will generally generate more income to finance the purchase of the Put hedges.

Also, the strikes chosen for the vertical spreads and/or butterflies can be adjusted to match personal reward/risk preferences.

Finally, when hedging a portfolio by using Index Options, an investor should determine the “beta” of his/her portfolio i.e. how it behaves in comparison with the Index being used (e.g. SPY). Assuming the portfolio is well diversified, the “portfolio beta” might only be ~ 30-50%, in which case the investor would use fewer options. For example, if the portfolio to be hedged was valued at $100,000 with a 40% beta, an investor would hedge using 2 Options (or Option Spreads) rather than the 5 used in the above examples. i.e. “insurance” would be cheaper.

David

Robert Ryan says

David,

Thanks so much of an overview than what I could possibly have done. Aren’t the tools/analysis/decisions of 1 SD vs 2 SD really using past data (yes momentum will be there as long as there are “traders”) as probability decisions? If I look at Fed policy and they say 0% interest I may think risk of significant drop in equity valuations is low. Or if I am 25 with 2 young children and am great health (with good genes-that’s next) I can buy a $1 Million life insurance for little given the history/probability of my dying at 35.

So maybe we make the decisions to buy insurance not when recent past says our portfolio will continue upward as it has for last 4+ years (OK whenever you got back in) and the SDs are stacked with recent data. But rather when momentums are carrying everything higher

Any studies about what core/index option call/put premiums give us hints about when we should buy insurance whether collars or butterflies? I prefer to watch a butterfly and not have a collar around my older neck :> ). But only buy flight insurance if there is bad weather before takeoff and a 4SD it might pay off to my beneficiaries

Thanks for education

Robert

HedgeHunter says

Robert,

Standard Deviations are based on past (historical) data but may be short-term or long-term. For example, in the Ranking SS I offer the choice of 10-day, 20-day or 60-day periods to calculate volatility (equivalent to % Std Dev). Whatever the time frame of the data used, volatility is usually annualized.

Projections of future volatility (standard deviations) are reflected in the Implied Volatility (IV) that can be extracted/calculated from the time value of Option premiums. This premium (IV) is established by the Market Makers who set the prices and reflects market supply/demand and level of uncertainty in the market. For equities, it is usual for Option premiums to increase in down markets/periods of greater uncertainty – thus, increasing Option premiums (Implied Volatility) is generally an indication of a potential bear market. Most Option traders will compare an asset’s historical volatility to the Implied Volatility in Option prices to determine whether an Option may be over or under-priced.

The volatility of the overall market (S&P 500) is characterized by the value of the volatility index (VIX), often referred to as the “fear” index. VIX correlates negatively with the S&P 500 (SPX or SPY).

Obviously, if we knew when the markets were going to decline, the decision as to when to buy insurance (or exit the market) would be easy. Unfortunately, when this becomes reasonably obvious, the price of insurance is usually high. It becomes a balance between risk and reward and a personal choice as to the best way to preserve wealth.

David

Steve Clark says

David,

Great example! I actually put it all on a spreadsheet, so I could see what was happening. It took me a bit of playing with the numbers but finally got everything to workout.

Two questions. If SPY tanked below 130, the bought and sold puts essentially offset each other and you have the actual loss of the equity (188.16-current price) + 2465 which is the initial costs of everything. Am I doing this correctly? Also does it make sense to sell a call at 205 to obtain $465 (or .5% or portfolio) to constrain oneself to only 5% higher in the market, even if one is bearish?

Thanks,

Steve

HedgeHunter says

Steve,

Yes, you’ve got it right regarding the losses below 130 (I’m assuming you’re referring to the Butterfly Hedge). Of course, this is a 30+% decline and there would be opportunities to adjust the hedge before the price dropped that far – I would probably be looking to adjust at ~160 (depending on time remaining in the Options). These adjustments go a little beyond the scope of this blog, but the butterfly can be converted into another “standard” Option position known as a Condor (you can Google it or look it up in any good (intermediate/advanced) Options book).

The question as to whether it is worth selling the Call Options is a good one – some investors may consider it an acceptable return (especially if neutral/bearish on the market), others may not. Personally I like to at least partially finance the cost of the hedge – however, as a rule of thumb, I look for a

monthlyreturn of at least 3.5% (preferably 5+%) on the “covered call” portion of the trade. In the above examples, this condition is not met (only 5-10% in 6 months). Generally, if I can find good premiums at ~1 SD from the current price and 5+% return (60% annualized) I will probably sell the Options. Whether this is possible depends, of course, on the volatility of the underlying asset. Technical analysis may also influence my decisions.David

Steve Clark says

David,

I was indeed taking about the butterfly hedge. It was the long time period involved that had me questioning the selling of the calls. If one could sell calls on a monthly basis I could see where that would be advantageous especially in a sideways market.

Thanks,

Steve

HedgeHunter says

Steve,

I agree regarding the Calls – also, in the example, I used the pricing of SPY Options – however, in practice an investor would not be selling SPY options, but Options on the underlying assets held in the portfolio (e.g. Hawking Portfolio). Often, as for example with UNG in the Hawking Portfolio, Option premiums on the individual assets will be greater than Option premiums on the index and it will be easier to cover the cost of the hedge by selling Options monthly (where we get the maximum decay in time value – i.e. time decay is not linear and increases significantly in the last 30 days of Option life).

David