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.