Options Strategy
Options strategy allows simple one-period rolling put and call options to be assigned to assets. This is a very powerful feature and can lead to drastic changes in portfolio allocations. Option-based allocation, like any asset allocation, should be approached cautiously and thoughtfully. The technology behind this feature is pending US patent approval. This feature is in beta testing, so please send us your feedback. In order to ensure that options are used properly, the feature requires a key update. Contact your relationship manager for a license update.
Substantial knowledge of options trading is assumed here, but in order to standardize terminology going forward, we provide the following basic definitions:
Put options are contracts that, when bought, guarantee an investor the right, but not the obligation, to sell a covered portion (at a fixed coverage rate) of an asset’s holdings at a guaranteed fixed strike price on or before a fixed date. Buying a put at a low strike price is like an insurance policy against the asset’s price falling below that price.
Call options are contracts that, when bought, guarantee an investor the right, but not the obligation, to buy a covered portion (at a fixed coverage rate) of an asset’s holdings at a guaranteed fixed strike price on or before a fixed date.
The type of options allowed in the Optimizer can be thought of as applying to every simulated or real return. When such an option is purchased, it will always be exercised according to its coverage when the corresponding return falls beyond its strike price. Thus, these are one-period options renewed at each period or some other long-term contract with similar payout characteristics. Strike prices are expressed as annualized returns in the same units as the forecasts. Coverage indicates what percentage of the asset is covered by the option. So, when the price is outside of the strike price, exercising the option means that the covered percentage will be at the strike price and the remaining percentage will be unaffected by the option. Options like these fit well into the simulation framework of the Michaud Resampled Efficient Frontier. The Optimizer currently can accept any level of coverage on a single put and/or call option for each asset, with user-input cost and strike price. Options with longer periods or multiple overlaid puts or calls are not currently implemented.
Options are activated through by enabling Options Strategy in the Advanced Options sub-menu of the Options Menu in the Optimizer ribbon. When activated, the blue Optimization Options bar indicate that options are enabled and additional columns appear on the Inputs Worksheet. Enter data for puts and calls.
Optimization proceeds with option overlays much the same as without. However, drastic changes in allocations may result from option overlays, as the risk inherent in an asset is clipped from above or below. A formerly risky equity, for example, may behave more like a bond when puts and calls are taken out to eliminate the tail risk of the equity. Options overlays can produce some curious results. The displayed frontier may fold back on itself to produce multiple portfolios with the same level of nominal risk. We leave it to the user to determine the appropriate use of these portfolios.
A Note on the Classical M-V Frontier
When classical frontiers are requested from the optimizer, the simulation framework which provided a natural framework for calculating allocations with options is no longer available. The classical frontier calculation requires only a set of means and variances, so the means and variances adjusted for any existing option overlays are recalculated within the software. This can be done analytically or through Monte Carlo, and depends on the choice of resampling function (normal, T, or 4-moment resampling). Currently, the Monte Carlo solution is implemented, with a high number of simulations to ensure convergence. Non-normal resampling distributions such as T or 4-moment with greater skewness or excess kurtosis will generally put more probability mass on certain extreme returns for which options are exercised, thus more drastically altering the behavior of the assets and the resulting portfolio.
How Means and Variances are Affected
There are two types of means and variances with option overlay. Applying an option will not affect the return on an asset. Thus the return observed on the asset price remains the same with or without the option overlay. However, the holder of the portfolio with the option has a guaranteed return and risk which is different from the nominal returns of the portfolio of assets. We refer to this as the portfolio means and variances, as opposed to the asset means and variances.
All reference portfolios are assumed in the software to be option-free, so the reference portfolio means and variances will reflect only asset means and variances. Similarly, individual assets, when plotted on a mean-variance frontier diagram, are plotted with their option-free means and variances. The optimal frontier, classical frontier, and simulated frontier portfolios will all be displayed with options-included means and variances.
Calculating the Value of an Option
The cost of returns are calculated as follows: result mean = simulated mean - put cost * put coverage - call cost * call coverage + put coverage * (put strike - min (put strike, simulated mean)) + call coverage * (max (call strike, simulated mean) - call strike) = simulated mean - coverages * costs associated with buying options + coverages * difference in prices if options are exercised.
Example 1: 50% coverage on a call at +5% strike price, cost of 2%
Raw Simulation: 3% Adjustment: 3% - 50%*2% = 2% (Pay 1% for option not exercised)
Raw Simulation: 6% Adjustment: 3% - 50%*2% + 50%*(6%-5%) = 2.5% (Pay 1% for option, benefit of 0.5% from option exercise)
Raw Simulation: 10% Adjustment: 3% - 50%*2% + 50%*(10%-5%) = 4.5% (Pay 1% for option, benefit of 2.5% from option exercise)
Example 2: 50% coverage on a call at +5% strike price, cost of 2%; 80% coverage on put at -3% , cost 2%)
Raw Simulation: 3% Adjustment: 3% - 50%*2% - 80%*2% = 0.4% (Pay 1% for call and 1.6% for put)
Raw Simulation: -6% Adjustment: 3% - 50%*2% - 80%*2% + 80%*(-3% - (-6%)) = 2.8% (Pay for options as above and get 80% of difference between -3% and -6% for exercise of put option)
Raw Simulation: +10% Adjustment: 3% - 50%*2% - 80%*2% + 50%*(10%-5%) = 2.9% (Pay for options as above and get 50% of difference between 10% and 5% for exercise of call option)
Unsupported Features
- Post-optimization, while available, will not use the options-overlaid means and variances. Thus caution should be exercised with postoptimizing, in order to avoid drastically altering the portfolios with extreme investability constraints.
- Tax and transaction cost models do not currently account for options; proper care must be exercised when using these features with options in interpreting the results. They can still be used, but must be interpreted carefully. Transaction costs for the options themselves are included in their prices.
- Long-short optimization requires special attention when using option overlays. Short assets with options will reverse the buy/write status for their options. For example, a put option which would normally be bought when its underlying instrument is long, will be written when the asset is short. It will no longer have the insurance function against losses resulting from changes in the underlying price.
- If you set up duplicate assets and apply options to the duplicates, you should disable the Ledoit Covariance Estimation option as it doesn't work well with perfectly correlated assets.
Please remember that this feature as a whole is relatively new and extremely powerful. Caution is strongly recommended when using this new technology for investment purposes.