Risk and Return of Equity Index Collar Strategies
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The Voices of Influence | iijournals.com The Journal The of of Alternative Investments Summer 2016 – Volume 19 Number 1 | www.iiJAI.com Risk and Return of Equity Index Collar Strategies RONI ISRAELOV AND MATTHEW KLEIN Volume 19 , Number 1 | Summer 2016 Risk and Return of Equity Index Collar Strategies RONI ISRAELOV AND MATTHEW KLEIN RONI ISRAELOV oss aversion leads many investors to In fact, the collar strategy buys one is a managing director at seek tail-protection strategies, but expensive instrument (a put option) and sells AQR Capital Management put options that provide the most another expensive instrument (a call option). in Greenwich, CT. direct insurance are expensive (both [email protected] Even if the dollar “costs” offset, this is a bad Lin terms of premium paid and lower expected deal relative to an alternative that does not MATTHEW KLEIN returns). One popular solution for mitigating systematically buy overpriced instruments, is an associate at AQR this cost is to finance the protective put option particularly when the purchased instrument Capital Management in by selling call options. This strategy is referred is more overpriced than the one being sold. Greenwich, CT. to as a collar, and this article investigates the We will show that the collar strategy’s [email protected] collar’s risk and return characteristics. expected return can be decomposed into its Index collars are typically described as equity risk premium and volatility risk pre- providing protection at little to no cost for mium components. A collar has lower equity those who are willing to trade upside poten- beta than the equity index, indicating that tial for reduced downside risk. For instance, it collects less equity risk premium. In the the Chicago Board Options Exchange case of the volatility risk premium, there is a (CBOE) answers the question of who should netting of volatility exposures from the put use equity collars (CBOE [2012a, 2012b]): and call options. The purchased put options provide negative alpha to the equity index • an investor who is looking to limit the because of the volatility risk premium paid downside risk of a stock position at little to put sellers, whereas the sold call options to no cost [emphasis added] provide some positive alpha. In the special • an investor who is willing to forgo case of a zero-cost collar, the put option’s upside potential in return for obtaining negative alpha should dominate because of this downside protection the implied volatility smile, which has been attributed to demand pressure by Bollen and Do collar strategies successfully protect Whaley [2004]; Gârleanu, Pedersen, and a position at little to no cost? The answer Poteshman [2009]; and Constantinides and depends on how one chooses to define Lian [2015]. “cost.” Although there may be no upfront Lower expected return due to reduced outlay if the put option and call option prices equity risk premium is incontrovertible: A are the same, this alone reveals absolutely collar mechanically has lower equity expo- nothing about the investment attractiveness sure than its underlying index. Buying a of the trade and its impact on returns. put option reduces the portfolio’s equity SUMMER 2016 THE JOURNAL OF ALTERNATIVE INVESTMENTS exposure, as does selling a call option. This is true received mostly or fully offsets the put option premium whether the collar provides a credit, provides a debit, paid). This objective typically drives collar portfolio or is self-financing. This is also true whether the options construction. For instance, a desired protection level are fairly, cheaply, or expensively priced. might be selected, such as three-month protection at Negative alpha due to the put option’s volatility risk 95% of the current index value. The call option’s strike premium is a well-documented, economically rational then might be selected such that its premium most empirical observation.1 The collar’s upfront net cost may closely matches that of the purchased 5% out-of-the- be negligible, but its negative alpha can have a material money put option. This approach provides the zero-cost impact on investors’ returns. Investing in a typical collar collar. Alternatively, the call option’s strike and matu- implementation has provided lower returns and a lower rity can be selected such that the strategy is zero-cost Sharpe ratio than investing directly in the S&P 500 Index.2 on average. In other words, investors would be better off simply The recently launched CBOE S&P 500 95-110 reducing their equity exposure. Collar Index (CLL) is an example of a collar implemen- tation that buys three-month put options that are about CONSTRUCTING A COLLAR 5% out-of-the-money at the time of purchase and sells one-month call options that are about 10% out-of-the- Exhibit 1 plots an example payoff diagram for money at the time of sale. This portfolio construction the simple collar strategy in which the purchased put is actually far from zero-cost. In fact, on average this option and written call option expire on the same date. strategy spends roughly $7.50 on put options for every The exhibit illustrates how the collar strategy trades off dollar it collects from selling calls. As far as we are aware, capped upside for limited downside. however, CLL is the only publicly available index that Many degrees of freedom exist when constructing tracks an S&P 500 Index collar strategy. Given that it a collar strategy. Most important are the strikes and was intended to serve as a benchmark for these strate- maturities of the purchased put option and written call gies, we feel that it is reasonable to treat CLL’s perfor- option. Collar strategies are often intended to be mostly mance as representative (or at least illustrative) of collars or fully self-financed (in that the call option premium in general.3 E XHIBIT 1 Illustrative Collar Payoff Diagram 120 115 110 short call option 105 caps upside 100 Collar Payoff 95 long put option limits downside 90 85 80 80 85 90 95 100 105 110115 120 Index Value Note: Illustration is long the equity index, long a put option with $90 strike price, and short a call option with $110 strike price. The prices of the two options are equal, and they expire at the same time. RISK AND RETURN OF EQUITY INDEX COLLAR STRATEGIES SUMMER 2016 E XHIBIT 2 CBOE Collar Performance Summary (1986–2014) S&P 500 Index CBOE Collar Index Excess Return 7.3% 3.2% Volatility 15.7% 10.7% Sharpe Ratio 0.47 0.30 Beta 1.00 0.62 Upside Beta 1.00 0.68 Downside Beta 1.00 0.58 Notes: The table shows summary statistics for the S&P 500 Index (SPX) and the CBOE S&P 500 95-110 Collar Index (CLL). The date range is July 1, 1986, to December 31, 2014. Returns are excess of cash. “Excess Return” is an arithmetic average annualized return. Volatility, beta, and upside/ 2 ∑ ()y −−yx*( x) ∑ ()x − x downside beta were computed using 21-day overlapping returns. We define downside beta as tx| t <00t t tx| t < t where yt is the collar’s trailing 21-day return on day t, x is the S&P 500’s trailing 21-day return on day t, and y– and x– are their full-sample average 21-day returns. The upside t 2 beta, similarly, is ∑ (y −−yx*( x ) ∑ ()x −x . tx| t >00t ) t tx| t > t COLLAR PERFORMANCE even after accounting for their reduced equity exposure. This article explores the reasons why. Exhibit 2 reports performance characteristics for The collar might be constructed such that it is self- CLL and the S&P 500 Index (SPX) over the period July financing, but the prices of the options traded are not 1, 1986, through December 31, 2014. Over this period, really what matter. What really matters is the options’ the collar earned significantly less return in excess of prices versus their fundamental or actuarially fair values. cash than had the S&P 500 Index: 3.2% per year for Equity index options tend to be expensive because of CLL versus 7.3% per year for the S&P 500 Index. It has investor preference for loss avoidance, and out-of-the- also had significantly lower volatility than the S&P 500 money put options tend to be more expensive than out- Index: 10.7% for CLL versus 15.7% for the S&P 500 of-the-money call options. Hence, buying protection is Index. The collar has realized a Sharpe ratio approxi- expected to hurt performance on a risk-adjusted basis mately 35% lower than the S&P 500 Index. because put options are expensive. Selling upside helps The collar is expected to have lower average risk-adjusted performance for the same reason, but not to returns than the S&P 500 Index because its limited a great enough extent, which is why the collar strategy loss and capped gain reduce its equity exposure. This has realized 1.3% per year of negative alpha. floor and cap are visible in Exhibit 3, which scatters To visualize, Exhibit 4 plots the payoff diagram to the collar returns against the S&P 500 over the period, an illustrative self-financing collar in which the sold call using 21-day overlapping returns. CLL’s 0.62 equity beta is cheap relative to the purchased put option. Comparing is also visible as the slope of the regression line in the the mispriced collar to a fairly priced one, the call option scatter. This number indicates that, as a starting point, strike in the former will be below the call option strike the collar is expected to earn 38% less equity risk pre- in the latter.