# Skating on thick ice

Designing an optimized defensive equity strategy

Stock markets have been a reliable source of investment returns in the long run. But over shorter time horizons, equities can be subject to sharp corrections and bear markets which erode capital and accumulated gains. This was starkly demonstrated in the 2008 global financial crisis and again in the sharp selloff in equity markets following the emergence of the COVID-19 pandemic in early 2020 when global equities fell by over 30% in a single month, wiping out several years of accumulated profits.

Investors are confronted with the question of how to allocate to equities when the risk of a bear market or crash is ever present. One answer is to remain fully invested for the long term and to ride out market lows. This has generally been good advice in the past as steep bear markets have often been followed by a sharp bounce back. However, investors may not be able to tolerate these drawdowns and, as the disclaimer on every piece of investment marketing literature states, past performance isn't necessarily a guide to future returns.

Human psychology also exerts a powerful influence on investment decision-making. It's well known that investors focus more attention on losses than the weight given to equivalent gains (called 'loss aversion bias' in behavioural psychology). When gains which have been slowly accumulated over several years are wiped out in a few weeks the pain is amplified, making it hard for investors to maintain a detached approach.

An alternative response to the question above is to consider a strategy which aims to systematically control equity downside risk. While equity investment will always carry risk, defensive equity strategies aim to provide high upside potential combined with smoother investment performance and lower drawdowns which can help investors to mitigate timing risks and stay invested through periods of heightened volatility to participate in subsequent market rallies.

Some defensive strategies are more defensive than others

Some defensive strategies are more defensive than others

There are many different approaches to designing a defensive equity strategy but we can categorise them into two buckets by their degree of predictability: lower precision, indirect strategies which depend on a repeat of historical patterns or correlations (e.g. minimum volatility equity portfolios, momentum strategies, 'just in time' hedging, cross asset hedging etc.) or higher precision strategies which directly hedge downside exposure (e.g. option-based approaches, dynamic exposure management strategies etc.).

The performance of lower precision strategies over time, and in the latest bear market, has been mixed with many strategies providing effective defensiveness in some market falls but not others. These strategies are appropriate where downside risk mitigation is not required at all times and investors are willing to accept a lack of predictability in all scenarios.

In this paper, we focus on higher precision strategies, in particular equity option defensive strategies which provide highly reliable drawdown control and minimize the path dependency associated with portfolio insurance approaches. Our aim is to identify strategies which avoid the additional costs and pitfalls of very simple option strategies without introducing unnecessary complexity.

To aid in the identification of viable option-based defensive strategies, we set out below our criteria for success:

**Predictable**– a defensive equity strategy should provide reliable downside risk control at all times and be simple and transparent**Systematic**– a rule-based strategy which doesn't rely on judgement to deliver consistent risk management**Efficient**– a strategy which optimizes risk-adjusted returns and controls costs to deliver long term value from downside risk management

The performance reference point for a defensive equity strategy is a simple portfolio which is allocated between an equity index and cash to target a similar level of risk. A successful defensive equity strategy should aim to deliver more upside and/or lower drawdowns than this reference portfolio for the same level of risk.

In the rest of this paper we investigate defensive equity strategies and attempt to provide a better understanding of some of the factors which drive cost and efficiency and, finally, identify optimal approaches that satisfy the criteria listed above.

Once we have decided to implement a defensive options overlay strategy we are faced with a long list of choices which need to be made. Which option combinations should we employ? Which strike prices should we choose? When should the options start and expire? How should the strategy be adapted as prices and market conditions evolve? These and many more questions make designing an efficient option strategy a complex task and mean that a simple approach may be ineffective. Furthermore, option markets have unique pricing characteristics which can have a significant impact on the expected returns and behaviour of individual strategies.

Selecting option parameters

Selecting option parameters

Consider the following simple example (which can be extended to any underlying equity market with a liquid option market). We start with a portfolio consisting of passive exposure to the S&P 500 index and buy a put option with the aim of flooring the market exposure in the event that the market falls. The option selected is a simple 3-month European-style put option on the S&P 500 index with a strike price set at 95% of the initial index level (for simplicity we assume a total return index including dividends).

At the end of 3 months the maximum loss on the portfolio will be 5% plus the percentage option premium paid. This premium amount can vary significantly with market conditions, which means the maximum loss can be less than 6% in periods of relative calm and more than 15% in periods of severe market stress, such as November 2008 and March 2020.

Furthermore, the maximum loss calculated above applies if we measure the return over the exact 3 month period. However, if we measure the return achieved between different dates then we see that, even with no changes to other market variables, the maximum loss will vary as the distance between the index level and the strike level varies.

We also have to consider what we will do at the end of the 3 month period (assuming we hold the option until expiry). If we replace the put option with another 3-month put option with a strike price set at 95% then our maximum loss over the combined 6 month period is now much greater and the performance over the period is not just determined by the index return but also by the path taken. As we extend the investment period this path dependency becomes a critical factor in the success or failure of the strategy.

**Observation 1: **There is no simple, passive approach to select an option strategy. The performance (and potential drawdowns) of any particular strategy will be affected by option prices and the path of market prices. An effective strategy should aim to control these factors and deliver more predictable outcomes.

With this observation in mind we investigate the historical performance of various common option strategies (listed below) in different market environments with the aim of assessing which parameters provide more effective and efficient downside protection.

Option strategies:

- S&P 500 Index + Short Dated Puts (95% strike, 3 month tenor)
- S&P 500 Index + Long Dated Puts (95% strike, 12 month tenor)
- S&P 500 Index + Long Dated Put Spreads Puts (Long 95% strike & Short 80% strike, 12 month tenor)
- S&P 500 Index + Put Ratios Overlay (Short 30% Delta Put & Long 2x 15% Delta Puts, 12 month tenor)

The two charts below show the results of these simulations on the S&P 500 index for each representative option strategy. We compare the impact of each option strategy on the annual return with the impact on the max drawdown recorded over two periods, first in Chart 2 the period from 2006 through to May 2020 (which includes the financial crisis in 2008 and the COVID-19 shock in 2020) and second in Chart 3 the calendar year 2018 only (which includes two less severe drawdowns).

Chart 2: Excess Return vs Max Drawdown for put option strategies (2006 to 2020)

Chart 2: Excess Return vs Max Drawdown for put option strategies (2006 to 2020)

Excess Return vs Max Drawdown for put option strategies (2006 to 2020): charts S&P 500 Index, S&P 500 Index + put ratios overlay, S&P 500 Index + long-dated put spreads, S&P 500 Index + Long dated puts and S&P 500 Index + short dated puts in a scatter chart showing excess returns vs. index and max drawdown, Dec. 2006 to February 2021.

Chart 3: Excess Return vs Max Drawdown for put option strategies (Calendar Year 2018)

Chart 3: Excess Return vs Max Drawdown for put option strategies (Calendar Year 2018)

Excess Return vs Max Drawdown for put option strategies (Calendar Year 2018) charts S&P 500 Index, S&P 500 Index + put ratios overlay, S&P 500 Index + long-dated put spreads, S&P 500 Index + Long dated puts and S&P 500 Index + short dated puts in a scatter chart showing excess returns vs. index and max drawdown, for calendar year 2018.

As we might expect, the performance of each strategy depends on the period chosen, with some strategies, such as put ratios, performing well in the long run but with marked underperformance in 2018, for example. We have also run this analysis on other sub-periods and other major global indices and we can draw some general conclusions about the relative performance of these option strategies.

One result that is broadly consistent over different time periods and indices is that long dated put options and put spreads (in above charts defined as options with a 1 year tenor, but this applies also for longer expiries) perform better than short dated put options (3 month tenor) with typically lower drawdowns and lower costs. We also note that put spreads generally have higher returns than put options but at expense of higher drawdowns in periods with severe market falls.

When we look for the underlying reasons for these results we note two critical factors that affect the performance of a put option strategy:

- Strategy parameters, in particular the degree to which parameters make the strategy sensitive to changing market conditions; and
- Volatility exposure, in particular the extent to which options are typically either expensive or cheap relative to theoretical fair value (known as the volatility risk premium)

We note, for example, that the reason for the outperformance of longer dated put options is because they are less sensitive to changing market conditions and are less expensive relative to theoretical fair value. However, longer dated put options by themselves still tend to trade at a premium to fair value so it is worth considering how we can construct strategies which are more attractively priced. To do this we need to understand a feature of option pricing known as the "volatility risk premium."

What is the volatility risk premium?

What is the volatility risk premium?

The Black Scholes option pricing model allows us to calculate a fair value for options if we know the key market inputs. Most of these inputs can be estimated fairly accurately from market data except for the key unknown which is the expected volatility of the underlying instrument. We can also reverse this equation, using the traded price of an option to calculate the 'implied' volatility, i.e. the forward-looking volatility which would be required for the option price to be fair.

When we compare implied volatilities from traded equity options with the volatilities which were actually realized during the option terms we observe that the average implied volatility from equity option prices is persistently higher than the realized volatility. This difference between implied and realized volatilities is known as the 'volatility risk premium'. There is substantial academic literature3 and empirical evidence from market practitioners4 which shows that this risk premium is persistent over time and is pervasive across global equity option markets (see below chart).

Chart 4: 1 Month Volatility Risk Premium (average of S&P 500, Eurostoxx50, and Nikkei 225 indices implied minus realized volatility for a 95% strike option)

Chart 4: 1 Month Volatility Risk Premium (average of S&P 500, Eurostoxx50, and Nikkei 225 indices implied minus realized volatility for a 95% strike option)

1 Month Volatility Risk Premium (average of S&P 500, Eurostoxx50, and Nikkei 225 indices implied minus realized volatility for a 95% strike option): charts volatility risk premium from November 2006 through May 2020.

As referenced above, the implied volatility premium varies with maturities as well as with strike prices. The chart below shows the volatility risk premium for an option strike price of 95% of initial level for various maturities and global equity indices. We note that, independent of the underlying market, the volatility risk premium is persistent but declines as we go further out on the option term structure. This implies that buying longer dated options is generally more efficient than buying shorter dated options and, equally, that selling shorter dated options is preferable to selling longer dated options.

Chart 5: Average Implied Volatility Risk Premium (95% Strike) vs Option Tenor

Chart 5: Average Implied Volatility Risk Premium (95% Strike) vs Option Tenor

Average Implied Volatility Risk Premium (95% Strike) vs Option Tenor: charts option tenor against average implied volatility risk premium for Eurostoxx50 Index, Nikkei 225 Index, S&P 500 Index and FTSE 100 Index, October 2006 to December 2019.

We also note that the volatility risk premium varies by market and index. For example, we observe a lower volatility risk premium for longer dated put options in Europe and Asia than in the US. One explanation for this is the higher issuance of structured products on European and Asian stocks which create a demand to sell longer dated options from the investment banks that create and hedge these products.

An additional feature of option markets is that the implied volatility varies according to the strike price of the option. Lower strike options (for instance put options with strike levels below the current index level) persistently exhibit higher implied volatility. This phenomenon is known as 'implied volatility skew' and partially reflects an adjustment for the fact that market returns aren't precisely normally distributed. Nevertheless, the implied volatility skew often overstates this effect and options with lower strike prices generally carry a higher implied volatility premium.

Chart 6: Implied Volatility vs Strike (Average of 1 year Options on S&P 500 index)

Chart 6: Implied Volatility vs Strike (Average of 1 year Options on S&P 500 index)

Implied Volatility vs Strike (Average of 1 year Options on S&P 500 index): chart runs from October 2006 to February 2021.

**Observation 2:** The volatility risk premium and implied volatility skew represent additional costs for investors who purchase put options to protect against drawdowns. These additional costs are particularly high for short dated out of the money put options and a simple strategy buying these options will suffer lower performance and lower risk-adjusted returns over time.

The above observations help us to understand some of the drivers of option prices but also highlight some of the pitfalls in designing and implementing defensive equity option strategies.

A better defensive equity strategy will avoid these pitfalls, or even turn them around to turn a cost into a benefit. We can achieve this by:

- Choosing parameters which offer more predictable outcomes; and
- Buying cheaper put options which are more efficient; and
- Selling more expensive options to harvest the volatility risk premium

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