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Enhancing CPPI with options

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Institutional investors have long sought robust strategies that give them exposure to risky assets but also maintain some form of capital protection. Here we address some of the acknowledged shortcomings of the popular Constant Proportion Portfolio Insurance (CPPI) strategy and discuss how options can be employed to enhance them. Moreover, we discuss how to optimise the strikes of the options in order to maximise returns according to an investor’s market outlook.
Portfolio managers who maintain exposures to major equity indices often seek out protection in the form of vanilla put options. Indeed, many managers have used the current low implied volatility environment to purchase ‘cheap’, at least relative to recent years, put protection. However, the increased demand for securing put protection at these lower volatility levels has contributed to an increase in volatility skews (ie, the relative cost of out-of-the-money puts to out-of-the-money calls), thus making this strategy less attractive. (See figures 1 & 2.)
Some portfolio managers do not employ these strategies due to regulatory or infrastructure issues. As a result, the market has developed an array of structured trading strategies to protect against losses, many of which attempt to replicate the performance of these options strategies. CPPI is one of the more popular portfolio insurance strategies, one in which options can further enhance its performance.
CPPI strategies (as well as many other portfolio insurance strategies) attempt to maximise participation in risky assets while simultaneously avoiding large losses.
One key distinction between CPPI strategies (see figure 2) and other option based strategies, is that CPPI hedging strategies are reactive to market moves. In other words, the core algorithm dictates how the portfolio gets adjusted after the market moves.
One well known issue with this is that when the market rallies, the risky exposures are increased, and when the market comes off, they are reduced. Consequently, these become known as buy high/sell low strategies. In derivatives terminology, they are described as being short gamma. One potential consequence of this type of risk is that the CPPI strategy can become cash-locked. So how can investors mitigate some of this risk through the use of options?
The answer is to integrate options into CPPI to mitigate the buy high/sell low nature of these strategies, and thereby avoid cash-lock. The basic premise is to maintain the required exposure to the risky assets using both the underlying assets as well as options on them. The degree to which options are used in place of the underlying should depend on the investor’s market outlook but could also be fixed from the start.
Naturally, there can be many variations on this theme, so investors should consult the advice of derivatives and CPPI professionals before implementing such strategies. Moreover, the underlying options market must be sufficiently mature so that the different maturities and strikes can be traded/hedged.
Suppose we have a regular CPPI strategy with a crash size of 20% and a bond floor at 70%, ie, 30% can be put at risk thus implying a 150% (= 30%/20%) of notional investment in equities. Here we first use a portion of the risk capital (assume a third of the 30%, so 10% of notional) to purchase a single call option over the entire investment horizon (eg, five years) and then leverage the remaining 20% into 100% exposure. This call option offers several benefits, some obvious and some subtle.
One obvious benefit is that once the call is purchased, it will maintain equity exposure over the entire investment period. So the investor will never be cash locked. While this is true, the exposure could be very small should the market fall and the option go far out-of-the-money.
Another benefit is that the option protects the bond floor to some extent as the option’s value cannot become negative. Consequently, the option enhanced strategy becomes more robust to downside moves and reduces the hedging requirements. This provides two primary benefits:
q A reduction in transaction costs: transaction costs are a concern with CPPI, especially for strategies with low crash size assumptions as they require more hedging. The option effectively increases/decreases participation itself when markets move, thus decreasing the overall hedging;
q A reduction in the short gamma nature of the strategy: but more importantly, the positive gamma from the option helps guard the strategy against the whipsaw effect. Indeed, two of the most detrimental scenarios for CPPI occur when the markets suffer an abrupt sell-off but is followed by a quick recovery, and when the market rallies sharply but then sells off soon after.
One last benefit that comes along with using calls options in this manner is a long exposure to implied volatility. This is similar to the long gamma one acquires with options but is slightly different. For mark-to-market purposes, this can be extremely beneficial (though the intent is to hold the call to maturity) because implied volatility levels are generally inversely related to the overall market (ie, volatility typically goes up when markets go down and vice versa).
The end result is that the call option will lose value when market deteriorates according to its participation (delta), but this loss will be cushioned by a likely increase in implied volatility.

A variation on this strategy could be to use short-term options over smaller periods. If an investor waited until the end of each period and then repurchased a new call option, then the strategy does become exposed to a potential cash-lock scenario. However, one could essentially pre-pay for this series of options he intends to purchase through the use of a cliquet option. This would avoid a cash-lock but maintain the positive gamma effect throughout.
Choice of strikes is crucial: while many options strategies often require the options to have specific strikes, here we are left to determine these ourselves.
An investor’s market outlook becomes critical to this selection. For example, consider an investor who decides to use the first option enhanced CPPI strategy above and expects medium- to low-range annual returns of say 5-7% from the equity markets over the next five years. Once it has been decided how much capital will be allocated to the call options, the maturity is determined but the strike is not. It is important to choose a strike that optimises the return of the option investment.
The 5-7% returns compound into a five-year return between 28-40%. Thus we would not choose call options that are more than 40% out-of-the-money as they would expire worthless under this scenario. So what strike should be choosen? Ideally, it would be a lower strike as the option would payoff more at expiry. However, these options cost more. So choose the strike such that the return on the option (given by the ratio option_payoff / option_cost ) is maximised.
For example, consider a five-year call option on the DJ EURO STOXX 50 index with a strike that is 75% of the current spot price. Assuming a financing rate of 4.3%, dividend yield of 3%, and implied volatility of 25%, this option would cost approximately 32% of spot. If the market returns 40% in five years, then this option would be worth 140% - 75% = 65% of the original spot level (ie, its intrinsic value). Since the option originally cost 32%, its return would be just over 100%. Figure 4 shows the returns for options across different strikes and for different market returns.
The payoff/cost ratio has been maximised and it has been determined that strikes between 64-78% (using DJ EURO STOXX 50 options) would maximise the returns on these call options should investor expectations play out.
As discussed, the typical CPPI algorithm has some inherent problems that portfolio managers would like to work around. Options offer a potential tool to mitigate these risks and reshape the risk/return profile of these strategies. Moreover, it is recommended that investors recognise the importance of strike selection in their options strategies and choose strikes in accordance with expectations of the market in order to optimise returns.
Peter Allen is head of equity derivatives strategy at JP Morgan in London

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