Tail Risk Hedging
Tail Risk Hedging

Tail Risk Hedging

The third alternative is to invest in strategies that are negatively correlated with tail risks. Essentially this approach balances risks in portfolios with risk-factor exposures that are likely to negate some of the adverse returns embedded inside the portfolio. Among the traditional established strategies, systematic, trend-following, managed futures strategy provides positive correlation with tail risk indicators such as the Volatility Index (VIX) while also being largely uncorrelated with the stock (LocationĀ 256)

that tail risks for typical diversified portfolios occur from systemic (LocationĀ 410)

even assets that are fundamentally uncorrelated may become correlated on the tails if they are affected by a common liquidity factor. (LocationĀ 427)

cursory observation of the closing prices shows that each new high happened at a rapidly decreasing time interval (roughly halving each time), which is ā€œamplification and oscillationā€ that precedes a correction in Sornetteā€™s theory (this is also observed in a variety of natural and social phenomena). (LocationĀ 460)

we expect, on average, to improve some hedging efficiency by moving to a reasonable (quarterly) hedging program. This also highlights two other major issues: (1) hedging has to be a systematic, repeated asset-allocation decision to obtain best long-term benefits, and (2) the hedge program has to be active and consider pricing levels (LocationĀ 638)

The two major secular exposures are the equity beta and interest-rate or duration exposure. (LocationĀ 655)

Generally, I believe that broadly diversified portfolios should have an attachment level anywhere from 10 percent to 15 percent below the current portfolio value. (LocationĀ 661)

My empirical and theoretical research, discussed in the next few chapters, validates the belief that over longer periods (three to five years), tail hedging is generally self-financing when one accounts for both the ability to tilt portfolios more aggressively and following a systematic approach to rebalancing in the presence of such hedges. (LocationĀ 672)

The moment the hedges become complicated, performance measurement takes a new twist. The reason simply is that the current price of the hedge does not reflect the potential it has for a large tail payoff, and because tail events are rare events, observation of a few nontail periods is not sufficient to identify the prospects of the tail hedge. (LocationĀ 712)

First, portfolio holdings often show increased correlation (tendency of holdings to move in lock step) when markets move downward while tracking equity markets less closely on the upside. (LocationĀ 737)

If uncertainty falls, the mark-to-market value of options also falls. The magnitude of the time decay also changes depending on what initial price was paid (the larger the price, the more time decay there is in absolute terms) and the distance to the optionsā€™ exercise price. (LocationĀ 747)

One keeps cash in his pocket in case of a flat tire or other more serious mishap but carries no insurance. Our second driver carries some insurance. (LocationĀ 762)

This chapter will focus on quantifying the long-term historical payoffs of rules based purely monetization strategies that may be suitable for an equity index portfolio. (LocationĀ 1036)

If there is a short-term shock in the market, the volatility curve flattens and inverts because the (LocationĀ 1044)

demand for shorter-term hedging exceeds the demand for longer-term hedging. This can be used as an opportunity to reduce shorter-expiry hedges and extend them out to reduce the cumulative long-term cost of hedging. (LocationĀ 1044)

Thus the rule of thumb is that when volatility is low, prefer straight puts (because they are more volatility sensitive), and for higher volatilities, prefer put spreads. Rotation refers to the exchange of direct hedges in one market for indirect hedges in other markets. For instance, if we can identify that the equity risk factor is responsible for the drawdown in many assets simultaneously, we want to sell options on assets that are more expensive and replace them with relatively cheaper options on other assets. Immediate examples would be replacing equity put options with credit-default swaps or puts on carry currencies. (LocationĀ 1049)

The option is sold whenever its value reaches a particular multiple, for example, five times the cost of the initial annual budget. (LocationĀ 1195)

It creates a commitment to a strategy that allows ā€œbuying on dipsā€ by monetizing an option or selling a hedging asset that has increased in value. As volatility subsides, the equity market tends to rise, and the risk premium embedded in the equity market also falls to normal levels. By rolling the profits from the tail hedge into the underlying equity market, the investor can turn a defensive strategy into an offensive strategy by taking profits from hedges, thus harvesting the benefit of the increased risk premium. (LocationĀ 1245)

Over the 60-year period it returns 16 percent less than the buy-and-hold strategy with no tail hedge, a loss of approximately 27 bp/year. (LocationĀ 1251)

As mentioned earlier, when volatility is low, we would naturally prefer outright put options because the potential gain from volatility rising is substantial. (LocationĀ 1421)

(buying a close to ATM put and selling a deeper OTM put) to essentially obtain the same profile of protection but with an added benefit from ā€œselling the skew.ā€ (LocationĀ 1423)

On the other hand, a small allocation (3 to 5 percent) to momentum-based strategies may provide significant risk-mitigation benefits. This is so because of the asymmetry and option-like behavior of the momentum factor returns: it tends to pay off large when the bounds of mean reversion break and effectively helps to provide portfolio diversification against large movements in asset (LocationĀ 1712)

Investors are averse to paying for tail risk hedging. Our research shows that (1) cost-effective tail hedging allows one to build more efficient portfolios with higher ex ante long-term expected returns, (2) tail hedging allows defense while allowing offense when its most productive, and (3) the ex post returns to active tail-hedged portfolios have been superior to passive buy-and-hold portfolios. (LocationĀ 1753)

The outcome where the hedge would expire worthless is the more normal outcome, and hence its impact is more salient. (LocationĀ 1947)

Intuitively, we note that when a large gain arrives together with a small loss, the gain and loss are generally aggregated or combined. (LocationĀ 1955)

People generally tend to overweight the probability of rare events and underweight the probability of more common events. (LocationĀ 1963)

Thus, despite well-known empirical literature and the belief that, on average, investors pay too much for insurance (as do home owners, automobile owners, etc.), there seems to be no immediate and riskless way to take advantage of a bias for tail insurance even if it did exist. (LocationĀ 1974)

is clearly borne out in the market for equity index options, where deeply OTM puts have consistently traded at a higher implied volatility (and price) than a deeply OTM call the same distance away from the forward price. (LocationĀ 1979)

For instance, immediately prior to the financial crisis, low-probability events were actually underweighted; that is, the probability of a fat-tailed event was underpriced, and tail protection was quite cheap. Once the crisis began, this shifted quickly, and the weighting function rapidly took on a familiar inverse-S-shaped structure, where low-probability events were being underweighted (see, e.g., Polkovnichenko and Zhao 2010; Wolff et al. 2009). (LocationĀ 2043)

As an exercise, I priced a one-year 25 percent OTM put on the S&P500 on March 22, 2013 (expiry March 21, 2014), which is a very typical benchmark option for a 60/40 equity/bond portfolio with a 15 percent portfolio-level attachment point. The price of the option with the implied volatility of 24.47 percent for the 25 percent OTM strike was approximately 1.46 percent, using Black-Scholes. (LocationĀ 2065)