Nine portfolio managers introduce their derivative hedging practices in Fabozzi's paper
These asset managers' practices are a good match to John Hull's biblical OFOD text.
I taught derivatives for years but only traded a few options (and have limited exposure to actual institutional hedging practices), so I did enjoy Fabozzi’s recently published Intricacies of Implementing Derivatives: Insights from Asset Management Experts, Part 1. In this first part, nine legit practitioners introduce some of their own derivative hedging practices. The good news is that we who studied John Hull’s biblical OFOD (e.g., FRM) did learn concepts that are actually applied! Some notes:
Application A: Asset allocation using futures
Simple example of altering equity/bond mix of a cash portfolio with stock (and bond) index futures. The example shows shifting from 60%/40% equity/bond to 65%/35% equity/bond with a long/short trade that buys MSCI World (equity) index futures and shorts bond futures. The cited advantages are lower explicit transaction costs, standard contract sizes, and the “obvious benefit of futures is that they are generally unfunded investments.”
Indeed, we always say that futures are unfunded, liquid and standardized. Liquidity is enabled by standardization. Derivatives are unfunded, by definition, but instead they require initial (and maintenance) margin. To me, what’s missing1 from the simple presentation is maturity (aka, the time dimension) and basis risk. Unlike stocks, the futures contracts mature on their deliver months, so (eg), you have to roll them. I don’t really know, maybe it’s the case that rolling such futures (in such a way that maturity is not really an issue) is easy and cheap.
Application B: Hedging with Stock Index Futures and Put Options
In regard to using stock index futures, this is a textbook approach to modifying the portfolio’s beta2:
And the author (Robert Harlow, CFA, CAIA) shows an alternative that buys a 20-delta put options:
His selected hypothetical scenario (starting on 2/28/2020 at the covid onset) is instructive because the options hedge outperformed due their complexity relative to the futures hedge. Options are nonlinear with gamma and vega exposure:
“The option approach was much more attractive than the futures approach in this example because the realized move in the underlying was so large. In other words, the option was underpricing subsequent volatility. However, most of the time, options tend to trade at a premium, a phenomenon known as the “volatility risk premium” (VRP). One way to measure the VRP is to compare option implied volatility to subsequent realized volatility. Historically, this spread is significant and positive, meaning implied volatility is on average a few percentage points higher than historical realized volatility and regular purchasers of index options tend to lose money. Because of the fact that futures contracts are not exposed to the VRP, they will tend to be less expensive hedging instruments than put options for the same amount of linear exposure reduction. Additionally, transaction costs on futures are far lower than transaction costs on options.” — Robert Harlow, CFA, CAIA
Application C: Using Options for Tail Risk Hedging
In this example, the portfolio manager “oversee[s] a $100 million investment in the S&P 500 index, via an exchange-traded fund such the SPDR S&P 500 ETF Trust (SPY) or the iShares Core S&P 500 ETF” and s/he hedges with a 90-day, 20% out-of-the-money (OTM) European put that’s “usually suitable if the portfolio manager expects a sharp and steep market shock like the one that occurred during the COVID-19 crisis.”
On my first read, I’ll admit that I wondered if the calculation was wrong because the cost of the put is only 17 basis points (I never see option prices so low …). But it really is that cheap3:
It’s so cheap because it’s -20% underwater and short-dated: 90/365 = 0.247 years is similar to 60/250 = 0.238 years (by habit, I tend to revert to trading days). The author (Vineer Bhansali) knows his subject: it’s worth reading the brief discussion on this option’s Greeks4.
About this tail hedge, this is my takeaway: it’s very specific (narrow?) crash insurance that will pay “extra” in the adverse outcome due to convexity but convexity’s price is time decay (theta). Indeed, I used to teach from Hull’s OFOD textbook, and per the BSM differential equation, we’d show why “theta can to some extent be regarded as a proxy for gamma in a delta-neutral portfolio.”5 Put another way, you pay for the benefit of high convexity (aka, gamma) with rapid time decay.
I’m less interested in Application D and Application E because they refer to liquidity management and cash equitization6.
Application F: Foreign Exchange Derivative Hedging for Equity Portfolios is detailed and I haven’t reviewed it yet.
Application G illustrated bond portfolio hedging with US Treasury Futures. It looks daunting—and I know from experience that T-bond futures are one of the hardest topics for CFA/FRM candidates—but it’s textbook (although to really grok it, best to supplement Hull with Bruce Tuckman because Tuckman goes deep similarly on P/L scenarios).
Application H is brief but necessary because it’s the only review of the hedge ratio, as given by the author (H.1):
And mathematically, that’s the same beta as above: it’s the (ex post) intercept of the regression of the strategy (aka, portfolio) returns, r, against the factor returns (aka, benchmark, index, or market). I’ll sometimes write beta β*(r, x) to explicate that it’s a beta of the portfolio with respect to the factors, just to remind that it’s not β*(x, r) because β*(r, x) <> β*(x, r) although ρ(x, r) = ρ(r, x, r). The hedge ratio is one of the most essential, elegant formulas in finance, but it’s almost too convenient: I highly recommend the author’s explanation of whether the minimum variance hedge is itself optimal, or advisable,
Application I refers not to hedging but rather how “derivatives are often used by proprietary traders to express active, speculative views”.
Don’t get me wrong. The author of the first case, Scott Hixon, CFA, certainly knows more about the practical nuances than me. He’s just illustrating the advantages of futures with the simplest possible example.
This formula is solving for target dollar beta. The example assumes a portfolio cash value of $150.0 million with a 1.15 beta while the S&P 500 index futures price is 2,951. This portfolio has a dollar beta of $150.0 million * 1.15 = $172.875 million. Each mini futures contract has a $50 multiplier so each e-mini futures contact has a dollar beta of 2,951 * $50 = $147,500. To neutralize the portfolio, you’d short $172.875 million ÷ $147,500 = 1,172 contracts. In the example, the manager only wants to achieve unit (1.0) beta, so he just needs to reduce dollar beta by $172.875 - $150.000 = 22.875 million, which requires 22.875 mm ÷ $147,500 = 155 e-mini futures contracts.
“The option also has higher-order Greeks such as the rate of change of delta with respect to time (called Charm or delta decay) which come into play when managing the risks of options over time.” — Vineer Bhansali
Hull, John C.. Options, Futures, and Other Derivatives (p. 411). Pearson Education. Kindle Edition.
“Cash equitization is a strategy designed to eliminate or effectively manage the cash drag by equitizing cash holdings mostly through trading derivatives. [It has become the industry convention that the word equitize applies to all asset classes including but not limited to equities. Therefore, the same cash management strategy in a fixed income fund is also referred to as cash equitization regardless if there are equities in the holdings or not.] In general, any easy to trade derivatives instruments with sufficient liquidity, relatively straightforward middle and back office operational.” — Wai Lee, PhD, and Eddie C. Cheng, CFA