Emlyn James Flint

Adapting to Market Regimes with Timed Hedging

We address a very topical – and to some extent, intractable – question: When should I hedge? By analysing South African historical market returns, we show that only a handful of extreme returns – which are well characterised by two simple quantitative indicators – can have a significant impact on portfolio performance. Motivated by this finding, we introduce a range of quantitative indicators grouped into separate return, risk and regime categories. We first outline a systematic process for creating a timed hedging strategy and then backtest how effective each of the proposed indicators are as hedge timing signals under real world market conditions. A total of 36 hedge timing indicators are tested using five common hedging structures. Detailed results and discussion are provided for each hedging structure. In general, the long-term timed hedge backtests show very promising results, producing timed hedged portfolios with returns as good or better than the index but with significantly lower volatility and tail risk.

Currency Hedging for Global Equity Portfolios: Historical Performance

Offshore assets present investors with an increased investment universe and additional opportunities for reward, but embedded exposure to exchange rates can result in additional risk. In this work, we consider a global equity portfolio of five equity indices (US, Japan, Europe, UK and Canada), and examine the historical performance of currency hedging strategies in the context of portfolio risk reduction. Two types of scenario are studied; namely, a holding in a single foreign equity index, and a model global equity portfolio. In the case of the global equity portfolio, it is assumed that the allocations to the equities are fixed and exposures to currencies are solved for in a single combined optimization, taking into account all interactions between the equity indices and currencies. We show that a theoretical minimum-risk currency exposure level can be calculated which results in less risk than portfolios featuring either full or zero currency exposure. Furthermore, we show that the risk reduction achieved historically by following an easily implementable dynamic currency hedging strategy is comparable to that given by the theoretical, perfect knowledge calculations. Given our focus on minimum-risk hedging strategies, we find that using certain hedging instruments can slightly reduce total portfolio returns. However, in all cases the significant reduction in volatility always leads to superior risk-adjusted returns for the global equity portfolios. Moreover, certain hedging instruments in our historical tests do actually provide both risk reduction and return enhancement.

Thinking About Theta: An Analysis of Time Decay, Early Unwind and Closeout Feedback Effects

Near-the-money options experience a rapid decline in time value over the weeks leading up to the expiry date. A possible strategy to alleviate the impact of the time decay effect is to unwind the hedge prior to expiry. However, appreciable time value is present for a reason: it is an indication that the final expiry value the option is uncertain and that there is a chance that the option could increase further in value. In this work, historical data is examined in order to determine whether or not a South African equity index exhibits any abnormal behaviour prior to expiry that would affect one’s view on the likelihood of a hedge expiring in-the-money. We present the results of analyses for two types of expiry-related effect in the local market, namely abnormal returns for periods immediately prior to expiry and price clustering where the underlying exhibits a higher probability of closing near a strike price on an expiry date. We also discuss the historical performance of a strategy aimed at reducing exposure to time decay in a systematic manner in which a derivative strategy is rolled well before the expiry date. It is shown that for the period analysed, an investor who wished to roll a hedge every 3 months achieved an appreciable increase in realised return for a moderate increase in risk by rolling a longer term option every 3 months compared to holding a 3 month option for the full term.

Regime-Based Tactical Allocation for Equity Factors and Balanced Portfolios

It is now an accepted fact that the majority of financial markets worldwide are neither normal nor constant, and South Africa is no exception. One idea that can be used to understand such markets and has been gaining popularity recently is that of regimes and regime-switching models. In this research, we consider whether regimes can add value to the asset allocation process. Four methods for regime identification – economic cycle variables, fundamental valuation metrics, technical market indicators and statistical regime-switching models – are discussed and tested on two asset universes – long-only South African equity factor returns and representative balanced portfolio asset class returns. We find several promising regime indicators and use these to create two regime-based tactical allocation frameworks. Out-of-sample testing on both the equity factor and balanced asset class data shows very promising results, with both regime-based tactical strategies outperforming their respective static benchmarks on an absolute return and risk-adjusted return basis.

Fractional Black-Scholes Option Pricing, Volatility Calibration and Implied Hurst Exponents

This paper addresses several theoretical and practical issues in option pricing and implied volatility calibration in a fractional Black-Scholes market. In particular, we discuss how the fractional Black-Scholes model admits a non-constant implied volatility term structure when the Hurst exponent is not 0.5, and also that one-year implied volatility is independent of Hurst exponent and equivalent to fractional volatility. Building on these observations, we introduce a novel 8-parameter fractional Black-Scholes inspired, or FBSI, model. This deterministic volatility surface model is based on the fractional Black-Scholes framework and uses Gatheral’s (2004) SVI pamaterisation for the fractional volatility skew and a quadratic parameterisation for the Hurst exponent skew. The issue of arbitrage-free calibration for the FBSI model is addressed in depth and it is proven in general that any FBSI volatility surface will be free from calendar-spread arbitrage. The FBSI model is empirically tested on implied volatility data on a South African equity index as well as the USDZAR exchange rate. Results show that the FBSI model fits the equity index implied volatility data very well and that a more flexible Hurst exponent parameterisation is needed to accurately fit the USDZAR implied volatility surface data.

Currency Options for Fund Managers

Options on a number of currency pairs involving the Rand are readily available to investors in the South African market. The most widely implemented strategies are those involving call options giving geared upside exposure to the underlying. However, overlay strategies such as collars and fences offer fund managers a powerful mechanism by which to control risk arising from exposure to foreign currencies.We motivate the need for consideration of downside protection against adverse currency moves and show that a weakening Rand is not a certainty. The behaviour of selected strategies over various historical periods is demonstrated in order to gain an intuitive understanding of performance under different types of currency scenario. Examples are considered both from the point of view of an investor holding foreign cash as an additional asset class, as well as investors holding foreign risky assets wishing to control the impact of currency moves on the returns of their offshore holdings. Finally, we discuss an interesting exotic variation of the vanilla zero-cost collar that allows one to increase potential upside without introducing the possibility of negative returns.

The Information Hidden in Derivatives Markets

One of the most important aspects in portfolio management is having an accurate understanding of the future possible returns of the underlying assets. Unfortunately, estimating such return distributions is anything but trivial. In this research, we consider the information embedded in the derivatives market. Derivatives are forward-looking instruments by design and thus should contain forward-looking information about their underlying assets. We describe how forward-looking information on the statistical properties of an asset can be extracted directly from options market data and how this can be used practically in portfolio management. While the extraction of a forward-looking risk-neutral distribution is well-established in the literature, obtaining information on future real-world distributions was until recently thought to be impossible. However, recent work by Ross (2015) has shown that it is indeed possible to derive exactly this distribution purely from options market data. We describe a robust implementation of Ross’s method on a history of weekly Top40 Index and USDZAR implied volatility surfaces. We outline some graphical ideas on how one can use this information descriptively and prescriptively and furthermore analyse the recovered moments – expected return, volatility, skewness and kurtosis – from the implied distributions. These recovered real-world moments are shown to be in line with economic rationale and also show promising results when used as signals within a simple TAA framework.

In Search of the Perfect Hedge Underlying

This report attempts to answer the question: What underlying portfolio should one use to hedge an active fund? We introduce a framework which allows us to conduct analysis on simulated realistic active portfolios in order to build intuition as to how hedge mismatch error affects the level of protection from a given hedge. We show that for typical market conditions, hedge effectiveness improves dramatically when using a hedge portfolio that more accurately reflects the underlying portfolio. This has clear consequences for using generic index options to hedge highly active portfolios. We also showcase several active return and tracking error decompositions that allow one to precisely quantify and thus manage the sources of risk and rewards within a given portfolio. We then discuss a mixed integer quadratic programming formulation that enables us to search across a large investment universe in order to find the subset of stocks that most closely replicates a given portfolio’s performance, whilst simultaneously complying with realistic market constraints. Motivated by these three elements, we introduce several alternative hedging methods for the fund manager to implement a better hedge for their active portfolio. In this report, we focus specifically on the use of long-only and long/short custom basket options as a means of creating an appropriate portfolio hedge.

Currency Hedge Design: Accounting for Uncertain Correlation and Volatility

In previous Peregrine Securities work, it was shown that currency hedge selection can be approached in an optimization framework and that the particular choice of hedge is strongly dependent on the correlation between the exchange rate and the foreign asset. Unfortunately, correlations between assets are generally unstable and it can be difficult to forecast an appropriate value to use as input to the optimizer. In this work we outline an approach to the determination of an optimal currency hedge in the presence of non-constant volatility and correlation. It is shown that implementation of the dynamic conditional correlation (DCC) model in a simulation framework allows one to incorporate the effects of time-varying parameters into the hedge selection process in a systematic and quantitative manner. An important finding is that the particular choice of short-term hedge depends to a large extent on the current value of correlation, emphasising the need for a modelling framework that provides accurate estimates of time-varying correlation.

Improving Portfolio Allocation Through Covariance Matrix Filtering

The sample covariance matrix is known to contain substantial statistical noise, making it inappropriate for use in financial decision making. Leading researchers have proposed various filtering methods that attempt to reduce the level of noise in the covariance matrix estimator. In most cases, these methods can be interpreted by analysing how they adjust the eigen-structure of the sample correlation matrix. This paper compares the filtering methods using a theoretical eigen-framework as well as a practical South African experiment. By focussing on the eigen-structure, the sources of statistical noise are identified. The sample correlation matrix suffers from excess dispersion in its eigenvalues and excess dispersion in its pairwise correlations. Bayesian shrinkage estimators that effectively remove the excess dispersion provide superior performance in terms of out-of-sample portfolio risk and turnover. Specifically, the optimal filtering method is a blend between the sample covariance matrix, its diagonal elements and the covariance matrix based on the constant correlation model.