In the fifth and final instalment in a series of articles on risk management techniques in asset management, NoÃ«l Amenc and Lionel Martellini look at the benefits of risk hedging with structured products
The use of a structured form of asset management by institutional investors has found its roots in constant proportion portfolio insurance (CPPI) and other forms of portfolio insurance strategies. Since then, a wide range of structured products has been developed, allowing institutional investors to customise their exposure to equity markets, so as to make it consistent with their preferences and liability-driven constraints. Generally speaking, structured products, which allow the user to achieve a non-linear, option-like exposure with respect to the return on traditional asset classes, are natural investment vehicles for institutional investors, who have a particularly strong preference for non-linear payoffs, because of the non-linear nature of the liability constraints they face (see for example Draper and Shimko, 1993). From an academic standpoint, Leland (1980) has shown – in a fairly general context – that investors whose risk tolerance increases with wealth more rapidly than the average will rationally wish to obtain portfolio insurance. This is the case in particular for institutional investors, whose portfolio value must at all costs exceed a given value, but thereafter can accept reasonable risks.
In an attempt to clarify the terminology used, it should be stated that we use interchangeably here the label ‘structured products’ or ‘structured investment strategies’ to refer to any contractual non-linear payoff resulting from a large variety of quantitative asset management techniques. The definition of ‘structured asset management’, as a family of investment strategies, is actually quite large, as it encompasses static asset allocation strategies as a trivial, specific case, dynamic allocation strategies such as CPPI and OBPI (option-based portfolio insurance), as well as payoffs resulting from the inclusion of exotic derivatives.
In what follows, we first present an overview of structured products, and also present the risk management benefits derived from including such assets.
The salient characteristic of structured products is the repackaging of strategies that involve long and short positions in derivatives, or alternatively in dynamic trading strategies that replicate derivatives-type payoffs, and the underlying asset into an investment vehicle that is easily accessible by investors. In particular, since the investor does not have to access derivatives markets himself, he is not constrained to respect margin requirements.
Historically, the first occurrence of a structured form of asset management was the introduction of portfolio insurance, such as the simple OBPI strategy. While any asset may be used in a structured product, we focus on the case of a stock index as an underlying. In the first part of our article, we provide an overview of the institutional aspects of structured products. We also review a range of structured products that are available to institutional investors.
The concrete investment vehicle that is used to provide a structured product to an investor may take on various legal or organisational forms. These obviously depend on the legal framework in the given legislation. However, in principle, structured products may be organised as bonds or as investment funds. Bonds allow a straightforward implementation of structured products that involve a capital guarantee. The guarantee is achieved because the holder of the bond is entitled to the payment of the face value at maturity. The coupon payment may then be linked to the price of an underlying asset. In this way, the bondholder effectively holds a portfolio of a zero-coupon bond and a derivative asset. In other words, one component of the payoff at maturity is certain while the other part depends on the price of the underlying asset. While bonds that have a limited lifetime may seem to be a more natural vehicle, investment funds also allow structured products to be implemented. Investment funds pool investors’ wealth into a portfolio whose management is delegated to a professional manager. The investment policy of the fund may then be defined as a strategy that achieves the desired payoff at maturity. In particular, the fund manager may make use of government bonds, an underlying asset and derivatives on the latter in order to achieve the desired payoff.
Since secondary markets exist for both bonds and investment fund shares, structured products may be exchanged between investors outside the subscription at the initial date and redemption at maturity. In fact, the issuer of the structured product often acts as a market maker for his product. It is typically argued that providers of structured products are more efficient than end users in managing products involving non-linear payoffs for a variety of reasons, including, among others, economies of scale, privileged market access (to the underlyings and to the derivatives), mutualisation effect (managing a portfolio of options is cheaper than managing each option individually), and efficient financing (better access to money markets compared to conditions that would be faced by end users if they had to borrow to implement the corresponding dynamic replication strategy).
While the immense variety of structured products makes it difficult to provide a clear classification, existing products may be distinguished among several areas. From an investor’s perspective, what matters is the type of payoff he/she obtains with the structured products. Therefore, the classification below builds on the payoffs and is partly based on a common way of classifying options.
Structured products offer payoffs that are non-linear functions of the price of an underlying. According to the type of non-linearity, one can divide these products into those with concave and those with convex payoffs. Convex payoffs are typical for products that include a capital guarantee, typically offered by an investment bank. This may be the most obvious form of non-linearity investors are looking for. Concave payoffs occur with discount certificates and other covered call writing strategies. These products allow investors to access the limited upside potential of a given asset at a lower price than full upside potential. More complex structured products may mix both types of non-linearity.
One of the reasons for investing in structured products is their exposure to changes in volatility of the underlying asset. Sensitivity (Vega) of the structured product may be positive or negative. Depending on their views on the evolution of volatility, investors may optimally select different types of exposure.
• Path dependency
Rather than depending on the observed price of the underlying asset at maturity, the payoff may be a function of the extreme (lookback or hindsight option) or average (Asian option) price observed during the lifetime of the structured product. For example, path-dependent products are used by investors who want to lock in the performance of a perfect timing strategy on a single asset (which corresponds to a lookback straddle strategy).
• Type of underlying asset
The underlying assets involved in a structured product may be an index or a basket of stocks. A number of structured products involve payoffs that depend on a large number of assets. Structures may include options to exchange one asset for another, or structures that pay the maximum return among a number of assets. Such products are used by investors who want to lock in the performance of a strategy that times perfectly among a number of assets.
It can be argued that typical institutional investors, with a strict focus on risk management driven by the presence of liability constraints, should optimally allocate a significant fraction of their portfolio to structured investment strategies, since such products allow investors to profit from the equity risk premium without being fully exposed to the downside risk associated with investing in stocks.
In order to show how this structured product can be used by an institutional investor, Goltz, Martellini and Simsek (2005) considered the following framework. Our investor maximises his or her holding period returns, subject to a level of Conditional Value-at-Risk (CVaR). As opposed to Value-at-Risk (VaR), which describes a given quantile – a maximum loss that will not be exceeded with a given confidence level – the CVaR measure summarises the distribution of returns that are below this threshold. This allows us to take into account both the existence of fat tails in the return distributions and institutional investors’ aversion towards taking on extreme risk.
In order to assess the inclusion of the structured product, they consider that the investor has access to a stock portfolio (such as a stock market index) and to a bond portfolio (such as a global bond index, which we model as a zero-coupon bond with constant time-to-maturity). We model an economy with stochastic interest rates and mean reversion in the excess returns on the stock index. We choose to introduce these two features because both effects are well-documented, stylised features of financial markets. More importantly, both of these features matter to institutional investors when it comes to their asset allocation decision. Time variation in the interest rate affects both the price of the bond holdings of an investor and the level of his liabilities. Mean reversion in long horizon returns, that is, the fact that periods with high returns are prone to be followed by periods of low returns and vice versa, obviously also has important implications for the asset allocation decision.
On each path, they calculate the returns for stocks, bonds and for the guaranteed structured product (GSP). The scenarios for the total returns on each asset class are then fed to the optimisation programme, which allows us to draw efficient frontiers. They minimise a convex combination of the portfolio CVaR and the negative of the expected portfolio return for different levels of risk aversion. Their results show that considerable improvement in the efficient frontiers depicting the risk return trade-off of the investor is achieved when the latter is allowed to invest in the structured product.
In the following figure, extracted from Goltz, Martellini and Simsek (2005), one may observe the change in asset allocation with respect to the change in risk aversion. These allocations correspond to portfolios labelled on the two efficient frontiers above. The GSP helps the risk-averse investors increase their returns by replacing the stock allocation in their portfolio and the risk-seeking investors to decrease the shortfall risk they are exposed to by replacing the bonds in their portfolio.
For investors with a strong aversion to risk (points 1–3) the weight of the structured product takes on values between 70%–90%. On the other hand, risk-seeking investors (points 5–9) can actually decrease shortfall risk exposure by replacing the bonds in their portfolio with a structured product. For this group of investors, optimal allocation to the structured product ranges from 10%–70%. In fact, only the most risk-seeking investors (point 10) would have a zero allocation for a structured product and invest 100% of their wealth in stocks.
Likewise, most portfolios, especially those corresponding to a high risk aversion parameter, contain a significant allocation to the structured product. On the one hand, this product helps the risk-averse investors increase their returns by replacing the stock allocation in their portfolio. The weight of the structured product for this type of investors takes on values between 70%–90%. On the other hand, the risk-seeking investors can actually decrease the shortfall risk they are exposed to by replacing the bonds in their portfolio with the structured product. Optimal allocation to the structured product for this group of investors ranges from 10%–70%. In fact, only the most risk-seeking investors have a zero allocation to the structured product and invest 100% of their wealth in stocks.
One may also study the impact of the presence of realistic levels of market frictions and heterogeneous expectations on volatility estimates. The inclusion of fees for the structured product is modelled by overpricing the option component relative to its theoretical value, which reduces the upside participation the structured product allows for.
As a consequence of the fees, the stock and bond indices become more attractive and replace part of the allocation to the structured product. The decrease in allocation to the structured product, however, has been found to be relatively small, even for high levels of fees.
The previous analysis has justified a demand from institutional investors for the structured product for the sole purpose of gaining access to non-linear return profiles. Another motivation for investors to buy a structured product may lie in expectations on volatility that diverge from those of the structurer. In fact, an underpricing of the structured product by the structurer according to the investor’s expectations of future volatility gives an additional motivation for investing. On the other hand, if the product is overpriced according to the expectations of the investor, this would reduce the allocation he chooses.
Since it is not reasonable to expect institutional investors to allocate a dominant fraction of their portfolio to structured products, one may also test the impact of imposing an upper bound on the allocation to the product. Obviously, the weight constraint is binding because the optimal allocation in the base case was very high. Overall, these results strongly suggest that adding even a limited fraction of the overall allocation to structured products allows for significant benefits.
It is important, however, to recognise that an institutional investor should always weigh the cost associated with the convexity (downside protection) involved in these standard types of structured products versus the expected benefits. In particular, one can argue that when the investor has accumulated a sufficient amount of realised gains in the management of the portfolio performance, it can be in a position to take on naked, as opposed to covered, positions. In other words, the institutional investor can always decide to self-insure against adverse market movements. The cost of the protection in this case is simply the cost of equity for the company, which should be compared to the cost of an outside protection provided for by the marketplace, which may or many not be higher.
Given the fair value principle that leads to a marked-to-market evaluation of assets in phase one, and assets and liabilities in phase two, the new IFRS accounting standards provide strong incentive for the use of advanced risk management techniques, based on risk diversification or risk hedging, that lie at the core of some of the most spectacular recent advances in portfolio theory.
The LDI approach to asset-liability management is consistent with a ‘separation theorem’ that advocates that the objectives of risk management and performance generation can be best dealt with when handled separately. On the one hand, the institutional investor can design a liability-matching or liability-hedging portfolio based on cash instruments, or derivatives for better customisation of the strategy. On the other hand, performance generation can be dealt with in the traditional context of asset management, with an enhanced focus on risk management justifying the use of such sophisticated techniques for risk diversification of risk hedging (with or without derivatives).
Unfortunately, however, implementing these risk management strategies requires a fair level of flexibility in the use of dynamic portfolio strategies and/or derivatives instruments. The problem is that neither the implementation of dynamic strategies nor the use of derivatives is facilitated by IFRS accounting standards. Hence, it seems that these new accounting standards lead companies to a rather schizophrenic situation, where on the one hand, the risks are emphasised more, but on the other, their management is made more difficult.
© fe December 2007 / January 2008
This article is based on research included in the EDHEC publication, The Impact of IFRS and Solvency II on Asset-Liability Management and Asset Management of Insurance Companies, by Noël Amenc, Philippe Foulquier, Lionel Martellini and Samuel Sender, November 2006. This research was sponsored by AXA Investment Managers.