Portfolio Insurance Strategies Research Articles

Asset allocation via life-cycle adjusted PPI strategy: evidence from the U.S. and China stock market

ABSTRACT In this article, we extend the Proportion Portfolio Insurance (PPI) strategy by a life-cycle adjusted multiplier to adapt to the scenario of multi-period investment with continuous cash inflows, such as variable annuity with minimal guarantees. Using variational methods, we establish the closed-form optimal risk multiplier that determines the proportion of risky assets. It is negatively correlated with the life-cycle phase and previous performance but positively correlated with market conditions. We test the effectiveness of the life-cycle adjusted PPI strategy in a discrete-time framework for application considerations. In the U.S. and China stock markets, the life-cycle strategies outperform benchmark strategies under various measurements with robust results. Variable annuity investors who are less risk-averse or accept a lower guarantee ratio can benefit most from our strategy.

Portfolio insurance using leveraged ETFs

This study examines the use of Leveraged Exchange Traded Funds (LETFs) within a constant proportional portfolio insurance (CPPI) strategy. The advantage of using LETFs in such a strategy is that it allows a greater percentage of the portfolio to be invested in the risk-free rate relative to a traditional CPPI. Where a standard CPPI strategy may require 50% of the portfolio to be invested in equities, using a 2x LETF only requires 25%, and a 3x LETF only requires 16.7% to attain the same effective exposure to equities. Results show when the risk-free asset is yielding at least 3% or the 1 year minus 90-day Treasury exceeds 1%, the use of LETFs within a CPPI framework results in annual returns approximately 1–2% higher with better Sharpe, Sortino, Omega, and Cumulative Prospect Values while reducing Value at Risk (VaR) and Excess Shortfall (ES) below VaR.

Portfolio insurance strategy in the cryptocurrency market

In this study, we perform a comparative analysis of portfolio insurance strategies for the cryptocurrency market. We examine performance evaluation regarding the various downside risks under different economic conditions and explore the impact of investors’ utility based on Expected Utility and Prospect Theory. We confirm evident economic gains using portfolio insurance in the cryptocurrency market and demonstrate reduced downside risks with a higher Omega ratio, implying reasonable risk-managed profit compared to buy-and-hold. Most importantly, portfolio insurance provides opportunities for a higher utility in cryptocurrency than in the traditional stock market, indicating a greater economic value of portfolio insurance.

Constant or Variable? A Performance Analysis among Portfolio Insurance Strategies

In this paper, we propose a comparison among three portfolio insurance strategies, namely the constant proportion portfolio insurance, the time-invariant portfolio protection, and the exponential proportion portfolio insurance, via an in-depth performance analysis. We aim to ascertain whether strategies characterized by variable parameters can outperform those with constant parameters by measuring potential returns, investment riskiness, downside protection capability, and ability to capture market upside. The results, achieved in a model-free framework by exploiting bootstrapping techniques, advise that no winning strategy exists overall, even when considering different volatility regimes, rebalancing frequencies, and protection levels.

A performance evaluation of portfolio insurance under the Black and Scholes framework: An application of the economic index of riskiness

The investment performance of an option-based portfolio insurance strategy is compared with a buy-and-hold strategy under the Black and Scholes framework. Under this setup, we can derive the return distributions for the portfolio insurance and buy-and-hold strategies. According to the economic performance measure, which generalizes the Sharpe measure, the portfolio insurance with no transaction costs almost outperforms buy-and-hold in all scenarios studied. Further, if the percent of principal protected is chosen optimally, the portfolio insurance is better than buy-and-hold. Although the portfolio insurance loses some ground for short investment horizons with transaction costs, the portfolio insurance performs relatively well for long investment horizons.

A Tail Measure With Variable Risk Tolerance: Application in Dynamic Portfolio Insurance Strategy

A Tail Measure With Variable Risk Tolerance: Application in Dynamic Portfolio Insurance Strategy

Hedge inflation risk of specific purpose guarantee funds

AbstractSpecific purpose guarantee funds (SPGFs) such as pension guarantee funds are popular among investors with both specific investment purpose and guaranteed return requirement but receive little academic attention. We propose a practical purpose‐oriented constant proportion portfolio insurance (PO‐CPPI) strategy that optimally allocates its assets into a risk‐free fund (floor) and a purpose‐related portfolio (cushion) to maximize prospect theory investors' utility with consideration of their purpose‐related inflation risk. Our closed‐form solution of optimal PO‐CPPI allocation derived in the continuous time case and Monte‐Carlo simulations in the discrete‐time and dynamic cases prove the superiority of PO‐CPPI over general portfolio insurance strategies.

Measuring and Managing the Opportunity Cost of Downside Risk Protection

Portfolio insurance targets the elimination of losses in excess of a predefined threshold while allowing for access to the upside potential of an underlying risky asset. This article studies the implications of the choice of the underlying asset on the frequency and magnitude of floor breaches and on the loss of performance associated with the protection against downside risk; it considers in particular the use of a diversified portfolio of stocks as opposed to a single stock. The authors find that gap risk is more prominent when insurance is applied to a stock than to a portfolio, but it can be reduced by implementing time-invariant portfolio protection or by letting the multiplier decrease when volatility rises. However, option-based insurance with dynamic option replication has a large probability of breaching, no matter the underlying asset. Among diversified portfolios, minimum variance portfolios minimize the opportunity cost of insurance, but the ranking of diversified portfolios in terms of long-term returns does not appear to be disturbed by insurance. <b>Key Findings</b> ▪ Floor breaches in a portfolio insurance strategy occur more frequently and larger if the risky asset of the strategy is a single stock than if it is a diversified portfolio of stocks. ▪ Option-based portfolio insurance with dynamic replication of the option involves large gap risk, whether the risky asset is a single stock or a diversified portfolio. ▪ The opportunity cost of insurance against downside risk, measured as the long-term return spread between the insured portfolio and its underlying risky asset, is minimized by taking the risky asset to be the minimum variance portfolio.

Investigating the Performance of Portfolio Insurance Strategies under a Regime Switching Markov Model in Tehran Stock Exchange

هدف: استراتژی‌های بیمه سبد، نوعی روش‌های ساختاری هستند که با تعیین مقداری برای کف، سطح مشخصی از اطمینان (بیمه) را ارائه می‌کنند. به بیان دیگر با استفاده از این استراتژی‌ها‌ی معاملاتی، می‌توان حداقل بازده از پیش‌ تعیین‌ شده‎ای را کسب کرد. این پژوهش ضمن بیان نحوه ساخت و تخصیص دارایی در این استراتژی‌ها، به بررسی عملکرد استراتژی بیمه سبد با نسبت ثابت (CPPI) و بیمه سبد بر اساس ارزش در معرض ریسک (VBPI) می‌پردازد. روش: ابتدا مدل ریاضی رویکرد با نسبت ثابت در حالت محدودشده، ارائه شد. در حالت محدودشده، استقراض با نرخ بدون ریسک امکان‌پذیر نیست. در ادامه با استفاده از تبدیل فوریه تابع مشخصه، تابع چگالی بازده استخراج شد. با استفاده از تابع چگالی بازده، ارزش در معرض ریسک در سطوح اطمینان مدنظر به‌دست آمد و در نهایت به‎کمک آن، مدل ریاضی رویکرد مبتنی بر ارزش در معرض ریسک ارائه‌ شد. به‌منظور برآورد روند حرکتی دارایی ریسکی، از مدل با رژیم متغیر استفاده شد که به واقعیت نزدیک‌تر است. یافته‌ها: نتایج نشان می‌دهد که هر دو استراتژی در کنترل ریسک نامطلوب موفق عمل کرده‌اند و این عملکرد با افزایش سطح اطمینان و تعداد دفعات تغییر چیدمان سبد در طول دوره سرمایه‌گذاری بهبود می‌یابد. در مقایسه دو استراتژی، سنجه امگا نشان می‌دهد که در آستانه‌های پایین عملکرد استراتژی با نسبت ثابت بهتر است. همچنین پراکندگی نتایج شبیه‌سازی‌شده برای ارزش نهایی سبد نشان داد که رویکرد با نسبت ثابت در محافظت از کف عملکرد بهتری دارد. نتیجه‌گیری: استراتژی‌های بیمه سبد، ریسک نامطلوب را نسبت به استراتژی خرید و نگهداری به‌طور چشمگیری بهبود می‌دهند و همچنین، استراتژی بیمه سبد با نسبت ثابت در قیاس با استراتژی بیمه سبد مبتنی بر ارزش در معرض ریسک عملکرد بهتری دارد.

Investors’ perspective on portfolio insurance

This study supports the use of behavioural finance to explain the popularity of portfolio insurance. Portfolio insurance strategies are important financial solutions sold to institutional and individual investors that protect against downside risk while maintaining some upside valuation potential. The way some of these strategies are engineered has been criticised and portfolio insurance itself blamed for increasing market volatility in depressed markets. Despite this, investors keep on buying portfolio insurance that keeps its solid market share. This study contributes to understand the phenomenon. We compare individual investors’ decision using two distinct frameworks: expected utility theory and behavioural theories. Based upon Monte Carlo simulation techniques we compare portfolio insurance strategies against uninsured basic benchmark strategies, for a wide variety of market scenarios. We conclude that cumulative prospect theory may be a viable framework to explain the popularity of portfolio insurance. However, among portfolio insurance strategies, naïve strategies seem to be preferable to most commonly traded strategies.

ASSET DEPENDENCY STRUCTURES AND PORTFOLIO INSURANCE STRATEGIES

The estimation of the multiplier parameter of portfolio insurance strategies is crucial for its implementation because it determines the risk exposure to the performance-seeking asset (PSA) at each point in time. Studies that address the estimation of the multiplier’s upper bound have been limited to strategies that use as the safe asset a short-term bank account, in which case the co-movements of the safe and the PSA become irrelevant. However, in several relevant applications, portfolio insurance strategies use stochastic reference assets different from cash, such as the control of active-risk relative to a benchmark, or insuring a minimum level of retirement income. We find that the implications of taking into account the assets’ co-movements in the multiplier estimation can be crucial. In Monte Carlo simulations the multiplier doubles in size across scenarios, and the strategy using the proposed approach presents stochastic dominance over the strategy that ignores the asset dependency structure.

One Year Later. Leveraged ETFs in Portfolio Construction and Portfolio Protection

One year after Coronovirus and three years later after initially suggesting them, we revisit the performance of balanced portfolios of leveraged ETFs that we initially suggested in the 2017 paper. Leveraged ETFs provide a convenient mechanism to dynamically change portfolio exposure and can be successfully used to construct robust portfolios that perform well during equity market drops. We start with a classical 60 percent Bonds/ 40 percent Stocks portfolio with monthly rebalancing that delivered 9.5 percent annually from January 1, 1986, to January 15, 2021. Its 120 percent leveraged cousin that is 72 percent Bonds/ 48 percent Stocks delivered 10.6 percent annually since 1986, same as SP500 but with lower volatility and drawdowns. Instead of leveraging with borrowing at the portfolio level, we can use a portfolio of leveraged ETFs.At the beginning of the paper we consider several balanced stocks/bonds portfolios created with leveraged ETFs but without borrowing money at the portfolio level and show that they present a very attractive risk-adjusted alternative to just stock index and classical stocks/bonds portfolios without leverage. A particular portfolio of 40 percent TQQQ, 20 percent TMF, 40 percent TLT with monthly rebalancing proposed by us in the 2017 paper as a leveraged ETF alternative to classical stocks/bonds portfolios performed well in 2018 and through the Coronavirus crisis up to January 15, 2021. We reviewed the performance of the 40-20-40 portfolio in our paper a year ago. Now after the Coronovirus crisis, we see that balanced portfolios suggested in 2017 sustained the crisis very well and performed well in 2020.A classical portfolio insurance strategy of Black-Jones-Perold can be easily implemented with leveraged ETFs. More complex dynamic portfolio strategies can also be implemented using leveraged ETFs.

Unfairly Defiled: A Long Term Perspective on Portfolio Insurance as a Strategy for Limiting Portfolio Losses

The invention of portfolio insurance as a strategy for limiting portfolio losses was introduced in the early 1980s and gained spectacular popularity throughout the decade, attracting between $60 billion to $90 billion from institutional money managers. The method provided downside protection against a long equity position by synthetically replicating a long put option using equity futures during an era when exchange-traded equity options were not sufficiently liquid. Unfortunately, the strategy came to a catastrophic end on the “Black Monday” of October 19, 1987, when the president of the New York Stock Exchange shut down the nascent technology used by index arbitrage program trading groups. This caused significant mispricings between futures and cash markets, making the required synthetic put option replication trading impossible. The portfolio insurance strategy was declared a complete failure and never has since regained widespread popularity. Three decades later, modern markets now fully embrace program trading, and the likelihood that program trading would be shut down for any reason ever again seems impossible. This paper examines how portfolio insurance would have performed during the 1991 to 2020 time period, during which 3 major stock market crashes occurred and program trading was never shut down. The paper concludes that portfolio insurance received unjust blame for the 1987 crash and its abandonment since then has been irrational and unfortunate for those seeking long equity exposure with a cost-efficient strategy for limiting portfolio losses.

Combination of Modern Portfoliotheory and Constant Proportion Portfolio Insurance Strategy(Application in the Context of Pension Fund Management)

Combination of Modern Portfoliotheory and Constant Proportion Portfolio Insurance Strategy(Application in the Context of Pension Fund Management)

Options on constant proportion portfolio insurance with guaranteed minimum equity exposure

In the present paper we study a new exotic option offering participation in a dynamic asset allocation strategy, which is an extension of the well‐known Constant Proportion Portfolio Insurance (CPPI) strategy. Our novel approach consists in assuming that the percentage of wealth invested in stocks cannot go under a fixed level, called guaranteed minimum equity exposure (GMEE). In particular, our proposal ensures to overcome the so‐called cash‐in risk, typically related to a standard CPPI technique, simultaneously guaranteeing the equity market participation. We look deeper into the valuation of call and put options linked to this new CPPI‐GMEE strategy. A particular attention is devoted to the analysis of key parameters' value as to gain a better understanding of the sensitivities of the option prices, when changing, for example, the embedded guarantee level. To show the effectiveness of our proposal we provide a detailed computational analysis within the Heston‐Vasicek framework, numerically comparing the evaluation of the price of European plain vanilla options when the underlying is either a purely risky asset, a standard CPPI portfolio and a CPPI with GMEE.

PORTFOLIO INSURANCE STRATEGIES FOR A TARGET ANNUITIZATION FUND

AbstractThe transition from defined benefit to defined contribution (DC) pension schemes has increased the interest in target annuitization funds that aim to fund a minimum level of retirement income. Prior literature has studied the optimal investment strategies for DC funds that provide minimum guarantees, but far less attention has been given to portfolio insurance strategies for DC pension funds focusing on retirement income targets. We evaluate the performance of option-based and constant proportion portfolio insurance strategies for a DC fund that targets a minimum level of inflation-protected annuity income at retirement. We show how the portfolio allocation to an equity fund varies depending on the member’s age upon joining the fund, displaying a downward trend through time for members joining the fund before ages in the mid-30s. We demonstrate how both portfolio insurance strategies provide strong protection against downside equity risk in financing a minimum level of retirement income. The option-based strategy generally leads to higher accumulated savings at retirement, whereas the constant proportion strategy provides better downside risk protection robust to equity market jumps/volatilities.

Behavioral portfolio insurance strategies

Portfolio insurance strategies that ensure a certain minimum portfolio value or floor such as the Constant Proportion Portfolio Insurance (CPPI) and the Option-based Portfolio Insurance are economically important and widely spread among the banking and insurance industries. In distress and volatile market environments, investors such as pension funds have a need to insure their portfolios against downside risk in order to meet certain future payments or liabilities. Non-anticipated shocks or negative interest rates, jumps, crashes, or overnight trading restrictions in stock prices could drop pension fund portfolios below desired levels (present value of pension obligations) making them underfunded with pension assets to pension liabilities ratio below 100%. In particular, within the current low interest rate environment, a high number of pension funds happen to be underfunded which is a severe practical problem. Because of such scenarios, there is a need for an investment strategy which covers both the case of funded and underfunded portfolios. This article introduces a novel strategy which generalizes the CPPI approach. It has the overall target of guaranteeing the investment goal or floor while participating in the performance of the assets and limiting the downside risk of the portfolio at the same time. We show that the strategy accounts for behavioral aspects of the investor such as distorted probabilities, a risk-averse behavior for gains, and a risk-seeking behavior for losses. The proposed strategy turns out to be optimal within the Cumulative Prospect Theory framework by Tversky and Kahneman (J Risk Uncertain 5(4):297–323, 1992).

Robust Leveraged ETF Portfolios Extending Classic 40/60 Portfolios and Portfolio Insurance

Leveraged ETFs provide a convenient mechanism to dynamically change portfolio exposure and can be successfully used to construct robust portfolios that perform well during equity market drops. We start with a classical 60 percent Bonds/ 40 percent Stocks portfolio with monthly rebalancing that delivered 9.4 percent annually over since 1986. Its 120 percent leveraged cousin that is 72 percent Bonds/ 48 percent Stocks delivered 10.4 percent annually since 1986, same as stocks but with lower volatility and drawdowns. Instead of leveraging with borrowing at portfolio level we can use a portfolio of leveraged ETFs. We consider several balanced stocks/bonds portfolios created with leveraged ETFs but without borrowing money at portfolio level and show that they present a very attractive risk-adjusted alternative to just stock index and classical stocks/bonds portfolios without leverage. In particular portfolio of 40 percent TQQQ, 20 percent TMF, 40 percent TLT with monthly rebalancing proposed by us in 2017 paper as a leveraged ETF alternative to classical stocks/bonds portfolios performed well in 2018 and through beginning of Coronavirus crisis up to February 28, 2020. What happens to this portfolio as crisis continues still to be seen. A classical portfolio insurance strategy of Black-Jones-Perold can be easily implemented with leveraged ETFs. More complex dynamic portfolio strategies can also be implemented using leveraged ETFs.

MULTIPLIER OPTIMIZATION FOR CONSTANT PROPORTION PORTFOLIO INSURANCE (CPPI) STRATEGY

Constant proportion portfolio insurance (CPPI) strategy is a very popular investment solution which provides an investor with a capital protection as well as allows for an equity market participation. In this paper, we propose a two-step approach to the numerical optimization of the CPPI main parameter, multiplier. First, we identify an admissible range of the multiplier values by controlling the shortfall probability (chosen as a measure of the gap risk). Second, within the admissible range, we choose the optimal multiplier value with respect to the omega ratio (chosen as a performance measure). We illustrate the performance of our optimization algorithm on simulated CPPI paths in the Black–Scholes environment with discrete trading as well as on the historical S&amp;P500 data using the block-bootstrap simulations.

Estimating portfolio risk for tail risk protection strategies

AbstractWe forecast portfolio risk for managing dynamic tail risk protection strategies, based on extreme value theory, expectile regression, copula‐GARCH and dynamic generalized autoregressive score models. Utilizing a loss function that overcomes the lack of elicitability for expected shortfall, we propose a novel expected shortfall (and value‐at‐risk) forecast combination approach, which dominates simple and sophisticated standalone models as well as a simple average combination approach in modeling the tail of the portfolio return distribution. While the associated dynamic risk targeting or portfolio insurance strategies provide effective downside protection, the latter strategies suffer less from inferior risk forecasts, given the defensive portfolio insurance mechanics.