Constant Proportion Portfolio Insurance Research Articles

Design risk: the curse of constant proportion portfolio insurance

Design risk: the curse of constant proportion portfolio insurance

Mean–variance optimization under affine GARCH: A utility-based solution

Affine GARCH models have recently been explored in the context of portfolio optimization, although in a quite narrow setting in terms of utility functions and risk aversion. This work notably extends existing results, accommodating a richer class of objective functions for a large family of GARCH models. In particular, our approach allows for connections to constant proportion portfolio insurance (CPPI) and mean–variance portfolio strategies. We explore the latter numerically based on S&P 500 market data, revealing that a GARCH model clearly outperforms a homoscedastic variant in terms of the efficient frontier.

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.

Comparing Downside Protection Strategies

In this article, the author uses a common framework to evaluate and compare various equity downside protection strategies including constant proportion portfolio insurance, volatility targeting, and a few option-based strategies in terms of the trade-off between downside protection and upside participation. Using the downside-to-upside performance ratio to measure that trade-off, the author finds that all these strategies offer the same trade-off over the many market cycles from 1996 to 2020. However, strategies with a concave payoff profile (such as put spread collar used in buffered exchange-traded funds or defined outcome exchange-traded funds) offer a better trade-off during the early stage of drawdown and recovery, and strategies with a convex payoff profile such as constant proportion portfolio insurance offer a better trade-off during the late stage of drawdown and recovery. The author’s results and insights allow investors to enhance their understanding of downside protection strategies and select the best strategy for their investment use case.

Practical Applications of Cash for Calls: A Quantitative Approach to Managing Liquidity for Capital Calls

In <b><i>Cash for Calls: A Quantitative Approach to Managing Liquidity for Capital Calls</i></b>, from the Fall 2022 issue of <b><i>The Journal of Alternative Investments</i></b>, <b>Jerome Schneider</b>, <b>Sean Klein</b>, <b>Wade Sias</b>, and <b>Simon Fan</b>, all of <b>PIMCO</b>, provide an approach to address the difficult task of minimizing cash drag while ensuring that limited partners can meet capital calls for private investments. By analyzing cash flow data for private equity, private debt, and private real estate funds, the authors quantify the extent of cash drag experienced when committed, but uninvested, capital is held in cash. They also illustrate the danger of holding the capital in public market equivalents (PMEs). Using historical call rates, the authors then simulate a tiering approach to holding committed capital in assets that have a range of risk and return characteristics and dynamically adjust the allocation. They show this strategy performs similarly to constant proportion portfolio insurance. The portfolio grows when the market outperforms, due to commitments that are partially allocated to PMEs, while an allocation to safe tiers protects the portfolio in market downturns.

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.

PORTFOLIO INSURANCE UNDER ROUGH VOLATILITY AND VOLTERRA PROCESSES

Affine Volterra processes have gained more and more interest in recent years. In particular, this class of processes generalizes the classical Heston model and the more recent rough Heston model. The aim of this work is hence to revisit and generalize the constant proportion portfolio insurance (CPPI) under affine Volterra processes. Indeed, existing simulation-based methods for CPPI do not apply easily to this class of processes. We instead propose an approach based on the characteristic function of the log-cushion which appears to be more consistent, stable and particularly efficient in the case of saffine Volterra processes compared with the existing simulation techniques. Using such approach, we describe in this paper several properties of CPPI which naturally result from the form of the log-cushion’s characteristic function under affine Volterra processes. This allows to consider more realistic dynamics for the underlying risky asset in the context of CPPI and hence build portfolio strategies that are more consistent with financial data. In particular, we address the case of the rough Heston model, known to be extremely consistent with past data of volatility. By providing a new estimation procedure for its parameters based on the PMCMC algorithm, we manage to study more accurately the true properties of such CPPI strategy and to better handle the risk associated with it.

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).

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.

Rebalancing Return and Hedge Effectiveness of Dynamic Portfolio Insurance Strategies: A simulation Based Study

Dynamic portfolio insurance strategies can be used to protect a stock market exposure against large losses. The implementation of these strategies entails a regular rebalancing which serves to adjust the current asset allocation to the one desired according to the strategy. An alternative to regular rebalancing could be a onetime portfolio allocation at the beginning of the investment period with no further adjustment up to the end of the period (“buy-and-hold”, B&amp;H). An essential criterion for deciding on a portfolio insurance strategy is its performance in comparison to the B&amp;H strategy.The aim of this paper is to study the performance of different dynamic portfolio insurance methodologies through a simulation process based on normally distributed stock returns. The analysis focuses on the Constant Proportion Portfolio Insurance (CPPI), Time Invariant Portfolio Protection (TIPP), and a modified version of the Time Invariant Portfolio Protection methodology (TIPP-M). The performance is measured using a rebalancing return and a hedge effectiveness measure. The results of the simulation analysis suggest that CPPI is the best strategy according to the rebalancing return while the TIPP strategy leads to the best hedge effectiveness results. TIPP-M is similar to TIPP but seems to be slightly worse. Keywords: Portfolio insurance, Constant Proportion Portfolio Insurance, CPPI, Time Invariant Portfolio Protection, TIPP, Buy-and-Hold, Rebalancing Return, Hedge Effectiveness, Monte Carlo Simulation JEL Classification: G11 DOI : 10.7176/RJFA Publication Date : DOI : 10.7176/RJFA/10-20-01 Publication date :October 31 st 2019

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 (OBPI) 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 (CPT) framework by Tversky and Kahneman (1992).

Portfolio rebalancing under uncertainty using meta-heuristic algorithm

In this paper, we solve portfolio rebalancing problem when security returns are represented by uncertain variables considering transaction costs. The performance of the proposed model is studied using constant-proportion portfolio insurance (CPPI) as rebalancing strategy. Numerical results showed that uncertain parameters and different belief degrees will produce different efficient frontiers, and affect the performance of the proposed model. Moreover, CPPI strategy performs as an insurance mechanism and limits downside risk in bear markets while it allows potential benefit in bull markets. Finally, using a globally optimisation solver and genetic algorithm (GA) for solving the model, we concluded that the problem size is an important factor in solving portfolio rebalancing problem with uncertain parameters and to gain better results, it is recommended to use a meta-heuristic algorithm rather than a global solver.

Portfolio rebalancing under uncertainty using meta-heuristic algorithm

In this paper, we solve portfolio rebalancing problem when security returns are represented by uncertain variables considering transaction costs. The performance of the proposed model is studied using constant-proportion portfolio insurance (CPPI) as rebalancing strategy. Numerical results showed that uncertain parameters and different belief degrees will produce different efficient frontiers, and affect the performance of the proposed model. Moreover, CPPI strategy performs as an insurance mechanism and limits downside risk in bear markets while it allows potential benefit in bull markets. Finally, using a globally optimization solver and genetic algorithm (GA) for solving the model, we concluded that the problem size is an important factor in solving portfolio rebalancing problem with uncertain parameters and to gain better results, it is recommended to use a meta-heuristic algorithm rather than a global solver.

Portfolio Insurance Strategies: A Comparison of Standard Methods When the Volatility of the Stock is Stochastic

ABSTRACT We compare the performances of the two standard portfolio insurance methods: the Option Based Portfolio Insurance (OBPI) and the Constant Proportion Portfolio Insurance (CPPI), when the volatility of the stock index is stochastic. In this framework, we provide a quite general formula for the CPPI portfolio value. We use criteria such as comparison of payoffs functions at maturity and various quantiles. We emphasize in particular the role of the insured percentage of the initial investment. JEL: G0, G15 Keywords: Portfolio insurance; OBPI; CPPI; Stochastic volatility I. INTRODUCTION One of the more popular strategies of portfolio insurance is the Option Based Portfolio Insurance (OBPI), introduced in Leland and Rubinstein (1976). It consists basically in buying simultaneously the stock (generally a financial index) and a put written on it. The value of this portfolio at maturity is always greater than the strike of the put, whatever the market fluctuations. Thus, this strike is the insured amount, which is often equal to a given percentage of the initial investment. The CPPI method has been analysed in Black and Rouhani (1989) and Black and Perold (1992). This method is based on a particular strategy to allocate assets dynamically over time. The investor starts by choosing a floor equal to the lowest acceptable value of the portfolio. Then, he computes the cushion that is equal to the excess of the portfolio value over the floor. Finally, the amount allocated to the risky asset (usually called the exposure) is determined by multiplying the cushion by a predetermined multiple. The remaining funds are invested in the reserve asset (for example, Treasury bills or other liquid money market instruments.) Initial cushion, multiple, floor and tolerance can be chosen according to the investor's own objective. The higher the multiple, the more the portfolio value increases in a bullish market. Nevertheless, the higher the multiple, the nearest the portfolio will be to the floor in a bearish market. As the cushion approaches zero, the amount invested on the risky asset approaches zero too. This feature implies that the portfolio value is below the floor only when there is a very sharp drop in the market before the investor can modify his investment weights. Therefore, the multiple must be bounded as shown in Bertrand and Prigent (2002a). Thus, this strategy is rather simple with respect to other approaches. The purpose of this paper is to compare these two strategies of portfolio insurance, when the volatility of the risky asset is stochastic. In section 2, we recall the basic properties of these two strategies. In section 3, we examine the impact of stochastic volatility for each portfolio insurance method. Finally in section 4, we analyse their properties and compare them. For this purpose, first we examine their payoffs and compute their expectations, variances, skewness and kurtosis of their returns. Second, we evaluate some of the quantiles of their returns. II. BASIC PROPERTIES OF THE OBPI AND THE CPPI We consider the following financial market: the period of time considered is [0,T]. Denote [B.sub.t] the riskless asset which has the following dynamics: [dB.sub.t] = [B.sub.t] r dt. Assume that the risky asset [S.sub.t] is a diffusion process: [dS.sub.t] = [S.sub.t] [a dt + [[sigma].sub.t] d[W.sup.1.sub.t]], where ([W.sup.1.sub.t])t is a standard Brownian motion. The volatility [[sigma].sub.t] is assumed to be stochastic and is defined as solution of the following stochastic differential equation: d[[sigma].sub.t] = [alpha] (t, [[sigma].sub.t])dt + [beta] (t, [[sigma].sub.t]) d[W.sup.2.sub.t], where [([W.sup.2.sub.t]).sub.t] is another standard Brownian motion independent from [([W.sup.1.sub.t]).sub.t]. We particularize the case of a stochastic volatility that evolves according to an Ornstein-Uhlenbeck process, as introduced in Scott (1987) and Stein and Stein (1991): d[[sigma]. …

CONIC CPPIs

Constant proportion portfolio insurance (CPPI) is a structured product created on the basis of a trading strategy. The idea of the strategy is to have an exposure to the upside potential of a risky asset while providing a capital guarantee against downside risk with the additional feature that in case the product has since initiation performed well more risk is taken while if the product has suffered mark-to-market losses, the risk is reduced. In a standard CPPI contract, a fraction of the initial capital is guaranteed at maturity. This payment is assured by investing part of the fund in a riskless manner. The other part of the fund’s value is invested in a risky asset to offer the upside potential. We refer to the floor as the discounted guaranteed amount at maturity. The percentage allocated to the risky asset is typically defined as a constant multiplier of the fund value above the floor. The remaining part of the fund is invested in a riskless manner. In this paper, we combine conic trading in the above described CPPIs. Conic trading strategies explore particular sophisticated trading strategies founded by the conic finance theory i.e. they are valued using nonlinear conditional expectations with respect to nonadditive probabilities. The main idea of this paper is that the multiplier is taken now to be state dependent. In case the algorithm sees value in the underlying asset the multiplier is increased, whereas if the assets is situated in a state with low value or opportunities, the multiplier is reduced. In addition, the direction of the trade, i.e. going long or short the underlying asset, is also decided on the basis of the policy function derived by employing the conic finance algorithm. Since nonadditive probabilities attain conservatism by exaggerating upwards tail loss events and exaggerating downwards tail gain events, the new Conic CPPI strategies can be seen on the one hand to be more conservative and on the other hand better in exploiting trading opportunities.

Dynamic portfolio insurance strategy: a robust machine learning approach

ABSTRACTIn this paper, we propose a robust genetic programming (RGP) model for a dynamic strategy of stock portfolio insurance. With portfolio insurance strategy, we divide the money in a risky asset and a risk-free asset. Our applied strategy is based on a constant proportion portfolio insurance strategy. For determining the amount for investing in the risky asset, a critical parameter is a constant risk multiplier that is calculated in our proposed model using RGP to reflect market dynamics. Our model includes four main steps: (1) Selecting the best stocks for constructing a portfolio using a density-based clustering strategy. (2) Enhancing the robustness of our proposed model with an application of the Adaptive Neuro-Fuzzy Inference Systems (ANFIS) for forecasting the future prices of the selected stocks. The findings show that using ANFIS, instead of a regular multi-layer artificial neural network improves the prediction accuracy and our model’s robustness. (3) Implementing the RGP model for calculating the risk multiplier. Risk variables are used to generate equation trees for calculating the risk multiplier. (4) Determining the optimal portfolio weights of the assets using the well-known Markowitz portfolio optimization model. Experimental results show that our proposed strategy outperforms our previous model.

ETFs, ETNs and Statistical Anomalies

We overview exchange-traded funds and notes mechanism and market. We consider different classes of ETFs: long, short, unleveraged, leveraged. We show tables and graphs of leveraged and short ETF behaviors for up and down moves for educational purposes. We describe historical behavior of several benchmark portfolios constructed using leveraged ETFs and describe their behaviors in different bull and bear markets. We describe implementation of constant proportion portfolio insurance strategy of Black, Jones, Perold using leveraged ETFs. Finally we describe different statistical anomalies: equal weighted ETFs anomaly and mispriced factors anomaly.