Constant Proportion Portfolio Insurance Strategy Research Articles

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)

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.

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.

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.

Three-fund Separation Constant Proportion Portfolio Insurance Strategy

Specific purpose guarantee funds such as pension guarantee funds are popular among loss-averse investors with common investment purposes, but their investment strategies, hedging techniques, and performance 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 and a purpose-related portfolio to maximize investors' utility with respect to their investment purpose and control the downside risk of the portfolio. The closed-form solutions of PO-CPPI derived in the continuous time case, followed by Monte-Carlo simulations in the discrete time case, also support the superiority of the proposed strategy.

On Path–dependency of Constant Proportion Portfolio Insurance Strategies

This paper evaluates the path-dependency/independency of most widespread Portfolio Insurance strategies. In particular, we look at Constant Proportion Portfolio Insurance(CPPI) structures and compare them to both the classical Option Based Portfolio Insurance(OBPI) and naive strategies such as Stop-loss Portfolio Insurance (SLPI) or a CPPI with a multiplier of one. The paper is based upon conditional Monte Carlo simulations and we show that CPPI strategies with a multiplier higher than 1 are extremely path-dependent and that they can easily get cash-locked, even in scenarios when the underlying at maturity can be worth much more than initially. The likelihood of being cash-locked increases with the size of the multiplier and the maturity of the CPPI, as well as with properties of the risky underlying’s dynamics. To emphasize the path-dependency of CPPIs, we show that even in scenarios where the investor correctly“guesses” a higher future value for the underlying, CPPIs can get cash-locked, losing the linkage to the risky asset. Thiscash-lock problem is specific of CPPIs, it goes against its European style nature of traded CPPIs, and it introduces into the strategy risks not related to the underlying risky asset – a design risk. Design risk does not occur for path-independent portfolio insurance strategies, like the classical case of OBPI strategies, nor in naive strategies.This study contributes to reinforce the idea that CPPI strategies suffer from a serious design problem.

Constant proportion portfolio insurance strategies in contagious markets

Constant Proportion Portfolio Insurance (CPPI) strategies are popular as they allow to gear up the upside potential of a stock index while limiting its downside risk. From the issuer’s perspective it is important to adequately assess the risks associated with the CPPI, both for correct ‘gap’ fee charging and for risk management. The literature on CPPI modelling typically assumes diffusive or Lévy-driven dynamics for the risky asset underlying the strategy. In either case the self-contagious nature of asset prices is not taken into account. In order to account for contagion while preserving analytical tractability, we introduce self-exciting jumps in the underlying dynamics via Hawkes processes. Within this framework we derive the loss probability when trading is performed continuously. Moreover, we estimate measures of the risk involved in the practical implementation of discrete-time rebalancing rules governing the CPPI product. When rebalancing is performed on a frequency less than weekly, failing to take contagion into account will significantly underestimate the risks of the CPPI. Finally, in order to mimic a situation with low liquidity, we impose a daily trading cap on the risky asset and find that the Hawkes process driven models give rise to the highest risk measures even under daily rebalancing.

A theoretical model of jump diffusion-mean reversion

PurposeThe purpose of this paper is to develop a theoretical model of a jump diffusion-mean reversion constant proportion portfolio insurance strategy under the presence of transaction cost and stochastic floor as opposed to the deterministic floor used in the previous literatures.Design/methodology/approachThe paper adopts Merton’s jump diffusion (JD) model to simulate the price path followed by risky assets and the CIR mean reversion model to simulate the path followed by the short-term interest rate. The floor of the CPPI strategy is linked to the stochastic process driving the value of a fixed income instrument whose yield follows the CIR mean reversion model. The developed model is benchmarked against CNX-NIFTY 50 and is back tested during the extreme regimes in the Indian market using the scenario-based Monte Carlo simulation technique.FindingsBack testing the algorithm using Monte Carlo simulation across the crisis and recovery phases of the 2008 recession regime revealed that the portfolio performs better than the risky markets during the crisis by hedging the downside risk effectively and performs better than the fixed income instruments during the growth phase by leveraging on the upside potential. This makes it a value-enhancing proposition for the risk-averse investors.Originality/valueThe study modifies the CPPI algorithm by re-defining the floor of the algorithm to be a stochastic mean reverting process which is guided by the movement of the short-term interest rate in the economy. This development is more relevant for two reasons: first, the short-term interest rate changes with time, and hence the constant yield during each rebalancing steps is not practically feasible; second, the historical literatures have revealed that the short-term interest rate tends to move opposite to that of the equity market. Thereby, during the bear run the floor will increase at a higher rate, whereas the growth of the floor will stagnate during the bull phase which aids the model to capitalize on the upward potential during the growth phase and to cut down on the exposure during the crisis phase.

Constant Proportion Portfolio Insurance Strategies in Contagious Markets

CPPI strategies are popular as they allow to gear up the upside potential of a stock index while limiting its downside risk. From the issuer’s perspective it is important to adequately assess the risks associated with the CPPI, both in order to charge the correct “gap” fee and for risk management. The literature on CPPI modeling typically assumes diffusive or Levy-driven dynamics for the risky asset underlying the strategy. In either case the self-contagious nature of asset prices is not taken into account. In order to account for contagion while preserving analytical tractability, we introduce self-exciting jumps in the underlying dynamics via Hawkes processes. Within this framework we derive the loss probability when trading is performed continuously. Moreover, we estimate measures of the risk involved in the practical implementation of discrete-time rebalancing rules governing the CPPI product. When rebalancing is performed on a frequency less than weekly, failing to take contagion into account will significantly underestimate the risks of the CPPI. Finally, in order to mimic a situation with low liquidity, we impose a daily trading cap on the risky asset and find that the Hawkes process driven models give rise to the highest risk measures even under daily rebalancing.

Constant Proportion Portfolio Insurance Strategy in Southeast European Markets

Abstract Background: In today’s highly volatile and unpredictable market conditions, there are very few investment strategies that may offer a certain form of capital protection. The concept of portfolio insurance strategies presents an attractive investment opportunity. Objectives: The main objective of this article is to test the use of portfolio insurance strategies in Southeast European (SEE) markets. A special attention is given to modelling non-risky assets of the portfolio. Methods/Approach: Monte Carlo simulations are used to test the buy-and-hold, the constant-mix, and the constant proportion portfolio insurance (CPPI) investment strategies. A covariance discretization method is used for parameter estimation of bond returns. Results: According to the risk-adjusted return, a conservative constant mix was the best, the buy-and-hold was the second-best, and the CPPI the worst strategy in bull markets. In bear markets, the CPPI was the best in a high-volatility scenario, whereas the buy-and-hold had the same results in low- and medium-volatility conditions. In no-trend markets, the buy-and-hold was the first, the constant mix the second, and the CPPI the worst strategy. Higher transaction costs in SEE influence the efficiency of the CPPI strategy. Conclusions: Implementing the CPPI strategy in SEE could be done by combining stock markets from the region with government bond markets from Germany due to a lack of liquidity of the government bond market in SEE.

PEROLD-SHARPE REBALANCING STRATEGIES IN PRACTICE

The purpose of this paper is to investigate the different strategies for portfolio rebalanc-ing (buy-and-hold, constant weights, and constant-proportion portfolio insurance (CPPI) suggested by Perold and Sharpe in a reallife environment using the actual market data and considering trans-action costs. Methodology. Exchange-traded funds were used to represent asset classes, and actual market prices in 2007-2015 for the ETFs used to conduct the research. The Monte-Carlo simulations were used to generate 400 portfolios over 3 different time horizons in order to get a representative sample. Two actual fee structures were used from the leading U.S. brokerage firms. Results of the portfolio dynamics research show outperformance of CPPI over other strategies on holding periods over 36 months, and on shorter time horizons CPPI and constant weights strategies clearly dominate over buyand- hold strategy. Contrary to the previous conclusions by Perold and Sharpe, there was no definite link between the stock market dynamics or volatility and the preferred strategy. We also see that after a bull market period the CPPI portfolio allocation shifts to 100% equity. The portfolio turnover is typically higher and much more dispersed for CPPI strategy than for constant weights strategy. We also found a strong negative correlation between the CPPI portfolio turnover and the initial equity allocation, whereas for constant weights strategy the turnover is higher at 50% allocation to both stocks and bonds. Practical implications. The strategy choice is shown to be more a matter of the holding period; CPPI seems the best choice over longer periods. Contrary to the widespread perception, our research shows that brokerage fees has not had a material influence on the simulated portfolio performance and, thus, should not be a factor for choosing a strategy. Originality/value. Unlike previous studies in this area that focused on analytical derivation based on sample statistics, we used the Monte-Carlo simulation on the actual asset prices and brokerage fees structures. The results of our research are much closer to the actual portfolio dynamics seen in practice. We also address issues like portfolio turnover and transaction costs that are often over-looked by academic researchers.

Optimal rebalance rules for the constant proportion portfolio insurance strategy – Evidence from China

The constant proportion portfolio insurance (CPPI) strategy is one of the most popular asset allocation strategies employed by guaranteed-return financial products investors. Rebalance disciplines play an important role in determining the CPPI performance in practice. This paper examines whether the selection of rebalance rules affects CPPI strategy performance in the context of Chinese equity markets and, if so, in what pattern, and whether an optimal parameter of rebalance exists. We find that, (1) the three alternative rebalance disciplines – time discipline, market move discipline and lag discipline – are indifferent in affecting the performance of CPPI strategy; (2) in terms of optimal parameters of each rebalance rule, the optimal rebalancing period for the time discipline is 3 trading days, the optimal trading threshold of the market move discipline 4%, and the optimal lag factor of the lag discipline 6%. These optimal parameters are not influenced by the length of investment.

A bootstrap-based comparison of portfolio insurance strategies

This study presents a systematic comparison of portfolio insurance strategies. We implement a bootstrap-based hypothesis test to assess statistical significance of the differences in a variety of downside-oriented risk and performance measures for pairs of portfolio insurance strategies. Our comparison of different strategies considers the following distinguishing characteristics: static versus dynamic protection; initial wealth versus cumulated wealth protection; model-based versus model-free protection; and strong floor compliance versus probabilistic floor compliance. Our results indicate that the classical portfolio insurance strategies synthetic put and constant proportion portfolio insurance (CPPI) provide superior downside protection compared to a simple stop-loss trading rule and also exhibit a higher risk-adjusted performance in many cases (dependent on the applied performance measure). Analyzing recently developed strategies, neither the TIPP strategy (as an ‘improved’ CPPI strategy) nor the dynamic VaR-strategy provides significant improvements over the more traditional portfolio insurance strategies.

Dynamic preferences for popular investment strategies in pension funds

In this paper, we characterize dynamic investment strategies that are consistent with the expected utility setting and more generally with the forward utility setting. Two popular dynamic strategies in the pension funds industry are used to illustrate our results: a constant proportion portfolio insurance (CPPI) strategy and a life-cycle strategy. For the CPPI strategy, we are able to infer preferences of the pension fund’s manager from her investment strategy, and to exhibit the specific expected utility maximization that makes this strategy optimal at any given time horizon. In the Black–Scholes market with deterministic parameters, we are able to show that traditional life-cycle funds are not optimal to any expected utility maximizers. We also prove that a CPPI strategy is optimal for a fund manager with HARA utility function, while an investor with a SAHARA utility function will choose a time-decreasing allocation to risky assets in the same spirit as the life-cycle funds strategy. Finally, we suggest how to modify these strategies if the financial market follows a more general diffusion process than in the Black–Scholes market.

Forecasting market turbulence using regime-switching models

We propose an early warning system to timely forecast turbulence in the US stock market. In a first step, a Markov-switching model with two regimes (a calm market and a turbulent market) is developed. Based on the time series of the monthly returns of the S&P 500 price index, the corresponding filtered probabilities are successively estimated. In a second step, the turbulent phase of the model is further specified to distinguish between bullish and bearish trends. For comparison only, a Markov-switching model with three states (a calm market, a turbulent bullish market, and a turbulent bearish market) is examined as well. In a third step, logistic regression models are employed to forecast the filtered probabilities provided by the Markov-switching models. A major advantage of the presented modeling framework is the timely identification of the factors driving the different phases of the capital market. In a fourth step, the early warning system is applied to an asset management case study. The results show that explicit consideration of the models’ signals yields better portfolio performance and lower portfolio risk compared to standard buy-and-hold and constant proportion portfolio insurance strategies.

Performance evaluation of optimized portfolio insurance strategies

We use S&P 500 index return data for the time period 1985–2013 to evaluate the performance of portfolio insurance strategies. We shed light on the question if the performance of a constant proportion portfolio insurance (CPPI) strategy can be improved by means of a time-varying multiplier which depends on the estimated future volatility. Neglecting any inter-temporal hedging demand, the theoretical foundation of the strategies is given by maximizing the expected utility of a HARA investor in a diffusion model setup. If the risk premium is assumed to be proportional to the variance, the optimal strategy is a CPPI strategy. Otherwise, the multiple is time-varying (PPI). It turns out that even time-varying multiple strategies based on a rolling window of historical volatility estimates give a significant improvement of CPPI strategies. The out-performance is robust w.r.t. alternative performance measures and is also true for proportional transaction costs and adequate trigger trading.