{"id":29750,"date":"2023-10-11T09:09:55","date_gmt":"2023-10-11T07:09:55","guid":{"rendered":"https:\/\/quantpedia.com\/?p=29750"},"modified":"2025-06-04T14:22:47","modified_gmt":"2025-06-04T12:22:47","slug":"time-invariant-portfolio-protection","status":"publish","type":"post","link":"https:\/\/vvv.quantpedia.com\/es\/time-invariant-portfolio-protection\/","title":{"rendered":"Time Invariant Portfolio Protection"},"content":{"rendered":"

INTRODUCTION<\/em><\/strong><\/h3>\n\n\n\n

In this article we are going to continue the discussion on portfolio insurance strategies. An exhaustive description of this methodology was already presented in the article Introduction to CPPI (<\/em>https:\/\/\\\/\\\/new-fmhwbzh6ghd9hede.swedencentral-01.azurewebsites.net\/introduction-to-cppi-constant-proportion-portfolio-insurance<\/em><\/a>). <\/em>This article will focus on an extension of the original model introduced by Estep and. Kritzman (1988), namely Time Invariant Portfolio Protection.<\/strong><\/p>\n\n\n\n

Constant Proportion Portfolio Insurance (CPPI) and Time-Invariant Portfolio Protection (TIPP) are two of the most famous portfolio insurance strategies that play an important role in the realm of investment management and risk mitigation. These strategies are designed to address the fundamental challenge of balancing the pursuit of financial growth with the imperative of capital protection against market downturns. Ideally, the guaranteed protection is achieved at the lowest possible premium for the investors.<\/strong><\/p>\n\n\n\n

THE MODEL<\/em><\/strong><\/h3>\n\n\n\n

CPPI is a dynamic approach that adapts to market conditions by actively adjusting the allocation between risky and risk-free assets, striving to preserve a predefined floor value while allowing participation in market upswings. In contrast, TIPP employs a more conservative methodology, where a fixed percentage of portfolio value is guaranteed throughout the investment horizon and the risky exposure is adjusted accordingly. The main difference is that while in CPPI the floor grows at a constant rate, in TIPP it is a function of the portfolio value and thus it has a path dependent nature. These two strategies offer distinct advantages and drawbacks, making them valuable tools for investors with varying risk appetites, investment objectives, and preferences for portfolio management.<\/p>\n\n\n\n

Both strategies prescribe an allocation to the risky asset that is equal to the cushion (difference between V0 and F0) multiplied by a risk-aversion coefficient m<\/em>. The higher the coefficient, the more aggressive the strategy, and conversely. The allocation to the risk-free is determined residually.<\/p>\n\n\n\n

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Let\u2019s show an example. If we assume an initial invested capital of 100$, an initial floor of 85$, and a multiplier of 4, we obtain a risky exposure of 60 (4x(100-85)) and risk-free allocation of 40. Many finance practitioners have introduced new extensions to the plain vanilla model. For instance, setting on the maximum and minimum exposure will avoid, on one side,  excessive risk taking and on the other hand, the absorption in state of 100% risk-free allocation. In our experiment, we force the exposure to lie in the range 40 to 120%.<\/p>\n\n\n\n

Figure (a) and Figure (b) show examples of the two methodologies. In the first case, the protection grows over time at a fixed rate as:<\/p>\n\n\n\n

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In the second case, the floor adjusts upwards to maintain the same level protection with respect to the portfolio value at each point in time t:<\/p>\n\n\n\n

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Now that we have explained the difference between the two approaches we focus on the statistical properties of TIPP. To do that, we follow the methodological approach used for CPPI by Khuman et al. (2008) and implement the same analysis to this new technique. In particular, we investigate the behavior of our risk metrics obtained by applying TIPP on two simulated processes: Geometric Brownian Motion (GBM) and Jump Diffusion Process (JDP). These processes represent a proxy for our risky financial assets. Given that we set an expected negative jump size to reflect the negative skewness of financial markets, we allow for fair comparison between the two processes by introducing a positive compensator to the JDP.<\/p>\n\n\n\n

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To validate the effectiveness of the strategy under two scenarios, we consider four relevant risk metrics:<\/p>\n\n\n\n