Portfolio Insurance with Adaptive Protection (PIWAP)

18 May 2015

Investors’ appetite for funds providing capital protection has been increasing in recent years. This is particularly the case for individuals saving for future life events such as retirement, buying a home or helping fund their children’s education. It can be explained in large part by the growth in defined contribution pension schemes and the rollercoaster performance of the equity markets over the past two decades.

Upside potential remains important to investors in capital protected funds, but not at any cost, and they demand that a certain minimum level of their capital be protected. With this in mind, we have investigated the best way to design and manage portfolios providing capital protection.

This document is a short summary of a research paper entitled ‘Portfolio Insurance With Adaptive Protection’, which provides a comprehensive mathematical explanation of our findings.


Funds protecting the capital invested in them have traditionally used the Constant Proportion Portfolio Insurance (CPPI) technique. This involves investing a portion of a fund’s capital in zero-coupon fixed income assets to ensure that at least some of the fund’s assets, known as the bond floor, can be recovered at a given future target date.

The remainder of the capital is invested in a risky asset, with the aim of increasing the value of the investor’s assets. The proportion of capital in the risky asset is adjusted in such a way as to avoid losing more than the cushion between the fund’s net asset value and its bond floor – so the proportion invested in risky assets is larger when the cushion is bigger. The size of the cushion depends on a number of factors, including the fund’s target date and the level of capital protection required at the target date.


But is it possible to improve upon the CPPI technique? We have researched this issue, looking in particular at:

  • how the initial time to target date and the Sharpe ratio of the risky asset should affect the initial cushion;
  • how the initial time to target date should affect theinitial guarantee;
  • how the maximum amount of assets in the cushion should change as the target date approaches; and
  • how the protection ratio should change as the target date approaches and as interest rates change.

According to our calculations, the optimal insurance strategy for a capital-protected portfolio involves increasing the protection of the invested capital up to the amount that keeps the cushion under a sufficient level, which will be a function of the remaining time until the maturity date and the investor’s aversion to risk or loss. This insurance strategy, which we call Portfolio Insurance with Adaptive Protection (PIWAP), is easy to implement and, in our view, offers a better trade-off between upside potential and protection at the target date.

Initial time to target date and Sharpe ratio of risky asset

First, we found that the proportion initially invested in risky assets should depend on the length of time until the target date. Figure 1 on the attached download shows the optimal initial cushion as a percentage of fund assets for two portfolios: one whose risky assets have a Sharpe ratio of 0.15, and the other whose risky assets have a Sharpe ratio of 0.40. It’s clear that the initial cushion should be bigger when the time until the target date is longer. The initial cushion also increases with the Sharpe ratio because the performance of the cushion is expected to be better if the Sharpe ratio is higher.

Interest Rates

Figure 2 on the attached download shows that the level of interest rates should have a considerable impact on the initial level of protection that investors choose – the higher the interest rate, the higher the initial level of protection that is necessary. It’s important to note that when interest rates are low – as they are currently – the optimal initial protection is below 100%. We can also see that the optimal initial protection actually ends up decreasing with the time to the target date when the Sharpe ratio of the risky asset is high.

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