Appetite among investors for funds with capital protection has been increasing in recent years. BNP Paribas Asset Management’ research examines the optimal design of such funds, which provide capital protection at a specific maturity. At inception the level of capital protection is often set at 100% for simplicity’s sake, but without any clearer rationale. In this article, we are proposing a framework for estimating the optimal level of protection.
BNP Paribas Asset Management has done extensive research on the design of target-date funds with explicit capital protection. Part of this work has been recognised as highly innovative and was recently published in the Journal of Investment Strategies (“Portfolio insurance with adaptive protection”, Thomas Heckel, François Soupé and Raul Leote de Carvalho, Volume 5, Number 3 (June 2016), Pages: 1-15).
Target-date funds with explicit protection are those with a given target date, e.g. 2030, and, for example, a guarantee that the net asset value (NAV) will not fall below 100. Such funds have been popular in the context of retirement planning as they provide a measure of certainty at the retirement date while still offering upside potential.
Managing these funds has been challenging in recent, crisis-ridden years. Volatility was at times high, particularly during the Great Financial Crisis of 2008/2009. This higher level of risk meant that some target-date funds not only forfeited a large part of their cushion – the money that can be lost without jeopardising the level of protection – but also the flexibility to take investment risk and benefit from upside potential.
Cushion management should be adjusted as a function of volatility
The first main conclusion of our research is that the cushion management – i.e. the allocation mechanism to the risky asset – should be adjusted dynamically as a function of volatility. The optimal approach is to ensure the risky asset allocation is proportional to the cushion. Rather than being constant, the proportion of risky capital relative to the cushion (the ratio between the two being known as the multiplier and usually written as ‘m’) should decrease as volatility rises. In other words, should volatility increase, one should cautiously reduce the allocation to risky assets even if the cushion suffers no impact as a result of the higher volatility.
Managing the capital protection involves controlling (‘leveraging’) the amount of cushion that can be lost without jeopardising the protection. This means investing more than the cushion in the risky asset – i.e. investing the multiplier times the cushion – to seek a higher return. However, this approach also leads to selling the risky asset after a loss because of the reduction in the cushion and to buying the risky asset after a gain. If one always follows the market – thus being ‘gamma long’ – one will lose money on average because one is selling after a loss and buying after a gain. It is therefore not optimal to ‘lever’ the cushion too much as the cost of doing so – the ‘gamma cost’ – will be too high. The optimal multiplier thus corresponds to the best trade-off between higher potential returns and higher gamma cost. The higher the volatility, the higher the gamma cost. One should therefore reduce the multiplier when volatility rises.
The empirical results in Exhibit 1 illustrate this conclusion. It compares managing a cushion either with a constant multiplier of two or five, or with a multiplier leading to the same average allocation to the risky asset but decreasing with volatility. The initial cushion is chosen arbitrarily at 100% (see the vertical axis). Too large a multiplier (five as opposed to two) leads to a large gamma loss and thus a poor average performance over the full period. Using a multiplier that decreases with volatility leads to better results (e.g. m=0.4/vol compared to m=2, or m=0.7/vol compared to m=5). Finally, note that the 0.4 and 0.7 in the numerator can be interpreted as the Sharpe ratio or risk-adjusted return of the underlying. The higher the Sharpe ratio, the more upside potential, thus the higher the optimal multiplier and the allocation to the risky asset.
Exhibit 1: Simulations of an investment with constant leverage (m=2 and m=5) or with leverage changing as a function of volatility (m=0.4/vol and m=0.7/vol)
Source: Bloomberg, BNP Paribas Asset Management as of 23/12/16
The capital protection level for target-date funds should at the outset depend on interest rates and loss aversion
Our research also concluded that the protection for target-date funds should initially be set at a level which reflects the level of interest rates and aversion to losses. Adapting the protection level to the current context of ultra-low interest rates is a particularly interesting exercise. Low interest rates mean that target-date funds offering 100% protection on the capital invested have little upside potential. As illustrated in Exhibit 2, the onset of ultra-low interest rates has indeed reduced the amount of cushion that such target-date funds could lose without jeopardising the protection level and has thus reduced the scope to invest in the risky asset.
As a result, target-date funds offering protection levels below 100% have been proposed to investors without any clear explanation of their rational. The thinking appears to be that the protection level needs to be reduced to create scope for upside potential. Our research addresses the question of the right level of protection in target-date funds: neither too large – to leave some upside potential – nor too small, to ensure a meaningful level of protection is maintained.
Our research demonstrates that the protection level of target-date funds does not have to be 100%. It can be higher if interest rates are high and lower if there is a low aversion to losses. The potential value of such an investment for investors indeed rises with an increasing protection level and potential upside at maturity in excess of this protection level. As both elements move in opposite directions (increasing the protection level reduces the upside at maturity), the right level for protection corresponds to the appropriate trade-off between the added benefit of increasing the protection level and the greater potential benefit of increasing the upside at maturity. The reasoning is similar to the trade-off between return and volatility in Markowitz’s theory, but it is applied here to the measure of risk linked to the level of protection, which is more relevant than volatility for target-date funds.
Exhibit 2: Small investment in a risky asset in a context of ultra low interest rates
Context of normal interest rates (around 5%)
Context of ultra low interest rates (below 1%)
Source: BNP Paribas Asset Management as of 23/12/16
When the fund performs well, the initial capital protection level needs to be raised via a ratchet mechanism
The third major conclusion of our research is that should the target-date fund perform well the initial protection needs to be raised using a specific ratchet mechanism. The strong fund performance increases the amount of cushion that can be lost while maintaining the protection level and also increases the upside potential to a point where it is too large in relation to the protection level. In such circumstances, it would be better to increase the protection level and reduce the upside potential relative to the new protection level. In short, the protection level needs to be adaptable. Hence the name Portfolio Insurance With Adaptive Protection = PIWAP.
In practice, the strategy is implemented via the use of a minimum protection ratio. The ratio indicates the proportion of the current protection level relative to the current NAV. It cannot be lowered because, by definition, the current protection level cannot be lowered. It can be raised, and hence a minimum protection ratio is imposed as a function of time left to maturity and the level of interest rates (see Exhibit 3). If the protection ratio falls below the minimum, it is increased to bring the ratio back to its minimum. For example, if interest rates are 0%, the minimum ratio is gradually increased from around 80% to close to 100% as maturity comes into sight. Should interest rates begin to rise, the minimum ratio will have to be adapted, rising to above 140% for instance when 15 years away from maturity.
Exhibit 3: Minimum protection ratio as a function of time to maturity for different interest rates levels (0%, 2% and 4%)
Source: BNP Paribas Asset Management as of 23/12/16
This article was written on 26 January 2017 by Thomas Heckel and François Soupé.