In Depth

​We really only get one chance to save for retirement.

An immediate consequence of this observation is that we cannot simply allocate our retirement dollars to the “market” and hope to have a safe nest egg when we are ready to retire. Averages matter for research and analysis, but the reality is that markets take one path, and the law of large numbers is no insurance against market crises. So the impact of a bad market, however short and episodic, can be substantial and permanent, forcing us to change expectations of our standard of living in retirement.

This is why we believe we need to look at the whole path taken by our investment portfolios and seek to keep risks tightly controlled. Tail risk management can help guard against market shocks, and this in turn means retirement assets can be managed within risk capacity (as PIMCO’s Stacy Schaus and Ying Gao wrote in “Loss Capacity Drives 401(k) Investment Default Evaluation” in May 2012).

Let’s examine some facts about – and methods designed for – hedging our retirement portfolios against so-called fat-tail losses.

The first thing to note is that long-term investors generally don’t seem to care about volatility if the volatility comes with the potential for ultimately higher gains. What retirees do care about are sharp falls in their portfolio value. These “drawdowns” not only can alter prospects for future savings, but also can force us into making irrational decisions at the wrong time, crystallizing losses and making them permanent. Hedging against such drawdowns is what a good risk management paradigm should be designed for.

We should also make clear the distinction between two types of drawdowns. As typically used, the term drawdown is defined as the percentage change in the value of an investment from a newly established high to a subsequent low. The maximum value of the peak-to-trough drawdown influences how we feel about the sudden loss in wealth. Slightly different is the maximum value of the loss from its initial value: This measures the economic loss of wealth. Higher volatility translates both into higher drawdowns and higher potential loss of economic wealth. Since we do not know with certainty when the drawdowns will occur and how large they will be, let’s focus our analysis here on the characteristics of expected maximum drawdowns, that is, the forecast of the average value of maximum drawdowns that could be expected (in practice it’s the average of a number of simulations we run (see description in Figure 1)).

We use a simple Monte Carlo simulation and assume that the NAV of a portfolio with the designated equity market beta follows a lognormal process, with the underlying equity risk factor volatility computed at 18% – consistent with long-term U.S. equity market results – and a mean annual return assumption going forward of 2% for the equity risk factor. Source: author’s computations. 

1. Expected maximum drawdown (from peak to trough) primarily depends on volatility, then on expected returns. For the more mathematically inclined this means that skewness (a measure of asymmetry in the distribution) and kurtosis (or how “fat” the tail of the distribution peak) matter relatively little, but doubling volatility can more than double drawdowns. In the language of risk factors that we at PIMCO use for our asset allocation approach, a higher equity beta or higher equity risk factor translates into higher volatility – and hence to higher expected maximum drawdowns. In Figure 1 we show how increasing the equity beta increases the potential maximum drawdown.
   
   
2. Increasing returns or decreasing volatility both tend to decrease maximum drawdowns, but the increase in returns has to be more than twice as much as the increase in volatility to keep the drawdown the same. In particular, increasing volatility and returns at the same time will keep the Sharpe ratio constant, but will increase the maximum drawdown. So we believe the often-used Sharpe ratio of volatility is simply not a good metric for deciding on what investments to pick for retirement – in this instance, volatility matters via its impact on the potential for large losses. In Figure 2 we show the non-linear dependence of the volatility normalized maximum drawdown on the volatility normalized Sharpe ratio for the same value of returns as the volatility changes. (We keep the returns constant at 2% per year in this example, too.) For all horizons, this relationship is non-linear, and the longer the horizon, the higher the normalized maximum drawdown for the same normalized Sharpe ratio.
   
   
   
    
3. Increasing the horizon will increase the expected maximum drawdown and depends very strongly and in a discontinuous manner on whether the expected returns are positive, negative or zero (as elegantly observed in an article by Malik Magdon-Ismail and Amir Atiya in Risk Magazine in October 2004). Further, the behavior is qualitatively different for the different signs of the expected return for long horizons that are relevant for retirees. Based on the analysis in this paper we can draw a number of conclusions:

1. If the expected return is positive, then the increase in horizon will increase drawdowns logarithmically with time (i.e., very slowly). As volatility doubles, the expected maximum drawdown grows four times as much. As returns double, the expected maximum drawdown halves.
   
2. If the expected return is zero, then the increase in horizon will increase drawdowns as the square root of time. The rule of thumb is that the expected maximum drawdown scales like one and a quarter times the volatility.
   
3. If the expected return is negative, then the increase in horizon will increase drawdowns linearly (i.e., very rapidly). The scaling of the expected maximum drawdown is largely immune to volatility and increases linearly with falling expected returns. 

Note particularly that as expectations of returns fall, the expected maximum drawdown rises quickly and results in catastrophic risk of ruin. In particular, if returns are zero or negative, the possibility of an investor losing over half of her investment over the not-very-far-out horizon is a very high likelihood event. In a world of structural imbalances and rising uncertainty that we are currently faced with, the positive benefits of high returns to equity markets should not be counted on to lower drawdowns. This calls for a high degree of caution to hedge against drawdowns like the ones experienced in 2008.

Having a longer horizon makes the portfolio risk management problem for a younger retiree more complex than an older investor close to retirement. Generally, the younger investor has to take more risk, and also has a larger length of time in which to recover from losses. But taking more risk means a higher chance of larger drawdowns.

Let’s make this concrete. Suppose we expect returns to be flat over the next few years. Then expected maximum drawdowns for a 20-year-old with 50 years to retirement will be more than twice the drawdown for a 60-year-old with 10 years to retirement (square root of 50/10 = square root of 5). But the 20-year-old will likely have a greater ability to withstand the drawdown because she has more time to invest and can expect periods where she can improve returns above zero. But her need to manage the downside still exists. So how should she do this in a disciplined manner?

First, typical investment portfolios, in our experience, suffer from too much asset class diversification and not enough risk diversification. In a cosmetically diversified asset mix it is very hard to tell what the potential is for drawdowns in the portfolio since we cannot easily decipher the risks of such a portfolio.

However, by using the coarser lens of risk factor exposures, we believe this exercise becomes somewhat simpler and a lot more practical. For instance, one can aggregate the equity beta of all types of assets in a portfolio and change the beta of the portfolio as desired to target a particular risk level. So as a practical tool, we recommend investors look at the composition of their investments using risk factors – the most important ones being the equity beta and the interest rate duration. But simply knowing the risks is not enough. We have to seek control against permanent damage from that risk using the framework of tail risk hedging.

 

So a relevant question is: How much should one be willing to pay for the option to hedge against a particular drawdown for a given horizon? This “budget” for hedging changes with two key variables. First, as the beta (market exposure) rises, the amount of premium spent implicitly (e.g., by keeping excess cash reserves) or explicitly (e.g., by buying put options) rises. Also, as the proximity of the threshold comes closer to the current value of the portfolio, the budget rises. So whereas for a 0.20 beta equity portfolio a 5% attachment level (the targeted maximum loss at the horizon of the investment hedge) would cost 31 basis points of premium per year (typical of a shorter-dated retirement portfolio), the same attachment level for a 0.50 beta portfolio would cost almost eight times as much (2.6%), again based on a Monte Carlo simulation using an 18% volatility for equity risk factor. On the other hand, if we take the attachment level to 15%, the hedge cost of the 0.50 beta portfolio drops back down to 30 basis points. In Figure 4 we show the relationship of cost to the horizon of the strategy for different betas. In these examples we have kept the volatility of the equity factor fixed at 18% per annum, which is close to the observed volatility over the last 80 years or so. As volatility rises and falls, the price of tail risk hedging will also rise and fall.

 

 

If we think of this essential tradeoff between hedge cost and beta, we see that for shorter-dated retirement strategies, there is very little time to make up for sharp drawdowns, hence most of the tail hedging has to be done both via defensive positioning and also via explicit tail hedges. On the other hand, if the portfolio has a long horizon, we can afford to take more risk via higher equity beta and can simultaneously move the attachment level further out to keep the cost of hedging against tail events relatively low.