Managing a key risk for investors : Disappointment

The cornerstone for any investment strategy is ensuring that an appropriate return is being earned for the level of risk being assumed. This requires that an assessment of expected returns be formulated which can be utilised to guide decisions. 

Yet even when everything works out as expected investors can often look back at realised returns and be disappointed as they lag what was initially expected. Often such disappointment can be the result of a simple mathematical bias, referred to as volatility drag, which it is possible for investors to manage.

What is Volatility Drag?

Volatility drag, also referred to as variance drain or volatility decay, results from differences in how investors frame forward looking expected returns versus how realised returns are generated. Usually investors consider expected returns in terms of simple arithmetic averages. In doing so such simplified approaches to framing forward looking expectations ignore the interaction of volatility with return generation.

Simple averages explicitly ignore the impacts of volatility as they view all returns as being of equal increments. For example with a simple arithmetic average a 10% increase is viewed as having the same incremental impact as a 10% decline. The result is that the volatility of returns around the mean has no impact on the expected return generated by a simple arithmetic average.

Though this is a perfectly reasonable simplifying assumption to make it ignores how actual returns are generated. In practice the returns generated by assets are driven by compounding which can have a material impact on the realised return. To see why consider an investor has $1 and suffers a 10% decline in value. To get back to the original $1 value now requires an approx. 11% gain generating a mean return of 10.5%. Once an investor takes into account compounding the mean return required to compensate for any volatility in returns increases. This is exactly the dynamic which is taken into account by the geometric mean.

The difference between the arithmetic and geometric mean of a series of returns is referred to as ‘volatility drag’. Volatility drag is accordingly ‘the mathematical reduction in long-term compound returns caused by price fluctuations’. Since geometric returns account for the compounding effect, volatility can negatively impact long-term realised returns. Importantly volatility drag does not change the mean or expected return, rather it affects the return the investor is most likely to realise.

Volatility drag can now be calculated as :

Volatility Drag = Arithmetic Mean - Geometric Mean

As the calculation suggests there are two ‘rules of thumb’ when it comes to volatility drag :

1. The higher the level of volatility, the more detrimental the impact of volatility drag, and
2. The longer the time period, the bigger the negative impact will be.

To achieve an approximation of volatility drag a simplified formula can be used. Over short holding periods the geometric mean return can be approximated by :

Geometric Mean = Arithmetic Mean – (StdDev² / 2)

therefore :

Volatility Drag = Arithmetic Mean - Geometric Mean = (StdDev² / 2)

Note this calculation is only an approximation and will understate volatility drag when applied over longer time horizons. For longer investment horizons investors should use a simulation to calculate volatility drag.

Why is this Important?

Though on the face of it volatility drag may simply appear to be an interesting mathematical phenomena it can have very real implications for investors. This makes understanding volatility drag important so that investors can appropriately manage expectations around returns. If two investments have the same arithmetic returns, but one has materially higher volatility, the more volatile asset may have a lower realised return due to the higher level of volatility drag. By not correctly taking into account this difference investors may either make incorrect investment decisions or be left disappointed even if the investment performs as planned. Indeed the difference between arithmetic and geometric returns can help explain why high volatility investment strategies may often disappoint by underperforming expectations even if everything goes as planned.

Managing Volatility Drag

Investors aim to construct portfolios which will provide an expected return in line with the risk they are taking. As volatility drag drives a ‘wedge’ between expected and realised returns the aim of investors should aim at minimising the impact of this ‘wedge’. To do this several actions could be considered.

a) Ensure Adequate Compensation for Risk:

The simplest step to take is to explicitly take into account the impacts from volatility drag when setting initial return expectations. Doing so assists to ensure that investors are adequately compensated for increases in volatility. Where a higher volatility is anticipated the increase in expected returns needs to be high enough to explicitly offset potential volatility drag.

Taking into account volatility drag is particularly relevant where leverage is involved as the impact on returns tends to be linear whereas the impact on volatility is non linear. Failure to appropriately account for the differing impacts of leverage on risk and return is often why many highly leveraged strategies disappoint in terms of realised versus expected returns to investors. Volatility drag is another reason the leveraging of investments should be approached with caution. As Warren Buffet said about leverage when investing ”If you're smart, you don't need it; and if you're dumb, you shouldn't be using it”.

b) Diversification :

The power of compounding is one of the key sources of wealth creation for long term investors. Volatility drag highlights how, to maximise the advantages from the power of compounding, investors should avoid large losses and recoveries requiring exponential growth. Optimisation of longer term returns accordingly requires the lowering of outright volatility and the potential for volatility drag. Volatility drag and diversification are accordingly intrinsically linked – appropriate levels of diversification reduces volatility and hence also reduces volatility drag.

c) Create Positive Convexity :

Positive convexity describes a non-linear payoff curve where gains accelerate faster than losses; i.e. positive convexity refers to an investment with more upside than downside. Positive convexity acts as a counterbalance to volatility drag by creating asymmetric returns that offset compounding losses. Adding a positively convex payoff profile to a portfolio creates positive skewness within a portfolio. When markets experience extreme moves, the convex leg spikes disproportionately, counteracting the volatility drag associated with volatile assets. Positively convex investment strategies are therefore expected to be highly correlated with the benchmark in typical market environments but diverge to the positive in extreme markets (see Figure 1). There are no free lunches though, and positive convexity strategies usually detract from performance during quiet markets as ongoing implementation/trading costs reduce returns.

Figure 1 : Stylised Positive Convex Payoff

Source : Simplify 101 : What is Convexity?

It may often be the case that portfolios exhibiting high positive convexity will also exhibit a high level of volatility; i.e. volatility drag may be a by product of positive convexity. It would however be risky for an investor to assume that simply because a portfolio exhibits a high level of volatility drag that if must also exhibit a high level of offsetting positive convexity or that the level of positive convexity is optimal. Where the level of convexity within a high volatility portfolio is sub optimal positive convexity can be added in several ways including the incorporation of :

• Options Strategies : Investors can overlay ‘cost effective’ options strategies exhibiting positive convexity. An example would be overlaying ‘out of the money’ call options or a straddle on an equity portfolio.

• Active strategies : There are a range of active strategies which aim to create positive convexity including specialised Exchange Traded Funds. For purely illustrative purposes two strategies will be outlined in more detail.

• Momentum strategies : Momentum (or trend following) strategies assume that assets with a current positive trend will continue to have a future positive trend and assets with a current negative trend will continue to have a future negative trend. The portfolio is long on assets with a positive past trend and short on assets with a negative past trend. This can be done in an absolute (long stocks) or relative sense (long and short stocks). The trading bias means that the payoff of the trend-following strategy is positively convex and is similar to a long exposure on a straddle option.

• Sub Par Fixed Income Strategies : An example of a strategy outside the equity space would be that of purchasing sub par bonds. Under certain conditions, such as heightened financial stress, the price of a fixed income instrument can decline to materially below its nominal value (also referred to as “face” or “par” value). This can create an opportunity to add positive convexity. When a fixed income instrument trades at a material discount to its nominal value it may benefit, in the absence of default, from a natural “pull” to the nominal value as it approaches maturity; referred to as “pull to par”. Such fixed income instruments have a bias to exhibit positive convexity given the potential for a material level of capital appreciation. A typical example of a ‘pull to par’ strategy is the purchasing of stressed/distressed debt.

d) Shorten investment horizon :

As volatility drag is a function of the investment horizon it can be managed by ensuring that high volatility strategies are utilised over shorter investment horizons. Leveraged, concentrated or non-diversified exposures/strategies can be useful as shorter-term exposures, but volatility drag highlights that they may be less suited for longer term investing. The obvious step for investors is for such strategies to be viewed opportunistically and not constitute a long term ‘buy and hold’ exposure where time will materially increase the exposure to volatility drag.

Investors may often face disappointment when the realised return from a strategy is materially below expectations. This risk of disappointment increases as the volatility associated with the strategy increases. Yet such disappointment may not reflect deficiencies within the strategy itself but simply expectations failing to correctly account for the risks associated with the increasing volatility of returns. 

As with any risk while it cannot be avoided it can be managed. The key is for investors to ensure that they are aware of the risk and then to take the necessary steps to combine strategies so that the risk adjusted outcomes for their portfolios are optimised. Doing so will ensure that they appropriately manage one of the key risks for investors namely disappointment with realised returns.