Many commonly used approaches to portfolio construction assume that, over time, the returns on financial assets will conform to a certain pattern called “normal distribution,” with most returns clustering symmetrically within a relatively small range of the mean.1
In a normal distribution, relatively thin tails trail off symmetrically around the mean, representing rare instances of extreme losses or steep gains.This, however, has not played out in practice. In reality, returns on assets tend to be “fat-tailed,” with far more instances of extreme losses and gains than a normal distribution would predict (see illustration in Chart). This means that many portfolio-construction frameworks are underestimating the risk that’s embedded in the markets.
There’s a big difference between the normal-distribution approximation of large gains or losses (which informs many investors’ portfolio decision making) and the actual occurrence of those large gains or losses. If S&P 500 equity returns were distributed normally, we would expect to see a daily gain or loss of more than 3% on only 54 days since 1 January 1930. In fact, the S&P 500 experienced a gain or loss of more than 3% on 568 days – nearly thirteen times more often than the normal distribution would predict (see Table).
This difference becomes more apparent as we move out on the tails. A normal distribution of returns would predict a daily gain or loss of more than 4% in the S&P 500 on only two days or so since 1 January 1930; this has happened on 263 days in this time period – more than 82 times as often as a normal distribution would anticipate. Under a normal distribution, we could reasonably expect never to have observed a daily gain or loss of more than 5% for the S&P 500 in this time frame. In reality, it has happened 127 times.
The observation that returns on assets – including equity-market returns – are fat-tailed is not especially new. For investors, however, the actual distribution of returns raises the question of whether their portfolio-allocation approaches adequately account for the possibility of large drawdowns, which can impair investment prospects for months and even years. Defensive equity strategies with a dual risk and return mandate can help investors to avoid large drawdowns and preserve capital, which in turn can help to create a smoother path to return objectives over time.
1 The mean value in a group of numbers is commonly called the “average.” The mean is calculated by adding all the values in a given set, then dividing by the number of values in the set.
Defensive equities: Defensive equities seek to provide a “best of both worlds”: delivering the equity risk premium to achieve wealth accumulation, but by investing in less-risky equity securities to promote wealth preservation.
Monte Carlo Simulation: Monte Carlo simulations are used to model the probability of different outcomes in a process that cannot easily be predicted due to the intervention of random variables. It is a technique used to understand the impact of risk and uncertainty in prediction and forecasting models.
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