Tail Risk – Downside Analysis (S&P500)

Tail Risk. The enemy for long term investing with leverage.

Lets express the 1 day daily returns in a box plot.


# Maximum Loss and Gain 
# Location of min/max
min.loc <- which.min(df$spx.clret)
max.loc <- which.max(df$spx.clret)
# Date of Min 
min <- df$Date[min.loc]
max <- df$Date[max.loc]
> min
[1] "1987-10-19"
> max
[1] "1933-03-15"
> min(df$spx.clret)
[1] -0.2289973
> max(df$spx.clret)
[1] 0.1536613

The maximum one day loss, -0.3558507% which occurred October 19th 1987 stock crash. The largest 1 day gain, 0.3522206% which occurred March 15th 1933.

If using leverage we obtain a 1 day loss of (-0.7117014 %,2x leverage) or (-1.0675521%, 3x leverage). These one day ‘shocks’ are what is known as tail risk. It means that one could be down to the above magnitude in one trading day.

If we check the frequency 1 day losses over over ‘n’ loss %:



Again if using leverage, these losses multiply by their leverage factor. Since 1928, there were 8 occurrences as example of > 20% one day losses. If we use 3x leverage this one day loss increases to >60%.

Furthermore, we also face bear market declines which again pose another issue when holding long term with leverage.


Inclusive of 1929 bear market, peak to trough draw downs can be in excess of 50%. Top of 08 to bottom in 09 is around 56%. Again if we buy and hold a leveraged product. We will see gains 2x or 3x this amount.

So these are the ‘issues’ with buy and holding with leverage. Is there a solution?

One method of exploration is to use a simple moving average as a low pass filter. Using monthly bars, a simple moving average tends to reduce over all volatility.


Areas in red are cash periods or periods below the 12sma.

The below plot shows the maximum draw down for any given simple moving average from 1928 to present day. The simple moving average moves the investor to cash when below:


Over the same period, buy and hold draw down is 0.89783016%. Depending on the sma used, we approx reduce draw downs by 40 to 50%.

The optimal monthly simple moving average ranked by cumulative returns 1928 to present day.


If we perhaps consider a ‘modern market’ 1950 onwards.

Over all draw down reduces from buy and hold 0.5687671 %… to the 25/30% area depending on the simple moving average used.


And the optimal look back for the monthly simple moving average:


The message is pretty clear. Using a simple moving average as a ‘low pass filter’ often reduces volatility of simple buy and hold. This strategy does well to avoid both bear market declines post 1999 and 2007.

The over all results of monthly 12 sma, 1988 to present:

One day shocks like the 1987 stock crash can yield a 1 day drown down using 2 / 3x leverage up to 70 or 90%.

Post 1987 stock crash we see maximum draw downs for varying simple moving averages. Note short term simple moving averages are invested during bear market declines:


The question going forward. Are one day shocks of the 1987 stock crash possible again in the future? Is there anything structural that can change this? Does HFT provide liquidity or will it evaporate during times of distress?

A maximum draw down of 19% since 1987 using the low pass filter approach seems pretty simple to bear. One could, from 1987 to present use a 2 or 3x leverage factor and increase gains SUBSTANTIALLY whilst matching a typical buy and hold draw down of 56%.

Leverage and risk is the trade off. If believe the next 40 years will be as rosy as the previous. One may wish to take this bet. Not to mention will the S&P500 even be the ‘king’ market and continue to provide the same level of returns as the past 100 years?

No one knows 🙂 If the risk profile suits. Then that’s up to you. Otherwise, a normal buy and hold investing approach using a simple moving average will avoid large negative compounding periods.

Long over 12 monthly sma:


The frequency of heavy 1 day losses reduces from buy and hold, This is partly due to avoiding the majority of bear market declines.


I believe the message is this: regardless of what you google about holding 3x leverage products, it should be studied whether the ETF is built soundly, ie has minimal tracking error for there are many ETFs with poor design.

Next – are you comfortable or can you stomach the sickening draw downs? There is no doubt spells of volatility and this is likely to continue.

Perhaps there are LESS VOLATILE instruments with smoother equity curves, perhaps less volatile strategies with smoother equity curves. With little volatility one may add a leverage multiplier at their will.

Author: Andrew Bannerman

Integrity Inspector. Quantitative Analysis is a favorite past time.

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