The Amount Of Capital Risked By Investing In The S&P 500
Computing the SPY's VaR & Max Drawdown Via Historical, Delta-Normal Simulations
The SPY’s monthly value at risk between 2005 - 2025: It’s illustrated that SPY’s VaR can reach circa 17.5%, yet flatline down to the 0% boundary, depending on methodology, confidence level, and market conditions.
A historical simulation conveys higher average VaR than a delta normal method, mostly due to the ocurrance of non-normal distributions.
Recent volatility spikes and clustering have resulted in delta normal VaR exceeding historical VaR.
An average average max drawdown of 36.06% is noted with a range of between 19.35% and 55.19%.
The SPDR S&P 500 ETF SPY 0.00%↑ tracks the S&P 500 via full replication. While it might be lucrative holding the S&P 500, it’s worth examining the risk of doing so. A myriad of risk-return methods exist. However, this article zooms in on Value-at-Risk and maximum drawdown. More specifically, I created models for historical Value-at-Risk and delta normal Value-at-Risk.
Historical VAR
The historical simulation method simply measures VaR by plotting past returns and phasing in a cutoff point. For example, let’s consider a sample of 100 returns and a VaR of 95%. We could rank the historical returns from best-to-worst, cut off at the 95th value and conclude that 95% of our returns won’t exceed the loss recorded at the 95th value. Furthermore, losses exceeding the 95th percentile are called exemptions–by averaging the exemptions, we find conditional VaR, which is a measure of extreme tail risk.
Trivially, VaR has limitations with one being: past returns aren’t fully correlated with future returns. However, despite its limitations, historical VaR still provides a solid baseline for inference, especially for non-normal return distributions. The key is to condition the model to market environments. For example, we could observe the values realized during the Great Financial Crisis to create future scenarios for credit crises.
Looking at SPY illustrates that it currently possesses a monthly historical VaR of 5.59% at the 99% level and a 4.50% historical VaR at the 95% level. History shows that these values can drift substantially higher. For instance, 99% VaR reached 16%+ during the GFC and 12%+ during COVID-19.
Delta Normal VAR
The delta normal method utilizes a parametric formula. Methodologically, delta normal isolates standard deviation and a t-stats. Specifically, the formula is written as: VaR = T-Stat x Monthly Standard Deviation. For the 95% confidence level, we use a t-stat of 1.65 and for the 99% level, we use a t-stat of 2.33. In simple terms, t-stats provide a standardized method of measuring how distant a data point is from the mean.
Compared to historical VaR, the delta normal method provided us with a lower overall Value-at-Risk. However, the end-date VaR settled higher. The lower structural result is mostly due to the assumption that returns are normally distributed. In contrast, the higher point-in-time result is likely due to volatility clustering, saturating values near the tail.
Max Drawdown
Maximum Drawdown is exactly what the name says, it measures an asset’s peak-to-bottom drawdown. It’s a true representation of tail risk. However, the periodicity and uniqueness of past events add limitations to the method, which is why we combine it with VaR instead of using it as a standalone. The SPY’s max drawdown communicates a range between 19.35% and 55.19%. Notably, recoveries can take long, especially if we incorporate a geometric return distributions into the thought process!
Averages
Herewith are the calculated throughout-the-cycle VaRs. Notably, the historical simulation’s average is higher than the delta normal’s. However, as previously mentioned, volatility clustering can cause the relationship to dislocate.
Max Drawdown averaged at 36.06%. The width of the drawdown range and infrequent occurrence presents challenges whenever conditioning for a market outlook, especially if idiosyncratic risk is considered.
Crucial: Disclaimer
This analysis is provided for informational and research purposes only. It does not constitute financial advice and should not be relied upon as such. The data and interpretations presented may contain inaccuracies or be subject to revision. This content is intended solely to foster further discussion and inquiry among peers. Always conduct your own due diligence or consult a licensed financial professional before making any investment decisions.
Related Tickers: TSLA 0.00%↑ NVDA 0.00%↑ AMD 0.00%↑ F 0.00%↑ GOOG 0.00%↑ $
Is there a book that I can read to help me understand your articles