Actual performance & risks

The Risks of Index Investing on Wall Street

An investor always runs a market risk on stock investments because asset values fluctuate randomly. During economic downturns, these fluctuations add up downward to a so-called Maximum Drawdown (MDD). The MDD serves as an accurate measure for the maximum interim loss an investor may suffer relative to their long-term expected annualized return. During market upturns, these fluctuations drive values to new heights.

DigiFundManager introduces the concept of a validation period—a period of "Out-Of-Sample" testing utilizing actual, historic cumulative value fluctuations of calculated portfolio time series. We optimize asset weightings using a gradient search to build optimal portfolios. This approach ensures that the backtest accurately represents actual value fluctuations over time, including stocks that have since become inactive.

We advise users to extend the validation period to include at least the last Global Financial Crisis (GFC), covering a minimum of 15 years, though 30 years is preferred. Major stock indices (such as the S&P 500 and the DJIA) are known to drop by roughly -50% during recessions. Interim losses of this magnitude are incredibly difficult to bear against a long-term annualized gain of 7% to 8%—and this applies to institutional players just as much as retail investors:

• Impact on personal capital: Large drawdowns on the way to a long-term average can leave you without the necessary means to sustain your daily life.
• Systemic risks: Several banks went bankrupt or required massive financial injections on their way to long-term averages during the last financial crisis because they were deemed "too big to fail."

The Risk-Reward-Ratio (RRR)

DigiFundManager uses the Risk-Reward-Ratio (RRR) to represent the balance between your capital at risk and your expected annualized result. We calculate this by taking the absolute value of the MDD as the Risk, and the annualized returns over the validation period as the Reward.

Professionals may be more familiar with the MAR ratio, which is simply the inverse of the RRR. For broad market indices, the RRR typically ranges between 6 and 8. This implies that the maximum interim value at risk is on the order of half your total investment when the annualized reward sits around 7% to 8%.

By implementing hedging and statistical techniques—such as the Mean-Variance Portfolio Theory developed by Harry Markowitz—one can reduce the RRR from a volatile 6 - 8 down to a balanced ratio of about 1 to 0.5 using properly screened and ranked portfolios.

Case Study: The Drawdowns of October and December 2018

October 2018 was characterized by a -10% downturn in the S&P 500. My own investment at the time consisted of an optimal portfolio containing 12 long positions hedged by 12 short positions. Calculated by DigiFundManager, these positions were purchased on September 27 for a 13-week holding period.

The weighting was determined using the Markowitz technique, utilizing the RRR as the objective function rather than the variance of the results. With hedging and the Markowitz framework in action, out-of-sample testing over a 30-year validation period projected a statistically expected annualized reward of 16%, with a maximum drawdown of just -11% after costs.

These simulated results showed a Year-To-Date (YTD) return of 15% at the end of the scan on September 26, 2018. The actual end-of-day (EOD) value fluctuations of my broker account (measured in Euros) over October 2018, compared against the S&P 500 benchmark, demonstrated that the strategy successfully mitigated the market shock.

Naturally, statistics provide no guarantees for future performance. However, the renowned mathematician and pioneer of quantitative investment strategies, Jim Simons, stated in 2005 that past performance remains the best predictor of success. Expectation values are derived from historical data. They indicate a measurable increase in your chances of future success, provided the underlying nature of the risks does not fundamentally change, as demonstrated by these empirical trading results on Wall Street.

Nassim Taleb's Black Swan

When the nature of risk does change and becomes unrecognizable within historical mathematical correlations, we enter the domain of Nassim Taleb. He formulates the mechanics of unpredictable, high-impact events.

DigiFundManager minimizes the maximum drawdown divided by the annualized result as one of three options to account for extreme randomness—the so-called "black swans" residing in the tail of a distribution function. This implies an optimization process that actively searches the extreme tail of a distribution. When these numerical correlation processes become mathematically unrecognizable, the effectiveness of any quantitative strategy will inevitably break down.

Markowitz and Hedging in Action

I rebalanced my long portfolio on Jun 08, 2026, as calculated by the software. Since September 26, 2018, my USD-denominated account gained +58.6% (including all costs) with an MDD of -47,1%. In comparison, the S&P 500 [$] rose by +155.7% but suffered an MDD of -34%. This is Markowitz and hedging in action.

In 2026, the current YTD USD results stand at -15.6% versus +8.6% for the S&P 500.

The Efficient-Market Hypothesis and Autocorrelations

Driven by a continuous stream of financial, political, and economic information, investors constantly attempt to construct and maintain portfolios that maximize returns while minimizing risk. Most financial models assume the Efficient-Market Hypothesis (EMH), which states that asset prices always reflect all available public information. This suggests that historical asset prices are all you need to compute optimal portfolios. Our software relies exclusively on historical end-of-day (EOD) exchange data and confirms this view.

This does not mean you cannot beat indices like the S&P 500. It means that market prices are fundamentally correct, allowing you to statistically predict the direction in which they will move.

To time these predictions (determining holding periods), one can apply the Wiener-Khinchin-Einstein theorem. This theorem enables a search for market timing windows that exhibit the strongest autocorrelations in portfolio value fluctuations across economic cycles. Consequently, past price movements provide the best predictor of future success.

This is exactly what quantitative strategies strive for. Elite hedge funds like Bridgewater, D. E. Shaw, and Renaissance all achieved double-digit returns in 2018, whereas the broader industry averaged roughly -5% compared to the S&P 500's drop of -6.2%. All three relied heavily on quantitative strategies. DigiFundManager proves that these superior results are entirely achievable for smaller, retail-sized portfolios using nothing more than historical EOD stock prices, volumes, dividends, and splits.

MiFID II and PRIIPs: Quantitative Risk Assessment

MiFID II (Markets in Financial Instruments Directive) and PRIIPs (Packaged Retail and Insurance-based Investment Products) regulate consumer investment products within the European Union, including ETFs and mutual funds. The MiFID II guidelines explicitly state:

"Market risk is measured by the annualised volatility corresponding to the value-at-risk (VaR) at a confidence level of 97.5% over the recommended holding period, unless stated otherwise. The VaR is the percentage of the amount invested, that is returned to the retail investor."

The manufacturing party of the PRIIPs product is required to calculate this VaR-equivalent volatility (VEV) and assign a Market Risk Measure (MRM) class. This MRM class is combined with Credit Risk Measures (CRM), if any, and translated into a single Risk Indicator (RI) ranging from 1 to 7. For example, if the VEV falls between 20% and 30%, the product is assigned an RI rating of 5 (assuming no significant credit risks are present).

PRIIPs products are broadly categorized into four separate categories.

Historical Scans vs. Fictitious Simulations

For Category 3 products, risks and annualized returns are often calculated from a minimum of 10,000 synthetic, fictitious data paths—essentially a lottery drawing. Jerzy Neyman, who pioneered confidence intervals, explicitly warned that a confidence interval (in this case, 97.5%) only yields information about the reliability of the drawing process itself. It carries no information regarding actual historical quantities, such as expected returns or structural risks.

Claiming that these fictitious fluctuations correlate with historical reality is a fundamental misunderstanding. You simply cannot extrapolate genuine historical risks from 10,000 synthetic data paths.

In our view, calculating a VEV based on an entirely artificial history cannot be used to establish a valid ex-post risk indicator. While Monte Carlo simulations are highly effective in fields like signal processing—where future propagation is dictated by immutable physical laws—the movement of stock market prices is fundamentally unpredictable. That is why we calculate expected annualized returns and maximum interim losses strictly from clean, unadulterated historical data.

Volatility-Based Risk vs. Maximum Drawdowns

We believe that calculating risk via VEV makes the issue unnecessarily complicated. A retail investor ultimately wants to know one thing: their maximum potential interim loss relative to their expected reward over a specific time horizon. DigiFundManager addresses this by focusing on the Risk/Reward ratio, aiming to optimize this value as close to 1 (or below) as possible.

In the professional investment space, risk is often treated as an average, with volatility (the standard deviation over a given time horizon) used as the primary metric. **However, this average risk metric is frequently a factor of three to four times smaller than the actual maximum interim loss.** Volatility works as a risk measure roughly 80% of the time, but it fails precisely when you need it most—when tail events kick in.

Modern Portfolio Theory (MPT) relies on standard MPT statistics. While standard deviation (volatility) is the baseline, a comprehensive risk analysis also incorporates the Sharpe ratio (reward relative to average risk against the S&P 500), beta (systematic risk relative to the S&P 500 minus the risk-free rate), and alpha (annualized reward relative to a risk-adjusted benchmark). Our free online version calculates all of these MPT statistics alongside the standard risk indicator.

The Risk Profile of the S&P 500

Portfolios composed of high-quality equities with healthy daily trading liquidity (excluding penny stocks and Over-The-Counter/OTC shares) carry virtually no credit risk. For these assets, market risk is the primary concern.

As an example, evaluating the annualized results of weekly trading the S&P 500 reveals that annualized returns vary by a factor of two when the validation period is compressed from 68 years down to 5 years. Skewness doubles, kurtosis shifts by a factor of four, and annualized volatility fluctuates between 12% and 18%.

Consequently, the sequence of weekly S&P 500 returns cannot simply be randomized to calculate a practical Value-at-Risk; only the actual historical sequence yields a realistic MDD risk level.

For compounded investments, the historical MDD stands at -56% for validation periods spanning anywhere between 12 and 68 years. For constant (non-reinvested) capital, that number drops to -75%. These are the true risk levels associated with broad Index investing. Because of this, the official MiFID II risk indicators for Category 3 products bear no formal relevance to actual risks and rewards.

How Does Market Risk Scale with Volatility?

For any given annualized volatility (σa), validation period (Nval), and economic investment cycle (Ninv) lasting roughly 7 to 11 years (the Clément Juglar cycle), it is mathematically straightforward to prove the existence of a minimum Value-at-Risk dictated by a strict inequality:

VaR is greater or equal to (Nval / 2Ninv) * σa

When the validation period spans two full investment cycles (approximately 20 years), the mathematical minimum of the Value-at-Risk equals the volatility. For a median volatility of 14.5%, your calculated market risk—or Value-at-Risk—would match that 14.5%, placing your Risk Indicator squarely at class 5.

But does this offer a realistic view of actual market behavior? Real-world data from index investing reveals that the practical Value-at-Risk is actually a factor of 3.5 times higher. Therefore, equating true market risk purely with volatility is fundamentally misleading.

Jan G. Dil and Nico C. J. A. van Hijningen,
Jun 13, 2026.