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Historical Simulation Method: Does It Really Help?

"simulation is an incredibly powerful technique to understand the impact on a variable due to changes in a number of factors."


Many theories have been authored on simulations that suggest either using the same outcomes generated in the past (called the historical simulation method) or generating a wider range of scenarios produced out of a probability distribution (called the parametric-based monte-carlo simulation method) to predict and understand the impact on a variable.


Our research says that the latter one i.e. the parametric-based monte-carlo simulation method has increasingly become a key method used for quantitative analysis. However, one needs to start with understanding the historical simulation method (being simple and easy) to understand the intuition behind the monte-carlo simulation.



Historical Simulation Method

the historical simulation simply assumes that history will repeat itself, which means one out of the past outcomes will repeat in the future.

for example, to estimate /predict the stock price, the historical simulation method uses shocks computed on the time-series data i.e. the outcomes that the stock has generated in the past, and the same shocks are then randomly picked by the simulator and applied to the current stock price to estimate the possibilities that the stock price can take in future (called simulated prices) under different scenarios. The scenario results are then averaged out together to provide a single-figure estimate.


Our algorithm extracted the time-series data of a stock, trading at $1453.00 dated 2022-10-04, for a lookback period of 250 trading days.

The time-series was then given to a scenario generator tool to compute proportional shocks.

It is important to note that, statistically, the scenario generator tool is computing the proportional shocks in a continuous timeframe though the timeframe is discrete to the end-of-day close time.


As per the historical simulation, the same past outcomes will repeat in the future but the order of occurrence may be different (the sequence of occurrence may change), and therefore, our simulator has randomly picked one shock (in-sample) from the series of shocks and applied to the current spot price $1453.00 to estimate the stock price at time t+1.

for better understanding, the below syntax can also be used in excel to approach the same.

=spotPrice*EXP(SMALL(spotShocks,RANDBETWEEN(1,COUNT(spotShocks))))

the same process of applying a randomly picked shock to the current spot price is repeated a number of times to simulate the current stock price to achieve the maximum possibilities that a stock price can take in one trading day period.

[grid:1million simulated stock prices]

these simulated prices were then averaged out to get a single-figure estimate of the stock price at t+1.

let's run the simulator by extending the timeframe to 250 trading days to estimate the stock price at t+250.

at each t'node, the simulator has randomly picked one shock (in-sample) from the series of shocks computed using the scenario generator tool and applied it to the immediate previous day's stock price (t-1'node) to estimate the stock price at t'node.

[columns:1simulation, rows:250t'nodes, grid:simulated stock prices]

[y-axis:values, x-axis:250t'nodes, grid:1random path]


Our algorithm triggered the simulator again and repeated the same process to generate multiple paths that the stock price may follow in the future until t+250.

at each t'node, the simulator has randomly picked one shock (in-sample) from the series of shocks computed using the scenario generator tool and applied it to the immediate previous day's stock price (t-1'node) to estimate the stock price at t'node.

[columns:10000simulations, rows:250t'nodes, grid:simulated stock prices]

[y-axis:values, x-axis:250t'nodes, grid:50random paths]

these simulated prices were then averaged out to get a single-figure estimate of the stock price at t+250.

for better understanding, some snippets from our excel model are attached!

Historical Simulation Method: Does It Really Help?

At the outset, this approach of simulation seems very intuitive as the algorithm tries to capture thousands (/millions) of possible values that the variable can take in the future, plus simple to understand, and easy to implement.

However, our algorithm together with other time-series models actually runs the parametric-based monte-carlo simulation to predict stochastic variables over a longer timeframe which actually resulted in a higher probability of estimated value getting achieved than running through historically observed data points.


Observation-1: one might have observed that, at the time of estimating the stock price over a longer timeframe, we had to reduce the number of simulations (generated 100k simulated paths instead of 1 million).

runtime recorded by our simulator through our time recorder tool.

It seems that these simulators are computationally heavy to run on a smaller machine and they are time-consuming too, they require high computational power /infrastructure to simulate a number of stochastic variables impacting multiple financial instruments.


Observation-2: the historical simulation method assumes that history will repeat itself, which means one out of the past outcomes will repeat in the future as it uses past historical outcomes to predict the future outcome which is not true in real life. Therefore, it fails to capture any new catastrophic event.


Limitations of the Historical Simulation Method


  1. Assumption of Stationarity:


    Historical Simulation and Stationarity: The historical simulation method is based on the assumption of stationarity, which means it presumes that the statistical properties of past data (such as mean, variance, and autocorrelation) will continue into the future. This assumption is critical because it underpins the belief that historical patterns and behaviors can be used to predict future outcomes.


    Non-Stationary Behavior of Financial Markets: However, financial markets are known for their non-stationary behavior. The statistical properties of financial data can change over time due to various factors, such as economic cycles, regulatory changes, technological advancements, and shifts in investor behavior. This non-stationarity implies that the historical data may become less reliable for future predictions as market conditions evolve.


    Inability to Capture Rare or Extreme Events: The historical simulation method relies solely on past data, which may not include rare or extreme events such as financial crises, recessions, or other significant market disruptions. These events, while infrequent, can have a profound impact on financial markets. Since historical data may not capture these events, the simulations might underestimate the risks and potential volatility associated with such occurrences.


  2. Limitations of the Lookback Period:


    Finite Time Period of Lookback: The lookback period in historical simulation covers a finite time span, which may not be sufficient to capture all the dynamics of the market, especially for long-term predictions. The chosen period might miss out on important historical events or trends that occurred outside of this timeframe, leading to incomplete or biased results.


    Challenges with Limited Market Data: This limitation is more pronounced when dealing with risk factors where market data is very limited. For example, emerging markets or newly listed securities may not have extensive historical data available, making it challenging to perform a robust simulation. In such cases, the limited data can restrict the ability to make accurate long-term predictions.


  3. Dependence on Data Quality and Completeness:

    Quality and Completeness of Historical Data: The accuracy of historical simulations heavily depends on the quality and completeness of the historical data used. Inadequate or incomplete data can lead to biased estimates and unreliable predictions. Data gaps, inaccuracies, or errors in the historical records can distort the results of the simulation, making them less reliable for future decision-making.


  4. Ignoring Fundamental Factors:


    Lack of Fundamental Analysis: Historical simulation relies solely on past price movements and does not incorporate fundamental factors such as economic indicators, company performance, and market sentiment. These fundamental factors can significantly influence future price movements. By ignoring them, the historical simulation may produce incomplete or misleading predictions.


    Impact of Economic Indicators and Market Sentiments: Economic indicators like GDP growth, inflation rates, and employment levels, as well as market sentiments driven by news and investor behavior, play crucial roles in shaping market dynamics. The absence of these factors in the simulation process means that it might miss important signals that could affect future market conditions.


  5. Equal Weighting of Historical Outcomes:


    Equal Treatment of Historical Outcomes: The historical simulation method treats all historical outcomes equally, regardless of their relevance to current market conditions. This approach fails to account for changes in market volatility or other factors that can vary over time.


    Relevancy to Current Market Conditions: Not all historical events have the same significance or impact on future predictions. Some events may be more relevant to current market conditions than others. By treating all outcomes equally, the simulation might not adequately reflect the current state of the market or the changes that have occurred over time.


  6. Backward-Looking Nature of Historical Simulation: The historical simulation is inherently a backward-looking method. It relies entirely on past data and does not incorporate any forward-looking information about future market expectations. This is a significant limitation because financial markets are influenced by both historical trends and future expectations. Forward-looking information, such as anticipated economic policies, technological advancements, or geopolitical events, is crucial for making accurate predictions about future market conditions.

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2 comentários


Wahid Syed
Wahid Syed
02 de mar. de 2023

Following is My observations on HUL Stock price for 3years(746 data points):

1.Expected Return distribution which is arrived by applying formula =spotPrice*EXP(SMALL(spotShocks,RANDBETWEEN(1,COUNT(spotShocks))))

2. Continue applying for total Equity price data and plot pivot and then group by to arrive Cummulative distribution

3.Finally bar chart is inserted based on pivot data.


I observe expected return distribution to be Symmetric which implies it is normally distributed by PDF. Historical Simulation method however has limitation if any sudden news came to limelight into market, then stock price don't follow this method.


When I estimate Point and Path estimation and draw line chart,it appears


Average the point(t) and path estimation(t+252d) and finally got expected return for 1 year



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srinath197987
srinath197987
01 de mar. de 2023

The expected return Distribution for 1000 iterations, even though after reducing the the number of Iterations the expected Price distribution seems to be normally distributed as this has been assuming the History will repeat again in the future, which also means the Historical Time series return distribution is also normally distributed.




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