Evidence-Based Individual Security Forecasting
One of the most popular methodologies for underwriting individual securities is the discounted cash flow (DCF) model—the analyst projects the free cash flows of a company into the distant future and discounts those cash flows to a “net present value” or fair price for the security today. The problem with the DCF is that there is no evidence that it or the theory upon which it is predicated works.
The reasons the DCF fails are twofold. First, traditional DCF models assume we can accurately forecast revenue and earnings 3–5 years into the future. But studies have shown that growth is neither predictable nor persistent. Second, traditional DCF models assume that the capital asset pricing model can be used to assess the riskiness of an investment and set an appropriate discount rate. But the capital asset pricing model has been empirically invalidated.
Two years ago, we proposed an alternative approach to financial modelling using Monte Carlo models. Most fundamental analysts will develop a downside scenario, an upside scenario, and a base case as they evaluate a potential investment—making deterministic forecasts for revenue, margins, and multiples. By contrast, a Monte Carlo model generates hundreds or thousands of independent scenarios to give probabilistic rather than deterministic insights into future returns.
To make this more tangible, consider how a traditional DCF model would work versus our Monte Carlo model for three key variables:
Figure 1: DCF Model vs. Monte Carlo Model
The Monte Carlo model then provides a distribution of potential investment returns given a thousand random trials with those assumptions—a thousand cases versus the traditional investment analysts’ three. Below is one example of a highly levered stock that goes bankrupt in roughly 25% of simulation trials (left of the first quartile – “Q1”) and pays off handsomely in 25% of trials (right of the third quartile – “Q3”).
Figure 2: Monte Carlo Model Results for a High-Leverage Stock
We can think of the Q1 outcome as analogous to the traditional downside case, the Q3 outcome as analogous to the upside case. The steeper the slope of the curve from the downside to upside, the higher the risk and the higher the return. The above Monte Carlo is a particularly high-risk, high-return investment.
To test if Monte Carlo underwriting forecasts work, we ran ~5,000 Monte Carlo simulations on the top 150 equities identified by Fama-French linear factor models in the US and Japan from 2000 to 2017. We wanted to compare how the Monte Carlo’s predictions stood up to those of the factor model.
We sorted the predictions of these 5,000 samples according to both the factor model rankings and the new Monte Carlo rankings independently in the US and Japan. We used the predicted average outcome of the 1,000 Monte Carlo simulations on each stock.
Figure 3: US and Japanese Backtested Portfolios - Factor Model vs. Monte Carlo Rankings
The Monte Carlo predictions were effective at sorting stocks from most attractive to least on one-year forward returns in both countries. It’s exciting to see that the results of the Monte Carlo model we created are almost as effective as the factor models that dominate the quantitative investment world.
Statistical analysis (Figure 4 below) of the Monte Carlo data suggests this did not occur by sheer chance. As expected, the factor model was reliably predictive in both geographies with T-stats of -3.45 and -4.37 (as the rank from #1 to #150 goes up, future returns go down).
We found that the slope of the probability distribution produced by the Monte Carlo model mattered. In the US, the third quartile (“Q3”) outcome, which is analogous to the upside case in a traditional DCF, was a reliable predictor of one-year forward returns. The stocks with the higher predicted upside did indeed do better on average.
In Japan, the first quartile (“Q1”) outcome, which is analogous to the downside case in a traditional DCF, was a good predictor of one-year forward returns. The stocks with worse predicted downsides had higher realized returns. The stocks that the Monte Carlo thought had the highest bankruptcy risk produced the best returns. In a country with almost no public company bankruptcies, investors were rewarded for investing in companies that would have had a higher probability of bankruptcy elsewhere.
Figure 4: Regression Output of One-Year Forward Returns vs. Factor Model and Select Monte Carlo Metrics
Finally, we wanted to test whether the Monte Carlo predictions systematically added value to our factor model rankings.
Figure 5: Backtested Portfolios Using Factor Model, Monte Carlo, and Combined Rules (2000-2017)
We are excited to find that adding Monte Carlo results to factor model results produced improved outcomes in portfolio construction. We hope this piece provides some insight into our process at Verdad. We aim to develop novel investment theories, subject them to rigorous falsification, and then integrate them into our investment decision making process systematically.
Monte Carlo models are more accurate than traditional DCF models because they embrace uncertainty—they take randomness as a fundamental given. Traditional DCF models assume the future is predictable, plannable, and understandable—and there is no more dangerous intellectual error to make in the world of investing than that assumption.