I am modeling a highly cyclical company; while the long-term trend is clear (at least in my head), forecasting the business cycle is a shot in the dark. What came to my mind is to introduce some random variable into the model and simulate it a few hundred times. Then, continue with the standard procedure, producing a “fair value” distribution for the equity.
Does any of you have done this / something similar? Can you recommend an article / video / sample model I can use as a starting point? Any ideas/recommendations how to improve it?
From this very vague description, it sounds like you have a formula for equity value whose input is revenue, which you intend to model as a random variable. There are many ways to do this, either with Monte Carlo simulation or without it. You need to first decide what your revenue distribution should look like. After that, it should be fairly simple to model the next period’s value.
If you are asking about fitting a proposed process (let’s say some autoregressive model) to historical data, the general approach is to set up the formula for that process in some computer program and solve for the independent variables that minimize the error term in the formula. Excel Solver should be good enough for this.
Edit: I should say though, that this approach might not be very precise for individual stocks, since observations are sparse and new developments might make different periods incomparable. The likelihood of statistically significant results will be low and the risk of spurious results will be high.
Again, your starting point is deciding what variables to include in your model. You can look up various mean reverting or other processes in the internets. The standard approaches are well documented.
Edit edit: Autoregressive processes or other processes are also not exclusive from Monte Carlo simulations. One is a model for price movements and the other is a way to simulate those movements given a known process.
First, thank you for the comment! Here’s the precise idea - I will use a standard DCF analysis with all descriptive variables but the revenue figures (which will be probabilistic). I was thinking of forecasting 5-10 period using some correlation between last year or two trends and introduce some noise (here’s where the Monte Carlo comes into play). So for example I projected Y_1 is Y_0 times some factor (say .1-.2) plus noise with expected value of, say an inverse log-normal distribution with 3% mean and standard deviation of 10%. The idea is to reproduce the wide variation in revenue growth while keeping a small portion of the momentum (via the first bit). The rest of the model will be defined by the revenues and their growth. The output will be a distribution of the fair value of the company. Do you think this might be a good approximation? We are talking about the semiconductor space here.
Still more reliable than technical analysis though
To answer your question, this is a complicated approach, since the result will be affected by many other variables. It is meaningful to perform quantitative analysis on stock indexes, as many effects are averaged over a large universe of stocks to product a continuous distribution of returns. Individual stock volatility, however, tends to be dominated by multi modal events, such as distribution contracts or important product releases. Furthermore, it will be challenging to produce a reliable price model using revenue alone as an input; you would have to quantify the effect of revenue on margins, future guidance, and other factors. This is a non trivial problem.
It might be interesting to try this approach anyway, to see the result. However, I have a feeling that many more layers of work will be required to produce and kind of accurate prediction.
I was thinking to use IF() function to model the margins (like, if revenue is growing, chances are demand outstrips supply implying expanding gross/operating margin (((i know this is not true in general, just for this particular example it might be relevant)))), similarly you can handle CapEx and change in working capital, while the D&A is a function of past period and past periods CapEx
I’m not an expert on this (time series modeling is very difficult!) – but if you’re facile with R (or a comparable language) you could get a lot of value from an ARIMA (or similar) kind of model.
Honestly I’m lost on how this approach is anything but a terrible response to looking at company and industry fundamentals. If you don’t know enough to loosely judge where you are in the business cycle, you shouldn’t be messing with highly cyclical companies. This is terrible because it ignores the fact that 1) each cycle is different in terms of amplitude and 2) a business may be operationally and financially very different from one cycle to the next.
brah, “inverse lognormal”? This generally describes the distribution of time it takes for a geometric brownian motion to reach a fixed point. Why would that be a reasonable model for the noise in the projected revenues of a cyclical company?
Bigger picture question is however, as alluded by my boy BS, what the actual f.uck? I’d use a Monte Carlo if I am dealing with several correlated variables which can collectively impact the distribution of free cash flows in a non-trivial way. Here, that’s not the case - your only stochastic variable is the revenue. I’d also use Monte Carlo if there is some contingency in the model which creates an asymmetrical output like an option payoff. Here, this doesn’t seem to be the case - when the simulated revenue goes up, the free cash flow goes up proportionally and vice versa. You are talking about possibly changing the margins as the revenue goes up or down, but it seems like an after thought and not a material impact.
Bottom line is, build a normal damn DCF producing a single point output using a base case forecast that reflects your best estimate for the revenue based on analysis of industry and company fundamentals. Then ask yourself, how certain I am in my terminal year revenue and estimate a low and a high which would produce the range of equity values around your single point conclusion.
It is a small database, so sticking to Excel might be more convenient in this case.
I have a clear idea where we are in the business cycle; problem is market is pricing equity as if we are at a different point which grinds my gears.
The logic behind is – as the company faces capacity constraints and management seems reluctant to expand in foreseeable future, revenues should be negatively skewed. Inverse log is the closest to normal you can get. Could you recommend a better suit if my reasoning is incorrect?
The idea, once again, was to have one random variable and lots of conditional ones leading to a fair value distribution rather than a point estimate. Okay, alternative case. At the moment I am looking at highly levered company – shall I use Monte Carlo here? What am I modelling? Straight down to share price or EPS?
That’s what I did – three scenarios with sensitivity analysis for each of them, varying the cost of capital and perpetual growth rate. I am still eager to build something that better represents the distribution of company’s fundamental value rather than sticking to the trivial – if we have this, we got that.
That’s silly logic and 90% of the battle using quant tools is proper application and logic, knowing nifty tricks is useless to investing without proper judgment. Your statement answers literally any valuation question you may have needed to know for an investment purpose. It’s also completely opposite from your opening statement:
Lastly, if you knew where we are in the cycle, then a fundamental forecast would by definition be better than any random simulation rendering it useless.
I think that choice of distribution seems reasonable in light of your explanation of capacity constraints and limited expansion options. That being said, I don’t see how it addresses the cyclicality of the industry which I thought was the primary concern. Why not model the interaction of certain macro factors whose joint impact can induce a regime shift in the industry? It seems to me that in your model framework your ending distribution of equity values, based on your selected distribution of future revenues, has nothing do with where you are in the business cycle at this moment.
Why is this the fundamental idea - what do you expect to gain by arriving at a distribution of equity values? Your output distribution of equity values is a direct function of the input distribution(s), so clearly subject to garbage-in garbage-out. For instance, if you are trying to get to the distribution of current equity values based on the uncertainty of where the industry might be in the economic cycle, I don’t see how you are accomplishing that with your model. You are getting *some* distribution of equity values, so what?
I think what Mobius and I are getting at (and correct me if I’m wrong Mobius) is that running this at the bottom of the cycle will give you one (generally lower value) distribution and running this at the top will give you another (generally higher value) distribution which fails to address this primary issue of getting one consistent “fair value” valuation through the cycle. In other words, you trading one set of valuations that will vary based on timing in the cycle for another set of simulation driven valuations that will vary based on timing in the cycle and be right back where you started after a pointless exercise.
What cracks me up about all this, was that in typical AF fashion all the pseudo quants jumped right in to talk Math 101 regression methods and modeling techniques in an effort to sound academic, without anyone stopping to ask if the premise even made any sense.
