# How would you try to predict the future behaviour of a stock price?

How does one answer this potential interview question? It's not a very clear question since there are clearly many factors.

My first guess would be to talk about looking at the expected (mean) return of the stock - is it increasing or decreasing in recent years. Could also then examine the volatility of this stock - using variance/standard deviation, we can see how reliable these returns have been over previous years. We could also use something like the Sharpe ratio to see how sensitive it is to fluctuations in volatility.

We could also look at its beta (or Treynor ratio) to see how sensitive it is to market risk.

We wouldn't want to look at things like Delta since this is to do with derivatives and not the underlying stock.

Are my ideas above correct? Is there anything important I have overlooked?

• What kind of interview is this for ? – noob2 Feb 17 '16 at 18:04
• I think I would not like to work for a company who asks such strange questions... – vonjd Feb 17 '16 at 18:21
• No specific company. I was reading it in a book of difficult/interesting interview questions. Any crucial information I have missed? – user11128 Feb 17 '16 at 18:32

The real answer is that you should never try to predict the future behavior of anything. Instead, ask yourself what sorts of risk you are comfortable taking and work back from there.

That being said, the quantitative finance textbook approach would look something like this:

Come up with a model for equity movement - this is typically some sort of brownian motion-based model, with a component for mean (drift) as you mentioned. You will also need assumptions/calculations for other things you mention such as volatility and/or beta (depending on your portfolio).

Simulate a whole bunch of these over your chosen time period. Price your portfolio (simple if you just want one equity) in each simulation. Use your method of choice (Value at Risk, Expected Shortfall, Worst-case scenario) to measure your loss against your risk appetite (first question).

Then, finally, realize that all of these models are technically 'wrong' but still potentially useful for answering interview questions!

• You are thinking as if you were pricing a derivative. Hft statistical arbitrage is all about predicting returns. Quants do that by searching for patterns in time series. – AFK Feb 18 '16 at 19:24
• Good point. It does depend on the time period you are talking about. HFT and other short term strategies can use entirely mechanical predictions. My main point was that you should first think about your risk appetite before trying to "predict" something - pretending you can actually predict something is a bad place to start. – Todd Page Feb 18 '16 at 19:36
• This is not limited to short term strategies. Momentum strategies can have a time scale of several years. I do agree that at this scale it requires a high tolerance for risk to be implemented though. – AFK Feb 18 '16 at 21:18

Everyone tries to predict the future in an endless variety of ways ranging from tarot cards and crystal balls, to elliot wave theory and neural networks. But, since this is a forum about quantitative finance, I think an appropriate answer to your question is historical backtesting of stock prices against a variety of indicators. These indicators could be economic indicators (ex: unemployment reports, interest rates), behavior indicators (ex: VIX, Put Call Ratio, COT, AAII Bull Bear ratio), or technical indicators (ex: broad indexes, linear regression, standard deviation, ATR). Some options players also try to predict moves by looking for signs of potential insider trading by looking for sudden spikes on a stock's historical implied volatility of options. So yes, in all of these cases, you merely try to predict the future by looking at the past.

The things you mentioned like sharpe ratio, beta, and delta are more for evaluating portfolio risk and are not useful for predicting the future.

I don't know how technical the job spec is but in quantitative finance:

You cannot use models to predict prices. You can however use simulations to predict the expected pay off of a certain scenario ASSUMING the underlying distributions of your model are correct....

...in the most conventional models (such as Black-Scholes) equity prices are assumed to evolve according to geometric brownian motion, including a drift term + some random noise component which is proportional to the volatility of the stock. This implies a number of assumptions, a large one being that prices are log-normally distributed.

# Central limit theory

The reasoning behind this is due to the central limit theorem, which states that if you take the mean of a very large number of independent random variables (which may have any distribution) is normally distributed. Given that daily returns are a function of a large number of intra-day returns, daily returns are normally distributed. A basic property states that if Returns0~Norm and S(t)=S(0)*exp(Returns) then S(t)~LogNorm.

# For simulations

Now you know how to simulate prices, but you can never actually take the expectations of simulations, because that's not exactly how they are used in real life. Simulation can be used for option valuation, but not very good at predicting an explicit price. The general idea is that if the underlying distributions are correct, then you can use it to model non-linear pay off functions. This is due to the Jensen Inequality, which states that E[f(x)] >= f(E[x]). You can do an example where the current price of 100 can go to either 50 or 200 with equal probability. The average expected price is 125. The pay off of an option with K=100 would be 25. If you now use prices models as they should be, you get a pay off of 0 of the option when S=50, and a pay-off of 100 when S goes to 200. The real expected value of the option is (0 + 100)/2 = 50. There is a fine line in how you apply price models, but it cannot be used to forecast an explicit price.

Interesting that no one provides an answer with more of an "active investment" take.

A lot of people think they can predict the future price of a stock (and hence its simplest behavior: up or down) by looking at the valuation of a company. A very simplistic way of looking at it is buying undervalued stocks and selling overvalue stocks (relative to ones opinion of that value).

The question is how do you form an opinion about the real value of the company :

-Fundamental analysis: specific knowledge/view about the industry or the company, management of the company, macro trends. etc.. (this list could go on forever)

-Behavioral Analysis, what behavioral bias are investors expressing in general and how to exploit them. (Value, Size, Momentum for example). Those are often linked to risk factors and links nicely to Todd Page answer.

Why, and whether this works is a big debate. I obviously oversimplify here and don't want to get into any debates whether the markets are efficient etc. Just want to give a different take to the answers you already have.

This can be applied each on their own or combined, applied to one stock or to a full cross-section of stocks. If this is an interview question I guess it might get asked in a form or another in a Quant Equity Shop (L/S Quant Hedge Funds and Active Equity Quant Managers which are all about doing cross sectional analysis of stocks fundamentals and behavioral factors).

The stylized answer is that naive factors will explain most of your predictive score. With the least amount of time, that's the first thing you'd do: You regress log returns against excess return over market mean, market capitalization and price-to-book ratio.

After that, the next lowest hanging fruit is to take into account a momentum factor or contrarian effects (covariance structure of cross-sectional returns).

As noted in a few comments, other answers appear to mistake this for a $\mathbb{Q}$ problem rather than $\mathbb{P}$ problem.