# Predict the behavior of a time series (P&L trading desk)

I work at the trading desk P&L department at a large bank. The trading desk has positions in almost all sorts of derivatives (options, futures) over a long list of stocks, currencies, commodities... My boss asked me to do the following:

1) Show that it is not possible to predict next years P&L

2) Build a working econometric model to predict next year's P&L

The daily P&L time series is really not stationary.

Can I tell my boss that:

Non-stationarity $\Rightarrow$Cannot be predicted based exclusively on the time series. Is it true? At least to start and show him that the time series is not enough to make predictions and that we will need, at least, a complex machine learning model to do so.

• I think your boss should be more concerned about P&L variations, and those could be stationary. However - before using heavy artillery such as machine learning - visual inspection and simple models are highly advisable: pick good predictors! – Lisa Ann Jul 20 '17 at 21:48
• suppose it is not stationary neither. Is it true that: Non-stationarity ⇒Cannot be predicted based exclusively on the time series? – John Jul 20 '17 at 21:57
• No, that's not true. – Chris Taylor Jul 20 '17 at 22:01

## 1 Answer

Without seeing your trading desk's P&L it's impossible to say whether it is predictable or not. But here are a few thoughts -

1. There's no reason to think that it isn't predictable. In general, financial time series are hardest to predict when the represent the return stream of an investible asset. A trading desk's P&L isn't really investible, so there is no reason to think that it will be unpredictable.

2. You certainly won't be able to predict the P&L with a large amount of certainty, but you may be able to make ballpark estimates.

3. Have you graphed the P&L to check if there is an obvious trend? For example, if markets are getting more efficient, you would expect P&L to be decreasing over time.

4. Is P&L correlated with other variables that you may be able to predict? For example, if the desk is engaged in market making, it will probably make more money when volatility is high and liquidity is low (as the desk is selling liquidity, and the price of liquidity is high when markets are more volatile).

5. If the desk is trading illiquid instruments (e.g. exotic derivatives) the P&L series may be autocorrelated. This is especially true if P&L is correlated with volatility or liquidity, since vol and liquidity measures are autocorrelated.

6. Are the markets the desk is engaged in becoming more heavily traded, or less? P&L from market making is correlated with volume, and you may be able to make a reasonable guess about whether volume will be higher or lower next year.

What you certainly do not need is a complex machine learning model. As Lisa Ann said in a comment, you will do much better with visualisations, simple linear models, and a healthy dose of insight.

• YOur answer makes total sense. But there is no market making activity. It is all concentrated on speculation. he bank is located in a country unstable politically, hence the volatilities are much function of what is on the news. Hence, the source of future variability in the time series is not contained in the own time series as it will depend on the news. The future news are impossible to model. That is why I think it is unpredictable. The past tells nothing about the future. One clue about this is that the time series is definetly not stationary. Do you agree? – John Jul 20 '17 at 23:41
• Chris Taylor, could you give an example of liquidity index? – John Jul 21 '17 at 12:29
• @John You can't draw any conclusion about the predictability of the time series based on what you have said. It may be predictable, it may not. To know for sure we would need to see the data (and try to make some out of sample predictions). I don't understand what you mean when you say "the time series is not stationary". First, stationarity is a property of a time series generating process, not of any particular time series. Do you mean that the P&L is steadily increasing or decreasing over time? Or something else? – Chris Taylor Jul 21 '17 at 12:57
• @John A commonly used liquidity index is the TED Spread, i.e. the excess yield of 3M LIBOR over 3M treasuries. You might also look at cost-based measures (e.g. average bid-offer spread), volume-based measures (e.g. ratio of turnover to market size) or impact-based measures (e.g. typical market move per unit of volume traded). – Chris Taylor Jul 21 '17 at 13:03