### Put-Call ratio as a measurement to gauge the overall mood of a market

The put-call ratio represents another information about the market. It is more or less sentiment information. If the ratio increases, that means that there are more new puts trades, so the investors are scared of a drop in price. Usually, when prices drop, many investors buy new puts to protect their assets (or just speculators buy puts to profit on the falling market). Either way, this information exposes more information about the market.

I heard about the put-call ratio for the first time sometime during 2014 when trading options. I saw it in some analysis by Lawrence G. McMillan (author of the excellent book, Options as a Strategic Investment). After seeing some connections between too high put-call ratios and drops in the stock prices, I occasionally looked at it. When you google for the put-call ratio, you can see some plots where it seems like some bulletproof predictor, but I have never done some more in-depth analysis before, so let’s do it.

### TYPES OF PUT-CALL RATIO

Actually, there are two types of put-call ratios:

- first one is calculated from the volume of puts divided by the calls’ volume
- second one uses open interest

Open interest is the number of all opened contracts for a given asset (stock, index, futures), not only daily volume. In this analysis, we will work with the volume-based put-call ratio, which is available at the web pages of CBOE (it is possible to download some daily data from there). We have already discussed some basics about the put-call ratio in the article about financial metrics, so it is not a new topic.

### Explanation of the put-call ratio on graphs

For explanation, we will use the prices of index S&P 500 and put-call ratio calculated from its options, exactly SPX + SPXW, but no SPY. It would be good to use SPY, too, because many traders trade SPY options.

We will start by looking at a plot of SPX and the put-call ratio for some sample time (put-call ratio data from CBOE were available from July 2010 until Oct 2019). On the plot, we have close prices of SPX Index; grey is an actual daily put-call ratio, which is very volatile, so we also used a 5-days moving average. We don’t use a moving average with a larger window because it will become a very delayed statistic, and we just need to have better-recognized tops and bottoms. After analyzing a plot, we will go through some statistical tests if it has some predictive power, and in the end, we will discuss how we can use it in practice.

When there is a new peak on the put-call ratio graph, the price has dropped, and the new growth begins. An interesting fact is, and it proves that the market is not symmetric, that the opposite logic does not work that visibly – when we have a new bottom. The problem with practical usage here is that we never know if we are on the peak or not, so after recognizing the peak, it can be too late. But when we see more significant drops in price, and then some visible peak is generated on the ratio plot, it can be a good indication to get in. Let’s look at some examples, in Feb 2018 (with smaller drawdown for two months but still right timing), or also April 2018 (even better timing than the peak before). In Oct 2018, we didn’t have a peak in the ratio after a bigger price drop, and the decline continued. At the end of 2018, we had another market correction and a visible lonely peak on the ratio plot, so it was an excellent opportunity to buy. We can study this graph and see some patterns. Let’s do some analysis on peaks on the whole dataset if they have some predictive value.

### Distribution of the put-call ratio

When analyzing the put-call ratio, it is essential to know the distribution so that we can have a look at another plot. This metric is distributed around a mean value of 1.75 and is a little bit skewed. According to distribution, we can see that the overall number of puts is higher than the number of calls because it is larger than 1. Actually, on average, there are 75% more puts than calls. There can be few explanations – buying put options is less risky than shorting the stock when you are bearish; long-term investors and funds can hedge their long positions with puts. We will compare observations that are a little extreme, those lower than 1.25 and higher than 2.25 (if we use a wider interval, we don’t have enough observations to do statistical tests).

### Predictive power of put-call ratio

In the table below, we compare the predictive power of both extreme sides. For comparison, we use statistical tests where we test the returns after a higher put-call ratio is larger than returns after a lower ratio. And we also test if they are larger than values for non-extreme ratio. If the p-value is lower than 0.05, we consider it a significant difference (p-value is the error that we falsely rejected the opposite hypothesis).

Return | Ratio < 1.25 | Neutral | Ratio > 2.25 | P-val High vs Low | P-val High vs Neutral |

1 day | -0.10% | 0.03% | 0.17% | 0.09 | 0.20 |

2 days | -0.07% | 0.07% | 0.51% | 0.02 | 0.03 |

3 days | -0.07% | 0.11% | 0.74% | 0.01 | 0.01 |

5 days | 0.05% | 0.20% | 0.94% | 0.00 | 0.00 |

7 days | 0.31% | 0.29% | 0.99% | 0.03 | 0.01 |

10 days | 0.43% | 0.43% | 1.18% | 0.04 | 0.02 |

Return | Ratio < 1.25 | Neutral | Ratio > 2.25 | P-val High vs Low | P-val High vs Neutral |

1 day | -0.10% | 0.03% | 0.17% | 0.09 | 0.20 |

2 days | -0.07% | 0.07% | 0.51% | 0.02 | 0.03 |

3 days | -0.07% | 0.11% | 0.74% | 0.01 | 0.01 |

5 days | 0.05% | 0.20% | 0.94% | 0.00 | 0.00 |

7 days | 0.31% | 0.29% | 0.99% | 0.03 | 0.01 |

10 days | 0.43% | 0.43% | 1.18% | 0.04 | 0.02 |

We have values of percent return on the stock price after a given put-call ratio in the table. Returns are always calculated as we buy 1st day on open and sell n-th day on close. So there is no look-ahead bias; we use yesterday’s put-call ratio to invest today. Since we don’t use any tops and bottoms here, only the extreme values, the results are usable immediately. We can see the low values of ratios do not have an opposite predictive power. The winning rate for investing long after the put-call ratio is higher than 2.25 is more than 60% (60% for 1st day, 70% for 2nd and 3rd day, 75% for 5th day, and over 60% for other days). These simple tests prove that the put-call ratio has real predictive value when it comes to predicting the long side of the market. Let’s have a look at local tops and bottoms in the plot and analyze predictive power (but recognizing the peaks in practice and jumping in can be challenging).

In the analysis of tops and bottoms, we will have a look of the immediate impact from the beak and if we invest three days after the peak to stimulate reality. Again we invest the next day on open or the third day on open.

Return | Bottoms | None | Tops |

1 day | -0.14% | 0.02% | 0.31% |

2 days | -0.27% | 0.04% | 0.49% |

3 days | -0.32% | 0.06% | 0.70% |

5 days | -0.34% | 0.11% | 0.81% |

7 days | -0.45% | 0.15% | 1.01% |

10 days | -0.33% | 0.22% | 1.31% |

3 days from 3rd day | -0.14% | 0.06% | 0.29% |

5 days from 3rd day | -0.10% | 0.11% | 0.57% |

10 days from 3rd day | 0.25% | 0.22% | 0.75% |

Return | Bottoms | None | Tops |

1 day | -0.14% | 0.02% | 0.31% |

2 days | -0.27% | 0.04% | 0.49% |

3 days | -0.32% | 0.06% | 0.70% |

5 days | -0.34% | 0.11% | 0.81% |

7 days | -0.45% | 0.15% | 1.01% |

10 days | -0.33% | 0.22% | 1.31% |

3 days from 3rd day | -0.14% | 0.06% | 0.29% |

5 days from 3rd day | -0.10% | 0.11% | 0.57% |

10 days from 3rd day | 0.25% | 0.22% | 0.75% |

In this article, we described the usage of the put-call ratio and showed its significance for generating some alpha on the long side when it comes to the high value of the put-call ratio. Visible peaks and bottoms on the put-call ratio plot can be used as alpha-generating signals, too. There are a few brokers/data providers who also provide a put-call ratio. Using this for algo-trading may be challenging, but for classical trading, it is usable.