In a previous post, we demonstrated the mean-reverting and trending properties of SP500. We subsequently developed a trading system based on the mean-reverting behavior of the index. In this installment, we will develop a trend-following trading strategy.

Trend following or trend trading is a trading strategy according to which one should buy an asset when its price trend goes up, and sell when its trend goes down, expecting price movements to continue.

There are a number of different techniques, calculations and time-frames that may be used to determine the general direction of the market to generate a trade signal (forex…


In a previous post, we demonstrated the mean-reverting and trending properties of SP500. In this follow-up post, we will develop a simple trading system exploiting the mean-reverting behaviour of this market index.

To generate buy and sell signals, we will use simple moving averages as noise filters. The simple moving average takes an average value of a stock over a certain period of time. It has been used for decades by technical traders and investors around the world. There exist other types of moving averages such as exponential moving averages, but we will use the simple ones in this post.


A technical or quantitative trading system on a linear (i.e. delta 1) instrument is basically a bet on the autocorrelation of the underlying. The autocorrelation properties of the underlying can be examined directly through autocorrelation functions or indirectly through the Hurst exponent.

In this post, we are going to examine the mean-reverting and trending properties of SP500 directly using the autocorrelation functions. We do so with the goal of designing quantitative trading systems on stock indices.

Recall that,

Autocorrelation, also known as serial correlation, is the correlation of a signal with a delayed copy of itself as a function of…


Dividend yield is an input into the option valuation model that often receives little attention from the practitioners. This is probably because the majority of companies do not pay dividends. And for those that pay, an inaccuracy in the estimation of the dividend yield often has a small impact on the fair value of the financial instrument, especially if the tenor of the instrument is short.

However, under some circumstances, dividend can become an important input in the valuation model, and an inaccurate estimation can lead to a severe financial loss. …


Historical volatility (HV) is a useful measure to gauge market uncertainty. Recall that,

In finance, volatility (usually denoted by σ) is the degree of variation of a trading price series over time, usually measured by the standard deviation of logarithmic returns. Historic volatility measures a time series of past market prices… Investors care about volatility for at least eight reasons:

  1. The wider the swings in an investment’s price, the harder emotionally it is to not worry;
  2. Price volatility of a trading instrument can define position sizing in a portfolio;
  3. When certain cash flows from selling a security are needed at…

In the previous installments, we presented the concept of Modern Portfolio Theory. We also provided an optimization algorithm, written in Python, for searching for the optimal portfolio.

To continue, we are going to perform some numerical experiments. Specifically, we are going to use the portfolio optimization program developed in the previous post in order to study the effect of diversification.

In finance, diversification is the process of allocating capital in a way that reduces the exposure to any one particular asset or risk. A common path towards diversification is to reduce risk or volatility by investing in a variety of…


In the previous installment, we presented a description of the Model Portfolio Theory and provided a concrete example in Python. We also explained the concept of an Efficient Frontier and provided a visual presentation of it. Recall that,

… the efficient frontier (or portfolio frontier) is an investment portfolio which occupies the “efficient” parts of the risk–return spectrum. Formally, it is the set of portfolios which satisfy the condition that no other portfolio exists with a higher expected return but with the same standard deviation of return (i.e., the risk). …


The Binomial tree is a standard method for pricing American style options. Recall that,

The Binomial options pricing model approach has been widely used since it is able to handle a variety of conditions for which other models cannot easily be applied. This is largely because the BOPM is based on the description of an underlying instrument over a period of time rather than a single point. As a consequence, it is used to value American options that are exercisable at any time in a given interval as well as Bermudan options that are exercisable at specific instances of time…


Last month, efinancialcarreeers published a post, stating that quant’s life is getting harder these days.

Back in the day, a quant in finance could devise a strategy, sit back and let the money roll in while lounging about in a silk robe with a fat cigar. Such are the halcyon dreams of the contemporary quantitative finance type who finds him/herself forced to grind continuously in front of a screen in search of illusory alpha while every man/woman with a piece of Python code does the same.

This wasn’t the exact complaint at today’s Quant Conference (held digitally this year), but…


Convertible bonds are complex, hybrid securities.

In finance, a convertible bond or convertible note or convertible debt (or a convertible debenture if it has a maturity of greater than 10 years) is a type of bond that the holder can convert into a specified number of shares of common stock in the issuing company or cash of equal value. It is a hybrid security with debt- and equity-like features. It originated in the mid-19th century, and was used by early speculators such as Jacob Little and Daniel Drew to counter market cornering. Read more

Previous studies have established a formal…

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