Academic Article Series: Economics and Finance 101:

Technical Analysis Indicators: Customisable Relative Strength Indices (and Moving Averages & Volatilities)

September 02, 2021

Jonathan Legrand

Developer Advocate

In this article, we build a data-frame to output an instrument's Daily (i) Close Prices, (ii) ln (logarithme naturel / natural logarithm) Return, (iii) Close Price's 10, 30 and 60 Day Moving Averages, (iv) Close Price's ln Return 10, 30 and 60 Day Moving Average, (v) Annualised Standard Deviation (i.e.: volatility) of the 10, 30 and 60 Day Rolling Window (Natural Log) Returns (based on CLOSE prices), and (vi) Relative Strength Index (RSI).

When it comes to the RSI data, a great article to read about its implementation can be found here (thank you Umer and Jason!). You may want to read into the installation of the TA-Lib library used to compute RSI data here. You may also want to read into how the way TA-lib calculates RSI; as per its GitHub documentation, it uses a Wilder Smoothing method to compute Moving Averages. Others may use different such methods (e.g.: Exponential Moving Average or Simple Moving Average). More information on Refinitiv Workspace's Chart App RSI can be found here and here. Previous RSI Python functions do not provide great amounts of customisation; in this article, we will create a Python function that does just that.

Webinar Video

This Webinar was broadcasted live on Twitch where I code live every Tuesday at 4pm GMT.

Using this Site

You may scale up or down the math figures at your convenience as per the below.

Relative Strength Index

The Relative Strength Index (RSI) is a value between 0 and 100 calculated for any one asset based on its historical price; it indicates an asset as oversold if bellow a certain threshold - idest (i.e.): it's underpriced - and overbought if above a certain threshold - i.e.: it's overpriced. RSI at time $t$ is calculated $RSI_{w, m, t}$ where $w$ is the window asked for (e.g.: 14) and where $m$ is either (i) $SMA$ (Simple Moving Average) or $Cutler$, (ii) $EMA$ (Exponential Moving Average), or (iii) $Wilder$ or $MEMA$ (Modified Exponential Moving Average):

(i) with $SMA$ (Simple Moving Average) or $Cutler$ such that $m_1=\{SMA, Cutler\}$: $$ RSI_{w, m_1, t} = \begin{Bmatrix} 100 & \text{if } \sum_{i=1}^w{|min(P_{t-i+1} - P_{t-i} \text{ }, \text{ } 0)|} = 0 \\ 100 - \frac{100}{ 1 +\frac{ \sum_{i=1}^w{max(P_{t-i+1} - P_{t-i} \text{ }, \text{ } 0)}} {\sum_{i=1}^w{|min(P_{t-i+1} - P_{t-i} \text{ }, \text{ } 0)|}} } & \text{otherwise} \end{Bmatrix} $$

(ii) & (iii) with $EMA$, or $Wilder$ / $MEMA$ such that $m_2=\{EMA, Wilder, MEMA\}$:

$$ RSI_{w, m_2, 1} = RSI_{w, m_1, 1} $$

and

$$ RSI_{w, m_2, \tau} = 100 - \frac{100}{ \left[ 1 + \frac{ a_m * \left( max(P_{\tau} - P_{\tau-i} \text{ }, \text{ } 0) \right) + (1 - a_m) * \left( \sum_{i=1}^w{max(P_{\tau-i+1} - P_{\tau-i} \text{ }, \text{ } 0)} \right)}{ a_m * \left( |min(P_{\tau} - P_{\tau-1} \text{ }, \text{ } 0)| \right) + (1 - a_m) * \left( \sum_{i=1}^w{|min(P_{\tau-i+1} - P_{\tau-i} \text{ }, \text{ } 0)|} \right)} \right]} $$

where $\tau > 1$, and

$$ a_m = \begin{Bmatrix} a_{MEMA} = a_{Wilder} = & \frac{1}{w} & \text{if } m \text{ is } MEMA \text{ or } Wilder \\ a_{EMA} = & \frac{2}{w + 1} & \text{if } m = EMA \end{Bmatrix} $$

And it is computed as such:

display response

Define a Python Function

	MSFT.O Close	MSFT.O's ln Return	MSFT.O's 1d Close	MSFT.O's Close 10D MA	MSFT.O's ln Return' 10D MA	MSFT.O's Ann. S.D. of 10D Roll. of ln Returns	MSFT.O's Close 30D MA	MSFT.O's ln Return' 30D MA	MSFT.O's Ann. S.D. of 30D Roll. of ln Returns	MSFT.O's Close 60D MA	MSFT.O's ln Return' 60D MA	MSFT.O's Ann. S.D. of 60D Roll. of ln Returns	MSFT.O's RSI14
30/03/2020	160.23	0.067977	10.53	146.431	0.016823	0.996665	158.844	-0.004855	1.170754	164.625167	-0.000041	0.847859	52.673834
31/03/2020	157.71	-0.015852	-2.52	147.545	0.007325	0.919086	157.86	-0.005719	1.170091	164.61	-0.000096	0.848196	51.337963
01/04/2020	152.11	-0.036154	-5.6	148.716	0.008011	0.904883	156.687667	-0.006933	1.174572	164.494667	-0.000741	0.852745	48.400379
02/04/2020	155.26	0.020497	3.15	149.971	0.008429	0.906763	155.715667	-0.005737	1.177938	164.456	-0.000247	0.854052	50.129028
03/04/2020	153.83	-0.009253	-1.43	151.619	0.011332	0.862599	154.890333	-0.004975	1.174237	164.351667	-0.000665	0.853384	49.321227
...	...	...	...	...	...	...	...	...	...	...	...	...	...
23/07/2021	289.67	0.012261	3.53	281.613	0.004134	0.178585	272.2775	0.003958	0.161648	260.488917	0.002153	0.206477	75.427556
26/07/2021	289.05	-0.002143	-0.62	282.786	0.004143	0.178457	273.316167	0.003802	0.162964	261.097917	0.002252	0.205188	73.90081
27/07/2021	286.54	-0.008722	-2.51	283.342	0.001959	0.182599	274.2045	0.003254	0.167933	261.670583	0.002129	0.20677	67.908078
28/07/2021	286.22	-0.001117	-0.32	283.713	0.001305	0.181845	275.133167	0.003414	0.165493	262.24325	0.002131	0.206756	67.16034
29/07/2021	286.5	0.000978	0.28	284.26	0.001928	0.176626	276.103833	0.003573	0.163726	262.888417	0.002419	0.20163	67.497578

Apendix: Mathematical Finction for $RSI_{w, m, 1}$:

$$ \begin{array}{ll} RSI_{w, m, 1} &= \begin{Bmatrix} 100 & \text{if } \frac{\sum_{i=1}^w{|min(P_{t-i+1} - P_{t-i} \text{ }, \text{ } 0)|}}{w} = 0 \\ 100 - \frac{100}{ 1 +\frac{ \frac{ \sum_{i=1}^w{max(P_{t-i+1} - P_{t-i} \text{ }, \text{ } 0)} }{w}} {\frac{ \sum_{i=1}^w{|min(P_{t-i+1} - P_{t-i} \text{ }, \text{ } 0)|} }{w}} } & \text{otherwise} \end{Bmatrix} \\ &= \begin{Bmatrix} 100 & \text{if } \sum_{i=1}^w{|min(P_{t-i+1} - P_{t-i} \text{ }, \text{ } 0)|} = 0 \\ 100 - \frac{100}{ 1 +\frac{ \sum_{i=1}^w{max(P_{t-i+1} - P_{t-i} \text{ }, \text{ } 0)}} {\sum_{i=1}^w{|min(P_{t-i+1} - P_{t-i} \text{ }, \text{ } 0)|}} } & \text{otherwise} \end{Bmatrix} \\ \end{array} $$