Friday, September 17, 2021

Sensitivity Analysis


What is Sensitivity Analysis?

The technique used to determine how independent variable values will impact a particular dependent variable under a given set of assumptions is defined as sensitivity analysis. It’s usage will depend on one or more input variables within the specific boundaries, such as the effect that changes in interest rates will have on a bond’s price.

It is also known as the what – if analysis. Sensitivity analysis can be used for any activity or system. All from planning a family vacation with the variables in mind to the decisions at corporate levels can be done through sensitivity analysis.

Sensitivity analysis works on the simple principle: Change the model and observe the behavior.

The parameters that one needs to note while doing the above are:

A) Experimental design: It includes combination of parameters that are to be varied. This includes a check on which and how many parameters need to vary at a given point in time, assigning values (maximum and minimum levels) before the experiment, study the correlations: positive or negative and accordingly assign values for the combination.

B) What tfo vary:The different parameters that can be chosen to vary in the model could be:
a) the number of activities
b) the objective in relation to the risk assumed and the profits expected
c) technical parameters
d) number of constraints and its limits

C) What to observe:
a) the value of the objective as per the strategy
b) value of the decision variables
c) value of the objective function between two strategies adopted

Measurement of sensitivity analysis

Below are mentioned the steps used to conduct sensitivity analysis:

  1. Firstly the base case output is defined; say the NPV at a particular base case input value (V1) for which the sensitivity is to be measured. All the other inputs of the model  are kept constant.
  2. Then the value of the output at a new value of the input (V2) while keeping other inputs constant is calculated.
  3. Find the percentage change in the output and the percentage change in the input.
  4. The sensitivity is calculated by dividing the percentage change in output by the percentage change in input.

This process of testing sensitivity for another input (say cash flows growth rate) while keeping the rest of inputs constant is repeated until the sensitivity figure for each of the inputs is obtained. The conclusion would be that the higher the sensitivity figure, the more sensitive the output is to any change in that input and vice versa.

Methods of Sensitivity Analysis

There are different methods to carry out the sensitivity analysis:

  • Modeling and simulation techniques
  • Scenario management tools through Microsoft excel

There are mainly two approaches to analyzing sensitivity:

  • Local Sensitivity Analysis
  • Global Sensitivity Analysis

Local sensitivity analysis is derivative based (numerical or analytical). The term local indicates that the derivatives are taken at a single point. This method is apt for simple cost functions, but not feasible for complex models, like models with discontinuities do not always have derivatives.

Mathematically, the sensitivity of the cost function with respect to certain parameters is equal to the partial derivative of the cost function with respect to those parameters.

Local sensitivity analysis is a one-at-a-time (OAT) technique that analyzes the impact of one parameter on the cost function at a time, keeping the other parameters fixed.

Global sensitivity analysis is the second approach to sensitivity analysis, often implemented using Monte Carlo techniques. This approach uses a global set of samples to explore the design space.

The various techniques widely applied include:

  • Differential sensitivity analysis: It is also referred to the direct method. It involves solving simple partial derivatives to temporal sensitivity analysis. Although this method is computationally efficient, solving equations is intensive task to handle.
  • One at a time sensitivity measures: It is the most fundamental method with partial differentiation, in which varying parameters values are taken one at a time. It is also called as local analysis as it is an indicator only for the addressed point estimates and not the entire distribution.
  • Factorial Analysis: It involves the selection of given number of samples for a specific parameter and then running the model for the combinations. The outcome is then used to carry out parameter sensitivity.

Through the sensitivity index one can calculate the output % difference when one input parameter varies from minimum to maximum value.

  • Correlation analysis helps in defining the relation between independent and dependent variables.
  • Regression analysis is a comprehensive method used to get responses for complex models.
  • Subjective sensitivity analysis: In this method the individual parameters are analyzed. This is a subjective method, simple, qualitative and an easy method to rule out input parameters.

Using Sensitivity Analysis for decision making

One of the key applications of Sensitivity analysis is in the utilization of models by managers and decision-makers. All the content needed for the decision model can be fully utilized only through the repeated application of sensitivity analysis. It helps decision analysts to understand the uncertainties, pros and cons with the limitations and scope of a decision model.
Most if not all decisions are made under uncertainty. It is the optimal solution in decision making for various parameters that are approximations. One approach to come to conclusion is by replacing all the uncertain parameters with expected values and then carry out sensitivity analysis. It would be a breather for a decision maker if he/she has some indication as to how sensitive will the choices be with changes in one or more inputs.

Uses of Sensitivity Analysis

  • The key application of sensitivity analysis is to indicate the sensitivity of simulation to uncertainties in the input values of the model.
  • They help in decision making
  • Sensitivity analysis is a method for predicting the outcome of a decision if a situation turns out to be different compared to the key predictions.
  • It helps in assessing the riskiness of a strategy.
  • Helps in identifying how dependent the output is on a particular input value. Analyses if the dependency in turn helps in assessing the risk associated.
  • Helps in taking informed and appropriate decisions
  • Aids searching for errors in the model
Credit :

Tuesday, March 31, 2015

Kaka's imagination - his first story

Vinayak, my year old has started weaving his own stories.  Here is one, probably the first documented one.  Its his imagination, his narration, i have just been a scribe, verbatim - its all his his words, as written on a sheet of paper 

ones upon a time there was a Lion called Don. He was the baddest King in the forest. He ate everyone in the forest.  Then a empire had a rule.  He said to Don that whenever  He saw somebody He will say to him that he will eat Him the next week.
Everybody was happy.  they cheered. Soon somebody was going his home the week had begin
One clever rabbit had an idea. He had 4 friends.  one was the crocodile called Likey, an elephant called Wes, and a tiger called lotty  and shonny the deer. they made an idea to make the lion a good lion.

the plan was that the rabbit came to behave as dead first but he said to the lion to close his eyes. Then the elephant will come to squash his neck with his trunk. then the crocodile will come to eat this legs. then when the lion would open his eyes the tiger right away jumped on his tummy and would not let him see them.  then the tiger will become good so that forest can be saved.

when his idea worked the Lion said sorry to everyone. 

============= the end ===================

Friday, February 27, 2015

dedicated to daughters

..पीहर आती है..
..अपनी जड़ों को सींचने के लिए..
..तलाशने आती हैं भाई की खुशियाँ..
..वे ढूँढने आती हैं अपना सलोना बचपन..
..वे रखने आतीं हैं..
..आँगन में स्नेह का दीपक..
..बेटियाँ कुछ लेने नहीं आती हैं पीहर..
..ताबीज बांधने आती हैं दरवाजे पर..
..कि नज़र से बचा रहे घर..
..वे नहाने आती हैं ममता की निर्झरनी में..
..देने आती हैं अपने भीतर से थोड़ा-थोड़ा सबको..
..बेटियाँ कुछ लेने नहीं आती हैं पीहर..
..जब भी लौटती हैं ससुराल..
..बहुत सारा वहीं छोड़ जाती हैं..
..तैरती रह जाती हैं..
..घर भर की नम आँखों में..
..उनकी प्यारी मुस्कान..
..जब भी आती हैं वे, लुटाने ही आती हैं अपना वैभव..
..बेटियाँ कुछ लेने नहीं आती हैं पीहर..
Dear Papa....

"बेटी" बनकर आई हु माँ-बाप के जीवन में,
बसेरा होगा कल मेरा किसी और के आँगन में,
क्यों ये रीत "रब" ने बनाई होगी,
"कहते" है आज नहीं तो कल तू "पराई" होगी,
"देके" जनम "पाल-पोसकर" b
जिसने हमें बड़ा किया,
और "वक़्त" आया तो उन्ही हाथो ने हमें "विदा" किया,
"टूट" के बिखर जाती हे हमारी "ज़िन्दगी " वही,
पर फिर भी उस "बंधन" में प्यार मिले "ज़रूरी" तो नहीं,
क्यों "रिश्ता" हमारा इतना "अजीब" होता है,
क्या बस यही "बेटियो" का "नसीब" होता हे??

"Papa" Says"...
बहुत "चंचल" बहुत
"खुशनुमा " सी होती है "बेटिया".
"नाज़ुक" सा "दिल" रखती है "मासूम" सी होती है "बेटिया".
"बात" बात पर रोती है
"नादान" सी होती है "बेटिया".
"रेहमत" से "भरपूर"
"खुदा" की "Nemat" है "बेटिया".
"घर" महक उठता है
जब "मुस्कराती" हैं "बेटिया".
"अजीब" सी "तकलीफ" होती है\
जब "दूसरे" घर जाती है "बेटियां".
"घर" लगता है सूना सूना "कितना" रुला के "जाती" है "बेटियां"
"ख़ुशी" की "झलक"
"बाबुल" की "लाड़ली" होती है "बेटियां"
ये "हम" नहीं "कहते"
यह तो "रब " कहता है. . क़े जब मैं बहुत खुश होता हु तो "जनम" लेती है
"प्यारी सी बेटियां"

Wednesday, February 18, 2015

Ganesh ji aarati - Shendur laal chaadaayo

शेंदुर  लाल  चढायो  अच्छा  गजमुख  को
दोंदिल  लाल  बिराजे  सुत  गौरीहर  को
हाथ  लिए  गुण लड्डू  साई सुरवर को
महिमा  कहे  न  जाए  लागत  हूँ  पद  को 
जय देव जय देव

जय देव जय देव
जय  जय जी गणराज विद्यासुखदाता
धन्य तुम्हारोदर्शन मेरा मन रमता
जय देव जय देव
जय देव जय देव

भावभगत से कोई शरणागत आवे
सम्पति संतति सबही भरपूर पावे
ऐसे तुम महाराज मुझको अति भावे
गोसावीनंदन निशिदिन गुण गावे
जय देव जय देव

जय देव जय देव
जय  जय जी गणराज विद्यासुखदाता
धन्य तुम्हारोदर्शन मेरा मन रमता
जय देव जय देव
जय देव जय देव

घालिन लोताङ्गन  वंदिन चरण डोळ्यांनी पाहीं रूप तुझे ।
प्रेम आलिङ्गिन आनंदन पूजिन भावें ओवाळीं म्हाने नमा  । ।

त्वमेव  माता पिता त्वमेव बन्धुश्च सखा त्वमेव ।
त्वमेव विद्या  द्रविणं त्वमेव, त्वमेव सर्वं मम देव देव । ।

काएं वाच मनसेंद्रियैर्वा बुद्ध्यात्मना वा प्रकृतिस्वभावा ।
करोमि यद्यत् सकलं पारसमई नारायणायेति समर्पयामि । ।

अच्युतम केशवं रामनारायणं कृष्ण दामोदरं वासुदेवं हरि  ।
श्रीधरम माधवं गोपिकावल्लभं जानकीनायकं रामधरान्द्रम भजे  । ।

हरे राम हरे राम, राम राम हरे हरे 
हरे कृष्ण हरे कृष्ण, कृष्ण कृष्ण  हरे हरे  । 

हरे राम हरे राम, राम राम हरे हरे 
हरे कृष्ण हरे कृष्ण, कृष्ण कृष्ण  हरे हरे  ।

हरे राम हरे राम, राम राम हरे हरे 
हरे कृष्ण हरे कृष्ण, कृष्ण कृष्ण  हरे हरे  । 

Rudhraashtak - Namamee shameeshan Nirvan roopam


Namaameeshameeshaan nirvana roopam, vibhum vyaapakam brahma veda swaroopam

Sunday, March 16, 2014

shuklaam vardhanam vishnu

I had to prepare my son for his shloka competition, but it was so hard to find it..
Finally, I managed to find the right sanskrit lyrics, hopefully, they are correct.

शुक्लां वर्धनम् विष्णुं  शशिवर्णं चतुर्भुजं ।
प्रसन्नवदनम् ध्यायेत् सर्वविघ्नोपशान्तये ॥ 
in roman,

Shuklaam Vardhanam Vishnum Shashivarnam chaturbhujam
prasannavadanam dhyaayet sarvavighnopashaantaye

Hope it helps

Wednesday, February 5, 2014

National Pension System (NPS) - India

The National Pension System (NPS) in India has been pushed for some time now. Government has been trying to increase the scope of the scheme, and hardly been successful at that.

One of the primary reasons has been the low cost structure for the Pension fund managers. While a regular mutual fund charges around 1.5% for the fund management effort, NPS fund managers were charging somewhere between 0.0009% to 0.25%.  At such low costs, it would have made little sense for anybody to be in business.

However, some of the fund managers persisted and are in relatively better standing today.  Some of them who did not continue (e.g. IDFC) continue to observe from a distance.

Over the last few years, returns from the NPS fund managers have been surpassing the general market returns, mostly in all categories.

Also, recently, govt regulations allowed hiking the fund management charges to 0.25%  in addition to allowing partial withdrawals from the NPS corpus.  Both of these measures have flamed the interest in NPS.  By and large, people are now taking notice of the possibility of considering NPS as a possible investment vehicle. 

Slowly, but surely, many private sector companies are also adopting the NPS route for their employees.  Beyond the long term investment option, NPS offers an instant benefit in terms of tax benefit above and beyond 80C.  10% of your Basic Salary + DA is the cap for Tax benefit under NPS. 

Therefore effectively, who falls in the 30% tax bracket, stands to shave of a substantial amount from his taxable income.  Furthermore, the returns on this additional investment are not as measly as the EPF (approx 8-9%), but much more controlled (you can chose ur fund options) and market linked.

All these measures are slowly resurrecting NPS as a possible investment vehicle.