# 4 types financial models - sensitivity analysis, scenario analysis, capital asset pricing and credit risk

Vidya Gopinath for keySkillset
30
March
2023

This is the 5th and final blog of the series on Financial Modeling, if you have directly landed on this blog then we recommend you read the 4 blogs preceding this blog. Here are the links

FM Blog 1:  What is financial modeling: uses, benefits and types of financial models

FM Blog 2: 4 different types of financial models-3 Statement Cash Flow model, Discounted Cash Flow model, Merger and Acquisition Financial model and Leveraged Buyout Financial model

FM Blog 3: Understanding financial modeling: uses and benefits

So, now let us get on with the 5th and final blog of the series.

## Types of financial models

### 1) Sensitivity analysis model

Sensitivity Analysis Model is a financial modeling technique used to evaluate the impact of changes in key assumptions on the financial performance of a company. It helps businesses make informed decisions by testing the impact of various scenarios on their financial performance and results.

#### Why is it used?

This model is used to identify the key drivers that impact a company's financial performance and to understand how changes in these drivers affect the company's profitability, liquidity, and solvency. The Sensitivity Analysis Model is particularly useful in scenarios where there is uncertainty or volatility in the business environment.

### To build the model, follow these steps:

The formula for a Sensitivity Analysis Model depends on the specific scenario being analyzed. However, the general approach involves creating a set of financial statements for the company under different scenarios, and then comparing the results to identify the most sensitive drivers.

Here is an overview of steps to be followed at a high level:

1. To measure sensitivity in a financial model, you start with a base case value for a particular input, let's say V1. You keep all the other inputs constant and calculate the output or NPV.
2. Then, you change the input to a new value, let's say V2, while keeping all other inputs constant, and calculate the new output.
3. Next, you find the percentage change in the input and the output.
4. Finally, to get the sensitivity, you divide the percentage change in the output by the percentage change in the input.

This helps you understand how sensitive the output is to changes in the input value.

Example: Let's say you're working on a financial model to analyze the feasibility of a new project. One of the inputs to your model is the expected sales volume, which you've estimated to be 10,000 units per month in your base case scenario. To measure the sensitivity of your model to changes in the sales volume, you first calculate the NPV of the project based on the base case sales volume of 10,000 units per month. Then, you increase the sales volume to 12,000 units per month and calculate the new NPV. You find that the NPV has increased by 20% due to the increase in sales volume.

So, the sensitivity of your model to changes in the sales volume can be calculated by dividing the percentage change in the output (20%) by the percentage change in the input (20%/20% = 1). This means that for every 1% change in sales volume, the NPV of the project will change by 1%.

In summary, there is no specific formula for a Sensitivity Analysis Model, as the approach will depend on the specific scenario being analyzed. However, the general approach involves creating a set of financial statements for the company under different scenarios, and then comparing the results to identify the most sensitive drivers.

### 2) Scenario analysis model

Scenario analysis is a powerful tool used by businesses to evaluate the potential impact of various future events or situations on their financial performance. The scenario analysis model is used to simulate different hypothetical scenarios, helping organizations to identify and prepare for potential risks and opportunities.

#### Why is it used?

This model helps businesses to identify potential risks and opportunities and evaluate their financial impact. It also provides a framework for stress testing different scenarios to better prepare for unexpected events. With help from this model, businesses make more informed decisions and create contingency plans based on potential outcomes.

### Now, to build the model, here is an overview of the steps to follow at a high level:

1. Define the Issue: The first step in scenario analysis is to clearly define the issue or problem you want to address. This involves identifying the decisions you want to make based on the analysis of different potential scenarios. It's important to keep track of assumptions regarding cause and effect, as you may need to modify them.
2. Gather Data: Once you've defined the issue, you need to gather relevant data to support your analysis. Identify the key variables and metrics involved and use reliable indicators of what you want to analyze. Keep track of which variables you will modify for each scenario and which ones you control.
3. Create a Scenario Template: After you have selected the metrics and variables, set up a template for the scenarios. You can adapt an existing financial document or model as the scenario template, which makes it easier to update and switch values.
4. Set Up Scenarios: With the scenario template in place, you can now set up each of the scenarios. This involves making assumptions about the values for the key variables in each scenario. It's important to think about less direct effects on other variables as well.
5. Evaluate Results: Once you have calculated and evaluated the different scenarios, you can start making decisions. It's best to evaluate at least three scenarios before making a decision. The base case should be the most realistic, but you should also consider extreme situations, both positive and negative. Evaluate as many scenarios as needed to make an informed decision.

Example: An example of scenario analysis could be a retail business considering expanding their product line. The first step would be to define the issue: how would adding a new product line affect their revenue and profitability? Next, they would gather data on their current sales, customer demographics, and potential costs and revenue for the new product line. They would create a scenario template that includes variables such as the cost of raw materials, pricing strategies, and marketing expenses. Then, they would set up scenarios with different assumptions, such as high demand or low sales. Finally, they would evaluate the results and make a decision on whether to proceed with the new product line based on the analysis of the different scenarios..

Now ,the formula for a scenario analysis model will depend on the specific variables being analyzed and the financial statements being simulated. However, the basic approach involves creating a set of assumptions for each variable, inputting those assumptions into a financial model, and analyzing the output to see how each scenario impacts your financial performance.

### 3) Capital asset pricing model

The Capital Asset Pricing Model (CAPM) is a widely-used financial model that helps investors determine the expected return of an investment by analyzing the relationship between risk and return. This model is used by investors to assess the risk and return of investments, especially in the stock market.

#### Why is it used?

This model helps investors make informed decisions when selecting investments. It provides a method for evaluating the expected return of an investment based on its risk. Investors are also able to better understand the risk-reward tradeoff in their investment portfolio with the help of this model.

### Step by Step overview of instructions at high level to build the CAPM model:

The CAPM formula is used to calculate the expected return of an asset based on its risk.

The formula is ERi = Rf + βi(ERm - Rf), where ERi is the expected return of investment, Rf is the risk-free rate, βi is the beta of the investment, and (ERm - Rf) is the market risk premium.

This formula accounts for the time value of money and the additional risk an investor takes on. By using the CAPM formula, investors can determine if a stock is fairly valued based on its risk and expected return.

Example: To calculate the expected return using the CAPM formula, we need the risk-free rate, the expected market return, and the beta of the stock. In this case:

Risk-free rate = 1.0%

Expected market return = 6.5% + 1.0% = 7.5%

Beta = 1.3

Using the CAPM formula, we get:

Expected return = Risk-free rate + Beta x (Expected market return - Risk-free rate)

Expected return = 1.0% + 1.3 x (7.5% - 1.0%)

Expected return = 1.0% + 1.3 x 6.5%

Expected return = 9.45%

Therefore, the expected return on the stock using the CAPM formula is 9.45%, assuming the market performs as expected and the company's stock has a beta coefficient of 1.3.

### 4) Credit risk model

A Credit Risk Model is a statistical tool used by financial institutions to evaluate the likelihood of a borrower or a company defaulting on a loan. It assesses the probability of default based on various factors such as credit history, financial statements, industry risk, and macroeconomic factors.

#### Why is it used?

The model is used by financial institutions to determine the creditworthiness of a borrower, set credit limits, and price loans. It also helps in managing credit risk by identifying potential defaulters and taking appropriate measures to minimize the risk of losses.

### To build a Credit Risk Model, this is the overview of steps to be followed at high level:

1. Define objectives: Determine the primary purpose of the credit risk model (e.g., estimating probability of default, credit scoring, loss given default, etc.).
2. Collect data: Obtain historical borrower data, which should include both financial and non-financial information (credit scores, payment history, outstanding debts, income, employment status, demographic information, etc.).
3. Preprocess data: Clean the dataset by addressing inconsistencies, errors, missing values, and transforming the data into a suitable format for analysis.
4. Select relevant variables: Identify the most important variables related to the borrower's likelihood of default, using feature selection techniques like stepwise regression, LASSO, or Recursive Feature Elimination (RFE).
5. Split the data: Divide the dataset into a training set (for model development) and a validation set (for model testing).
6. Develop the model: Choose a suitable statistical or machine learning technique (e.g., logistic regression, decision trees, random forests, support vector machines, neural networks, etc.) and train the model on the training set.
7. Validate the model: Test the model's performance on the validation set using relevant performance metrics (accuracy, precision, recall, F1-score, AUC-ROC, etc.) to evaluate its ability to predict credit risk accurately.
8. Backtest the model: Assess the model's robustness and generalizability by testing its performance on historical data under various market conditions and credit cycles.
9. Implement the model: Integrate the credit risk model into the organization's credit decision-making processes, which may involve developing user interfaces, automating processes, and training staff.
10. Monitor and update the model: Regularly evaluate the model's performance, update it with new data as needed, and refine it to ensure continued accuracy and relevance in changing market conditions and borrower behavior.

Conclusion

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