Welcome to Banking Quest

Introduction

• Concept of Average 
• CAGR
• Correlation & Covariance 
• Alpha 
• Beta 
• R-Square 
• Concept of Normal Distribution
• Concepts of NDTL & ANBC

 Concept of Average

• The mean (also called arithmetic mean), in everyday language called the average, is the sum of the values of a group of numbers divided by the amount of numbers in the group.

Example:

• We have 9 numbers in a group: 10, 12, 11, 15, 13, 35, 41, 23, 20. The sum of these 9 numbers is 180. Then the sum of 180 is divided by 9 in order to get the average. The average is 180/9 = 20.

 Concept of Mean

• Let us compared the two data sets:
• It can be told that the statistical tool Mean (Average) camouflages (disguises), the highest profit of +25 and highest loss of -15 made in the scrip X.
• Strangely, the mean of both the scrips are coming to Rs. 20/-.
• It means, the average measurement is not a good instrument from risk perspective to capture the actual risk in the business or venture. 
• A low risk appetite investor, if he invests in the scrip X based on Mean, he will be thoroughly misguided. 
• On the contrary, a high risk taking investor, if he invests in Scrip Y again, he will  also be disappointed to get a monthly return of Rs. 5/-
• To conclude, the investors or traders in risk management should actually go behind the mean and look into the actual cash flows and invest or take position based on their risk appetite level. 

 Compound Annual Growth Rate (CAGR)

• CAGR is a very useful method to calculate the growth rate of an investment. It can be used to evaluate the past returns or estimate the future returns of an investment. CAGR is helpful in finance in the following ways

1. Better investment decisions: The CAGR calculator is a very handy tool to help you analyze your investment decisions every year. For instance, if you have purchased an equity mutual fund five years ago, the CAGR calculator gives you the average rate of returns you have earned every year over the past five years. This can help you understand whether the fund's returns are as per your expectations or not. If the fund is not performing well, you may want to reconsider your investment in the future.

2. Compare returns between different funds and benchmarks: You can also use the CAGR calculator to compare the returns you earn on a particular fund against similar funds. This can help you understand how well the mutual fund or any investment is performing compared to its peers or other investment avenues in the market. 

• Hence, investors can also compare against the benchmark indices for greater clarity.
• The compound annual growth rate (CAGR) is the rate of return (RoR) that would be required for an investment to grow from its beginning balance to its ending balance, assuming the profits were reinvested at the end of each period of the investment’s life span.

 Example of How to Use CAGR:

• Imagine you invested $10,000 in a portfolio with the returns outlined below:
• From Jan. 1, 2018, to Jan. 1, 2019, your portfolio grew to $13,000 (or 30% in year one  - (3,000/10,000 x 100 = 30% - Annual Growth Rate - AGR).
• On Jan. 1, 2020, the portfolio was $14,000 (or 7.69% from January 2019 to January 2020. (1,000/13,000) x 100 = 7.69% - AGR).
• On Jan. 1, 2021, the portfolio ended with $19,000 (or 35.71% from January 2020 to January 2021. (5,000/19,000 x 100 = 35.71% - AGR).
• On the other hand, the compound annual growth rate smooths the investment’s performance and ignores the fact that 2018 and 2020 were vastly different from 2019. The CAGR over that period was 23.59% and can be calculated as follows:
• CAGR = ((19,000/10,000)^(1/3)) – 1
• =((1.9)^0.33) – 1
• = 1.2359 – 1 = 0.2359 x100
• =23.59%
• Only concern in CAGR, we have to use a scientific calculator or EXCEL. 

Comparing Investments: The CAGR can be used to compare different investment types with one another. For example, suppose that in 2015, an investor placed $10,000 into a Savings account with an interest rate of 3% and another $10,000 into a stock mutual fund. The rate of return in the stock fund will be uneven over the next few years, so a comparison between the two investments would be difficult.

Assume that at the end of the five-year period, the savings account’s balance is $10,510.10 and, although the other mutual fund investment has grown unevenly, the ending balance in the stock fund was $15,348.52. 

Using the CAGR to compare the two investments can help an investor understand the difference in returns: (given in the next slide)

 What are other uses of CAGR?

• Understanding the formula used to calculate CAGR is an introduction to many other ways that investors evaluate past returns or estimate future profits. 
• The formula can be used algebraically into a formula to find the present value or future value of money, or to calculate a hurdle rate of return.
• For example, imagine that an investor knows that he needs $50,000 for his child’s college education in 18 years and they have $15,000 on hand to invest today. 
• How much does the average rate of return need to be to reach that objective?
• The CAGR calculation can be used to find the answer to this question as follows: (Please refer next slide)

 Conclusion:

• CAGR is a very useful method to calculate the growth rate of an investment. It can be used to evaluate the past returns or estimate the future returns of your investments.
• However, remember that CAGR works suitably for lumpsum investments only. 
• In case of Systematic Investment Plans (SIPs), it does not take the periodic investments into account as it only considers the initial and final values for the calculation.
• Overall, the CAGR calculator is a very useful tool and it can help you analyze your investments.

 Alpha Ratio

• Alpha Ratio: When it comes to quantifying value and risk, two statistical metrics, alpha, and beta, are useful for investors. Both are risk ratios used in risk management and help to determine the risk/reward profile of investment securities.
• Alpha measures the performance of an investment portfolio and compares it to a benchmark index, such as the S&P 500/ BSE Sensex/NSE Nifty etc. The difference between the returns of a portfolio and the benchmark is referred to as alpha. 
• A positive alpha of one means the portfolio has outperformed the benchmark by 1%. Likewise, a negative alpha indicates the underperformance of an investment.
• In measuring capital under Operational Risk (Basel-III) under Basic Indicator Approach, 15% specified by RBI is the measure of Alpha or Gross return or income of the bank. 

 Beta Ratio

• Beta Ratio: Beta measures the volatility (and not the returns) of a portfolio compared to a benchmark index. The statistical measure beta is used in the CAPM, which uses risk and return to price an asset. 
• Unlike alpha, beta captures the movements and swings in asset prices. A beta greater than one indicates higher volatility, whereas a beta under one means the security will be more stable.
• In risk management, risk is represented by volatility of market prices. Hence, Beta measures this volatility which is a replica of risk.
• In measuring capital under Operational Risk (Basel-III) under The Standardized Approach (TSA), risk of 8 business lines is measured by Beta.
• Trading & Sales would carry a Beta of 18% (high risk) whereas lending to retail carries a Beta of 12% (low risk). 

Difference between Alpha and Beta Ratios

• 2020: A year of great volatility in commodity and financial markets
• On 1st January, 2020, it started with 41,306 and on 31st December, 2020, it ended with 47,751. Growth in the index is 6,445 points (47,751 minus 41,306)
• The earnings (Alpha) of the index during the year is 15.60% (6,445/41,306 x 100).
• But, if we take the BSE Sensex during the year 2020, the daily volatility (Beta) was  81% approx. (refer graph given in the next slide).
• The BSE Sensex, India’s benchmark stock market index, suffered its biggest ever inter-day fall of 13.15% on March 23, a day before the Prime Minister announced a nationwide lockdown. The Sensex fell from its previous day’s close of 29,915.96 to 25,981.24, the lowest value since 26 December, 2016. The year 2020 included 3 trading sessions -- 12, 16 and 23 March that saw among the top 10 biggest inter-day falls in the index history.

Correlation and Covariance Measures

• Covariance and correlation are two key concepts in statistics and probability theory, but what do they actually mean in practice? More importantly, when do we use them? 
• Put simply: we use both of these concepts to understand relationships between data variables and values. 
• We can quantify the relationship between variables and then use these learnings to either select, add or alter variables for predictive modeling, insight generation or even storytelling using data. 
• Thus, both correlation and covariance have high utility in Statistics, machine learning and data analysis. 
• Example working of correlation is given in the next slides.

 Covariance Working

• Calculate covariance for the following data set:
  x: 2.1, 2.5, 3.6, 4.0 (mean = 3.1)
  y: 8, 10, 12, 14 (mean = 11)
• Substitute the values into the formula and solve:
  Cov(X,Y) = ΣE((X-μ)(Y-ν)) / n-1
  = (2.1-3.1)(8-11)+(2.5-3.1)(10-11)+(3.6-3.1)(12-11)+(4.0-3.1)(14-11) /(4-1)
  = (-1)(-3) + (-0.6)(-1)+(.5)(1)+(0.9)(3) / 3
  = 3 + 0.6 + .5 + 2.7 / 3
  = 6.8/3
  = 2.267

 Correlation and Covariance Measures

• COVARIANCE VS. CORRELATION
• Both covariance and correlation measure the relationship and the dependency between two variables.
• Covariance indicates the direction of the linear relationship between variables.
• Correlation measures both the strength and direction of the linear relationship between two variables.
• Correlation values are standardized (-1  to +1). The values of the correlation coefficient can range from -1 to +1. The closer it is to +1 or -1, the more closely the two variables are related. The positive sign signifies the direction of the correlation (i.e. if one of the variables increases, the other variable is also supposed to increase).
• Covariance values are not standardized.

 R-Square Measure

• R-Squared: In statistics, R-squared represents a notable component of regression analysis. 
• The coefficient R represents the correlation between two variables—for investment purposes, R-squared measures the explained movement of a fund or security in relation to a benchmark. 
• A high R-squared shows that a portfolio’s performance is in line with the index. 
• Financial advisors can use R-squared in tandem with the beta to provide investors with a comprehensive picture of asset performance.
• R-squared measures the degree to which the fund's performance can be attributed to the performance of the selected benchmark index. 
• R-squared is reported as a number between 0 and 100. A hypothetical mutual fund with an R-squared of 0 has no correlation to its benchmark at all. 
• A mutual fund with an R-squared of 100 matches the performance of its benchmark precisely.
• Beta and R-squared are two related, but different, measures. A mutual fund with a high R-squared correlates highly with a benchmark. If the beta is also high, it may produce higher returns  than the benchmark, particularly in bull markets. 
• R-squared measures how closely each change in the price of an asset is correlated to a benchmark. Beta measures how large those price changes are in relation to a benchmark. 
• Used together, R-squared and beta give investors a thorough picture of the performance of asset managers.

 Concept of Normal Distribution

• It is assumed in the statistics that a large sample size, is approximately normally distributed. As long as the sample size is large, the distribution of the sample means will follow an approximate normal distribution.
• Hence, it is believed in Statistics that all kinds of variables in natural and social sciences are normally or approximately normally distributed. Height, birth weight, reading ability, job satisfaction, or SAT scores are just a few examples of such variables.
• Because normally distributed variables are so common, statisticians  have designed many statistical tests for normally distributed populations.
• Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. In graph form, normal distribution will appear as a bell curve.
• The normal distribution is the most common type of distribution assumed in technical stock market analysis and in other types of statistical analyses. The standard normal distribution has two parameters: the mean and the standard deviation. For a normal distribution, 68% of the observations are within +/- one standard deviation of the mean, 95% are within +/- two standard deviations, and 99.7% are within +- three standard deviations.
• Advantages of the normal distribution:
• The normal distribution is widely used partly because it does genuinely often occur. 
• It is also often used even when it is just a rough approximation because it is easy to handle. 
• The normal distribution can be manipulated algebraically much more easily than alternatives, so it can be used to derive formulae. This means that it is possible to derive results that can easily be applied.
• Disadvantages of the normal distribution:
• Uniform distributions exist, and so do skewed distributions. Ceiling effects, floor effects, you name it, plenty of things don't fit normal and that's a real disadvantage when using a normal distribution.
• If the size of the population is inadequate, it may not fit into a normal distribution and hence, normal distribution requires large sample size. 

 NDTL

• The Net Demand and Time Liabilities or NDTL shows the difference between the sum of demand and time liabilities (deposits) of a bank (with the public or the other bank) and the deposits in the form of assets held by the other bank.
• As per RBI Circular (Annexure 1) Net Liabilities of the Banks is defined as follows:
• While computing liabilities for the purpose of CRR and SLR, the net liabilities of the bank to other banks in India in the ‘banking system’ shall be reckoned, i.e., assets in India with other banks in the ‘banking system’ will be reduced from total liabilities to the ‘banking system’. 
• In other words, the net demand and time liabilities of a bank can be calculated by using the following formula:
• Bank’s NDTL = Demand and time liabilities (deposits) – deposits with other banks
• Suppose a bank has deposited  Rs. 5000 with the other bank and its total demand and time liabilities (including the other bank deposit) is 10,000. Then the net demand and time liabilities will be 5,000 (10,000-5,000).
• Thus, the deposits of a bank are its liabilities that can be in the form of demand liability, time liability and other demand and time liabilities.

Demand Liabilities: The demand liabilities include all those liabilities of a bank which are payable on demand. Such as current deposits, cash certificates and cumulative/recurring deposits, outstanding telegraphic transfers, Demand drafts, margins against the letter of credit/guarantees, credit balance in cash credit account, etc., all are paid on demand.

Time Liabilities: Time liabilities are those liabilities of a bank which are payable otherwise on demand. These include fixed deposits, cash certificates, staff security deposits, time liabilities portion of saving deposits account, margin held against the letter of credit (if not payable on demand), gold deposits, etc.

Other Demand and Time Liabilities: These include all those miscellaneous liabilities which are not covered in above two types of liabilities. Such as interest accrued on deposits, unpaid dividend, suspense account balances showing the amount due to other banks or public, participation certificates issued to other banks, cash collaterals, etc.

ANBC

• Adjusted Net Bank Credit (ANBC), include total credit disbursed by bank together with other investments made by it which are not its obligation. The investments which are made under no obligation include bill discounted, bill or bond purchased etc. 
• Banks also purchase government securities under their obligations to maintain Statutory Liquidity Ratio (SLR). This SLR factor is not included in ANBC. In other words and to make it simple, we can say ANBC means loans & advances given by the Bank + investment.
• Definition of ANBC is: It is the net bank credit plus investments made by banks in non-SLR bonds held in the held-to-maturity category.