Chapter 11: Fundamentals Of Risk And Return

Chapter 11: Fundamentals Of Risk And Return – NISM-Series-XV Research Analyst Exam Study Notes Download PDF Book 

Return of Investment and Return on Investment

Topic Pointers:

  1. Investment Objective:
    • Capital investment in various products to earn returns.
    • Focus on both earning returns and preserving the invested capital.
  2. Evaluating Investment Returns:
    • Importance of return level, return volatility, and return nature (periodic or capital appreciation).
    • Emphasis on the safety of capital alongside the expected return.
  3. Return on Investment (ROI):
    • Measures the efficiency of an investment.
    • Calculated as: 
    • Higher ROI indicates better investment efficiency.
    • Useful but requires caution in unpredictable investments like equity and mutual funds.
  • Return on Investment (ROI): A financial metric comparing the profit generated by an investment to the amount of capital invested, expressed as a percentage. It is a key indicator of the efficiency and potential profitability of an investment.


If an investor puts $1,000 into a stock and it earns a net profit of $100 in a year, the ROI is calculated as:

This means for every dollar invested, the investment returned 10 cents in profit.

Calculation of Simple, Annualised, and Compounded Returns

  1. Purpose of Calculating Returns:
  • To assess if returns meet investment goals and compensate for risks.
  • To compare different investments based on returns.
  • To evaluate investment performance relative to a benchmark.
  1. Types of Returns:
  • Periodic payouts (interest, dividends, rent).
  • Appreciation or depreciation in investment value.
  1. Components of Total Returns:
  • Periodic income (fixed or variable).
  • Gain or loss in investment value.
  1. Calculating ROI:
  • Formula: ROI (%) = (Total Returns / Total Cost) × 100.
  • Reflects the return over a specific period.

Simple Return:

  • Calculated as: 
  • Represents single period or absolute return.
  • Does not consider the period of the investment.

Annualized Return:

Converts absolute return to a yearly basis.


Useful for comparing investments held for different periods.

Compounded Annual Growth Rate (CAGR):

  • Considers time value of money.
  • Formula:
  • where n is the holding period in years.
  • Reflects the smoothed rate of return over the investment period.


Return on Investment (ROI): A financial ratio that calculates the percentage return on an investment relative to its cost. It includes both periodic income and changes in the value of the investment.

Example: An investor bought 150 shares of ABC company at Rs.25 each, paying Rs.20 as a broker commission. The shares were later sold for Rs.30 each, with another Rs.20 commission. Additionally, the investor received Rs.1 per share as dividends. 

The total cost was Rs.3,770, calculated as 150 shares×Rs.25 per share+Rs.20 =150 shares×Rs.25 per share+Rs.20.

The total cost was Rs.3,770 (150 shares x Rs.25 + Rs.20), and the total returns were Rs.4,630 (150 shares x Rs.30 – Rs.20 + 150 shares x Rs.1 in dividends).

The simple return on the investment was 23%, calculated as or

However, this simple return doesn’t consider the holding period. To compare investments over different periods, the return is annualized. For example, if the investment was held for 15 months, the annualised return is 

The Compounded Annual Growth Rate (CAGR), which takes into account the time value of money, is used for a more accurate assessment. CAGR assumes reinvestment of periodic returns. In this example, if the investment was held for 5 years, the CAGR is calculated as  

CAGR provides a clearer picture of stock performance over time, considering both the investment period and the time value of money. It’s the standard measure of return for periods longer than a year.

CAGR for Multiple Cash Flows

Calculation of Compound Annual Growth Rate (CAGR) Using XIRR in Excel

  • CAGR provides a smoothed average annual growth rate of an investment, ignoring volatility.
  • The XIRR function in Excel calculates the internal rate of return for a schedule of cash flows that are not necessarily periodic.
  • XIRR is useful when cash inflows/outflows are at irregular intervals.
  • It requires two sets of data: the dates of cash flows and the corresponding cash flow amounts.
  • Negative values represent cash outflows (investments), and positive values represent cash inflows (returns).
  • The dates should be in a consistent format, and the cash flows should match each date accordingly.

The Compound Annual Growth Rate (CAGR) is the mean annual growth rate of an investment over a specified time period longer than one year.

It represents one possible measure of an investment’s return and assumes the investment grows at a steady rate.

The XIRR function returns the internal rate of return for a series of cash flows that occur at irregular intervals.

Example: An investor purchases an equity share for Rs. 150 and receives dividends over three years, followed by the sale of the share.

  • Purchase date and price: 31 Jul 2011 for Rs.150 (cash outflow: -150).
  • Dividends received: Rs.5 on 31 Oct 2011, Rs.6 on 31 Oct 2012, Rs.4 on 31 Oct 2013 (cash inflows).
  • Sale of share: 15 Jan 2014 for Rs.165 (cash inflow).

Applying the XIRR function in Excel with the above cash flows and dates, the CAGR is calculated to be 8.06%.

To use the XIRR function:

  1. Input dates in one column and corresponding cash flows in another.
  2. Select the range of cash flows and dates in the XIRR function.
  3. If necessary, provide a ‘Guess’ for the rate of return to start the calculation.
  4. The result is the CAGR, which in this example is 8.06%.

Risks in Investments

  • The interplay of risk and return is fundamental in investing; higher returns often entail higher risks.
  • Investment risk entails the volatility and potential loss of the capital invested.
  • The discrepancy between actual and expected returns is also a measure of investment risk.
  • Different investment vehicles come with varying degrees of risk.
  • Fixed deposits are typically low-risk; they offer lower, but more predictable returns.
  • Equity investments carry higher risk due to uncertain dividends and potential for capital value fluctuation.
  • Investors need to assess risks in relation to their personal situations and investment goals.

Risk in investments refers to the uncertainty and potential variability in the returns of an investment, which at its extreme can result in the loss of the initial capital.

Risk is inherently tied to the expected returns from an investment, where typically the possibility of higher returns comes with a higher level of risk.

Example: A bank fixed deposit is considered low-risk as the bank is expected to honour both the interest payments and the return of the principal.

Conversely, investing in equities is considered high-risk due to unpredictable dividends and significant price volatility.

A retired individual may prefer a fixed deposit for stable income, avoiding the higher risks associated with equity investments despite their potential for higher returns.

Inflation Risk in Investments

  • Inflation risk is the risk that investment returns may not keep up with the rate of inflation, reducing purchasing power over time.
  • This risk is most relevant for fixed-income investments like bonds, fixed deposits, and debentures.
  • As inflation increases, the real rate of return on investments decreases.
  • Fixed return instruments promise a set amount in interest payments, which can become less valuable as inflation rises.
  • In equity investments, inflation risk is generally lower because businesses can increase prices to match inflation, potentially leading to higher profits and stock prices.

Inflation risk, or purchasing power risk, is the risk that the cash flows from an investment will be worth less in the future due to inflation. It represents the decline in purchasing power of money, resulting in a decrease in the real value of investments.


  • Lata’s fixed deposit giving Rs.10000 per month faces inflation risk if inflation rises by 10%, reducing her purchasing power to needing Rs.11000 to maintain the same standard of living.
  • A bond with an 8% coupon rate in a 7% inflation scenario gives a real return of 1%. If inflation increases to 9%, the real return becomes negative.
  • During hyperinflation in Venezuela, bond investments eroded in value, while the Caracas Stock Exchange Index rose significantly, reflecting the lower inflation risk for equities compared to fixed-income securities.

Interest Rate Risk

  • Interest rate risk is the risk that changes in interest rates will affect the price of bonds.
  • There’s an inverse relationship between bond prices and interest rates.
  • When interest rates fall, existing bonds with higher interest become more valuable, increasing their market price.
  • Conversely, when interest rates rise, the market price of existing bonds with lower rates falls.
  • The market adjusts bond prices to align the internal rate of return (IRR) with current interest rates.
  • This risk not only affects bonds directly but also impacts debt funds that hold such assets.
  • Equity investments can also be affected by interest rate risk since higher rates can lead to lower present values of future cash flows and reduce corporate borrowing and investment.

Interest rate risk is the potential for investment losses due to fluctuations in interest rates, which inversely affect bond prices. As interest rates rise, bond prices typically fall, and as rates decline, bond prices usually increase.


  • An investor buys a 5-year bond with an 8% annual interest rate. If the Reserve Bank of India reduces policy rates, new bonds may offer 7.5%, making the older 8% bonds more attractive and pushing their prices up.
  • If policy rates increase and new bonds offer 9%, the older 8% bonds become less attractive, driving their market price down.
  • The change in bond prices is a result of the market aligning the yield of existing bonds with the new market interest rates, ensuring the IRR for the bonds matches the prevailing market rate.
  • In equity markets, higher interest rates increase the cost of capital, potentially decreasing the present value of company cash flows and lowering equity prices due to reduced demand.

Business Risk

  • Business risk refers to the potential for a company to experience losses due to factors that affect its operations.
  • It is also termed operating risk.
  • Factors contributing to business risk include fluctuations in the cost of raw materials, labour costs, the emergence of competing products, and expenses related to marketing and distribution.
  • The impact of these risks varies across different companies and industries.
  • Diversifying one’s investment portfolio is a strategic way to mitigate business risk.

Business risk, or operating risk, is the risk associated with the day-to-day operations of a company. It arises from various operational factors that can lead to financial losses for the company.


  • A company may face increased costs for raw materials due to market shortages, which could reduce profit margins.
  • Introduction of a new competitor’s product might lead to a loss of market share and decreased sales.
  • Rising employee costs due to wage increases or changes in labor laws could impact the company’s operating income.
  • A diversified portfolio, including investments across different sectors or geographical regions, can reduce the impact of business risks associated with any single company or industry.

Market Risk

  • Market risk is the potential for an investment to lose value due to adverse price movements in the market.
  • This risk is influenced by changes in the intrinsic value of an asset, which can be affected by various factors such as interest rates or currency values.
  • Specific types of market risk include interest rate risk (e.g., bond prices falling due to rising interest rates) and currency risk (e.g., a currency appreciation affecting export-oriented companies).
  • Market risk is relevant to assets traded in financial markets, like equities, bonds, gold, and real estate.
  • Non-marketable securities, like deposits or small savings schemes, are not subject to market risk but also don’t benefit from potential increases in market value.

Market risk, also known as systematic risk, is the potential for an investor to experience losses due to factors that affect the overall performance of the financial markets.


  • If the Reserve Bank increases interest rates, the market value of existing bonds with lower rates will likely decrease (interest rate risk).
  • For a company that relies on exports, an appreciation in the domestic currency could reduce its revenue when converted back, potentially leading to a decrease in its stock price (currency risk).
  • Conversely, investments like fixed deposits, which have a fixed return and are not traded on open markets, do not face market risk but also do not have the opportunity to increase in value due to market movements.

Credit Risk in Debt Instruments

  • Credit risk, also known as default risk, is the risk that a bond issuer will fail to make expected payments.
  • Debt instruments like bonds carry default risk because they have pre-set payment schedules.
  • Issuers’ ability to service debt can change, affecting the default risk for investors.
  • Sovereign governments typically don’t face default risk for local currency borrowings because they can raise funds via taxation or printing money.
  • Credit ratings by agencies assess and express the creditworthiness of borrowers using standardized symbols.
  • High credit ratings (e.g., AAA, A1) indicate low default risk, while low ratings (e.g., D) indicate high default risk or actual default.
  • The credit rating reflects the issuer’s fundamentals and can change if those fundamentals change.
  • Lower credit ratings correlate with higher yields demanded by investors to compensate for higher risk.
  • Diversification across different bonds can mitigate default risk.

Credit risk is the possibility that a bond issuer will be unable to meet its obligations for interest payments or principal repayment, thus affecting the value of debt instruments.


  • A corporate bond with an A1 rating is considered to have a high degree of creditworthiness, suggesting a low chance of default.
  • If the issuing company’s financial health deteriorates, its credit rating may be downgraded, indicating a higher risk of default.
  • This would typically lead to a higher yield on the bond to compensate new investors for the increased risk.
  • A diversified bond portfolio might contain a mix of government and corporate bonds with varying credit ratings to balance the overall default risk.

Liquidity Risk

  • Liquidity risk is the risk that an investor may not be able to quickly sell an investment at its intrinsic value.
  • It can result in having to sell the investment at a discount, facing high transaction costs, or not being able to sell at all.
  • This risk is particularly relevant in markets with low trading volumes, such as corporate bonds in India, real estate, and art.
  • Lock-in periods can also contribute to liquidity risk, as they prevent selling during that time.
  • The bid-ask spread is an indicator of liquidity; a wide spread indicates higher liquidity risk.

Liquidity risk refers to the potential difficulty of selling an investment without a significant change in price due to a lack of buyers or market activity.


  • The Sovereign Gold Bond (December 2025) order book snapshot as of 17-Jul-2020 shows a bid-ask spread of over Rs.80, which is about 2% of the bond’s value, indicating high liquidity risk.
  • The small quantity available for trade also suggests a lack of liquidity, as there may not be enough volume for an investor to sell a significant position without affecting the price.

Call Risk in Bonds

  • Call risk pertains to the possibility of a bond being redeemed by the issuer before it reaches maturity.
  • It is often associated with reinvestment risk because investors may have to reinvest the returned funds at a lower interest rate.
  • This risk is heightened in environments where interest rates are declining.
  • Issuers may choose to call higher-interest bonds to reissue new bonds at the current, lower rates to reduce their debt expenses.

Call risk is the risk to bondholders that a bond may be repaid early by the issuer, especially during times of falling interest rates, which can force investors to reinvest at lower yields.

Example: An investor holds a bond with a 10% coupon rate. As market interest rates drop to 5%, the issuing company might decide to call the bond early to refinance its debt at the lower rate. The investor is then faced with call risk, as they must find a new investment for their funds, likely at a lower interest rate than the original bond.

Reinvestment Risk

  • Reinvestment risk concerns the chance that cash flows (like interest from bonds) will have to be reinvested at a lower rate than the original rate.
  • It occurs when fixed-income investments yield periodic payments that need reinvestment.
  • The total return from an investment is affected by the rate at which these reinvestments are made.
  • When market interest rates decrease, reinvestment risk increases, as new investments may yield lower returns.
  • Conversely, if interest rates increase, reinvestment risk decreases or is eliminated because the new investment may yield higher returns.
  • Opting for a cumulative option in debt investments can mitigate reinvestment risk by accumulating interest until maturity instead of paying it out periodically.

Reinvestment risk is the probability that the investor may have to reinvest income flows from an investment at a return that is lower than the original investment’s rate of return.

Example: An investor holds a bond paying annual coupons. If the current interest rates fall by the time the coupon is paid, the investor faces reinvestment risk as they may have to reinvest that coupon at the new, lower interest rate, reducing their overall returns from the investment.

Political Risk in Business and Investment

  • Political risk involves the uncertainty due to government actions that can affect businesses and investments.
  • This risk includes potential actions like nationalisation of industries, changes in tax laws, or alterations in licensing requirements.
  • Government’s ability to change laws and regulations means nearly all businesses and securities are subject to political risk.
  • Political risk is more pronounced in countries with unstable or unpredictable political climates.

Political risk refers to the risk that a business’s or investment’s profitability or viability may be affected by changes in government policies, regulations, or political stability.

Example: A company operating in a country where there is a sudden change in government might face increased taxes, stricter regulations, or even nationalisation, all of which could significantly impact its operations and profitability.

Country Risk and Investment Risks Classification

  • Country Risk: Involves the risk associated with a specific country’s ability to meet its financial commitments. Country risk can impact all securities within that country and can extend to international relations.
  • Systematic Risk: These are market-wide risks that affect a broad range of investments. They are also known as undiversifiable risks and are caused by factors like government policy changes, global events, and economic shifts. Inflation, exchange rate, interest rate, and reinvestment risks fall under this category.
  • Unsystematic Risk: Specific to individual securities or a narrow group of investments. These risks can be mitigated through diversification. Examples include credit risk, business risk, and liquidity risk.
  • Both systematic and unsystematic risks are inherent in most investments.
  • Country Risk: The risk that a country will not be able to honour its financial commitments, affecting the performance of all securities issued within that country.
  • Systematic Risk: Market-wide risks that impact a wide range of investments and cannot be diversified away.
  • Unsystematic Risk: Risks specific to individual securities or sectors that can be mitigated through diversification.


For Systematic and Unsystematic Risks: Ajay’s investment in an infrastructure company’s equity shares carries business risk (unsystematic) and market risk (systematic). Diversification can reduce business risk but not market risk. Similarly, Ashima’s bond investments are subject to credit risk (unsystematic) and interest rate risk (systematic). While she can mitigate credit risk through diversification, interest rate risk impacts all debt investments and cannot be diversified away.

Measuring Risk in Investments

Measure of Uncertainty:

  • Risk is often defined as the uncertainty or unpredictability in returns.
  • Standard deviation (ss) is a common measure, calculated as 
  • ​where Xˉ is the average return and n is the number of observations.

Measure of Sensitivity:

  • Risk is assessed based on how sensitive an asset’s price is to different risk factors.
  • For equities, beta measures sensitivity to market movements.
  • For bonds, duration measures sensitivity to interest rate changes.
  • For options, delta measures sensitivity to changes in the price of the underlying asset.

Measure of Loss:

  • Risk can be seen as the probability or potential size of losses.
  • Value at Risk (VaR) is a common tool, measuring the maximum expected loss over a given time period at a specific confidence level.

Risk measurement in finance is the quantification of the likelihood and magnitude of negative financial outcomes in investment decisions. It typically encompasses measures of uncertainty, sensitivity to market factors, and potential loss.


If a portfolio has a VaR(1%) of 12%, it means there’s a 99% chance that the loss will not exceed 12%, or conversely, a 1% chance that the loss will be more than 12%. This helps in understanding and preparing for the worst-case scenario in terms of portfolio losses.

Concepts of Market Risk (Beta)

    • Beta Definition: Beta measures a security’s volatility relative to the market, indicating systematic risk.
    • Interpretation of Beta Values:
  • A beta of 1 implies the security moves in tandem with the market.
  • Beta less than 1 indicates less volatility than the market.
  • Beta greater than 1 suggests more volatility than the market.
  • Beta in CAPM: Used in the Capital Asset Pricing Model (CAPM) to calculate expected returns based on market risk.
  • Limitations of Beta:
    • Beta views risk purely from the perspective of market price volatility.
    • It overlooks business fundamentals, economic developments, and price levels.
    • Assumes equal upside potential and downside risk, based solely on market volatility.
    • Beta’s reliance on past price volatility is argued to be a poor indicator of future performance or risk.

Beta is a measure of the relative volatility of a security in comparison to the overall market, representing the extent of its systematic risk.

Example: If a stock has a beta of 1.2, it is theoretically 20% more volatile than the market. This implies that if the market goes up or down, the stock is expected to move up or down by 20% more than the market movement. However, as critiqued by value investors like Seth Klarman, beta may not comprehensively describe the risk in a security, as it fails to consider factors beyond past price fluctuations.

Sensitivity Analysis in Financial Modeling

  • Importance of Inputs in Financial Models: The reliability of a financial model depends on the quality of its inputs, which often include assumptions about future business aspects.
  • Risk of Inaccurate Assumptions: If assumptions are not well-researched or evaluated, the model’s output can be unreliable.
  • Critical Variables Identification: It’s vital to identify and focus on the critical variables in a valuation model.
  • Conducting Sensitivity Analysis: This involves analysing how changes in key variables affect the model’s output.
  • Application in DCF Models: For instance, in a Discounted Cash Flow (DCF) model, the discount rate is a primary variable. Its accurate assessment is crucial as it reflects the risks in the business.
  • Scenarios in Sensitivity Analysis: Typically, best case, worst case, and most likely scenarios are analysed to understand the range of possible outcomes.

Sensitivity analysis is a technique used in financial modelling to evaluate how the different values of key variables impact a model’s output.

Margin of Safety in Value Investing

  • Origin of the Concept: Popularised by Benjamin Graham, known as the father of value investing, and further advocated by Warren Buffett.
  • Definition: The margin of safety refers to buying securities at a price significantly lower than their intrinsic value.
  • Significance: The greater the difference between the intrinsic value and the purchase price (with the intrinsic value being higher), the higher the margin of safety.
  • Risk Mitigation: Provides a cushion against downside risk and errors in valuation judgement.
  • Subjectivity in Valuation: Determining a company’s intrinsic value is subjective, and the margin of safety provides a buffer for this uncertainty.
  • No Fixed Standard: The extent of the margin of safety varies among investors; there’s no universally accepted standard for its size.

Margin of Safety is a principle in value investing that involves purchasing securities when their market price is significantly below their intrinsic value, thus providing a cushion against investment errors and market volatility.

Example: If an investor calculates the intrinsic value of a stock to be $100 but can purchase it for $70, the $30 difference represents the margin of safety. This margin serves as a buffer against potential losses due to unforeseen factors or calculation errors in the stock’s intrinsic value.

Comparison of Equity Returns and Bond Returns

Nature of Returns:

  • Bonds: Primarily from coupon income and sometimes value gains due to falling interest rates.
  • Equities: Mainly from appreciation in value, with dividends being a smaller component.

Risk and Return Levels:

  • Bonds are lower-risk due to predefined coupon returns and potential security for bondholders, resulting in generally lower returns.
  • Equities are higher-risk with no assurance on dividends or appreciation, but have the potential for higher returns.

Influencing Factors:

  • Bond returns are influenced by credit risk and interest rate changes.
  • Equity returns are influenced by company performance and external economic factors.

Investment Strategy Advice by Warren Buffett:

  • Compare the Rate of Return on stocks and bonds before investing.
  • Choose stocks when their Rate of Return is higher than bonds, and vice versa.
  • During economic distress, when interest rates are low, equities might offer higher returns even on a dividend yield basis.

The comparison of equity and bond returns involves analysing the nature, level, and composition of returns from both investment types, considering factors like inherent risks, potential returns, and market conditions.

Example: In a scenario where bond yields are at 3% and the expected return on equities is 6%, an investor following Buffett’s advice would opt for equities due to the higher potential return. Conversely, if bond yields rise to 5% and equities are expected to return only 4%, bonds would be the preferable choice for their higher return and lower risk.

Calculating Risk Adjusted Returns

Risk-Adjusted Returns in Investment Analysis

  • Purpose: To compare investment performances accurately by accounting for risk.
  • Necessity: High-risk strategies might yield higher returns, which makes it unfair to compare absolute returns with lower-risk strategies.
  • Volatility: High-risk investments are often more volatile, which should be considered over the holding period.
  • Risk-Adjusted Measures: Use metrics that balance returns with the level of risk taken to achieve those returns.

Risk-adjusted return measures are financial metrics used to compare the returns of investment portfolios or strategies by normalising for risk, allowing for an apples-to-apples comparison regardless of the level of risk involved.

Jensen’s Alpha as a Measure of Performance

  • Alpha’s Definition: Represents the excess return of an investment relative to a benchmark’s return.
  • Risk Consideration: Traditional alpha doesn’t account for risk levels; Jensen’s Alpha does.
  • Use of CAPM in Jensen’s Alpha: Adjusts for risk by using the Capital Asset Pricing Model (CAPM) to calculate the expected return.
  • Formula for Jensen’s Alpha: Jensen’s Alpha = Return on Portfolio – (Risk-Free Rate + β * (Market Return – Risk-Free Rate)).
  • Interpretation: A higher Jensen’s Alpha indicates better performance relative to the risk taken, after adjusting for the market’s performance.

Jensen’s Alpha is a risk-adjusted performance measure that evaluates the excess return of a portfolio over its expected return based on the CAPM model.

Example: If a portfolio has a return of 15%, the risk-free rate is 3%, the market return is 10%, and the portfolio’s beta (β) is 1.2, then Jensen’s alpha is calculated as:

Jensen’s Alpha = 15% – (3% + 1.2 * (10% – 3%))

15% – (3% + 1.2 * 7%) = 15% – 11.4% = 3.6%

A Jensen’s Alpha of 3.6% indicates the portfolio has outperformed its expected return based on the risk taken.

Understanding the Sharpe Ratio

  • Function of Sharpe Ratio: It evaluates the performance of an investment by adjusting for its risk.
  • Calculation of Risk Premium: The risk premium is the return of an investment above the risk-free rate.
  • Sharpe Ratio Formula: 
  • Interpretation: A higher Sharpe Ratio implies that the investment has a better risk-adjusted return, making it a more efficient choice for investors.

The Sharpe Ratio is a risk-adjusted measure used to determine the extra return an investor receives per unit of increase in risk, calculated by dividing the risk premium of the portfolio by the standard deviation of its returns.

Example: Assume an investment portfolio has an average annual return of 12%, a risk-free rate of 3%, and a standard deviation of the portfolio returns is 10%. The Sharpe Ratio would be calculated as follows:
Sharpe Ratio = (12% – 3%) / 10% = 0.9
This Sharpe Ratio of 0.9 suggests that the investment is earning 0.9 units of return for every unit of risk, which would be considered a favourable level of compensation for the risk taken.

Treynor Ratio

  • Purpose: The Treynor ratio assesses investment performance by measuring the risk premium earned per unit of Beta.
  • Calculation: It is calculated as follows: 
    • Return on portfolio: The total return generated by the investment portfolio.
    • Risk-free rate: The return from a risk-free asset, often represented by government bonds.
    • Beta: A measure of an investment’s volatility relative to the market; it represents systematic risk.
  • Interpretation: A higher Treynor ratio indicates superior performance in relation to the systematic risk taken.
  • The Treynor ratio is a measure of investment performance that quantifies the risk premium earned per unit of Beta. It is calculated by subtracting the risk-free rate from the investment return and dividing the result by the investment’s Beta.

Example: If an investment portfolio generates a return of 12%, the risk-free rate is 3%, and the portfolio has a Beta of 1.5, the Treynor Ratio is calculated as follows: 

A Treynor Ratio of 6% suggests that the portfolio has earned a 6% risk premium per unit of Beta.

Behavioural Biases in Investments

Definition: Behavioural Biases in Investments refer to the psychological and emotional factors that influence individuals’ financial decisions, often leading to irrational or unpredictable behaviour.

Conventional Financial Theory:

According to traditional financial theory, individuals are assumed to be rational and make decisions to maximise their wealth prudently.

Role of Emotion and Psychology:

Despite the rationality assumption, real-world decisions are often influenced by emotions and psychological factors, causing deviations from logical choices.

Benjamin Graham’s Insight:

Benjamin Graham, known as the “Dean of Wall Street,” emphasised in his book “The Intelligent Investor” that financial markets are more driven by psychology than pure logic.

Behavioural Finance:

Behavioral finance is a relatively new field that combines behavioural and psychological theories with economics and finance to explain why people make irrational financial decisions.

Inbuilt Behavioural Biases:

Simon Savage, co-head of European and global long/short strategies at GLG Partners, suggests that everyone has inbuilt behavioural biases to varying degrees.

Awareness as a Defense Mechanism:

Awareness of these biases is crucial for fund managers to build a defence mechanism against making poor investment choices influenced by these biases.

Practical Advice:

Savage advises fund managers not to ignore these biases and to be mindful of them to avoid financial vulnerabilities in their decision-making.

“Behavioural Biases in Investments are the psychological and emotional factors that deviate from the rational wealth-maximising assumptions of conventional financial theory. Behavioural finance seeks to explain and understand why individuals make financial decisions influenced by these biases.”

Loss-Aversion Bias

Topic Pointers

Loss-aversion bias refers to the psychological tendency of investors to strongly prefer avoiding losses over acquiring gains. It is characterised by the fear of experiencing a financial loss, which often leads to inaction.

Magnitude of Loss Aversion: Studies have shown that the pain or emotional distress associated with experiencing a financial loss is approximately twice as strong as the pleasure derived from gaining an equivalent amount of money.

Preference for Inaction: Investors affected by loss-aversion bias tend to prefer doing nothing when faced with decisions that may result in a loss, even if analysis and information support a different action.

Examples of Manifestations:

Holding onto losing stocks: Investors may resist selling stocks that have incurred losses, hoping that they will eventually recover.

Avoiding riskier asset classes: During periods of market volatility, investors may avoid investing in riskier assets like equities, despite discussions and information suggesting potential gains.

Frequent Portfolio Evaluation: Loss-averse investors often monitor their portfolio’s performance more frequently, as they are sensitive to even short-term losses. This heightened awareness can lead to a preference for inaction.

Preferred Strategy:Inaction becomes the preferred strategy for loss-averse investors when they perceive that taking action might lead to a potential loss.

Confirmation Bias

Topic Pointers:

  1. Definition: Confirmation bias, also known as my-side bias, is a cognitive bias characterised by the tendency to actively search for, interpret, or prioritise information in a way that aligns with one’s existing beliefs or hypotheses.
  2. Inductive Reasoning Error: It is considered a systematic error of inductive reasoning, where individuals gather evidence or information selectively to support their preconceived notions, often disregarding contradictory evidence.
  3. Example in Trading: In the context of trading, confirmation bias may manifest when a trader initially buys a stock for a specific reason. If that reason does not materialise as expected (e.g., the stock’s price doesn’t rise), the trader might invent another reason to justify holding the position, rather than objectively reassessing the investment.
  4. Decision Precedes Information: Confirmation bias often involves the sequence of making an intuitive or preconceived decision and then seeking information that confirms or supports that decision, rather than making a decision based on unbiased analysis.

“Confirmation bias is a cognitive bias in which individuals have a propensity to seek, interpret, or give priority to information that reinforces their existing beliefs or hypotheses. This bias can lead to a selective and skewed perception of information, as individuals tend to favour evidence that aligns with their preconceived notions while downplaying or ignoring contradictory evidence.”

Ownership Bias (Endowment Effect)

Topic Pointers:

  1. Definition: Ownership bias, also known as the endowment effect, is the cognitive bias that makes individuals assign a higher value to things they own compared to the value assigned by others. It leads to an overestimation of the worth of one’s possessions.
  2. Endowment Effect: The term “endowment effect” is often used interchangeably with ownership bias to describe this psychological phenomenon.
  3. Subjective Valuation: This bias results in individuals valuing their possessions subjectively and irrationally higher than their objective market value.
  4. Investment Implications: In the context of investments, ownership bias can cause investors to hold onto positions that they would not choose to buy at the current market price. They attach a higher value to their existing holdings simply because they own them.

“Ownership bias, also referred to as the endowment effect, is a cognitive bias characterised by the tendency for individuals to ascribe a greater value to things they own compared to the value assigned by others or their objective market worth. In the context of investments, this bias can lead individuals to overvalue their existing holdings, potentially causing them to retain positions that they would not acquire at current market prices.”

Gambler’s Fallacy

Topic Pointers:

  1. Definition: Gambler’s fallacy is a cognitive bias where individuals make predictions about entirely random events based on previous outcomes or attempt to identify trends when none exist.
  2. Misguided Belief: It is the mistaken belief that if a particular event occurs more frequently than expected in a certain period, it will happen less frequently in the future, or if it occurs less frequently than expected, it will happen more frequently in the future. This belief is often based on the idea of “balancing nature.”
  3. Example of Misconception: For example, if a roulette wheel has landed on red for several consecutive spins, a person influenced by the gambler’s fallacy may believe that black is now more likely to come up in the next spin, as if the wheel is “due” for a change.
  4. Inaccurate Predictive Behaviour: The gambler’s fallacy leads to inaccurate predictions because it assumes that random events have a memory or are influenced by past occurrences, which is not the case for truly random events.

“Gambler’s fallacy is a cognitive bias characterised by the erroneous belief that the likelihood of a random event is influenced by past occurrences of the same event. It involves making predictions about future events based on the assumption that if an event has occurred more or less frequently than expected in the past, it will ‘balance out’ in the future, leading to incorrect predictions.”

Winner’s Curse

Topic Pointers:

  • Competitive Bidding Context: The Winner’s Curse primarily occurs in situations where multiple parties are bidding competitively for an asset, such as in auctions or tender processes.
  • Overvaluation Tendency: Bidders tend to overestimate the value of the asset, leading them to bid more than what the asset is objectively worth.
  • Behavioural vs. Financial Outcomes: Behaviorally, winning the bid feels like a success. However, financially, it often results in a loss because the asset is not worth the price paid.
  • Risk of Overpayment: The Winner’s Curse highlights the risk of overpaying in competitive situations, emphasising the need for careful valuation.

The Winner’s Curse refers to the tendency to ensure winning a competitive bid at the cost of overpaying for the asset. While behaviorally perceived as a victory, it can lead to a financial loss.

Herd Mentality

Topic Pointers:

  • Behaviour in Investing Community: Herd mentality is a behavior disorder prevalent among investors, particularly during times of uncertainty.
  • Influence of Others’ Decisions: Investors often follow the investment choices of others, driven by the belief that others may possess superior information.
  • Impact of Uncertainty: This bias stems from uncertainty in the market, leading investors to seek validation from others’ actions.
  • Short-term Validation, Long-term Risks: Although following the herd can seem correct and may be supported by short-term gains, it often contributes to market bubbles and subsequent crashes.
  • Small Investors’ Tendency: Smaller investors tend to enter the market late, often when it is overheated and poised for a correction, influenced by the actions of others.
  • Psychological Barrier to Contrarian Actions: Most individuals avoid going against the crowd, as going with conventional wisdom is seen as less risky for one’s reputation, echoing the sentiment of economist John Maynard Keynes.

Herd mentality is a behavioural disorder in the investing community, characterised by the tendency to follow others’ investment choices due to uncertainty and the belief that others have better information. This often leads to market bubbles and crashes, as investors seek confirmation from others and enter overheated markets.”


Topic Pointers:

  • Cognitive Bias in Decision Making: Anchoring is a cognitive bias where individuals rely too heavily on the first piece of information received.
  • Impact on Investors: Investors often cling to initial information, even if it becomes irrelevant, and base their decisions on this outdated data.
  • Disregarding New Information: New, potentially more relevant information is often labeled as incorrect or irrelevant and is consequently ignored.
  • Influence on Selling Decisions: Investors waiting for the ‘right price’ to sell, even when new information suggests that the expected price is unrealistic, are influenced by anchoring.
  • Detrimental to Portfolio Performance: Holding onto losing stocks with the hope that they will regain their past value, despite current information suggesting otherwise, can negatively impact overall portfolio returns.
  • Importance of Current Information: Decisions should be based on the current price and value difference, considering the latest available information, rather than on past prices.

Anchoring is a cognitive bias that refers to the tendency to heavily depend on the first piece of information when making decisions. In investing, this bias leads to holding onto outdated information and making decisions based on it, often ignoring new and relevant data.”

Projection Bias

Topic Pointers:

  • Focus on Recent Past: Projection bias involves focusing primarily on recent events or experiences when considering the future.
  • Ignoring Distant Past: This bias leads to the neglect of long-term historical trends or patterns.
  • Overemphasis on Current Trends: It causes an overestimation of the likelihood that current trends or situations will continue into the future.
  • Lack of Comprehensive Analysis: Because of this bias, there is often a failure to analyze situations or predict future outcomes using a comprehensive view of past data.
  • Influence in Decision Making: Projection bias can significantly influence personal and professional decisions, potentially leading to skewed judgments or unrealistic expectations.

Projection bias is the tendency to project the recent past into the distant future, while completely ignoring the distant past. This cognitive bias affects how individuals perceive and predict future events based on recent experiences.”

Investment Wisdom from Renowned Gurus

Topic Pointers:

  1. Stock Market Cycles:
    • Bull Market: Characterised by rising stock prices, optimism, business expansion, and profitability. Can lead to overvaluation.
    • Bear Market: Follows a bull market, marked by falling stock prices, economic downturns, business stress, and lower demand.
  2. Benjamin Graham’s Allegory:
    • Mr. Market: Represents the market’s daily price assessments, often influenced by emotions.
    • Investment Strategy: Investors should not be swayed by Mr. Market’s emotions but should look for mispricing opportunities.
  3. Investment Wisdom from Gurus:
    • Benjamin Graham:
      • Investment success is achievable; superior results are challenging.
      • Short-term market is like a voting machine, long-term like a weighing machine.
    • Charlie Munger: Good investing skills enhance business management.
    • David Dreman: Psychology is crucial and often misunderstood in the market.
    • John Templeton: Invest at the point of maximum pessimism.
    • Peter Lynch: Choose businesses that can be run by anyone.
    • Walter Schloss: If no good investments are available, hold cash.
    • Warren Buffett:
      • Rule No.1: Never lose money.
      • Rule No.2: Never forget Rule No.1.
  • Bull Market: A market condition where stock prices are rising, and the economic outlook is optimistic.
  • Bear Market: A market condition where stock prices are falling, often due to economic downturns and reduced business profitability.

Measuring Liquidity of Equity Shares

Topic Pointers:

  1. Purpose of Stock Exchanges: Provide liquidity, meaning the ease of buying and selling shares.
  2. Liquidity Determination: High liquidity is achieved when there are numerous buyers and sellers for a stock.
  3. Liquidity Measurement Metrics:
    • Stock Turnover Ratio:
      • Formula: Stock Turnover Ratio = Number of Shares Traded / Number of Outstanding Free Float Shares.
      • Time Frame: Usually calculated over a one-year period.
      • Free Float Shares: Refers to shares held by non-promoter group shareholders.
    • Traded Value Turnover Ratio:
      • Formula: Traded Value Turnover Ratio = Traded Value of Shares / Market Capitalization of the Company.
      • Similarity: It is akin to the stock turnover ratio but uses the traded value instead.
  • Liquidity: In the context of stock markets, liquidity refers to how easily equity shares can be bought and sold in the market.
  • Free Float Shares: Shares that are available for trading in the market, excluding those held by promoters.

Important Formulas

  • Future Value of a Single Cash Flow (FV):
  •  Where PV is the Present Value, r is the interest rate, and n is the number of periods.
  • Future Value of a Series of Cash Flows (Annuity): 
  • Where P is the periodic payment, r is the interest rate, and n is the number of periods.
  • Present Value of a Single Cash Flow (PV): 
  • Where FV is the Future Value, r is the interest rate, and n is the number of periods.
  • Present Value of a Series of Cash Flows (Annuity): 
  • Where P is the periodic payment, r is the interest rate, and n is the number of periods.
  • Yield to Maturity (YTM) for Bonds:
  • This is a more complex calculation, often done through iterative methods or financial calculators. It’s the internal rate of return (IRR) for a bond investment.
  • Total Return: 
  • Income from investment includes interest or dividends, and capital gains are the change in the value of the investment.
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