QFE University

Portfolio Theory (22 Q&A)

Q1. What does it mean for an investor to be risk-averse, risk neutral, risk seeking and risk tolerant?

Risk-Averse: A risk-averse investor is one who prefers lower-risk investments with relatively stable returns over higher-risk investments with potentially higher returns. They prioritize protecting their capital and are willing to accept lower returns in exchange for reduced risk. They tend to avoid highly volatile assets and seek investments with more predictable outcomes.

Risk-Neutral: A risk-neutral investor is indifferent to risk and makes investment decisions solely based on the potential returns. They evaluate investments based on their expected return, regardless of the level of risk involved. This type of investor would typically make choices based purely on mathematical expectations, without being swayed by the degree of risk.

Risk-Seeking: A risk-seeking investor is willing to take on higher levels of risk in exchange for the possibility of higher returns. They are inclined towards investments that have a higher potential for volatility and greater uncertainty. Risk-seeking investors might be more comfortable with aggressive, speculative investments and are willing to accept the possibility of losses for the chance of significant gains.

Risk-Tolerant: This term refers to an investor’s ability to endure the fluctuations and potential losses in their investment portfolio without changing their long-term investment strategy. A risk-tolerant investor may have a higher capacity to handle market volatility and fluctuations in the value of their investments without feeling the need to make sudden changes to their portfolio.

Q2. What is Arbitrage?

Arbitrage refers to the practice of exploiting price differences in different markets, or within the same market, to make a profit without incurring any risk or requiring additional investment. It involves buying and selling assets, securities, or currencies simultaneously in different markets to take advantage of the price discrepancy.

Arbitrage opportunities are often short-lived and disappear quickly as market participants quickly exploit them. The presence of arbitrageurs helps ensure that prices across different markets remain relatively consistent, as their actions tend to eliminate price discrepancies.

However, efficient markets tend to minimize arbitrage opportunities, making it difficult for traders to consistently profit from price differences. As technology advances and markets become more efficient, arbitrage opportunities become increasingly rare and challenging to exploit.

Q3. What is Hedging?

Hedging is a risk management strategy used to offset or reduce the potential losses from adverse price movements in assets, investments, or positions. It involves taking an offsetting position that serves to mitigate the risk of adverse price movements in another position or portfolio.

Investors can use financial instruments like options, futures contracts, swaps, or derivatives to hedge against price movements in stocks, commodities, currencies, or interest rates. While hedging helps minimize downside risk, it also limits the potential for large gains. Hedging involves a trade-off between reducing risk and potential profits.

Implementing a hedge often involves costs, such as transaction fees, premiums for options, or margins for futures contracts. These costs need to be considered against the potential benefits of reducing risk. Hedging can be a crucial aspect of portfolio management, especially for investors or businesses with exposure to volatile markets or uncertain economic conditions.

Q4. What is Speculation?

Speculation refers to the practice of making investment decisions with the aim of earning significant profits, typically by taking on a higher level of risk. Unlike investing, which often involves a longer-term approach and focuses on the fundamental value of assets, speculation is more short-term and revolves around attempting to profit from market price movements.

Speculators usually have a shorter time horizon, seeking to capitalize on short-term price fluctuations rather than holding assets for the long term. Speculators might frequently use derivatives like options, futures, or other complex financial instruments to magnify their exposure to the market and potentially increase their returns. This amplifies both potential gains and losses.

Speculation often occurs in highly volatile and liquid markets where price movements can be rapid and unpredictable, allowing for quick buying and selling of assets. While speculation can lead to substantial profits, it also carries a high risk of substantial losses. The speculative nature means that success isn’t guaranteed, and market movements can quickly erode gains.

Q5. What is different kind of risks faced in the Portfolio?

In a portfolio, various types of risks can impact investment performance. Understanding and managing these risks are crucial for effective portfolio management. Here are some key risks:

a) Market Risk: Also known as systematic risk, it refers to the risk associated with overall market movements. Factors such as economic conditions, interest rate changes, geopolitical events, and market sentiment affect all investments in the market.

b) Interest Rate Risk: Fluctuations in interest rates affect bond prices inversely. When interest rates rise, bond prices typically fall, impacting the value of fixed-income investments in a portfolio.

c) Credit Risk: This risk arises from the possibility of an issuer defaulting on its debt obligations. It affects bond investments, with lower-rated bonds carrying higher credit risk compared to higher-rated or government bonds.

d) Liquidity Risk: It refers to the risk of not being able to sell an investment quickly without significantly impacting its price. Investments in less liquid assets might face challenges in finding buyers at desired prices, especially during market stress.

e) Inflation Risk: The risk that the purchasing power of money will decrease over time due to inflation. Inflation erodes the real returns on investments, especially on fixed-income securities, if their returns don’t outpace inflation.

f) Currency Risk: For portfolios with international investments, fluctuations in exchange rates can impact the value of those investments when converted back to the investor’s home currency.

g) Political and Regulatory Risk: Changes in government policies, regulations, or geopolitical events can impact the performance of investments. Political instability, trade policies, or sudden regulatory changes can affect market conditions and asset prices.

h) Volatility Risk: It refers to the potential for investments to experience rapid and significant price movements in either direction. High volatility can lead to uncertainty and potential losses.

i) Event Risk: Unforeseen events like natural disasters, terrorist attacks, or corporate scandals can have sudden and significant impacts on investments.

Q6. What are different Asset Classes investor can invest in?

Investors have various asset classes to consider when building a diversified investment portfolio. These asset classes differ in risk, return potential, and characteristics. Here are some common asset classes:

a) Stocks (Equities): Ownership shares in publicly traded companies. Stocks offer the potential for high returns but come with higher volatility and risk. They can be categorized based on company size (large-cap, mid-cap, small-cap), sector, or geographical location.

b) Bonds (Fixed-Income Securities): Debt instruments issued by governments, municipalities, or corporations. Bonds provide regular interest payments and return of principal at maturity. They vary in risk, with government bonds considered less risky than corporate or high-yield bonds.

c) Cash and Cash Equivalents: Highly liquid and low-risk assets, including cash, treasury bills, money market funds, and certificates of deposit (CDs). These provide stability but typically offer lower returns compared to other asset classes.

d) Real Estate: Investments in physical properties or real estate investment trusts (REITs). Real estate offers potential for rental income and capital appreciation. It’s considered an inflation hedge and can diversify a portfolio.

e) Commodities: Physical goods like gold, silver, oil, agricultural products, etc. Commodities can act as a hedge against inflation and provide diversification but can be volatile and sensitive to supply and demand factors.

f) Derivatives: Financial instruments derived from underlying assets, such as options, futures, and swaps. Derivatives can be used for hedging, speculation, or leveraging positions. They often involve higher risk due to leverage and complex structures.

g) Foreign Exchange (Forex): Trading currencies in the foreign exchange market. Forex trading involves buying one currency by selling another, aiming to profit from fluctuations in exchange rates.

h) Alternative Investments: These include hedge funds, private equity, venture capital, art, collectibles, cryptocurrencies, and other non-traditional assets. They often have limited liquidity and higher barriers to entry but can provide diversification and uncorrelated returns.

i) Structured Products: Complex financial instruments designed to provide customized risk-return profiles. These might combine elements of various asset classes to suit specific investor preferences.

Q7. What is Efficient Frontier?

The Efficient Frontier is a fundamental concept in modern portfolio theory that illustrates the optimal set of portfolios that offer the highest expected return for a given level of risk or the lowest risk for a given level of expected return. It’s represented graphically as a curve on a graph where the x-axis denotes risk (standard deviation or volatility), and the y-axis represents the expected return.

Key points to remember about Efficient Frontier:

a)     Risk and Return Tradeoff: The Efficient Frontier demonstrates the tradeoff between risk and return. As you move along the curve, you can achieve higher returns, but this generally comes with an increase in risk.

b)    Optimal Portfolio Selection: Portfolios lying on the Efficient Frontier are considered optimal because they offer the highest expected return for a given level of risk or the lowest risk for a given level of expected return. These portfolios are considered efficient because they maximize returns while minimizing risk.

c)     Diversification Benefits: The concept of diversification is integral to the Efficient Frontier. By combining different assets that don’t move in perfect correlation with each other, investors can construct portfolios that optimize returns for a given level of risk or minimize risk for a given level of return.

d)    Rebalancing and Optimization: As market conditions change, the shape and position of the Efficient Frontier may also change. Portfolios need to be periodically rebalanced or optimized to maintain the desired risk-return profile.

Q8. What is Global Minimum Variance Portfolio?

The Global Minimum Variance Portfolio (GMVP) is a concept in portfolio theory that refers to the portfolio with the lowest possible volatility or variance among all possible portfolios comprised of a set of assets. It represents the combination of assets that, when combined in various weights, produces the least amount of overall risk or volatility.

The green point in the above figure represents the Global Minimum Variance Portfolio 

Q9. Define systematic risk and non-systematic risk? What are some examples of it?

Systematic risk, often referred to as market risk, is the risk inherent to the entire market or an entire market segment. It’s not specific to a particular company or industry but affects the overall market. Factors such as interest rate fluctuations, political instability, natural disasters, inflation, and recession are examples of systematic risks. They are unpredictable and can’t be diversified away because they impact the entire market.

Non-systematic risk, also known as unsystematic or specific risk, pertains to risks that are unique to a particular company, industry, or sector. These risks can often be reduced through diversification. Examples of non-systematic risks include company management changes, labor strikes, competitive pressures within an industry, and regulatory changes affecting only specific companies or sectors. Diversification across different assets or industries can help mitigate non-systematic risks as they tend to be specific to certain entities or sectors and can be managed through portfolio diversification.

For instance, if you invest all your money in a single tech company, your investment is highly exposed to the risks associated specifically with that company—like poor management decisions or a product failure. But if you diversify your investments across various industries (such as tech, healthcare, consumer goods), you can reduce the impact of these specific risks on your overall portfolio.

Q10. Explain CAPM Model?

The Capital Asset Pricing Model (CAPM) is a financial model that aims to determine the expected return on an investment based on its risk. It helps in calculating the appropriate expected return for an asset considering its risk compared to the overall market and the risk-free rate.

Here are the key components of the CAPM:

1. Risk-Free Rate: This is the theoretical return on an investment with zero risk, typically approximated using government bonds. It serves as a baseline return that an investor would expect without taking any risk.

2. Market Risk Premium: It represents the additional return expected by investors for taking on the extra risk of investing in the overall market rather than the risk-free asset. It’s calculated as the difference between the expected return of the market and the risk-free rate.

3. Beta (β): Beta measures the volatility or systematic risk of an asset in comparison to the entire market. A beta of 1 means the asset’s price moves in line with the market, less than 1 indicates lower volatility than the market, and greater than 1 signifies higher volatility.

The CAPM formula is:

Expected Return=Risk-Free Rate+(β×Market Risk Premium)

This formula states that the expected return of an asset is the sum of the risk-free rate and a risk premium based on the asset’s beta and the market risk premium.

Q11. What are the assumptions of the CAPM Model?

The following are assumptions made by the CAPM model:

  • CAPM assumes that all investors are rational, risk-averse, and have the same expectations about future investments.
  • CAPM assumes that markets are perfectly efficient, meaning all investors have access to all information simultaneously, and there are no transaction costs.
  • There is unlimited capital to borrow at the risk-free rate of return.
  • Investors have the same time period to evaluate information.
  • Investments can be divided into unlimited pieces and sizes.
  • Investors can take short positions in assets without any restrictions or costs.
  • There are no taxes, inflation, or transaction costs.

Q12. Explain Fama French Three Factor Model?

The Fama-French Three Factor Model is an extension of the Capital Asset Pricing Model (CAPM) that was developed by Eugene Fama and Kenneth French. It aims to provide a more comprehensive explanation of stock returns by considering additional factors beyond the single-factor (market risk) approach of CAPM.

The model introduces two additional factors besides the market factor (as represented by the market return):

· Size (SMB – Small Minus Big):This factor captures the historical tendency of small-cap stocks to outperform large-cap stocks. It calculates the excess returns of a portfolio of small-cap stocks over the returns of a portfolio of large-cap stocks.

· Value (HML – High Minus Low): The value factor captures the historical tendency of value stocks to outperform growth stocks. It calculates the excess returns of a portfolio of high book-to-market (value) stocks over the returns of a portfolio of low book-to-market (growth) stocks.

The Fama-French Three Factor Model’s equation for expected return is:

  • Expected Return Expected Return is the expected return on the asset.
  • Risk-Free Rate Risk-Free Rate is the risk-free rate of return.
  • βMarket is the sensitivity of the asset’s returns to the overall market returns.
  • βSize measures the sensitivity of the asset’s returns to the size factor.
  • βValue measures the sensitivity of the asset’s returns to the value factor.
  • Market Risk Premium is the excess return expected from the market portfolio.

  This model suggests that the returns of a stock can be better explained by considering not only its sensitivity to market movements but also its sensitivity to size and value factors. It acknowledges that small-cap and value stocks have historically exhibited certain return patterns that are not adequately captured by the single-factor CAPM.

Q13. What are some of the measures to evaluate the performance of the portfolio?

There are several measures used to evaluate the performance of a portfolio, each offering insights into different aspects of how well the portfolio is doing. Some key measures include:

1.     Sharpe Ratio: It assesses the risk-adjusted return of a portfolio by considering the excess return (returns above the risk-free rate) per unit of risk (standard deviation). A higher Sharpe Ratio indicates better risk-adjusted performance.

  • Rp is the portfolio’s expected return.
  • Rf is the risk-free rate of return.
  • σp is the standard deviation of the portfolio’s returns.

2. Sortino Ratio is a measure used in finance to evaluate the risk-adjusted
return of an investment or portfolio, similar to the Sharpe Ratio. However,
unlike the Sharpe Ratio that considers total volatility (both upside and
downside), the Sortino Ratio specifically focuses on downside volatility or the
volatility of negative returns.

  • Rp is the portfolio’s expected return.
  • Rf is the risk-free rate of return.
  • σd is the standard deviation of the downside returns, often calculated using returns below a certain threshold (such as the minimum acceptable return or target return).

3. The Treynor Ratio, named after Jack Treynor, is a financial metric used to
evaluate the risk-adjusted performance of an investment or portfolio. It
measures the excess return generated by a portfolio per unit of systematic
risk, represented by beta.

  • Rp is the portfolio’s expected return.
  • Rf is the risk-free rate of return.
  • βp is the portfolio’s beta, which measures the sensitivity of the portfolio’s returns to the overall market returns.

4. Jensen’s Alpha, named after Michael Jensen, is a measure used in finance to assess the risk-adjusted performance of an investment or portfolio. It evaluates the excess return generated by an investment or portfolio compared to its expected return, considering the asset’s level of systematic risk as measured by its beta (from the Capital Asset Pricing Model – CAPM).


  • Rp​ is the actual return of the portfolio.
  • Rf​ is the risk-free rate of return.
  • βp​ is the beta of the portfolio.
  • Rm​ is the market return.

Q14. How does the Sortino Ratio differ from the Sharpe Ratio in evaluating portfolio performance?

The Sortino Ratio and the Sharpe Ratio are both widely used measures for evaluating portfolio performance, but they differ in their approach to assessing risk and their focus on downside volatility.

Here are the primary differences between the Sortino Ratio and the Sharpe Ratio:

Focus on Risk:

  • Sharpe Ratio: Considers total volatility or standard deviation of returns, whether positive or negative, as a measure of risk. It assesses the risk-adjusted return by dividing the excess return over the risk-free rate by the total volatility.
  • Sortino Ratio: Focuses specifically on downside volatility or the standard deviation of negative returns below a certain threshold (often the minimum acceptable return or target return). It emphasizes the risk of negative returns, penalizing the portfolio for downside deviation only.


  • Sharpe Ratio: Measures the risk-adjusted return per unit of total volatility, providing a broader view of the portfolio’s performance.
  • Sortino Ratio: Focuses on the risk-adjusted return per unit of downside volatility, specifically targeting the risk of negative returns.

Investor Preference:

  • Sharpe Ratio: Suitable for investors concerned with both upside and downside risk and seeking a broader view of risk-adjusted performance.
  • Sortino Ratio: More suitable for risk-averse investors primarily concerned with minimizing the risk of negative returns and downside volatility.

Q15. What is Tracking Error? Can you tell the formula for tracking

Tracking Error is a measure used in finance to assess the consistency of a portfolio’s returns compared to those of a chosen benchmark. It quantifies the variability or deviation in performance between the portfolio and its benchmark over a specific period. Essentially, it helps investors and fund managers evaluate how effectively a portfolio mirrors the performance of its benchmark.

In essence, Tracking Error measures the standard deviation of the difference in returns between the portfolio and its benchmark. A low Tracking Error implies that the portfolio closely follows the benchmark, while a higher Tracking Error indicates greater deviation or variability in performance compared to the benchmark.

It’s a crucial metric in evaluating the effectiveness of a portfolio manager’s strategy: lower Tracking Error generally signifies that the manager is closely tracking the benchmark, whereas higher Tracking Error might suggest either intentional deviations due to an active management strategy or potential issues in portfolio management.

The formula for calculating Tracking Error involves taking the square root of the average of the squared differences between the portfolio returns (Rp) and benchmark returns (Rb) over a specified time period n:

Q16.    What is the Modern Portfolio Theory (MPT)?

Modern Portfolio Theory (MPT) is a framework developed by Harry Markowitz in the 1950s that revolves around the idea of constructing an investment portfolio to maximize returns while minimizing risk. At its core, MPT suggests that by diversifying investments, an investor can optimize their portfolio’s expected return for a given level of risk or minimize the risk for a targeted level of return.

Key principles of Modern Portfolio Theory include:

a) Diversification: MPT emphasizes spreading investments across various asset classes (such as stocks, bonds, real estate, etc.) to reduce overall risk. The idea is that when one asset underperforms, others may perform better, thus offsetting potential losses. 

b) Risk vs. Return: MPT quantifies the trade-off between risk and return. Higher expected returns typically come with higher risk. Investors should seek an optimal balance between the two based on their risk tolerance and investment goals.

c) Efficient Frontier: This is a graph that illustrates the maximum expected return achievable for a given level of risk or the minimum risk for a targeted level of return. Portfolios lying on the efficient frontier are considered optimal as they offer the best risk-return trade-off.

d) Asset Allocation: MPT stresses the importance of allocating assets based on their correlation with each other. Ideally, assets in a portfolio should have a low correlation to minimize overall risk.

Q17. What are the assumptions of the Modern Portfolio Theory (MPT)?

Modern Portfolio theory has a certain assumption that is to be considered while making any decisions in order to arrive at the conclusion that risk, return, and diversification relationships hold true. The different assumptions of the modern portfolio theory are as follows:

a) Returns from the assets are distributed normally: MPT assumes that asset returns follow a normal distribution, which implies that extreme events or outliers are rare. However, real market returns often exhibit non-normal distributions with fat tails, suggesting more frequent extreme events than expected. Due to this assumption, various statistical measures like standard deviation or correlation in analysis or portfolio can be used.

b) Rational Investors: The theory assumes that the investor making the investment is rational and will avoid all the unnecessary risk associated. This implies that any decision maker who acts in a rational manner will have the aim of maximising the utility and will evaluate their investments based on the return and risk associated with it. This assumes investors have access to all relevant information and make rational decisions based on this information.

c) Mean-Variance Framework: MPT assumes that investors evaluate portfolios solely based on their expected returns and the standard deviation (or variance) of those returns. This assumes that risk is solely measured by volatility and that investors are risk-averse.

d) Constant Risk and Return: MPT assumes that risk and return expectations for assets remain constant over the investment horizon. This assumption doesn’t account for changes in economic conditions, market dynamics, or shifts in investor sentiment over time.

e) No Taxes, Transaction Costs, or Market Frictions: MPT assumes a frictionless market environment where there are no taxes, transaction costs, or constraints on the market participants. In reality, these factors can significantly impact portfolio performance and management.

Q18. What are the limitations of the Modern Portfolio Theory (MPT)?

Modern Portfolio Theory (MPT) has faced several criticisms over the years, challenging its assumptions and practical implications. Some of the notable criticisms include:

a) Uncertainty and Black Swan Events: MPT assumes a normal distribution of asset returns, failing to adequately address extreme events or “black swan” events—highly unpredictable occurrences with significant impacts, which can lead to substantial losses not accounted for in MPT’s risk models.

b) Assumption of Rationality: MPT assumes that investors are rational and always make decisions based on maximizing returns for a given level of risk. In reality, investors might not always act rationally due to emotions, cognitive biases, or imperfect information, which can lead to deviations from the theory’s predictions.      

c) Failure to Account for Tail Risks: One main criticism of MPT is that portfolios are assessed on variance, rather than downside risk. Quick definition: variance is a measure of volatility (or measure of the dispersion) of returns, over time. MPT doesn’t adequately address tail risks, which are extreme and infrequent events that can have a disproportionate impact on portfolios. These risks might not be captured effectively within MPT’s standard deviation-based risk measures.

d) Correlation and Covariance Estimations: The accuracy of MPT heavily relies on accurate estimates of asset correlations and covariances. Critics argue that these estimations might not hold during turbulent market conditions, leading to unreliable risk assessments and portfolio constructions.

e) Single-Period Analysis: MPT primarily focuses on single-period analysis and assumes that risk and returns are constant over time. In reality, market conditions, risk factors, and returns can fluctuate significantly over different time frames, which challenges the simplistic single-period approach.

f) Efficient Markets Hypothesis Assumption: MPT relies on the Efficient Markets Hypothesis, which posits that asset prices reflect all available information. Critics argue that markets might not always be perfectly efficient, leading to mispricings and inefficiencies that MPT fails to account for adequately.

Q19. What is Arbitrage Pricing Theory (APT)?

Arbitrage Pricing Theory (APT) is an alternative asset pricing theory developed by economist Stephen Ross in the 1970s. APT provides a theoretical framework for understanding the relationship between expected returns on assets and their systematic risk factors.

·     APT assumes that asset returns are determined by multiple factors or sources of systematic risk rather than just one factor, as in the Capital Asset Pricing Model (CAPM).

·  APT does not specify the exact factors that drive asset returns. Instead, it suggests that multiple macroeconomic, industry-specific, or other systematic factors influence asset returns. These factors could include interest rate changes, inflation rates, market volatility, changes in exchange rates, or other economic indicators.

·   APT asserts that the expected return of an asset should be related to its exposure or sensitivity to various risk factors. Assets with higher sensitivity to these factors should command higher expected returns to compensate for the additional risk.

·   APT is often expressed in a mathematical equation that relates the expected return on an asset to its sensitivity to different systematic factors. The equation resembles a linear factor model but doesn’t specify the exact factors or their coefficients.

The APT formula for expected return for an asset i is given by:


In essence, APT aims to explain the relationship between an asset’s expected return and various risk factors by identifying and quantifying the sensitivities of assets to these factors. It provides a framework for understanding asset pricing beyond the constraints of a single market factor, as in the CAPM.

Q20.     What is the role of covariance in Portfolio Theory?

Covariance plays a crucial role in portfolio theory as it measures the degree to which the returns of two assets move together. In portfolio theory, understanding covariance helps in assessing how the returns of different assets co-vary or behave in relation to each other.

Here’s the significance of covariance in portfolio theory:

·  Diversification: Covariance helps in assessing the diversification benefits within a portfolio. Assets with low or negative covariance tend to move independently or in opposite directions, offering greater diversification benefits when combined in a portfolio. Diversification can reduce overall portfolio risk by spreading it across uncorrelated assets.

·    Risk Assessment: Covariance is a measure of the joint variability between two assets. High covariance implies that the returns of the assets move in tandem, increasing the overall risk of the portfolio. It contributes to the overall volatility of the portfolio, affecting its risk profile.

·  Efficient Frontier: When constructing an efficient portfolio using Modern Portfolio Theory, covariance plays a critical role. The efficient frontier represents the set of portfolios that offer the highest expected return for a given level of risk. Covariance influences the shape of the efficient frontier as it determines how different assets interact in terms of risk and return when combined in a portfolio.

Q21.  Explain the concept of diversification in portfolio theory?

Diversification is a fundamental concept in portfolio theory that involves spreading investments across a variety of assets to reduce risk without necessarily sacrificing potential returns. The primary goal of diversification is to create a portfolio where the risks of individual assets are mitigated by combining them with other assets that behave differently under various market conditions.

Key aspects of diversification in portfolio theory include:

·   Risk Reduction: Diversification aims to minimize the overall risk of a portfolio by combining assets with different risk profiles. When assets are chosen carefully and have low correlation or move independently of each other, adverse movements in one asset may be offset by positive movements in another, reducing the impact of individual asset volatility on the overall portfolio.

·  Asset Allocation: Diversification is closely tied to asset allocation, where investors allocate their investments across different asset classes (such as stocks, bonds, real estate, commodities) and within each asset class to different securities or sectors. The mix of these assets and their correlations determine the overall risk and return characteristics of the portfolio.

·  Optimal Risk-Return Tradeoff: Diversification allows investors to seek an optimal balance between risk and return. A well-diversified portfolio aims to achieve the highest possible return for a given level of risk or the lowest possible risk for a target level of return. This aligns with the principles of Modern Portfolio Theory (MPT) developed by Harry Markowitz.

Q22. How can you compute standard deviation of a portfolio having 2

For a portfolio with assets X and Y, the portfolio variance can be calculated as follows:

Portfolio standard deviation will be:

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