Risk and Return Analysis PDF

**[Introduction To Portfolio Management]** [Introduction To Portfolio Management] [Risk and Return] [1- The concept of risk and its types] This section aims to identify the concept of risk and the types of investors in terms of their attitudes towards risk. It also sheds light on the types of r...

**[Introduction To Portfolio Management]** [Introduction To Portfolio Management] [Risk and Return] [1- The concept of risk and its types] This section aims to identify the concept of risk and the types of investors in terms of their attitudes towards risk. It also sheds light on the types of risks, whether in light of the possibility of reducing them through diversification or in light of the possibility of managing them through financial decisions. [1/1- The concept of risk:] Risk is defined as \"The Chance of Loss\", and it is also known as \"The Possibility of Loss\", and it is also known as \"Uncertainty\". It is also defined as \"the dispersion of actual results from expected results\" The presence of risk\" means the possibility of achieving different returns, The presence of risk \"means that the investor is no longer tied to one case of the asset\'s returns, as there are multiple cases, and thus, different returns, expressed in the form of \"probability distributions\". In the same context, risk can be defined as \"the state of the possibility of a negative deviation from the desired, expected or hoped-for returns. In light of the previous definitions, we find that there are two basic trends in\ this regard: the first is limited to the case of a negative deviation of the actual from the expected and the second is expanded to include the deviation of the actual from the expected, whether negative or positive. Although the term is the same in English. Investors\' attitudes towards return and risk differ, as investors want to receive compensation for the risk associated with the investment, and the higher the degree of risk, the higher the rate of return they demand. However, the shape of this direct relationship between return and risk differs according to the attitudes of those continuing towards risk. The following In this regard, investors can be classified into three categories as:\ [Risk-Averters], who are investors who are not willing to pay more than or even equal to the expected return. [Risk-Neutral] investors who are willing to pay equal to the expected return. [Risk-Takers], investors who are willing to pay more than the expected return. [2/1- The Risk and Types of Risk:] Total risks can be divided - in light of the possibility of reducing them through diversification - into two types: Systematic Risk and Unsystematic Risk, where: [1- Systematic risks] are defined as general risks or market risks or non-diversifiable risks, as these risks are related to factors that affect the market as a whole, and thus their impact extends to all companies operating in the market. These general factors are related to variables of fiscal and monetary policy and interest rates, exchange rates, and business cycles. [2- Unsystematic risks] are defined as special risks or company risks or diversifiable risks, as these risks are related to factors that affect a specific company or sector, and thus their impact extends to this company or sector only. These special factors are related to variables such as financial leverage, operating leverage, marketing strategies, and workers\' strikes. [2- The relationship between return and risk] It can be said that the most important relationship in finance is the relationship between return and risk. [Is There a Positive Correlation Between Risk and Return?] Yes, there is a positive correlation (a relationship between two variables in which both move in the same direction) between risk and return. with one important caveat. There is no guarantee that taking greater risk results in a greater return. Rather, taking greater risk may result in the loss of a larger amount of capital. A more correct statement may be that there is a positive correlation between the level of risk and the potential for return. Generally, a lower risk investment has a lower potential for profit. A higher risk investment has a higher potential for profit but also a potential for a greater loss. As models have multiplied have that addressed this relationship. And perhaps the most important of these models is the Capital Asset Pricing Model (CAPM). As this model provides an analysis for the relationship between systematic risks and the required rate of return. And thus, this model does not use total risk. This section focuses on analyzing the relationship between return and risk -- graphically using this model, without addressing the assumptions of the model. This model is mainly concerned with analyzing the relationship between return and risk by describing the relationship between the required rate of return and the \"systematic risk coefficient\". But first it is necessary to analyze and study the [Capital] Market Line to analyze this relationship: [A- Capital Market Line (CML)] CML is limited to analyzing the relationship between return and risk, by describing the relationship between the expected rate of return and the \"standard deviation\" of expected returns. The CML represents the best possible group of portfolio assets that makes the most out of the expected level of returns at a given level of risk (as defined by volatility/ standard deviation). Thus, investors should choose a portfolio with a combination of both risk-free investments and market portfolio. It is noted that when investors have identical expectations the market portfolio and efficient frontier coincides. [What Does the Coefficient of Variation (CV) Tell Investors?] The [coefficient of variation](https://www.investopedia.com/terms/c/coefficientofvariation.asp) (CV) is the ratio of the standard deviation of a data set to the expected mean. Investors use it to determine whether the expected return of the investment is worth the degree of volatility, or the downside risk, that it may experience over time. Dividing the volatility, or risk, of the investment by the [absolute value](https://www.investopedia.com/terms/a/absolute-value.asp) of its expected return determines its CV. An investor can calculate the coefficient of variation to help determine whether an investment\'s expected return is worth the volatility it is likely to experience over time. A lower ratio suggests a more favorable tradeoff between risk and return. A higher ratio might be unacceptable to a conservative or \"risk-averse\" investor. [What Is Variance?] The mean is the mathematical average of a set of two or more numbers. To find an arithmetic mean, add up the numbers in a set and divide by the total quantity of numbers in the set. Variance is a statistical measurement of the spread between numbers in a data set. It measures how far each number in the set is from the [mean](https://www.investopedia.com/terms/m/mean.asp) (average), and thus from every other number in the set. Variance is often depicted by this symbol: σ2. It is used by both analysts and traders to determine [volatility](https://www.investopedia.com/terms/v/volatility.asp) and market stability. The [square root of the variance](https://www.investopedia.com/ask/answers/021215/what-difference-between-standard-deviation-and-variance.asp) is the [standard deviation](https://www.investopedia.com/terms/s/standarddeviation.asp) (SD or σ). Which helps determine the consistency of an investment's [returns](https://www.investopedia.com/terms/r/return.asp) over time. In particular, it measures the degree of dispersion of data around the sample\'s mean. Investors use variance to see how much risk an investment carries and whether it will be profitable. Variance is also used in finance to compare the relative performance of each asset in a portfolio to achieve the best asset allocation. What Is Variance? [First, The Mean] The mean is the mathematical average of a set of two or more numbers. To find an arithmetic mean, add up the numbers in a set and divide by the total quantity of numbers in the set. [The Variance] Variance is a statistical measurement of the spread between numbers in a data set. It measures how far each number in the set is from the mean (average), and thus from every other number in the set. **Variance is often depicted by this symbol: σ^2^** - It is used by both analysts and traders to determine [volatility](https://www.investopedia.com/terms/v/volatility.asp) and market stability. - The [square root of the variance](https://www.investopedia.com/ask/answers/021215/what-difference-between-standard-deviation-and-variance.asp) is the [standard deviation](https://www.investopedia.com/terms/s/standarddeviation.asp) (SD or σ). - Which helps determine the consistency of an investment's [returns](https://www.investopedia.com/terms/r/return.asp) over time. - In particular, it measures the degree of dispersion of data around the sample\'s mean. - Investors use variance to see how much risk an investment carries and whether it will be profitable. - Variance is also used in finance to compare the relative performance of each asset in a portfolio to achieve the best asset allocation. [What Is Standard Deviation?] - Standard deviation is a statistical measurement that looks at how far individual points in a dataset are dispersed from the mean of that set. - If data points are further from the mean, there is a higher deviation within the data set. - It is calculated as the square root of the variance. - Standard deviation, in finance, is often used as a measure of the relative riskiness of an asset. - A volatile stock has a high standard deviation, while the deviation of a stable blue-chip stock is usually rather low. - Standard deviation is also used by businesses to assess risk, manage business operations, and plan cash flows based on seasonal changes and volatility. [What Is Covariance?] - Covariance is a statistical tool that measures the directional relationship between the returns on two assets. - A positive covariance means asset returns move together, while a negative covariance means they move inversely. - Covariance is calculated by analyzing at-return unexpected (standard deviations from the expected return) or multiplying the correlation between the two random variables by the standard deviation of each variable. - covariance is different from the correlation coefficient, a measure of the strength of a correlative relationship. - Covariance is an important tool in modern portfolio theory (MPT) for determining what securities to put in a portfolio. - Risk and volatility can be reduced in a portfolio by pairing assets that have a negative covariance. +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | [** * | | | | | | | | | | *Risk | | | | | | | | | | & | | | | | | | | | | Retur | | | | | | | | | | n | | | | | | | | | | Analy | | | | | | | | | | sis | | | | | | | | | | By]{. | | | | | | | | | | under | | | | | | | | | | line} | | | | | | | | | | | | | | | | | | | | [1- | | | | | | | | | | Using | | | | | | | | | | coeff | | | | | | | | | | icien | | | | | | | | | | t | | | | | | | | | | of | | | | | | | | | | Varia | | | | | | | | | | tion] | | | | | | | | | | {.und | | | | | | | | | | erlin | | | | | | | | | | e} | | | | | | | | | +=======+=======+=======+=======+=======+=======+=======+=======+=======+ | Time | Econo | | | | | | | | | serie | mic | | | | | | | | | s | statu | | | | | | | | | | s | | | | | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 4 | Ṝ | 1 | --- | | | | | | | | = | | --- | | | | | | | | ∑R | | ----- | | | | | | | | --- | | Ṝ | | | | | | | | --- | | = | | | | | | | | ---- | | ∑Rꓑ | | | | | | | | | | --- | | | | | | | | | | --- | | | | | | | | ⴖ | | ----- | | | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | σ^2 | 2 | --- | | | | | | | | ^ = | | --- - | | | | | | | | ∑) | | -- -- | | | | | | | | R- Ṝ | | ----- | | | | | | | | ^2^( | | ----- | | | | | | | | --- | | -- | | | | | | | | --- - | | σ^2 | | | | | | | | -- -- | | ^ = | | | | | | | | ----- | | ∑) | | | | | | | | ----- | | R- Ṝ | | | | | | | | - | | ^2^(ꓑ | | | | | | | | | | --- | | | | | | | | | | --- - | | | | | | | | ⴖ- | | -- -- | | | | | | | | 1 | | ----- | | | | | | | | | | ----- | | | | | | | | | | -- | | | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | | R | ꓑ | Rꓑ | R- Ṝ | ) R- | ) R- | | | | | | | | | Ṝ^2^( | Ṝ^2^( | | | | | | | | | | ꓑ | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | | | | | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | ∑ | | | = Ṝ | | | = | | | | | | | | | | σ^2^ | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 | --- | 3 | --- | | | | | | | | --- | | --- | | | | | | | | ----- | | ----- | | | | | | | | --- | | --- | | | | | | | | σ | | σ | | | | | | | | = | | = | | | | | | | | √ σ^2 | | √ σ^2 | | | | | | | | ^ | | ^ | | | | | | | | --- | | --- | | | | | | | | --- | | --- | | | | | | | | ----- | | ----- | | | | | | | | --- | | --- | | | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 1 | cv | 4 | cv | | | | | | | | = | | = | | | | | | | | Σ | | σ | | | | | | | | --- | | --- | | | | | | | | - --- | | - --- | | | | | | | | --- | | --- | | | | | | | | | | | | | | | | | | | | | | | | | | | | Ṝ | | Ṝ | | | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ [EX-1 (Economic status)] Stock X is expected to achieve a return of 10% with a probability of 20% and a return of 20% with a probability of 80% While stock Y is expected to achieve a return of 12% with a probability of 20% and a return of 17% with a probability of 80% Which one to choose? And why? [1- For the stock] Stock X --------- ----- ----- R.10.20 P.20.80 1 & 2 R ꓑ Rꓑ R- Ṝ ) R- Ṝ^2^( ) R- Ṝ^2^(ꓑ ------- ----- ----- ------ ------ ------------ -------------.10.20.02 -.08.0064.00128.20.80.016.02.0004.00032.18.0016 Σ = Ṝ = σ^2^ σ = √ σ^2^ --- --- -------- = √.0016 =.04 cv = Σ ---- --- ------ Ṝ =.04.018 =.22 [2- For the stock Y] Stock Y --------- ----- ----- R.12.20 P.17.80 1 &2 R ꓑ Rꓑ R- Ṝ ) R- Ṝ^2^( ) R- Ṝ^2^(ꓑ ------ ----- ----- ------- ------ ------------ -------------.12.20.024 -.04.0016.00032.17.80.0126.01.0001.00008.16.0004 Σ = Ṝ = σ^2^ σ = √ σ^2^ --- --- -------- = √.0004 =.02 cv = σ ---- --- ------ Ṝ =.02. 16 =.125 In view of the above we choose the stock Y because it achieves the lowest coefficient of variation. [EX-2 (Time series)] Stock X is expected to achieve a return of 6%,5%,9%,8%At the end of the next four years. The required: 1- risk-return analysis of this stock. 2- do you recommend buying the stock (X) or the stock (y), note that the stock (Y) achieves a return of 10%,11%,13%,14%At the end of the next four years. \-\-\-\-\-\-- [1- risk-return analysis of Stock X: ] N R R- Ṝ ) R- Ṝ^2^( --- ----- ------ ------------ 1.06 -.01.0001 2.05 -.02.0004 3.09.02.0004 4.08.01.0001 ∑.28 \-.001 1- Ṝ **^=^** ∑R **^=^**.28 ,07 ---- --- --------- ---- --------- ----- ----- ⴖ 4 2- σ^2^ **^=^** ∑) R- Ṝ^2^( **^=^**.001.00033 ---- ------ --------- ------------- --------- ------ -------- ⴖ-1 3 ---- --- --------- -------- --------- ------ 3- σ **^=^** √ σ^2^ **^=^**.018 ---- --- --------- -------- --------- ------ 4- cv **^=^** σ **^=^**.018 ,26 ---- ---- --------- --- --------- ------ ----- Ṝ ,07 [2- risk-return analysis of Stock y: ] N R R- Ṝ ) R- Ṝ^2^( --- ----- ------ ------------ 1.10 -.02.0004 2.11 -.01.0001 3.13.01.0001 4.14.02.0004 ∑.48 \-.001 1- Ṝ **^=^** ∑R **^=^**.48 ,12 ---- --- --------- ---- --------- ----- ----- ⴖ 4 2- σ^2^ **^=^** ∑) R- Ṝ^2^( **^=^**.001.00033 ---- ------ --------- ------------- --------- ------ -------- ⴖ-1 3 ---- --- --------- -------- --------- ------ 3- σ **^=^** √ σ^2^ **^=^**.018 ---- --- --------- -------- --------- ------ 4- cv **^=^** σ **^=^**.018 ,15 ---- ---- --------- --- --------- ------ ----- Ṝ ,12 In view of the above we choose the stock Y because it achieves the lowest coefficient of variation.