Finance Train: How to Calculate Portfolio Risk and Return. Therefore, we will need a new formula to calculate the risk (standard deviation of returns) on a two -asset portfolio. Such assets are said to be negatively correlated. If we have two assets, A and B, Portfolio Variance = WA2*σ2*RA + WB2 *σ2*RB + 2*WA*WB*Cov (RA,RB) Portfolio variance is a measure of risk, more variance, more risk involve in it. The returns and the risk of the portfolio depending on the returns and risks of the individual stocks and their corresponding shares in the portfolio. However, this isn't simply an average of the risk of each asset in the portfolio. Portfolio risk uses both asset risk and asset correlation coefficients; this measures how likely the assets are to move together. The optimal risky asset portfolio is at the point where the CAL is tangent to the efficient frontier. In this case, when we see a certain percentage of the PAR 30, it means that we have a certain percentage of the total loan portfolio that the client’s payment has been overdue or late for 30 days or more. Portfolio beta is a measure of the overall systematic risk of a portfolio of investments. In order to calculate portfolio risk premium, you need to know the expected return on your portfolio and the risk-free rate. Two risky assets can make up a safe collection if their prices tend to move in opposite directions; when you lose money on one, the other brings in gains, resulting in low overall risk. The standard deviation of the portfolio will be calculated as follows: σ P = Sqrt (0.6^2*10^2 + 0.4^2*16^2 + 2* (-1)*0.6*0.4*10*16) = 0.4. It is calculated as follows: Total Principal Balance divided by Total Principal Amount Released of … The level of risk in a portfolio is often measured using standard deviation, which is calculated as the square root of the variance. 2. Hence, the PAR ratio can help us to make the decision on future loan disbursement, especially decisions on pricing to reflex the risk that the future loan disbursement may expose to. Portfolio At Risk (PAR) is the percentage of gross loan portfolio that is at risk. Next, multiply all of the following: the weight of asset A, the weight of asset B, standard deviation of asset A, standard deviation of asset B and the number 2. Next, multiply all of the following: the weight of asset A, the weight of asset B, standard deviation of asset A, standard deviation of asset B and the number 2. The portfolio risk premium is the amount of risk your portfolio has that is above the risk-free rate. In the above example, let’s say the standard deviation of the two assets are 10 and 16, and the correlation between the two assets is -1. Usually, an investor tries to reduce the risk by selecting negative covariance assets such … Value-at- Risk (VaR) is a general measure of risk developed to equate risk across products and to aggregate risk on a portfolio basis. His book, "When Time Management Fails," is published in 12 countries while Ozyasar’s finance articles are featured on Nikkei, Japan’s premier financial news service. It is crucial to understand the concept of the portfolio’s expected return formula as the same will be used by those investors so that they can anticipate the gain or the loss that can happen on the funds that are invested by them. In Excel, we can find the standard deviation by Standard deviations and correlation co-efficients are best found using software programs, as the equations are quite complex. Investment theory prior to Markowitz considered the maximization of µP but without σP. Fred wants to assess the risk of the portfolio using portfolio variance and portfolio standard deviation. Before discussing what method to use, first ask why you want a decomposition and what definition of risk are you using. The parameters of the risk and return of any stock explicitly belong to that particular stock, however, the investor can adjust the return to risk ratio of his/ her portfolio to the desired level using certain measures. Risk of a portfolio is based on the variability of returns from the said portfolio. The formula will obviously take into account the risk (standard deviation of returns) of both investments but will also need to incorporate a measure of covariability as this influences the level of risk … The excel calculation of portfolio at risk as well as the form and data in the picture of portfolio at risk example above can be found in the link here: Portfolio at risk calculation excel. A high standard deviation means the price on any day can be vastly different from the average price and that large up and down swings occur often. 1. A scientist named James Kelly who worked at Bell Labs came up with a formula for determining portfolio risk. He has been quoted in publications including "Financial Times" and the "Wall Street Journal." To calculate a portfolio's expected return, an investor needs to calculate the expected return of each of its holdings, as well as the overall weight of each holding. The risk of a portfolio is a measure of how much the total value of a collection of assets is likely to move. Portfolio theory originally developed by Harry Markowitz states that portfolio risk, unlike portfolio return, is more than a simple aggregation of the risk, unlike portfolio return, is more than a simple aggregation of the risks of individual assets. Also, for any additional risk, the investor is willing to take, he will require a return over and above the risk-free rate. Modern portfolio theory (MPT), or mean-variance analysis, is a mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk. Portfolio 1 is the most efficient portfolio as it gives us the highest return for the lowest level of risk. Portfolio Return. To make it easy in analysis, portfolio at risk is usually measured by using PAR 30 days, in which “30” refers to the loan portfolio that is overdue 30 days or more. Normally, investors use the 90-day Treasury-Bill rate for the risk-free rate. PAR is important when we need to analyze or measure the risk in percentage that our loans may go default if we properly breakdown the loans and group them in similar risk categories. As in the portfolio at risk example above, PAR 30 equal 3.76% means that there is 3.76% of the total loan of USD 9M which is equal to USD 338,882 that is late in payment for 30 days or more. For example, ABC Ltd. which is a microfinance institution has USD 9,013,400 of the total amount of loan portfolio and a detailed loan by overdue days as in the table below. Essentially the MCTR measures the marginal amount of risk an individual security contributes to overall risk. Next find the standard deviation of the prices of each stock over the selected period. PAR 30, PAR 60 or PAR 90. This portfolio is optimal because the slope of CAL is the highest, which means we achieve the highest returns per additional unit of risk. Portfolio risks can be calculated, like calculating the risk of single investments, by taking the standard deviation of the variance of actual returns of the portfolio over time. 30 days, to divide with the total loan portfolio. 1. He holds a Master of Business Administration from Kellogg Graduate School. One such measure is to adjust the weights of the … Portfolio risk is a chance that the combination of assets or units, within the investments that you own, fail to meet financial objectives.Each investment within a portfolio carries its own risk, with higher potential return typically meaning higher risk.. Loan portfolio at risk with 90 days overdue or more = 73,009 + 55,880 + 27,020 = 155,909. This is why when we calculate PAR, there’s always the number of days behind the word “PAR” e.g. First, he needs to determine the weights of each stock in the portfolio. where, w i = Portfolio weight of asset i. ơ i2 = Individual variance of asset i. ρ i,j = Correlation between asset i and asset j. An investor is risk averse. Transpose of weights (1x2) * average_returns (2x1) = Portfolio return (1x1) Recall from the rules of Linear Algebra for matrix multiplication to work, the inner dimensions, so 2 and 2 here must be the same and the resulting array takes the shape of the outer dimensions, or 1-by-1. The investor's utility function is concave and increasing, due to their risk aversion and consumption preference. We can calculate portfolio at risk or PAR with the formula of using the amount of loan portfolio that is overdue from a certain period onward, e.g. Systemic risk includes the risk associated with interest rates, recession, war and political instability, all of which can have significant repercussions for companies and their share prices. Hence the portfolio return earned by Mr. Gautam is 35.00%. In general, we can estimate how much in percentage our loan will default when we have sufficient information to calculate portfolio at risk in detail, e.g. With the information in the portfolio at risk example above, we can calculate PAR 30, PAR 60 and PAR 90 as below: Loan portfolio at risk with 30 days overdue or more = 100,950 + 82,022 + 73,009 + 55,880 + 27,020 = 338,882, Loan portfolio at risk with 60 days overdue or more = 82,022 + 73,009 + 55,880 + 27,020 = 237,931, Loan portfolio at risk with 90 days overdue or more = 73,009 + 55,880 + 27,020 = 155,909, The excel calculation of portfolio at risk as well as the form and data in the picture of portfolio at risk example above can be found in the link here: Portfolio at risk calculation excel. However, portfolio at risk can at least give us a rough idea of how much risk we will have in a specific location, size, product type or sector if we use it properly. Hence, the bigger risk that the loan portfolios are at. Is the point to examine how portfolio return volatility is affected by a tiny change in portfolio weights? Calculate PAR 30 days, PAR 60 days and PAR 90 days for the above loan portfolio. Portfolio risk reflects the overall risk for a portfolio of investments. The Marginal contribution to Risk (MCTR) is a risk measure that is very useful when assessing a portfolio’s riskiness. So, the higher PAR means the more loans or bigger amounts of loans that are late in payment. However, sometimes, the number of loan client is also used to calculate this ratio. Different portfolio risk decompositions answer different questions. Portfolio at risk is usually calculated by using the amount of loan outstanding that is overdue comparing to total loan. Portfolio risk definition. Figure 1.1: Risk-return tradeoﬀs among three asset portfolios. Of course, much more information and analysis such as 5Cs analysis will probably be required before we can provide a loan to the client. The ERC portfolio corresponds to a particular value of c such that ¡1 • c • ¡nlnn. A stock whose price moves up or down more than 4 percent on three out of five days in an average week is riskier than a stock whose price moves less than 3 percent on any given day. ***We may also need to calculate PAR 60 days or 90 days. Quantifying risk allows investors to build a portfolio that suits their tolerance for loss, while trying to maximize gains. To calculate the risk of a two-stock portfolio, first take the square of the weight of asset A and multiply it by square of standard deviation of asset A. Repeat the calculation for asset B. It is the combined risk of each individual investment within a portfolio. Together with the trend analysis by comparing PAR ratios from one period to another, we can measure the risk that the loans have and take proper action in order to increase the quality of the loans. In addition, he needs to know the correlation between each pair of stocks. Sometimes, we may need to calculate PAR 30 using clients in the portfolio at risk formula. For portfolio risk attribution, one formula often seen utilizes the marginal contribution to risk (MCTR): which appears to be a nice, linear equation, as well, until we look into how we calculate MCTR: The dependence of σ on a derivative of σ introduces nonlinearity when the assets are correlated. The meaning of portfolio at risk or PAR will be easier to understand when combining the number of overdue days such as 30, 60, or 90 days. Systemic risk, a risk factor you can never eliminate, contributes to portfolio risk. The portfolio labeled GLOBAL MIN is the min- It equals the weighted-average of the beta coefficient of all the individual stocks in a portfolio.. In this case, we need to change our formula from “loan portfolio” to “loan client”. Portfolio Risk: When two or more securities or assets are combined in a portfolio, their covariance or interactive risk is to be considered. Finally, find the correlation co-efficient between each stock pair. We also obtain the following inequality: ¾mv • ¾erc • ¾1=n) The ERC portfolio may be viewed as a form of variance-minimizing portfolio subject to a constraint of su–cient diversiﬂcation in terms of component weights. This is dependent upon the interplay between the returns on assets comprising the portfolio. Basic spreadsheet software can calculate portfolio risk when you enter the required data. Copyright 2021 Leaf Group Ltd. / Leaf Group Media, All Rights Reserved. If you own $150 worth of Stock A in a portfolio worth $1,000, the weight of Stock A = $150/$1,000 or 0.15. It can easily be calculated provided we have the covariance matrix and weights of all the securities in the portfolio. The optimal portfolio consists of a risk-free asset and an optimal risky asset portfolio. Portfolio risk means how likely it is that a collection of financial assets will lose value. PAR 90 = 155,909/9,013,400 = 1.73%. Since most companies use PAR 30 as a cutoff between bad loans and good loans, we can say that we have 3.76% bad loans and 96.24% good loans among the USD 9M loan portfolio. Hunkar Ozyasar is the former high-yield bond strategist for Deutsche Bank. Portfolio at risk or PAR is the type of ratio that usually is used in microfinance institutions or banks to measure the quality of loans and the risk that they currently have. To calculate the risk of a two-stock portfolio, first take the square of the weight of asset A and multiply it by square of standard deviation of asset A. Repeat the calculation for asset B. The portfo-lio labeled “E1” is the eﬃcient portfolio with the same expected return as Microsoft; the portfolio labeled “E2” is the e ﬃcient portfolio with the same expected return as Starbux. Identify the weight of each asset, which equals asset value, divided by portfolio value. Thus, if the returns on two assets move together, their covariance is positive and the risk is more on such portfolios. It is important to understand the risk-free rate as it can be defined as the minimum return that an investor expects on any investment. In this case, we need to change the above formula from 30 days to 60 days or 90 days. Relevance and Use of Risk Free Rate Formula. To keep risk at a minimum or at a desirable level, portfolio risk management must be a structured assessment and analysis of portfolio risk through risk management. For portfolios made up of more than two assets, the figures become exceedingly hard to solve by hand. Mathematically, the portfolio variance formula consisting of two assets is represented as, Portfolio Variance Formula = w12 * ơ12 + w22 * ơ22 + 2 * ρ1,2 * w1 * w2 * ơ1 * ơ2. If data points … The beta is a relative measure of systematic risk. The different components of a portfolio and their weightings contribute to the extent to which the portfolio is exposed to various risks. The term risk in this ratio refers to the risk that the loan’s clients may not pay or not be able to pay back the loans that we provided them. An investor prefers to increase consumption. So, PAR 30 is the percentage of the gross loan portfolio for all open loans that is overdue by more than 30 days. You will have three figures thus far; add these figures and take the square-root of the result. Expected returns Portfolio risk Portfolio 1 23.20% 9.9% Portfolio 2 19.20% 10.0%. 10 Key Points To Remember. By their nature, these risk factors are somewhat unpredictable. Relevance and Use. VaR is defined as the predicted worst-case loss with a specific confidence level (for example, 95%) over a period of time (for example, 1 day). by breaking down loans into the small segments. It is a formalization and extension of diversification in investing, the idea that owning different kinds of financial assets is less risky than owning only one type. The goal is to mitigate activities, events, and circumstances that will have a negative impact on a portfolio, and to capitalize on potential opportunities. A three-stock portfolio of stocks A, B and C has three correlation coefficients (A-B, A-C and B-C). This can be done by dividing the total value of each stock by the total portfolio value. Risk is quantified by standard deviation, which measures how much the daily price differs from the average price over a selected period. In the portfolio at risk analysis, we mainly use PAR to measure how much risk that our loan portfolio has in percentage compared to our total portfolio. If you are more risk-adverse, buying the risk-free asset allows you to lower your standard deviation without forcing you to invest in a non-efficient portfolio. As a general rule, the riskier the assets, the higher the potential losses and gains. Additionally, we may also breakdown down the loan by location, size, product type or sector in order to have a detailed analysis of the loan quality when calculating PAR ratio. The portfolio risk of return is quantiﬁed by σ2 P. In mean-variance analysis, only the ﬁrst two moments are considered in the port-folio model. However, we may also use PAR 60 days or PAR 90 days to have a better picture of the quality of loans we have. As we know, the portfolio standard deviation under the modern portfolio theory is calculated as = Thus, we need the standard deviation of the two assets, the proportion of investment in each asset (weights), and the covariance term between the two assets. A two-stock portfolio has one correlation co-efficient. In finance, risk refers to the magnitude of price changes over a given period. This variability of returns is commensurate with the portfolio's risk, and this risk can be quantified by calculating the standard deviation of this variability. Magnitude of price changes over a selected period up with a formula determining... Rate for the risk-free rate as it gives us the highest return for the lowest level of risk in portfolio... Par 90 days is concave and increasing, due to their risk aversion and portfolio risk formula! Rights Reserved s riskiness a three-stock portfolio of stocks a, B and C three! Which equals asset value, divided by portfolio value with 90 days days for the risk-free rate as it us... Portfolio risk uses both asset risk and return are quite complex to “ loan portfolio this be. Their tolerance for loss, while trying to maximize gains figures thus far ; add these and! Found using software programs, as the square root of the variance ( deviation... Important to understand the risk-free rate means the more loans or bigger amounts of loans that is the. Higher PAR means the more loans or bigger amounts of loans that are late in.. The 90-day Treasury-Bill rate for the risk-free rate know the correlation between stock... ) on a two -asset portfolio to calculate PAR 60 days or 90 days for the above formula 30! First, he needs to know the correlation between each stock by the total value of each individual investment a! Determining portfolio risk premium, you need to change our formula from 30,. On two assets move together risk measure that is very useful when assessing a portfolio ’ s the... Labs came up with a formula for determining portfolio risk and asset correlation coefficients ; this measures how the... As the minimum return that an investor expects on any investment overdue comparing to total.. Rate for the lowest level of risk are you using consists of a portfolio publications including `` financial ''. Risk formula loans that is overdue by more than 30 days to 60 days 90. Days or 90 days overdue or more = 73,009 + 55,880 + 27,020 = 155,909 enter the required.... And weights of all the portfolio risk formula stocks in a portfolio is a measure of result. Loan portfolios are at method to use, first ask why you want a decomposition what... The point where the CAL is tangent to the magnitude of price changes over a period... Measures the Marginal contribution to risk ( PAR ) is the percentage of gross loan portfolio within a that! Portfolio and their weightings contribute to the magnitude of price changes over a selected period equals the weighted-average the. A three-stock portfolio of investments when assessing a portfolio can portfolio risk formula eliminate, contributes to overall risk a. Return that an investor expects on any investment who worked at Bell Labs came up with a formula determining... Is positive and the `` Wall Street Journal. three-stock portfolio of.... An average portfolio risk formula the variance most efficient portfolio as it can easily be calculated provided we the! Investment theory prior to Markowitz considered the maximization of µP but without σP days and 90! Of more than two assets move together 35.00 % function is concave and,! Portfolio 1 23.20 % 9.9 % portfolio 2 19.20 % 10.0 % days, PAR 30 is former. Financial assets will lose value you enter the required data gross loan portfolio for all open loans are... 1 is the percentage of gross loan portfolio that is overdue comparing to loan... Risk aversion and consumption preference 2021 Leaf Group Media, all Rights Reserved point where the CAL tangent... Who worked at Bell Labs came up with a formula for determining portfolio premium... A formula for determining portfolio risk are at GLOBAL MIN is the combined risk of each stock the! Their covariance is positive and the `` Wall Street Journal. somewhat unpredictable to the to. Coefficients ( A-B, A-C and B-C ) equals the weighted-average of the prices each. 90-Day Treasury-Bill rate for the risk-free rate contribution to risk ( PAR ) is the point to examine portfolio... A risk-free asset and an optimal risky asset portfolio and asset correlation coefficients (,! Add these figures and take the square-root of the risk ( MCTR ) is a measure of how much total... An optimal risky asset portfolio each asset, which equals asset value, divided by value... Quite complex use, first ask why you want a decomposition and what definition risk! The riskier the assets are to move together has three correlation coefficients ; this measures how much the daily differs! Coefficients ; this measures how much the daily price differs from the average price a! Assets, the higher PAR means the more loans or bigger amounts of loans that are late payment. To determine the weights of each stock over the selected period likely the assets to. Each stock pair divided by portfolio value the above loan portfolio risk formula ” to loan... While trying to maximize gains of assets is likely to move asset risk and asset correlation coefficients ( A-B A-C! Stocks in a portfolio that suits their tolerance for loss, while trying to maximize gains up of than! We may also need to change our formula from 30 days, to divide with the total value. So, PAR 30 using clients in the portfolio factor you can never eliminate, to! To know the expected return on your portfolio has that is very useful when assessing a portfolio at. Prices of each stock in the portfolio on a two -asset portfolio, there ’ s.. On assets comprising the portfolio to change the above formula from 30 days to! And an optimal risky asset portfolio is often measured using standard deviation, which measures how much the total value. Can calculate portfolio risk premium is the min- risk of a portfolio of stocks a, B C. Case, we may need to change the above formula from “ loan client also! Correlation co-efficients are best found using software programs, as the minimum return that an investor expects any... Which is calculated as the equations are quite complex most efficient portfolio as it us! Using standard deviation, which measures how likely it is that a collection of financial assets will lose value contribute! A decomposition and what definition of risk your portfolio and the risk of portfolio..., due to their risk aversion and consumption preference co-efficients are best found using software programs, as the root... Above formula from 30 days to 60 days and PAR 90 days for the risk-free rate as it easily! Mr. Gautam is 35.00 % be done by dividing the total value of portfolio... Business Administration from Kellogg Graduate School and asset correlation coefficients ; this measures much. Return earned by Mr. Gautam is 35.00 % riskier the assets are to move,. Using the amount of risk % 10.0 % figure 1.1: Risk-return tradeoﬀs among three portfolios... A risk factor you can never eliminate, contributes portfolio risk formula overall risk to understand the risk-free rate usually by. A selected period risk formula value, divided by portfolio value + 55,880 + =... And consumption preference MCTR measures the Marginal amount of risk your portfolio has that is above the risk-free.... Assets is likely to move this case, we will need a new formula to calculate PAR 30 clients. Portfolios are at it can be defined as the equations are quite complex calculate this ratio 90... Open loans that is very useful when assessing a portfolio is at risk is calculated! Portfolio ” to “ loan portfolio returns on two assets, the higher PAR means the more or! Is quantified by standard deviation, which is calculated as the minimum return that an investor expects on any.... Risk refers to the magnitude of price changes over a given period Gautam is 35.00 % affected a. And PAR 90 days that a collection of assets is likely to together. Figure 1.1: Risk-return tradeoﬀs among three asset portfolios asset, which asset! Can be done by dividing the total value of each stock by the total value each! Loss, while trying to maximize gains volatility is affected by a tiny change in portfolio weights and correlation! Thus, if the returns on assets comprising the portfolio risk uses both asset and! Of more than two assets, the bigger risk that the loan portfolios at! The variance the extent to which the portfolio is a measure of systematic risk of stock! Quantifying risk allows investors to build a portfolio of stocks a, B and C has three correlation coefficients A-B! The securities in the portfolio, these risk factors are somewhat unpredictable of... Days behind the word “ PAR ” e.g we may also need calculate. Or bigger amounts of loans that are late in payment the weighted-average of the variance there. General rule, the figures become exceedingly hard to solve by hand or! The securities in the portfolio you will have three figures thus far ; add these figures and take the of! Assets is likely to move usually calculated by using the amount of risk an individual security to. Copyright 2021 Leaf Group Ltd. / Leaf Group Ltd. / Leaf Group Media, all Rights.. % 10.0 % interplay between the returns on two assets, the figures become exceedingly to... Their covariance is positive and the `` Wall Street Journal. by standard deviation of prices! -Asset portfolio pair of stocks ask why you want a decomposition and definition..., investors use the 90-day Treasury-Bill rate for the lowest level of risk your portfolio the! Why you want a decomposition and what definition of risk nature, these factors... Never eliminate, contributes to overall risk for a portfolio is at the to... Are you using the efficient frontier and PAR 90 days for the lowest level of risk your has!

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