Variance of a portfolio with n assets Excel

Portfolio Variance Formula (example) How to Calculate

  1. Step 4: Finally, the portfolio variance formula of two assets is derived based on a weighted average of individual variance and mutual covariance, as shown below. Portfolio Variance formula = w 1 * ơ 1 2 + w 2 * ơ 2 2 + 2 * ρ 1,2 * w 1 * w 2 * ơ 1 * ơ 2. Example of Portfolio Variance Formula (with Excel Template
  2. imizes the standard deviation of the portfolio while maintaining the desired return.A series of sample stocks are included, but the spreadsheet can be adapted to other stocks selections
  3. O (2): The standard deviation of the second asset in the portfolio squared. Q(1,2): The correlation between the two assets in the portfolio has been denoted as q (1,2). Examples of Portfolio Variance Formula (With Excel Template) Let's take an example to understand the calculation of Portfolio Variance Formula in a better manner
Investment Style of Portfolio Management: Excel Applications

This video discusses the Global Minimum Variance Portfolio (GMVP) and how to construct it in excel. This example applies to a portfolio with any number of as.. The covariance matrix is utilized in modern portfolio theory in the estimation of risks. The measures of the covariance matrix are used in anticipating the returns on the financial assets. Examples of Covariance Matrix in Excel. Given below are some of the examples to use the covariance matrix in excel Formula for Portfolio Variance. The variance for a portfolio consisting of two assets is calculated using the following formula: Where: w i - the weight of the ith asset; σ i 2 - the variance of the ith asset; Cov 1,2 - the covariance between assets 1 and 2 . Note that covariance and correlation are mathematically related #portfolioanalysisOptimizing a portfolio of multiple assets in Excel using Solver. #portfolioanalysisOptimizing a portfolio of multiple assets in Excel using Solver

Mean-Variance Portfolio Optimization with Exce

Review - Discuss why Linear Algebra is the preferred method for calculating portfolio return and risk.; Returns - Calculate portfolio return using array math.; Risk - Find three measures of portfolio risk after creating a covariance matrix with arrays in Excel.; Looking forward - See how we move forward to make the process less theoretical and more practical #portfolioanalysi

(Download excel file: http://www.codible.com/pages/85) Compute the minimum variance of a two-stock portfolio using Excel Solver.Some good books on Excel and. Expected portfolio variance= SQRT (W T * (Covariance Matrix) * W) The above equation gives us the standard deviation of a portfolio, in other words, the risk associated with a portfolio. In this equation, ' W ' is the weights that signify the capital allocation and the covariance matrix signifies the interdependence of each stock on the other the global minimum variance portfolio with no short sales and the highest single asset expected return • Solve the Markowitz algorithm with no-short sales for each target expected return in the grid • Test to see if feasible solutions exist for target expected returns above the highest single asset expected retur

Chapter 2: The Mean-Variance Approach of Portfolio Optimization The mean-variance portfolio optimization method was one of the foundations of portfolio selection modelling recommended by Markowitz along with the concept of diversification and the efficient frontier of a portfolio.8 In order to understand the mean-variance approach of portfolio. important to solve, for any given set of n assets (with given rates of return, variances and covariances), the weights corresponding to the minimum-variance portfolio. We start on this problem next. 1.3 Minimal variance when n = 2 When n = 2 the weights can be described by one number α where α 1 = α and α 2 = 1 − α

Summary Mean-Variance optimization can be profitably applied to portfolio management. An Excel spreadsheet for optimization of portfolios with three assets is freely available from the author for. Similarly, we can create a function for a portfolio with n number of assets where there are n number of terms of products of squared asset weighted and variances and n(n-1)/2 number of covariance terms. A better way is to use the variance-covariance matrix to find portfolio variance. Exampl I'm currently implementing a CAPM model in Excel: A portfolio of n risky assets when n=6 (in this case) A riskless borrowing rate of 8% and riskless lending rate of 3%; I'm given the expected return and standard deviation for each risky asset. The first task was to create a minimum variance portfolio

Portfolio Variance Formula How to Calculate Portfolio

Minimum Variance Portfolio in Excel: Multi-asset case

Analytical Approach to Calculating VaR (Variance

Covariance Matrix in Excel Step By Step Guide (with

But Did You Check eBay? Check Out Buy Portfolio On eBay. Looking For Great Deals On Buy Portfolio? From Everything To The Very Thing. All On eBay Variance is a measurement of the spread between numbers in a data set. The variance measures how far each number in the set is from the mean. Using a data set chart, we can observe what the linear. The global minimum variance portfolio (GMV portfolio), is the portfolio with the lowest possible standard deviation (risk) out of all possible levels of expected return. The investor can use the Efficient frontier of Portfolio excel formula to get a combination of assets that has the optimal level of expected return for a given level of.

Portfolio Variance - Definition, Formula, and Exampl

Note that this graph was created with just two assets in the portfolio. The efficient frontier can be created using multiple assets. This frontier represents all the feasible portfolio combinations that one can create. There is also a minimum variance portfolio (MVP) for which there is minimum risk Preface vii Preface For more than 20 years, since the emergence of PCs, Lotus 1-2-3, and Microsoft Excel in the 1980's, spreadsheet models have been the dominant vehicles fo This Excel spreadsheet will calculate the optimum investment weights in a portfolio of three stocks by maximizing the Sharpe Ratio of the portfolio.. This is known as the Sharpe Optimal Portfolio.Sample investment returns for the three stocks are provided, but the spreadsheet can be easily adapted to other stocks and a larger investment space 6 Minimum Variance Portfolio of Two Assets The minimum variance portfolio achieves the lowest variance, regardless of expected return. For two assets, it is easy to solve for the minimum variance portfolio. (We shall see that it is also easy to solve for the minimum variance portfolio for the general case.) From the two-asset portfolio variance.

Portfolio of four assets: Optimization with Solver - YouTub

Due to complex correlatio n patterns between individual assets, portfolio optimization is a key idea in investing. Mean-variance model as a good o ptimizer can exploit the correlation, the. Question 1: Markowitz Mean-Variance Optimization. The basic problem is to maximize expected return, w′E, where w is an (n x 1) (rows x colums) vector of portfolio weights and E is an (n x 1) vector of expected returns on n assets, subject to at least two constraints. [Remember w′ takes a (n x 1) vector and transposes it into a (1 x n) vector. When assets are held as part of a portfolio, an important consideration is the amount of co-movement between portfolio components. Portfolio Analysis the same value as the population variance returned by the Excel VARP function shown in figure 1 cell G28. Fig 5: Variance covariance matrix - ATP and COVAR version The return is associated with a portfolio of weightages (asset-allocation) to help decide investment strategies. The optimization strategy that will be used in this analysis is Modern Portfolio Theory (Markowitz, 1952), commonly known as Mean Variance Optimization (MVO) introduced by Harry Markowitz in 1952 7.12 The N Asset Case. For an N asset portfolio, the portfolio return is just the sum of the asset returns times the weights each of the assets has in the portfolio. In matrix notation, this is just the product: r p = w' r (Eq 3) w is a vector containing the respective weights of the N assets

Portfolio Choice: n Risky Assets and a Riskless Asset XIII. Additional Readings Buzz Words: Minimum Variance Portfolio, Mean Variance Efficient Frontier, Diversifiable (Nonsystematic) Risk, Nondiversifiable (Systematic) Risk, Mutual Funds Asset (portfolio) A mean-variance dominates asset (portfolio) Basset (portfolio) B if μ A ≥μ B and σ A < σΒ or if μ A >μ B while σ A ≤σ B. • Effi i t f tiEfficient frontier: lifllloci of all non-ditddominated portfolios in the mean-standard deviation space. B d fi iti ( ti l)By definition, no (rational) mean-variance

Calculate the standard deviation of each security in the portfolio. First we need to calculate the standard deviation of each security in the portfolio. You can use a calculator or the Excel function to calculate that. Let's say there are 2 securities in the portfolio whose standard deviations are 10% and 15% * Portfolio Variance in the 2-asset case We have: Hence: * Covariance Between Two Portfolios (Matrix Form) Define w1 as the (vertical) vector of weights on the different assets in portfolio P1. Define w2 as the (vertical) vector of weights on the different assets in portfolio P2 Portfolio Optimization also known as 'Optimal Asset Allocation' is a part of the 'Modern Portfolio Theory (MPT)' by Harry Markowitz. It aims at creating a balanced portfolio that will yield the maximum possible return while maintaining the amount of risk that the investor is willing to carry where \(w\) refers to the set of weights for the portfolio assets, \(\sum\) is the covariance matrix of the assets, \(\mu\) is the expected asset returns and \(\mu_t\) represents the target portfolio return of the investor. Note that this represents a very basic (and a specific) use-case of portfolio allocation where the investor wants to minimse the portfolio risk for a given target return Page 6 of 20 The variance of a portfolio not only depends on the variance of the assets but also upon the covariance of any two assets, this is how closely the returns on every two assets in the portfolio move with respect to each other, this is mainly due to the fact that financial markets interact, meaning that the investments do not vary.

Variance Covariance Method - Examples Example 1 - Two Asset Portfolio It is easy from there to expand the calculation to a portfolio of n assets. But be aware that you will soon reach the limits of Excel as we will have to calculate n(n-1)/2 terms for your covariance matrix. Previous Lesso N-asset diversification Selecting an optimal portfolio from N>2 assets An optimizer (using quadratic programming) is used to identifying the set of permissible optimal portfolios. Given the efficient frontier (EF), selecting an optimal portfolio for an investor who are allowed to invest in a combination of N risky assets is rather straightforward The mean-variance portfolio optimization problem is formulated as: min w 1 2 w0w (2) subject to w0 = p 0be the vector of portfolio weights on the nrisky assets so that 1 P n i=1 w iis the weight on the risk-free security. An investor's portfolio optimization problem may then be formulated as min w 1 2 w0w (3 Portfolio Variance. Any investor can benefit from diversifying his portfolio with assets that are not perfectly correlated. The portfolio variance reduces as the correlation among assets decreases Two-asset portfolio Consider two assets with known means R1 and R2, variances ¾12 and ¾2 2, of the expected rates of returns R1 and R2, together with the correlation coe-cient ‰. Let 1 ¡ fi and fi be the weights of assets 1 and 2 in this two-asset portfolio. Portfolio mean: RP = (1 ¡ fi)R1 + fiR2;0 • fi • 1 Portfolio variance: ¾2 P = (1 ¡ fi)2¾2 1 + 2‰fi(1 ¡ fi)¾1¾2.

PPT - Portfolio Construction PowerPoint Presentation, free

To calculate the variance of a portfolio with two assets, multiply the square of the weighting of the first asset by the variance of the asset and add it to the square of the weight of the second. Part 3: Many-asset portfolio • The last section was concerned with a two asset portfolio. • In general, we don't want to restrict our portfolios to two assets. • Thus, in this section, we consider the variance generalized to a many-asset portfolio. Learning objectives for Part 3 Multi-asset portfolio • To appreciate why the portfolio formula should be a summation of all covariance

assets, also providing the Risk-Return Trade-off measure, graphing the portfolio possibilities frontier, and calculating the weights for the Minimum-Variance portfolio. II System Requirements Portfolio Builder 1.1 runs as MS Excel spreadsheet, but would not run if the security level is hig Variance is a measurement of the spread between numbers in a data set. Investors use the variance equation to evaluate a portfolio's asset allocation According to standard portfolio theory, the tangency portfolio is the only efficient stock portfolio. However, empirical studies show that an investment in the global minimum variance portfolio. Excel has a variance function, Mean-variance analysis enables investors to construct a portfolio of assets that maximizes expected return for a given level of risk. In this framework, risk is. From the perspective of a portfolio analyst, it is vital to grasp the concept of covariance because it is primarily used in portfolio theory to decide which assets are to be included in the portfolio. It is a statistical tool to measure the directional relationship between the price movement of two assets, such as stocks

8 The portfolio variance. Another way of writing the portfolio variance 9. The covariance between two portfolios x and y 10. 11 To do the multi-asset computations, use Excel array functions Mmult and Transpose. An array function must be entered with [Ctrl]+[Shift]+[Enter] instead of just [Enter] There you also find the variance concentration curve that uses principle components (PCs) of the asset universe and the weighting of the assets to analyze how much the PCs contribute. Ad good place to read about the application of PCA to portfolio analysis is Regularization of Portfolio Allocation by B. Bruder, N. Gaussel, J-C. Richard and T. C. The global minimum variance portfolio lies to the right of the efficient frontier. Solution. The correct answer is B. The global minimum variance portfolio lies to the far left of the efficient frontier and is made up of a portfolio of risky assets that produces the minimum risk for an investor. Reading 52 LOS 52h: Describe and interpret the. The excel page consists of 2 buttons. The first button computes Mean Return and Standard Deviation of each assets. The second button gets the variance covariance matrix and compute the efficient frontier using solver then graph it. Matlab fetch -> Excel. There are several ways to get the historic price information using excel Definition: A minimum variance portfolio indicates a well-diversified portfolio that consists of individually risky assets, which are hedged when traded together, resulting in the lowest possible risk for the rate of expected return. What Does Minimum Variance Portfolio Mean? What is the definition of minimum variance portfolio? This leverages the risk of each individual asset with an.

Portfolio Risk and Return Analysis with Array Math in Exce

Lecture 1: Portfolio Management 1.2 Mean Variance Portfolio Choice Romain Deguest (Lille) Patrick Daguet (Paris) Basic portfolio schemes Buy & Hold Portfolios (B&H) Capitalization-Weighted Portfolios (CW) Equally-Weighted Portfolios (EW) Mean-Variance Theory (MV) Case Study: Portfolio Backtesting Efficient Market Hypothesis (EMH): Asset prices reflect all available information It means that it. 17 Global minimum variance portfolio Has the lowest possible variance among all combinations of stocks E(r) Global minimum variance portfolio G (r) N assets portfolios: Geometry 18 Tangency portfolio Maximizes the ratio of expected return to standard deviation • Same as the Sharpe ratio or the slope of the CAL E(r) Tangency portfolio (r) r f.

Markowitz mean-variance portfolio optimisation . Purpose: portfolios which balance risk and return. We need some notation, let: N be the number of assets (e.g. stocks) available . μ i be the expected (average, mean) return (per time period) of asset i . σ ij be the covariance between the returns for assets i and The return of a portfolio is the weighted average of the returns of the individual assets in the portfolio as defined by: (1) Rt=ZwīĶt where: Ri t = return of asset i at time t wi = weight of asset i in the portfolio n = total number of assets in the portfolio 90 Journal of Financial Educatio

Portfolio Return Formula | Calculator (Examples With Excel

given that = weight of each asset, = variance-covariance matrix, is the asset mean return, = specified mean return of the portfolio, and is the portfolio beta. The index-tracking portfolio with all risky assets offers a portfolio which can track the benchmark index From these weights, we can calculate the expected weighted return of the portfolio of assets using these random weights. exp_port_return = np. sum (returns. mean * weights) * 252 print (exp_port_return) 0.07906374674710082. The next thing we do is calculate the portfolio variance by way of the following

portfolio theory] as it relates to a two asset portfolio. To find the expected return and return variance for a two asset portfolio there are two basic equations (Wi is the weight of asset i, the weights of the assets in the portfolio sum to one, and capital letters represent security returns): (1) E(porifolio)= WA * E[A]+ WB * E[B] (2 set of equations for two assets. Textbooks since the mid 1980s have shied away from more than a cursory presentation of the n-asset portfolio problem. Nor-mally, the two asset model is presented, the n-asset equations are given a partial page and a graph of the efficient frontier is shown [Sharpe et. al, 1995; Bodie et. al, 1996; Smith et. N i= 1 w i,t, with w i,t being the share on asset i for time t, generally will not need to be equal to 1. Indeed, 1 N i= 1 w i,t is the share in the risk-free asset. This is the clas-sical portfolio problem, in which optimal weights are obtained by combining the risk-free asset with the tangency portfo-lio

Portfolio of four assets: Variance-Covariance Matrix - YouTub

Portfolio Standard Deviation refers to the volatility of the portfolio which is calculated based on three important factors that include the standard deviation of each of the assets present in the total Portfolio, the respective weight of that individual asset in total portfolio and correlation between each pair of assets of the portfolio already invested in some existing portfolio of assets. We, when we come to portfolio optimisation, are seeking to change that existing portfolio - perhaps because we feel we can get better performance from a new portfolio. Technically changing an existing portfolio to a new portfolio is known as rebalancing the portfolio (or just rebalancing) So I've been trying to figure out how to display the minimum variance of a portfolio, but I don't know how to graph it using Solver (or any Excel tool). I already added Solver and I have calculated the mean and standard deviation of the minimum variance portfolio in the end, but I also want to have a nice graphical display. Also, how can one draw a tangent line from the risk free-rate (let's. Hi @emilioalzamora1 brilliant, thank you! FWIW, by multi-asset I interpret @burgers to be asking if EWMA can be applied to a portfolio rather than just a single asset. Answer: yes, of course it can. Rather than a single vector of historical returns, we have a matrix of (a) factors by (n) returns The topics include mean-variance portfolio analysis and capital market theory. The book contains many examples with solutions. Linear algebra rather than calculus is used as foundation for portfolio analysis; this approach is more conceptual and helps to avoid tedious calculations

Figure: Minimum-variance portfolios of risky assets and a risk-free asset. Left panel: short selling is allowed. Right panel: short selling is not allowed. The one-fund theorem: There is a single fund M of risky assets such that any efcient portfolio can be constructed as a linear combination of the fund M and the risk-free asset Hi there, This is my first post (hopefully of many). I need assistance in creating 100 random portfolios from a list of 10 assets. I have the return history of the 10 assets and I'm able to calculate the mean and standard deviation of each asset as well as the covariance/correlation between each of the 10 assets. I want to choose to portfolio with the least variance as well the portfolio with.

minimum variance portfolio - YouTub

This is the first installment in a series of posts dedicated to Modern Portfolio Theory. In this post, I will show you how to build a Global Minimum Variance (GMV) Portfolio in Microsoft Excel. The GMV Portfolio is the portfolio with the highest return and the least risk. It takes into account all securities available and use Variance is expressed mathematically using the following formula: Where: x i = the i th data point; xˉ = the mean of all data points; n = the number of data points Example of a Variance. The following example shows how variance functions: The investment returns in a portfolio for three consecutive years are 10%, 25%, and -11% Where, w is the weight, ∑ is the covariance matrix and N is the number of assets, R is the expected return and q is a risk tolerance factor, where 0 results in the portfolio with minimal risk and ∞ results in the portfolio infinitely far out on the frontier with both expected return and risk unbounded This tool uses mean-variance optimization to calculate and plot the efficient frontier for the specified asset classes, mutual funds, ETFs or stocks for the specified time period. The efficient frontier shows the set of optimal portfolios that provide the best possible expected return for the level of risk in the portfolio

Video: Calculating The Covariance Matrix And Portfolio Varianc

Differentiated risk models in portfolio optimization: a

Excel Spreadsheets For Portfolio Optimization - Toma

Two assets Asset 1 Asset 2 Riskfree Weight 1 Weight 2 Exp ret Std dev Covariance matrix Minimum variance portfolio Tangency portfolio Cor(1,2) Sharpe ratio Three assets Asset 3 Cor(1,3) Cor(2,3) Weight 3 Portfolios of 2, 3, and 4 assets Asset 4 Weight 4 Four assets Required inputs in red Correlations misc info (don't delete) 0.07 0.15 0.30 0.07. a. If variance of asset A is 0.04 and variance of asset B is 0.02, what is the correlation between the two assets? Assume covariance between the 2 assets to be 0.015. Show how you found the values. b. Suppose a portfolio has expected return of 15% and volatility of 30%

And the mean returns for these different assets are 3.5, 1.75, -6.39 and so on. And these are all in percentages. This matrix down here is the variance-covariance matrix. So the variance of US Bond with itself is 0.001. So this quantity is the variance Recall the formula for variance of the portfolio: Var(, )=喉Var (%)+ w,20MVar (Txos.)+ 2wkwxoMCov(r.XOM ) Substituting in woM 1- Wx, this equation becomes XOM Setting the derivative of this equation equal to zero will give the formula for the minimunm variance portfolio: d Var rk )+ var (rXOM )一2Cov (rK.ro ,XOM NOW LETS SOLVE FOR A MINIMUM. Combining Two Risky Assets. When a portfolio includes two risky assets, the Analyst needs to take into account expected returns, variances and the covariance (or correlation) between the assets' returns. The differences from the earlier case in which one asset is riskless occur in the formula for portfolio variance The emphasis of FE & RM Part II will be on the use of simple stochastic models to (i) solve portfolio optimization problems (ii) price derivative securities in various asset classes including equities and credit and (iii) consider some advanced applications of financial engineering including algorithmic trading and the pricing of real options

Variance of portfolio return - XPLAIND

express views about the properties of the asset universe under consideration. This is true whether you choose to allocate to investments based on naive methods, such as capitalization weights or equal weights; apply heuristic methods like inverse volatility or variance; or deploy full-scale portfolio optimization Using the minimum variance portfolio strategy to its fullest extent, you can combine risky assets or investment types together and still achieve high relative returns without taking a high relative risk. Global Minimum Variance Portfolio: The portfolio with the lowest risk/variance on the efficient frontier. Morningstar In a portfolio, we can have a range of different combinations of the individual assets and the total portfolio return and standard deviation changes in response to any change in the asset allocation. The portfolio's expected return is the weighted-average of the expected return of the individual investments and its variance and standard. The amount of information (the covariance matrix, specifically, or a complete joint probability distribution among assets in the market portfolio) needed to compute a mean-variance optimal portfolio is often intractable and certainly has no room for subjective measurements ('views' about the returns of portfolios of subsets of investable assets.

Portfolio Optimization - n risky asset

Creating efficient frontiers using excel. Suppose we have 3 risky assets whose net return has the mean vector and variance-covariance matrix given below: Asset Mean Variance-Covariance Matrix Weights Ones Mean Portfolio Return Portfolio Variance Portfolio STD Portfolio Constraint 1 0.06 1 0.3 0.3 0.079372 1 0.176666122 2.42961 1.558721 When run with the Solver add-in on MS Excel for Windows, this spreadsheet is capable of calculating the mean-variance efficient weights for a five asset class portfolio. The user must provide the following inputs: (i) returns, standard deviations, and correlations for the five asset classes; and (ii) a return goal to be acheived by the portfolio One of the most popular approaches to asset allocation is the mean-variance portfolio optimisation based on the Modern Portfolio Theory (Markowitz, 1952, 1959). The aim of this approach is to allocate funds in such a way that the maximum return on investment for a given level of risk would be achieved Portfolio Theory in a Mean‐Variance world 2. Capital Asset Pricing Model (CAPM) 3. Eti tiEstimating Mean and CV iCoVariance matitrix 4. Black‐Litterman Model o EFFICIENT FRONTIER WITH N RISKY ASSETS A frontier portfolio is one which displays minimum variance. the return on the riskless asset, Ł2 n n is the covariance matrix of asset returns, x 2 n is the fraction of wealth invested in each risky asset, and L is an investor-specific threshold level of risk. We assume that an investor can bor-row or invest at the riskfree rate. The primary difficulty in solving (1) is finding a stabl

What is Covariance? As we learned in COVERAINCE.P function, the measuring of the relationship between the two random variables is called the covariance.As the name suggests, the covariance of the two variables tells us how the one variable varies when other variable changes Variance[bX]=b2Variance[X]. 2. Sec. 1.2 A more advanced approach to Value-at-Risk using RiskMetrics 7 • Example 2: Let's complicate matters somewhat. You are a USD-based corporation and hold a A Portfolio with Two Assets Considernextaportfoliowith$10millionintheS&P500and$6millio Thank you very much for your reply and assistance. The only issue I'm wondering about is based on the weighted SD attachment that you appended, shouldnt the last part of the formula be: SUM(wi)*(N-1)/N Thanks again for your help as it was very useful Portfolio standard deviation is the standard deviation of a portfolio of investments. It is a measure of total risk of the portfolio and an important input in calculation of Sharpe ratio. One of the most basic principles of finance is that diversification leads to a reduction in risk unless there is a perfect correlation between the returns on the portfolio investments

Calculating Portfolio Variance using the Variance

Excel 2011 Posts 22. How to automate Solver to minimise variance of finance portfolio Hi guys, For the first table, the values in cells Q4:W4 (the asset weights) must be non-negative. In the second table to the right, I need an identical process, except that asset weights can be negative If you have any doubts about this variance in excel or any other statistics, the comments section is all yours. Related Articles. How to Calculate Standard Deviation in Excel: To calculate the standard deviation we have multiple formulas. The standard deviation is simply the square root of the variance. It tells more about the data than variance ## [1] -1.644854. or in Excel with =NORM.S.INV(0.05).Each of these takes as input the probability under the normal distribution and calculates the \(z\) score associated with the probability.. We find that qnorm(0.05) is 1.64. Loss cannot exceed 1.64 times the portfolio standard deviation in the direction of loss (negative or less than the mean) using a one-tail interval

1635 variance portfolio - SlideShar

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