Investment management- Portfolio management

Investment management- Portfolio management

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  To The Worldof Investment
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  • Standard Deviationof a Portfolio Investment • Three Assets Portfolio • Estimation Issues • The Effective Frontier • The Effective Frontier and Investor Utility Objectives
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  STANDARD DEVIATION OFA PORTFOLIO  Portfolio standard deviation is the standard deviation of the rate of return on an investment portfolio and is used to measures the inherent volatility of an investment.  It measures the investment’s risk and helps in analyzing the stability of returns of a portfolio
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  Example:: Weight Expected returnSD. Stocks A .5 .20 .10 Stocks B .5 .20 .10 (0.5)2 (0.10)2 + (0.5)2 (0.10)2 + 2 (0.5) (0.5) (0.01) (0.25) (0.01) + (0.25) (0.01) + 2 (0.25) (0.01) (0.0025) + (0.0025) + (0.005) 0.01 0.10 = = = = =
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  When the co-relationis :: 0.5 (0.5)2 (0.10)2 + (0.5)2 (0.10)2 + 2 (0.5) (0.5) (0.005) (0.0025) + (0.0025) + 2 (0.25) (0.005) 0.0075 0.0866 = = = =
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  A Three AssetPortfolio Model A demonstration of what occurs with a three assets portfolio is useful because it shows the dynamic of the portfolio process when assets are added. It shows the rapid growth in the computation required, which is why we generally stop at there. Three is a better option…. The assets are Stocks, Bonds, Cash or any Cash equivalent………..
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  Assets classes E(𝑹𝒊) E (ɕ𝒊) 𝑾𝒊 Stocks (S) 0.12 0.20 0.60 Bonds (B) 0.08 0.10 0.30 Cash Equivalent(C) 0.04 0.03 0.10 Calculation Here the co relation are : 𝑟𝑆,𝐵 = 0.25; 𝑟𝑆,𝐶 = -0.08; 𝑟𝐵,𝐶 = 0.15 The weights specified, the E(𝑅 𝑝𝑜𝑟𝑡) is E(𝑅 𝑝𝑜𝑟𝑡) = (0.60) (0.12) + (0.30) (0.08) + (0.10) (0.04) = 0.072 + 0.024 + 0.004 = .100 = 10.00% E (𝑹𝒊) = Expected Risk E (ɕ𝒊) = Expected Standard Deviation 𝑾𝒊 = Weight of the Investment
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  When we applythe generalized formula, the expected standard deviation of a three asset portfolio, it is ɕ2 𝒑𝒐𝒓𝒕 = (𝑤𝑆 2 ɕ 𝑆 2 ) + (𝑤 𝐵 2 ɕ 𝐵 2 ) + (𝑤 𝐶 2 ɕ 𝐶 2 ) + (2 𝑤𝑆 𝑤 𝐵ɕ 𝑆ɕ 𝑩ɕ 𝑺.𝑩) + (2 𝑤𝑆 𝑤 𝐶ɕ 𝐶ɕ 𝑪ɕ 𝑺.𝑪) + (2 𝑤 𝐵 𝑤 𝐶ɕ 𝐵ɕ 𝑪ɕ 𝑩.𝑪) ɕ 𝒑𝒐𝒓𝒕 𝟐 = [(0.6)2 (0.20)2 + (0.3)2 (0.10)2 + (0.1)2 (0.03)2 + {[2(0.6)(0.3)(0.20)(0.10)(0.25)] + 2(0.6)(0.1)(0.20)(0.3)(-0.08)] + 2(0.3)(0.1)(0.10)(0.3)(0.15)] = [0.015309 + (0.0018) + (-0.0000576) + (0.000027)] =(0.0170784) 1/2 = 0.1306, = 13.06%
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  ESTIMATION ISSUES To allocatethe portfolio asset we have to consider some factors, which will effect our portfolio asset allocation, this portfolio asset allocation depends on the accuracy of the statistical inputs. This means that for every asset being considered for inclusion in the portfolio, we must estimate its expected return and standard deviation. So this factors which we have to consider before portfolio asset allocation are called estimation issues.
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  Steps to befollowed ::  To consider the accuracy of the statistical inputs  To calculate the correlation estimates  To calculate the estimation risk  To reduce the estimation risk
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  SINGLE INDEX MARKETMODEL :: 𝑅𝑖 = 𝑎𝑖 + 𝑏𝑖 𝑅 𝑚 + 𝑒𝑖 Here, 𝑅𝑖 = that part of security i’s return, which is independent of market performance 𝑏𝑖 = the slope coefficient that relates the returns for security i to the returns for the aggregate stock market 𝑅 𝑚 = the retunes for the aggregate stock market 𝑒𝑖 = unsystematic risk of the security of the i.
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  DOUBLE INDEX MARKETMODEL :: rij = 𝑏𝑖 𝑏𝑗 ɕ 𝑚 2 ɕ 𝑖ɕ 𝑗 Here , rij = the correlation coefficient of returns 𝑏𝑖 = the slope coefficient that relates the returns for security i, to the returns for the aggregate stocks market 𝑏𝑗 = the slope coefficient that relates the return for security j, to the returns for the aggregate stock market ɕ 𝑚 2 = the variance of returns for the aggregate stock market ɕ𝑖 = the standard deviation of Rij ɕ𝑗 = the standard deviation of Rji
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  THE EFFICIENT FRONTIER TheEfficient frontier is the set of optimal portfolios that offer the highest expected return for a define level of risk or the lowest risk for a given level of expected return. Portfolios that lie below the efficient frontier are sub-optimal because they do not provide enough return for the level of risk.
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  EFFICIENT FRONTIER FORALTERNATIVE PORTFOLIOS
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  The Efficient Frontierand investment Utility Objectives:: Use utility to determine the optimal risk portfolio The efficient frontier and the utility curve recover the highest possible utility.
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  Any Question???