Fully supports the multi-period investment paradigm;
Fully supports portfolios featuring assets with highly non-Gaussian distribution of returns, or non-linear inter-dependencies, including options and hedge funds. This is achieved through direct simulation of portfolio dynamics with no model assumptions.
Choose either MS Access-database or Excel spreadsheet format to store your data;
Import historical data from a text file, Yahoo!Finance, Excel table,and Bloomberg Professional;
Batch import support;
Automatic update from all 4 sources.
Simultaneous creation of two environments for portfolio analysis:
Analytical environment: logarithmic price increments are assumed to be independent normally distributed random variables
Historical environment: optimization and other procedures are performed directly on historical prices
Riskless asset Other notations are Risk-free asset or Numeraire. It is the asset, in units of which portfolio wealth is measured. As a rule, the investor is nearly indifferent to changes in value of the riskless asset. option;
Factor-selection option for a factor-based asset pricing model A regression model which imposes additional structure on the parameters of the Analytical model. This is achieved by imposing conditions on regression coefficients. The one-factor case corresponds to CAPM. Fama-French 3-factor model is another commonly used asset pricing model..
Representation of risks in three equivalent forms simultaneously: covariance matrix Symmetric matrix containing covariances between portfolio components annual returns. Its diagonal elements are equal to squared volatilities of corresponding assets.; volatility matrix Upper triangular matrix such that its square is equal to the Covariance matrix. Computed from the covariance matrix using Cholessky decomposition. Used in the equations of the Analytical model.; correlation matrix Symmetric matrix containing correlations between portfolio components returns. Its diagonal elements are equal to 1. together with vector of standard deviations.
Option of manual model parameters editing;
Sample estimates of returns and covariances;
Black-Litterman model of incorporating investor's views in estimation of expected returns;
Stambaugh combined-sample estimates, used if asset histories differ in length; [Stambaugh; 1997];
Jorion estimate of expected returns, which shrinks sample expected returns towards a common value [Jorion; 1986];
Ledoit-Wolf estimate of the covariance matrix, which shrinks the sample covariance matrix towards the constant correlations covariance matrix [Ledoit, Wolf; 2003];
Pastor-Stambaugh-Wang joint estimate of expected returns and covariances, which shrinks sample estimates to their respective counterparts, implied by the selected factor model [MacKinlay, Pastor; 2000], [Kan, Zhou; 2005];
MacKinlay-Pastor joint estimate of expected returns and covariances, based on the assumption that prices are explained by an unobservable factor [Pastor, Stambaugh; 1999], [Wang; 2003].
Excel Solver
Three optimization criteria:
Maximization of an expected utility with constant relative risk aversion
Minimization of target shortfall probability [Stutzer; 2003]
Benchmark tracking
Worst-case scenario optimization: the resultant portfolios demonstrate optimal behavior under the worst-case scenario [Garlappi, Uppal, Wang; 2004].
Lower and upper bounds on individual asset weights
Lower and upper bounds on asset groups
Short-selling constraint
Margin constraint
Zero weight in the riskless asset Other notations are Risk-free asset or Numeraire. It is the asset, in units of which portfolio wealth is measured. As a rule, the investor is nearly indifferent to changes in value of the riskless asset.
Zero weight in factors An asset which plays the role of an independent variable in the context of Factor-based asset pricing models.
Lower bound for expected excess growth rate Expected instantaneous rate of return (including Dividend yield) over the risk-free rate.
Upper bound for portfolio volatility The most common measure of risk. Defined as annualized standard deviation of returns.
Upper bound for portfolio semi-volatility Special case of Downside volatility corresponding to the threshold equal to the average increment size. Under the assumption of independent normally distributed logarithmic returns it is equal to Volatility / 2.
Upper bound for portfolio beta Measure of portfolio sensitivity to changes in price of the only Factor. Under the CAPM assumptions portfolio beta is calculated as the sum of products of individual betas and the corresponding portfolio weights.
Portfolio volatility The most common measure of risk. Defined as annualized standard deviation of returns.
Portfolio normalized semi-volatility Equal to doubled Semi-volatility. Under the assumption of independent normally distributed logarithmic returns it coincides with Volatility.
Portfolio beta Measure of portfolio sensitivity to changes in price of the only Factor. Under the CAPM assumptions portfolio beta is calculated as the sum of products of individual betas and the corresponding portfolio weights.
Portfolio Value-at-Risk Maximum portfolio loss (measured in % of the initial wealth) over a given time interval at a given level of statistical confidence.
Portfolio Mu Vector parameter of the Analytical model. Asset Mu can be viewed as the expected simple annual rate of return in the asset, as opposed to the expected geometric rate of return, measured by the expected growth rate.
Portfolio expected excess growth rate Expected instantaneous rate of return (including Dividend yield) over the risk-free rate.
Calculation of target shortfall probabilities according to selected ranges for the investment horizon and target rate. This procedure is a key to identifying investor's goals.
Simultaneous calculation of two risk measures: Value-at Risk Maximum portfolio loss (measured in % of the initial wealth) over a given time interval at a given level of statistical confidence. (VaR) and Conditional Value-at Risk Conditional expectation of losses beyond VaR (measured in % of the initial wealth) over a given time interval at a given level of statistical confidence. (CVaR)
Various techniques for calculation of VaR and CVaR, including:
Delta-Normal Method (DNM)
Empirical distribution
Implied normal distribution
Implied non-central t-distribution
Cornish-Fisher expansion
Simulations of portfolio strategies with continuous rebalancing;
Simulations of portfolio strategies with continuous rebalancing and portfolio insurance — these strategies are optimal a predetermined portion of the initial wealth and/or accumulated profits must be maintained;
Portfolio-strategy simulations with "inaction region" rebalancing — these strategies are optimal in the presence of proportional transaction costs;
Portfolio-strategy simulations with "inaction region" rebalancing and portfolio insurance.
"Three-fund" portfolio calculation — utility-based portfolio, optimal in the presence of an estimation error in the model parameters;
Utilization of block bootstrapping algorithm in the calculation of VaR-CVaR, and shortfall probabilities;
Determine inaction region optimal size in the presence of proportional transaction costs, based on a multidimensional extension of the Davis-Norman approach;
Wide range of optimization constraints, which also include:
Constraints on assets groups
Highly non-linear margin constraint to account for margin requirements in portfolio components
Various performance measures including Information ratio, Sortino ratio, STARR ratio.