The covariance of one asset’s return to that of another asset. This time frame covers a few market crashes including the Asian Financial Crisis (Michael & John, n.d.) in 1997, the Dotcom Crash (Beattie, Market Crashes: The Dotcom Crash (2000-2002), n.d.) from 2000-2002, and the Housing Bubble/Credit Crisis (Beattie, Market Crashes: Housing Bubble and Credit Crisis (2007-2009), n.d.) of 2007-2009. The portfolio’s standard deviation is calculated below: To maintain consistency in periodicity of different parameters, standard deviation is annualised as follows: Annualizing Factor = SQRT(Number of Periods a Year), Note: Since MarketXLS uses monthly values, the annualizing factor is sqrt(12). The only downside is if an API is deprecated, your code breaks. If you’d like, you can download the excel workbook here. As expected, portfolios with a higher return were exclusively in equities which have higher risk and portfolios with the least amount of risk were heavily weighted into the fixed-income assets. Meanwhile, securities on the left end of the efficient frontier would be suitable for more cautious investors. This refers to the number of points for which data is calculated for plotting the frontier. Before we do anything, it is important to remember to annualize the Expected Returns and Standard Deviations. The MVO model only takes into consideration historical results and thus is limited to that. Negative correlation implies that if one asset goes up, the other will go down and vice versa. This article will discuss what it is, how it is then calculated, and how MarketXLS calculates it of your Portfolio. In order to avoid high active management costs, I’ve elected to use Index Funds as the selected assets for the optimization. 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. Python has a great library called pandas_datareader that allows you to pull in historical information right into a pandas dataframe. Those would likely have a high degree of risk coupled with high potential returns. The covariance matrix is calculated for the portfolio: Note: This is a two and three asset example and can be done for as many assets as a portfolio might have. Data was collected from July 1st, 1996 to March 1st, 2018 to account for approximately 22 years of data. 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. A more robust model that could be incorporated in future optimizations is the Black-Litterman Model (Black & Litterman, 1992) that enhances the asset-allocation process by introducing user input for specific opinions on market returns. For instance, if taking daily data, seeing as a trading year has 252 days, multiply the ratio with the square root of 252. The MVO model only takes into consideration historical results and thus is limited t… for yearly returns, annualizing factor = SQRT(1), for monthly returns, annualizing factor = SQRT(12), for weekly returns, annualizing factor = SQRT(52), for daily returns, annualizing factor = SQRT(252). The weights of each asset i, is wi. The standard deviation for each asset was taken by looking at the monthly returns. Black, F., & Litterman, R. (1992). Currency conversion was not required as the percentage return was calculated for returns. Adjusted monthly close price was pulled from Yahoo Finance (Historical Stock Data) by applying filters to pull from the following parameters: Data for each asset was collected in that indices’ respective currency and outputted to a csv file.

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