Every once in a while we remember that we have some money invested

Every once in a while we remember that we have some money invested. If you are part of this bunch, you probably want to make sure you are getting the most of your portfolio. Portfolio Optimization deals with the notion that there is a line, a frontier, where the most efficient portfolios are. There is a lot of material about Portfolio Optimization ,however, not a lot of practical, step by step examples showing how you can optimize your own.

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To start, we shall define what we mean by optimization: let's assume your portfolio has 3 assets you can choose from-cash, bonds and stocks. You can have an infinite number of portfolios, each with a different percentage of the named assets. Each of these portfolios would also yield a different return and risk. Your goal as a portfolio manager (or owner of a 401k plan) is to make sure your portfolio yields a maximum amount of return, with minimum risk.

In this part of the article, we will go through the steps necessary to gather and prepare the data needed for analysis of our portfolio.

  • Define your portfolio assets: if you are in a 401k plan, you have a certain number of mutual funds you can choose from. Go through the list of possible mutual funds, and mark down the ones you are considering for analysis. Make sure that you select assets from the whole range of risk low, moderate and aggressive. For practical reasons, you should probably want to keep the number of assets less than 10.
  • Gather the financial data of each asset: your objectives are to determine the rate of return of each asset, as well as the risk involved. However, you will probably not find this data readily available from your brokerage firm. So you will have to do some homework. There are a whole range of sites on the internet you can go to in order to retrieve financial data for your assets. One of such sites is yahoo finance. Type the ticker symbol of your asset in Yahoo and then select historical prices. Go as far back in time as you can (typically more than 10 years). Select download to spreadsheet.
  • Prepare the data for analysis: by now you should have a spreadsheet containing the historical prices for each of your assets. You are going to add columns I and K. Column I is merely a copy of column E , which holds the closing asset prices, in this case. Column K is the calculated 7-day Moving Average of the Closing Prices. We use Moving Average so that we filter out noise in the historical prices. The formula, on cell K8 is AVERAGE(I2:I8) . You can then copy this cells formula to the remaining of the cells on the column by dragging and extending. After theK8column is populated with the Moving Average, it is time to calculate yearly returns, going back as far as practical. The formula for the rate of return is ((Return-Capital)/Capital)* 100% . As an example, if the asset price is the beginning of the year is $12 and at the end of the year it is $14, you have: Return = ((1412)/12)*100% . Use the prices on the Moving Average column. At the end of this exercise, you should have a rate of return for each year of the life of your asset
  • Calculate Mean, Standard Deviation of your returns: if you have the data analysis package installed on excel, all you should have to do is to select the data related to the yearly returns and select Descriptive Statistics . This summary statistics will include the mean (arithmetic mean) and standard deviation.

If you have completed all the above steps, the first part of Optimizing your Portfolio is finished. All of the tasks above serve one single objective, which is to arrive at a Mean and Standard Deviation of the Returns of each of the possible assets in your portfolio. The Mean gives you an idea of the average yearly return you can expect our of the asset. The Standard Deviation relates to the risk involved.

In the 2nd part of this article, we will see how we can use Monte Carlo simulation to cycle through a number of different arrangements for our portfolio, each one with it's own combined rate of return and risk.

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