First, select the subject Markowitz Diversification. If you are using data from your Excel Spreadsheet (see topic 2.3.2 chapter 2) click OK to "Grab data from Excel." If you have previously initialized the Excel Link then just select each stock you want to use by clicking on the cell above each stock name to toggle between Yes and No. If you have not previously read in any data follow the steps described in chapter 2’s topic 2.3.2.

Once you have completed the required steps click on the button Create CAPM Tutor Data Set. Next click OK to see the Markowitz action and display screens. The fifteen stocks in the data set are listed, as well as the weight of each stock in the portfolio.

To start with, plot all individual securities. If only one security appears check that you appropriately toggled each security to be turned on. You can then repeat Plot Individual Securities. This will show you the expected return and standard deviation for each of the securities.

Next plot several naively diversified, or equally weighted, portfolio. Look at the row labeled "Eq. Wtd." For "equally weighted." If you click on the cell, to toggle between Yes and No, you can create an equally weighted portfolio from any subset of securities by clicking the button market "Eq. Wtd." Now you can examine naive diversification using both risk and return, rather than only risk (e.g., in Chapter 4).

The Display shows you the plot of each portfolio in risk/return space. That is, the X-axis is expected return and the Y-axis is volatility.

For example, plot an equally weighted (naively diversified) portfolio. The dot shows you the expected return and standard deviation (volatility) of a portfolio with every stock having an equal weight. The expected return and volatility numbers are displayed in the Action Window. Alternatively, you can read off the (pixel approximate) coordinates by using CAPM Tutor’s Scale Lines. To do so click on the Options menu item, then select Scale Lines and then select View Scale Lines. This lets you click on any point in the Display window directly to see the X and Y coordinates.

You can see that the equally weighted portfolio usually does significantly better than any of the individual stocks in terms of variance (or standard deviation). In fact, you can see that this portfolio generally dominates most of the individual stocks. That is, for the same expected return it has strictly less volatility. This illustrates the point that you can form portfolios with better risk return properties than is the case if you held only individual stocks.

Before continuing further you may want to first experiment a little with the scaling before continuing too far. CAPM Tutor will select the scale automatically but you may prefer to see more or less detail. Thus, the numbers on the X- and Y-axes of the graph can be edited directly using either the Delete or Backspace keys. In the current data we are using monthly returns so the numbers should be relative to this time period.

Next, you can check whether it is possible to improve upon the risk/return tradeoff provided by scrolling portfolio weights for one security. That is, start with the current equally weighted portfolio and change the weights for a pair of securities. You only need do this for one security and CAPM Tutor will automatically adjust the portfolio weights to sum to one against the security identified in the bottom left of the Action Window.

To see the best you can do given your estimated inputs click the button labeled "Frontier." CAPM Tutor automatically computes and plots the minimum variance frontier. This displays the minimum standard deviation attainable for a given target return. The set of portfolios on the upper part of this frontier cannot be dominated. As a result, this upper portion is referred to as the efficient frontier.

To interpret the above screen, look at Microsoft (MSFT) the stock labeled number 4. This stock has the highest expected return in the picture. To find out what this return is, select Edit from the menu items and then View Covariance Matrix from the submenu items. This displays the variance/covariance matrix of returns as well as expected returns computed from whatever historical data you use. For example, CAPM Tutor calculates monthly returns/volatility from monthly closing prices. You can copy and paste this data to other Windows applications if you want to.

Here you can see that Microsoft had an average return of 0.03653 per month over this 10-year period! You can also read off the mean/volatility numbers for Microsoft (recall volatility is the standard deviation whereas variance is computed in the above matrix for the diagonal term), by plotting an equally weighted portfolio consisting of only Microsoft. That is, click No beside Eq. Wtd for all other stocks except Microsoft and then plot.

By itself it has an expected return of 0.0365 with a volatility of 0.091. An immediate question is whether there exists a portfolio that can dominate holding Microsoft by itself? To check this we will first identify the volatility (standard deviation) of the Markowitz portfolio that has the same expected return as Microsoft (0.03653). In the Action Window, enter your target return as a number into the box labeled Expected Return and press the Enter key. CAPM Tutor will now display the resulting minimum variance portfolio that provides this same target return . You can set the plot size by clicking on the menu item Options and then the sub-menu item Colors. By clicking on the name Porfolios you will see that you can change the width by scrolling the width scroll bar):

The portfolio weights are automatically displayed on the screen. If you want to store these weights for use in another subject you can via the Edit menu, followed by the folling sub-menu items Portfolio Weights, Store Weights, Set x. If you are trying this exercise online (for any stock or fund of your choice) you will see that the minimum variance portfolio attains your target return with lower volatility.

(C) Copyright 1999, OS Financial Trading System