lessNaive

Benefits from Naive Diversification

Describe the effect of the number of stocks in a portfolio on the portfolio variance using your own data set.

You can answer this problem using the "Naïve Diversification" subject of CAPM Tutor. Run CAPM Tutor by double clicking it’s icon. From the Main Screen click on the button to the left of "Naïve Diversification."

The program will ask you for a data source. For example, you can use beta/volatility data in this subject from MorningStar’s mutual fund site or you can use historical price data from Microsoft’s Investor site. We will continue our example assuming that you are using the Excel Spreadsheet link. To do so, click on Grab Data from Excel, select Prices for Data format and Discrete compounding.

Click OK to get to Excel Data Link.

If you have previously entered data into CAPM Tutor using Excel Link then this is remembered. For example, if you have worked through 2.3.2 in chapter 2 in this current session you need only select the subset of securities you are interested in. Once selected click on the button Create CAPM Tutor Data Set. Otherwise, refer back to topic 2.3.2 to read how to get data into CAPM Tutor via Excel Link.

This window, lets you control what you will see in the Display Window, which is where you see most of the graphics produced by CAPM Tutor. In the middle of your screen, if you see:

"Your Y-Scale is too wide. Attempt to reset scale?"

The program is simply telling you that relative to your data, the default scale for plotting is too wide. Click "Yes" to change the scale automatically. The Display Window for Naive Diversification will then appear. You can at any time manually change the scale by click beside any scale number, deleting, and typing in a new number followed by the Enter (or Return) key.

The example above has the names displayed (PG (i.e., Proctor and Gamble), BA (Boeing), etc.). The program allows you to pick specific stocks and plot the resulting portfolio variance. It also allows you to pick randomly from within a specified subset of stocks.

Interpreting the Axis

The Y-axis is portfolio variance (traditionally naive diversification was measure in variance not volatility (square root of portfolio variance). The X-axis is the number of securities in the naive portfolio. That is, 1, 2, 3, 4, 5, and so on. What you are looking at is the relationship between portfolio variance and the number of stocks in your portfolio. You will also observe that for a particular number, e.g., 5-stocks, different 5-stock naive portfolios will have different levels of variance. The goal of naive diversification is to select a portfolio (from your acceptable set of stocks) with minimum variance.

Specifying a subset of stocks

Click the row corresponding to the name of the stock under the column marked "On/Off." This will toggle the stock from On (i.e., included in your subset) to Off (excluded). If you turn off all stocks, the program will switch on the last stock, so that you always are studying at least one stock.

Plot the Results of a Subset of Stocks

Click next to the name of the stocks under the column marked "Included." This will toggle it from "Yes" to "No." After you are done, click the Plot button to see the results. You will see the variance of a naively diversified portfolio with only the included stocks.

To start, let us include all stocks, and see the results. Click Plot, and observe that the portfolio variance for the equally weighted portfolio is given and the portfolio is plotted in the Display Window.

Tip1: The variance (square root of variance equals volatility) is always measured relative to your input data source. For example, if you used monthly price data, variance is measured in time units equal to 1-month.

Tip2: If you dont like the appearance of the Display Screen you can change colors and sizes of points plotted by selecting the Options menu, then the sub-menu item Colors, and the sub-sub-menu item Change Colors.

To get a feel for the effect of the number of stocks on portfolio variance, click the Random button a few times. This will pick randomly from the subset of stocks you have specified. After about 10 random picks, you will see a scatter plot of portfolios containing different numbers of stocks. The number of stocks is on the X-axis, so you can see the effects of one stock, two stocks, and so on. You will see that portfolio variance can decrease as we increase the number of stocks.

Clicking the Random button a bunch of times is tedious so CAPM Tutor lets you select all possible combinations for a portfolio of n stocks from the m securities you are working with. To do this select Plot Random and select the number of portfolios you want to be automatically sampled for you. If you are not working with too many securities you can specify the number of securities you want in your portfolio. Next click on Plot All to see the results from all possible combinations.

The display illustrates the effect of increasing the number of stocks on portfolio variance. However, you can see that the variance first declines but then rises again. That is, it is not guaranteed to decrease as you increase the number of stocks.