Page 3: Portfolio Allocations and Monte Carlo Outcomes

This page of the QPP Contents Guide goes over Page 3 of the Portfolio Report, the main body of QPP. This guide will describe what the inputs and outputs mean. Also, default settings, if any, are given. Furthermore, links to articles illustrating the specific features will be given.

NOTE: Quantext is not a registered investment advisor.  No information in this document should be taken as advice to buy or sell any asset.  Any and all information obtained from Quantext is on an "AS IS" basis. Please note that the numbers/tickers used in the QPP screen shots and examples are for illustrative purposes only and are not to be taken in any way as advice.
Figure 3a: This is the left hand side of QPP’s page 3.

Fund Name: This column of tickers (funds, individual equities, etc.) is carried from page 2 to this page by QPP. If you change the tickers on page two of QPP, remember to hit GET DATA before considering the output!

Percentage of Funds: This is where the user allocates the portfolio to the tickers. These can be changed repeatedly without updating the historical data (without hitting GET DATA.) In the screen shot in Figure 3a, the first ten tickers have been (carelessly) allocated to ten percent each. Any combination of the twenty tickers will work, as long as the total (Sums to) equals 100%.

Average Annual Return: This column contains the Monte Carlo results (forward-looking projections) for the individual tickers in the portfolio. (Even if they are allocated to zero in the portfolio.) This return is the total projected return for the specified portfolio; it includes dividends and splits.

Sums to: This is an extremely important little box to keep an eye on. Every time that you reallocate funds to the portfolio, check to make sure that 100% of the portfolio has been allocated!

Portfolio Stats: This is the turquoise box to the right side of page 3. These are the projected (forward-looking) Average Annual Return and Standard Deviation (Annual) for the portfolio. Many of Quantext’s articles illustrate the usefulness of this quantity. Below, are some older articles that illustrate the use of QPP. For more recent articles, please see our Library:

Risk and Return
Risk Return 2

All ETF
Sector Outlook
Market Neutral
Performance Prediction QQQQ
Performance Prediction
Making Sense of Trailing Performance
Diversification Premium
Investing At Home
Real Estate 2

These projections are long-term average annual return and Standard Deviation in annual return (SD).  The market evolves, so these values evolve, but Quantext thinks of them (and tests them) as though they are for several years or so into the future. Please understand that Average Annual Return is not the same as compounded annual return (often abbreviated as CAGR):

Cost of Volatility

Keeping in mind that returns and standard deviations change in time, testing on a regular basis is a good idea.  The projected default risk of Bear Stearns (BSC) increased dramatically in one month (see this article: Bear Stearns.)  However, this is unusual. 

QPP’s projected portfolio performance assumes annual rebalancing. Rebalancing is actually more complex than many people think. For some thoughts on the role of rebalancing, the reader may find this article to be of interest: Rethinking Rebalancing 2.

Average Annual Return (under Portfolio Stats): This is the projected return based on QPP’s calculations. This return is the total projected return for the specified portfolio; it includes dividends, splits, and all expenses other than loads. (Accounting for loads will be covered in this document towards the end of this “Page 3” section.)

QPP’s projected returns are expected average returns—not a specific forecast for the coming year. If you measure the height of every person in a group, the average value is a measure of what you will average out to if you measure a number of people but this may be quite far off the mark as a prediction for any individual.

QPP assumes dividends are reinvested.

QPP does not handle taxes, but taxes can have a large effect.  A number of users manage two QPP portfolios--one for their taxable and one for their tax advantaged portfolios. (Tip 11 in the Troubleshooting Guide will help you set this up successfully.)

Over what time period is the "projected" average annual return?  The long term expected returns and volatility are given -on the order of a year or more. (Momentum effects can be powerful influences out to a year but at a year or more, reversion to the mean is a stronger force.)  Though the projections are long term, you can re-check a portfolio every quarter, say, and note any changes in the projections.  (As new information is processed in, the results can change.)

If you want to see the historical returns for a specific ticker, allocate 100% to that ticker and look at the table labeled Historical (see below).  (You do not need to hit “Get Data” again.) Another option is to unhide the Excel sheet called “Historical”. To do this, go to Format > Sheet > Unhide > Historical > OK.

As well as understanding what you’re seeing with regards to historical vs. projected returns, it is important to understand the asymmetry associated with volatility (positive and negative movement in stock price.)  It is possible for a stock to have a positive average annual return and a negative cumulative return.  Consider a stock with the following returns:

Yr 1   100%
Yr 2   50%
Yr 3   -80%

At the end of the three years, $1 invested is worth $0.60, a cumulative loss of 40%.  (After one year, you have $2. After the next year, you have $3. After the third year you have lost 80% of that; you have $.60.) BUT the average annual return is 23% (average of 100%, 50%, and -80%). For more details: Cost of Volatility.

Annual Standard Deviation (Annual) (under Portfolio Stats): This is the projected, long-term annual standard deviation of the portfolio. This is an indicator of how risky the portfolio is.

Historical Data: This yellow box contains historical data for the time period that specified on page 2 of QPP. The Start and End Dates of the period are repeated at the top of the yellow box. The Average Annual Return and Annual Standard Deviation for the portfolio, for this time period, are given. These are total returns, including splits and dividends.

Historical Beta is the beta for the portfolio over the specified time period.

Historical Yield is the yield (dividends) for the portfolio over the specified time period.

Portfolio R^2 is the R-squared of the portfolio over the given time period.

For definitions of the above mentioned quantities, please visit Investopedia at http://www.investopedia.com/terms.

Performance of S&P500 over historical period, both the Average Annual Return of the S&P500 and the Annual Standard Deviation of the S&P500, are given as a reference for comparison. These are, again, for the historical period specified by the user.

Market Index (S&P500): In the gray box in the lower right portion of page 3 of QPP, the assumed future performance of the S&P500 is shown. These pieces of information were specified (and are adjustable by the user) on page 1 of QPP. These greatly influence the Monte Carlo outcomes of the portfolio. The user can manipulate both the expected (average) annual return of the market and the annual standard deviation on market returns (on page 1 of QPP) and instantly see the effect that these views have on the projected Portfolio Stats. Please see “PAGE 1”, above, in this document, to review Quantext’s default settings for these quantities.

Simulated Portfolio Beta: Beta is preserved in QPP. Therefore, Simulated Portfolio Beta and Historical Beta are similar. Simulated Portfolio Beta is an indicator of how closely the portfolio tracks the S&P500.

Diversification Metric: In all versions of our portfolio planning software, we have an analytical function that accounts for non-market correlation between portfolio components.  This is important because many asset classes have correlation to one another beyond what can be captured by Beta. (Beta, by definition, captures correlation to the S&P500, “the market”.)  Looking at non-market correlation is important for many portfolios, especially those with concentrations in a sector. 

We offer a pdf about the Diversification Metric and its usefulness. Furthermore, diversification is discussed in these articles:

True Diversification
Diversification Premium
Better Portfolio Planning
Market Neutral

Our software generates a statistic, Diversification Metric (DM), that measures how effectively the non-market components of returns actually diversify one another.  In the best possible case, the non-market component of returns would be totally uncorrelated with one another.  In the worst case, they would be highly correlated.  DM measures how un-correlated the non-market returns are across the portfolio.  Higher values of DM mean that the non-market component of returns shows low correlation across the portfolio.  Higher DM means that you are getting more real diversification out of your portfolio.  There seems to be an upper limit of about 60% -70%.

Note: The Correlation Matrix in Quantext’s portfolio planners helps one to determine how correlated each asset in a portfolio is to the portfolio as a whole, as well as to each of the other individual components—this is historical correlations for the historical period used. QPP’s projections do not simply preserve the correlation matrix. The Correlation Matrix is found by clicking on the tab marked Correlations at the bottom of the Excel screen.


Figure 3b: This chart is the right hand side of QPP’s page 3.

Ticker: QPP merely carries the list of tickers to this chart.

Beta: These are the historical Beta’s for the individual holdings.

Increase in Average Return (%): This is where one can adjust the projected return on the individual tickers in the portfolio.

The user can account for loads. The Returns given in QPP automatically account for annual expenses (fees), but not loads. The way to account for loads is to go to page 3 of QPP and scroll over to the right, just past the data ‘check’ column. You will see a column in RED type where you can manually change the returns for the individual tickers. To account for loads, you can think about how long you might keep a fund, and then spread the load over that amount of time. For example, if the load on a fund is 5%, and you are thinking you might keep the position for five years, you can lower the annual returns of that fund by 1% by putting a “-1%” in the RED ink column. Sometimes, one may wish to use an index as a proxy for a fund. For example, DJP is an ETF that, as of 2008, does not have the requisite three years of historical data. A proxy that can be used for DJP is the Dow Jones AIG commodity index, ^DJC.  As this is an index, and not an ETF, you need to account for fees.  In the case of including an index in a portfolio, you can use the Increase in Average Return (%) column to account for fees.  Using ^DJC as a proxy for DJP, we use -0.7% in the RED INK column. (This is captured in the above screen shot.) If you have a varying view on a specific ticker’s outlook from what is given on the left hand side of QPP’s page 3, you can adjust the projected expected return of that ticker in this column. Historical Annual Dividend Yield: Average annual dividend yield for the historical period. Minimum Rolling Annual Yield: Lowest dividend yield for any 12-month period in the sample data. If this is substantially different from the average yield, this indicates that there might have been a one-off special dividend in the sample period, for example. SD Multiplier: This is a redundant feature—ignore it.


Figure 3c: This is the lower right side of page 3 of QPP.

Portfolio Autocorrelation: QRP and QPP both calculate an historical statistic called portfolio autocorrelation.  Portfolio autocorrelation is the correlation in portfolio returns from one month to the next.  If it is positive then high returns tend to be followed by high returns and vice versa.  If portfolio autocorrelation is negative, then the portfolio returns tend to be 'mean reverting' which means that very high return months tend to be followed by returns closer to the mean--the portfolio tends to damp out periods of very high or very low returns.

Portfolio theory generally assumes that autocorrelation is zero--the random walk.  QPP and QRP model the market as though autocorrelation is zero, and the metric shown is for historical performance.  If you have a portfolio that shows a lot of positive autocorrelation (absolute value >20%), this is a flag--this means that big swings get amplified.  Good to keep an eye on. These effects are widely debated, but there is evidence that they can be meaningful: Stock Return Autocorrelation is Not Spurious, Robert Anderson et al, U-Cal Berkeley, 2005