Model Portfolios, updated

January 23, 2019

Portfolio Visualizer is a highly rated online tool for designing investments (ref. 1). I used it to backtest the model portfolios listed in the following chart:


Legend: The top row shows the trading symbols of six index funds selected to build the model portfolios in rows 2-5.  The portfolios were backtested from December 2018 to January 2010.  $1.00 was initially invested in each portfolio and allowed to grow in value to the final balances shown in the righthand column.  The performance benchmark is Standard&Poors 500 TR Index in row 6.

Four-sector models in rows 2-4 represented diversified investments in stocks (VT, VTI), real estate investment trusts (VNQ), investment grade U.S. bonds (AGG), and gold bullion (GLD).  Several observations:

  • Four-sector models outperformed the bond market as determined by comparing their balances to the $1.32 that would result from investing only in AGG.
  • Portfolio performance was affected by the percentages of the index funds. The final balance of  four-sector models increased with the total percentage of stocks (VT, VTI) and real estate (VNQ) investments. 
  • Four-sector models underperformed the benchmark.

The one-sector model in row 5 held diversified investments in U.S. stocks. SCHX is a proxy for U.S. large-cap stocks and VTI is a proxy for all U.S. stocks. Among models, only the final balance of this model surpassed that of the benchmark in row 6.


Four-sector models are ideal portfolios for making short term investments of 1-5 year time periods. The goal of four-sector models is to improve safety by reducing the downside risk of investing in one sector.

The one-sector model of diversified U.S. stocks is ideal for making long term investments of 10 or more years.


Last year’s SmallTrades Portfolio, in 2018, was a four-sector portfolio that underperformed the benchmark.  In 2019, the new SmallTrades Portfolio will hold a group of actively managed stocks plus the passively managed Schwab U.S. Large-Cap ETF (SCHX). The initial allocation will be 20% stocks and 80% SCHX.

Thesis: SCHX is designed and tested to match the performance of the benchmark. Successful management of the stocks will raise the portfolio’s total performance above that of the benchmark.


  1. Vikram Chandrasekhar, 2016.  What is the best tool to backtest a portfolio online?


The total return of a portfolio is estimated by the following formula:

RT = aRA + bRB+ cRC + dRD

For example, what is the estimated total return for the following portfolio?;  

25% VT + 25% VNQ + 25% AGG + 25% GLD

  • a, b, c, and d = 0.25.
  • RA = 7.19%, RB = 10.21%, RC = 3.13%, and RD = 1.37%.
  • RT = 0.25*7.19% + 0.25*10.21%+ 0.25*3.13% + 0.25*1.37% = 1.80% + 2.55% + 0.78% + 0.34% = 5.47%

By comparison, the Portfolio Visualizer  reported RT = 5.93% with a final balance of $1.68.  

Copyright © 2019 Douglas R. Knight 



January 19, 2019
Once again, the SmallTrades Portfolio failed to outperform 
the Standards & Poor 500 TR Index ('benchmark'). In 2019, I
will replace five exchange-traded funds (ETFs) with a single ETF.

The SmallTrades Portfolio is actively managed within a tax-protected Roth IRA.  No cash has been added or removed from the account since the time of inception in 2007.  Figure 1 describes the portfolio and its investment strategy:

portfolio 2018 v3

Fig. 1. The holdings as of 12/31/2018.

The following strategies are used to earn capital gains:

  • The passive strategy is to collect dividends and capital gains from exchange-traded index funds (ETFs).  Each ETF is ‘passively’ managed to match the performance of a market index rather than ‘actively’ managed to outperform or underperform a market index.
  • The swing strategy is to buy the stock at a low price (‘bargain’) and sell it at a high price, however long the price-swing happens to occur.
  • The growth strategy is to purchase a reasonably priced stock and hold it until the company stops growing over several-to-many years.  The stock price should increase with the company’s profit.
  • The drip strategy is to buy a reasonably priced stock to collect dividends and reinvest them in additional shares of stock.  The beneficial effect of ‘drip’ increases as the stock survives several market cycles.

2018 Performance

Figure 2 shows the changes in value for every $1 invested in the Portfolio (solid blue line) and Benchmark (dashed blue line) after 12/31/2007.  The market value of the benchmark was consistently higher than that of the portfolio.

invested $ portfolio

Fig. 2.


In 2013, I replaced the Portfolio‘s mutual funds with ETFs that match the performance of 4 market sectors based on a model portfolio of global stocks, U.S. real estate investment trusts (REITs), U.S. bonds, and gold bullion.  I rebalanced the ETFs as needed and continued to actively manage a group of stocks.  Figure 3 shows annual fluctuations of the stock values (solid red line) and ETF values (dashed red line) as if $1 were invested in each group on 12/31/2013.

invested $ stocks

Fig. 3.

The benchmark (solid blue line) underperformed the stocks and outperformed the ETFs until 2018, when the benchmark surpassed both groups of investments (Fig. 3).


Several events in 2018 worked against the portfolio.

  • The U.S. stock market lost its collective annual earnings in the last quarter of 2018.  Most stocks declined in value.
  • Stop-loss trading orders triggered steep losses from 5 stocks in the portfolio.  Four were high-risk investments in small companies that failed to generate returns.  One investment was a large company with steadily declining earnings.
  • The 4-sector model portfolio predicted that the portfolio’s ETFs would collectively grow by nearly 9% every year, but instead they grew at half that rate, 4.4% annually.  The databases for the model portfolio were outdated (limited to the time period of 1997-2011) and have not been updated.


The new SmallTrades Portfolio will hold one index fund, the Schwab U.S. Large-Cap ETF (i.e., SCHX), and a group of stocks.  The SCHX is designed and tested to match the performance of the benchmark (more information in Model Portfolios, updated). The stocks will initially comprise 20% of the portfolio’s market value and they will be actively managed to outperform the SCHX.  Consequently, the portfolio’s growth should outperform the benchmark’s growth.

Copyright © 2019 Douglas R. Knight

What is a stock and how much is it worth?

August 21, 2018

A stock is an offering of part ownership in a company.  Each part, — called a share—, is worth the price that buyers are willing to pay.  

A new stock is sold for the first time in the primary market.  The primary market is a private one comprised of the company’s founders, venture capitalists, and third parties such as banks and advisors.  Venture capitalists take a big risk that the company might fail.  In return, they have considerable influence on how the company is governed and operated.  They hope to earn a generous profit from selling their shares.

The stock may be sold again in the secondary market by public auction.  The secondary market is the familiar stock market where thousands of investors, —like us—,  trade cash for stocks and other exchange-traded securities.  We also hope to earn a generous profit from selling shares. Some companies may occasionally choose to pay us a cash bonus called a dividend.

Wise buyers seek the best price for a good company.  The best price is determined by ‘valuation’ and the quality of the company is assessed by ‘fundamental analysis’.

Copyright © 2018 Douglas R. Knight

The joy of stock returns

August 5, 2018

A good reason for investing in stocks is to earn more money than the interest paid by a bank account or savings bonds.  Some investors ignore their stocks until it’s time to cash in.  Most prefer to watch the growth of returns, in which case they need to know the total return and holding period.   

Total Return

Stock profits depend on the capital gains and dividends.  A capital gain is the amount earned when the current stock price exceeds its purchase price.  A capital loss is the amount lost when a current price is below the purchase price.  The capital gain (or loss) is “unrealized” if the investor doesn’t sell the stock or “realized” if the investor sold the stock.  Some companies make occasional cash payments, called dividends, to their stock holders.  

Total Return is the total profit from your stock investment.  It represents the stock’s change in market value combined with all dividends you received from the company.  In equation 1, the change in market value is equal to “market value – total cost”.  

total return = market value – total cost + dividends

  • Market value is the combined value of all shares owned at the current market price (market value = current price * volume; volume is the number of shares).  
  • Total cost is the value of all shares purchased (cost = purchase price * volume) during the holding period 
  • Holding period is the period of stock ownership.  

Trading fees are ignored in order to simplify this discussion. In actual transactions, trading fees reduce the market value and increase the cost by small amounts so as to reduce the total return by a small amount.  The impact of trading fees on profits is lower in larger transactions.  For example, a $5.00 trading fee is 5% of a $100 purchase compared to 0.5% of a $1,000 purchase. 

Return on Investment (ROI)

ROI is the basic measurement of profitability (ref 1).  It is the ratio of total return to total cost (equation 2).

ROI = total return/total cost

Significance: the ROI shows how much profit you earned from every invested dollar.  If the ROI were 0.2/1, which is 20%, then you earned 20 cents per invested dollar.

“Price performance” (equation 3) may not measure the ROI.  Price performance = (price2 – price1)/price1, where price1 is the earlier number and price2 is the later number.  Price 1 may neither be the purchase price nor the only purchase price.  ROI includes all purchase prices.

Rate of Return

The rate of return measures profitability with respect to time.  Think of if it as the ROI for the holding period (equation 4). 

Rate of Return = ROI/holding period

Don’t forget that the ROI compares profit to cost when the time period is anchored to the date of the initial purchase.

ISSUE: The rate of return is most precise when there is just one purchase.  Serial purchases require a more complicated calculation of the “annual return”.  

Annual return

The annual return is a number that represents the average rate of growth per year of the holding period.  The annual return has several important properties:

  1. It doesn’t change during the holding period.
  2. It’s a geometric average, not an arithmetic average.  The graph of geometric growth is a curved line (“exponential”) rather than a straight line (“linear”).
  3. The geometric average represents the phenomenon of compounded growth known as “compounded interest”.

Stock investors are interested in 2 types of compounded growth:

  1. The compound annual growth rate (“CAGR”) of a single purchase.
  2. The internal rate of return (“IRR”) for a series of purchases.  

There are free calculators which are posted online to determine the CAGR (ref 2) and the IRR (ref 3).  

ISSUE: The annual return is usually inaccurate during the first year of compounded growth and becomes more accurate over longer time periods.  

Rule of 72 

The payback period is something to celebrate!  It’s the point when the investment doubles your money.  Payback is measured by the ratio of total cost to the rate of return.  Or, it can be estimated by the Rule of 72 (equation 5).  

Rule of 72 = 72/assumed annual return

Significance: the Rule of 72 is used to forecast the holding period needed to double your money (ref. 4).  For example, assume that your total return will grow at a constant rate of 10% per year [approximately the same rate as the growth of the U.S. Stock Market].  The expected payback period is 7.2 years (7.2 = 72/10).  


The total profit of your stock investment is called the total return.  The simplest way to measure profitability is to calculate the ROI with equation 2.  The ROI is insensitive to time until you calculate the rate of return with equation 4, which allows you to compare the profitability of several stocks in your portfolio.  The annual return of compounded growth is a refined measurement of your calculated rate of return.  After a holding period beyond one year [to avoid the chance of considerable inaccuracy], the annual return may be determined with an online calculator for a single investment (CAGR) or serial investments (IRR).    


1. Return on Investment (ROI). 

2. Compound annual growth rate (CAGR) calculator.  . 

3. XIRR calculator to calculate IRR of non-periodic cash flows.   . 

4. Brian Beers. What is the Rule of 72? , 1/2/2018.

Copyright © 2018 Douglas R. Knight

Ways to invest in stocks

July 19, 2018

There are thousands of  investors who want to own ‘good’ companies that avoid ‘trouble’.

  • they invest in stock shares [stock shares are equal units of part ownership]
  • a good company
    • operates a profitable, growing business
    • avoids financial distress and regulatory penalties

Investors purchase and sell shares in the stock market.  They hope to sell their stock at a desirable price and may also receive cash rewards from companies that pay dividends.  Investors earn a profit (called a capital gain) when the sales price is above their cost of investment or lose money (called a capital loss) when the sales price is below cost.  

Stock Analysis

Two ways of evaluating a stock are called technical analysis and fundamental analysis.  Technical analysis measures the performance of share prices and share volumes in the stock market.

  • Shares are units of part ownership which are traded in the stock market.
  • Price: the price of a share in the stock market.
  • Volume: the total number of shares traded in the stock market 

Fundamental analysis evaluates the business performance of a company by way of searching through its quarterly and annual filings.  The business description, financial statements, and CEO’s annual letter to shareholders are important sections of the filings.

  • CEO: Chief Executive Officer; top manager of the company.
  • Filings: periodic reports to shareholders that are required by the U.S. Securities and Exchange Commission (SEC).

Business performance is also assessed by the company’s market share and competitive advantage within its industry.  This information is available online.

Investment Strategies

The most common investment strategies for stocks are swing trading, value investing, and growth investing.  

Swing trading (cyclic trading) uses brief upward or downward trends in share prices to determine when to buy or sell stocks.  The typical holding period is from one day to several weeks.  The investor hopes to earn a capital gain (–if seeking a profit–) or capital loss (–if seeking to reduce the short term capital gains tax–).  The investor uses either a technical analysis or guesswork to judge the price trend.  The main risks of incurring a loss are due to price volatility and taxation of returns.

  • Hold: to own.
  • Short term: one year or less.
  • Short term capital gains tax: the taxation of a capital gain at the regular income tax rate.
  • Price volatility: the random fluctuation of prices based on the market forces of supply and demand.
  • Return: the profit or loss from an investment.

Value investing seeks a capital gain by purchasing the stock at an unusually low price (e.g., 60% of intrinsic value) and then selling it at approximately double the purchase price.  The holding period depends on the length of time for the stock price to become profitable. During the holding period, an investor will receive any dividends paid by the company.  The informed investor uses a fundamental analysis to assess the quality of the company and the intrinsic value of its stock.  The causes of an unusually low price include a market downtrend (e.g., economic recession) and poor company performance.  The main risks of incurring a loss are due to an eventual delisting of the company and taxation of returns.  

  • Intrinsic value: the share price calculated by a professional analyst’s secret formula.  However, you can estimate the intrinsic value as the net worth of the company (book value) per share, based on the idea that a wealthy investor could acquire the company at its intrinsic price by puchasing all shares of stock at the book value per share.   
  • Dividend: a cash reward paid to share holders from the company’s profits or cash reserves.
  • Delisting: removal of the stock from the stock market for various regulatory reasons, including bankruptcy of the company.    

Growth investing is a long term strategy for using the upward momentum of share prices to earn a capital gain. The capital gain is earned by simply holding the stock and reinvesting all dividends.  The rule of 72 estimates the holding period needed to double the purchase price of the stock at an assumed rate of annual return.  The growth investor uses a fundamental analysis of the company and market valuation to judge the fairness of the stock price.  The main risks of incurring a loss are due to deterioration of the company, decline in market value, and taxation of the returns.

  • Long term: after one year.
  • Momentum: an upward trend of share prices.
  • Rule of 72: [ Years to double the price = 72/percentage annual rate of return ] For example, a 15% annual rate of return will double the share price in 4.8 years. 
  • Annual rate of return: a constant percentage change in value every year that accelerates the growth of an investment; CAGR is an acronym for the annual rate of return.
  • Valuation: the art of judging if the price is low (discounted, undervalued) or high (expensive, overvalued). 

disclaimer: this article may not increase your investment profits.

Copyright © 2018 Douglas R. Knight


January 1, 2018

My SmallTrades Portfolio holds stocks and broad-market index ETFs (chart 1).

chart 1. SmallTrades Portfolio in 2017.

Chart 2 shows the diversification of ETFs as measured by percentages of year-end market values among ETF classes.

chart 2. Diversification of ETFs in 2017.

Chart 3 shows the diversification of stocks among 8 market sectors as measured by percentages of year-end market value for each stock sector and the ETFs.

Chart 3. Distribution of stocks and ETFs by market sectors.

Chart 4 shows the distribution of stocks according to market capitalization.

Chart 4. Combined market capitalizations.


My investment goal is to outperform the “Benchmark” Standard & Poors 500 Total Return Index, yet my portfolio has never outperformed the Benchmark (chart 5).

Chart 5. Portfolio performance.

Chart 5 shows growth trends for the benchmark (blue dashed line) and portfolio (solid blue line) since 2007 [the benchmark represents a passively managed, buy-and-hold investment; my portfolio is an actively managed investment].  On the Y axis, a unit value of $1.00 was assigned to both the total market value of the Portfolio and the Benchmark on December 31, 2007. Ratios of subsequent market- and benchmark values to the 2007 baseline are displayed line plots on the chart.

In 2014, my investment policy was modified to buy stocks of good companies and hold them for the long term. Chart 6 shows the result of my stock investments (red line) compared to the Benchmark Index (blue line) and ETF investments (red dashed line). The unit value of $1.00 was calculated on December 31, 2013. Since then, the stock group clearly outperformed the Benchmark and ETFs.

Chart 6. Stock and ETF performances.

Risk Management of ETFs

Broad-market index ETFs are primarily protected against stock losses by the passive management of investment portfolios which mimic the composition and performace of reputable market indices.

ETFs are secondarily protected by rebalancing significant allocation errors as described in the SmallTrades Portfolio’s strategies for risk management. In theory, a significant drift of asset classes occurs when one asset class surpasses a 24-28% allocation error. My preferred allocation of ETF market values is 30% stocks, 30% REITs, 20% bonds, and 20% gold bullion.

A perfect allocation of ETFs would result in 0% allocation error.  Furthermore, allocation errors would reflect disproportional gains or losses of market value.  Chart 7 shows the year-end allocation errors (blue bars) and error limits (red dashed lines) of my ETFs. There was growth of the Global Stocks ETF and decline of the remaining ETFs. Any allocation error that exceeds an error limit (red dashed line) should trigger trades that rebalance the ETFs to the preferred allocation.  My ETFs were not rebalanced in 2017.

Chart 7. ETF allocation errors in 2017.

Risk management of Stocks

My stocks are primarily protected against risks of steep loss by diversification of the market sectors, as illustrated in the preceding chart 3. The second line of defense is stop-loss orders.  In keeping with the investment goal of holding good stocks for the long run, I set ‘stops’ at a wide margin to prevent recent market fluctuations from triggering an unwanted sale.


The SmallTades Portfolio will continue to be actively managed for long term success. The ETFs will be rebalanced anytime there’s a 24% allocation error or a modification of the ETF holdings. In 2017, I failed to sell large cap stocks in order to buy good small cap and mid cap stocks. Consequently, 60% of the total market capitalization of my stock portfolio was in the Large Cap category.  In 2018, I would like to reduce the Large Cap category to 40% total market capitalization and boost the market capitalization of small- and mid cap stocks issued by good companies with potential growth of earnings.

Portfolio history

  1. On 12/31/2007, the portfolio held a group of actively managed mutual funds in a tax-deferred Roth account. Since then there have been no cash deposits or withdrawals and the portfolio still resides in a Roth account.
  2. During 2007-2010 the actively managed mutual funds were traded for stocks in an attempt to earn a 30% annual return by process of turning over short term ‘winners’.  Four mistakes led to a big loss:
  3. mistake #1: after a couple of short term capital gains from Lehman Brothers Inc., I ignored the dangers of the company’s large debt and lost $45,000 during Lehman’s decline to bankruptcy.
  4. mistake #2: substantial long term profits from good companies were lost by selling holdings for short term profits. My strategy was to earn a quick 30% in the first year and re-invest in the next winners. It was too difficult to identify the next winners.
  5. mistake #3: day-trading was a game of chance that I played and managed to break even; meanwhile, good stocks grew in value.
  6. mistake #4: a trial of investing in leveraged ETFs resulted in losses due to negative compounding.
  7. I abandoned the goal of a 30% annual return in 2012 by adopting a more realistic, but still aggressive, goal of outperforming the benchmark. That same year, I changed my investment strategy to that of holding a mixed portfolio of 80% broad-market index ETFs and 20% stocks for the long term. ‘Good’ companies attract and retain investors for many years. I will search for profitable companies with growth potential that are undervalued by the stock market. My search methods include reading reputable sources of business news, partiicipating in an investment club, using stock screeners, and attending investor conferences. Then I include and exclude stocks by reading analyst reports, financial statments, SEC filings, and market analyses. Valuation critieria help me decide if the stock price is worth paying.
  8. Prior to March, 2016, five ETFs were allocated to four asset classes with each asset class holding 25% of the combined market value. Since my retirement income didn’t depend on making withdrawals from the SmallTrades Portfolio, I increased my ETF exposures to global stocks and REITs by decreasing my exposures to investment-grade bonds and gold bullion. The new allocation rule was 30% stocks, 30% REITs, 20% bonds, and 20% gold. Any drift in allocation to a 24% error will be rebalanced.

What is a good company?

December 15, 2017

Good companies attract investors.  They do so by selling a desirable product that sustains the company’s growth of sales and earnings.  The growth of sales is a good measure of market success.  Durable companies convert their sales invoices into cash and use the cash wisely.  Accounting items such as the free cash flow, sustainable growth rate, quick ratio, and debt-to-equity ratio are easy measures of the company’s health and durability.  Growth stocks should be assessed by the quality of the company.

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