R-squared, the linearity of investment returns.

December 24, 2016

[updated 12/25/2016: R2 is a useful measure of indexing]

The R-squared (R2) statistic describes a pattern of plotted data with respect to a straight line. R-squared is called the coefficient of determination (ref 1,2).


The black dots in figure 1 represent investment returns that are poorly related to market returns. There is a random distribution of investment returns with respect to market returns. The blue line is an inadequate representation of the relationship simply because there is no relationship. The R2 score for this distribution is 0.03. Conversely, the black dots in figure 2 show the ‘herding’ of data around a straight line.


Figure 2’s investment returns are highly related to market returns with an R2 of 0.997.


The R2 score represents the degree of alignment of data to a best-fit line as determined by regression analysis. The lowest possible score of 0 indicates a random pattern of data with absolutely no alignment. The highest possible score of 1 represents complete alignment.

The product of R2 X 100 represents the percent of variation in investment returns that are related to market returns (ref 1,2). In other words, R2 measures the relavance of the best-fit line to a set of data. Relavance increases as the R2 score varies from 0 to 1.

The lowest score of 0 defies any financial analyst to draw a meaningful line for investment returns as they relate to market returns. In figure 1, the incline (β) and Y-intercept (⍺) of the blue line are unreliable measurements of investment performance.

The highest R2 score of 1.00 identifies a straight line of near-perfect predictions of returns. Any R2 above 0.75 identifies a straight line for making predictions of returns. Lower scores represent increasingly random events. In figure 2, the incline (β) and Y-intercept (⍺) are reliable measurements of investment performance.

R-squared is an excellent measure of index fund performance.  Websites for index mutual funds and ETFs publish R2 as a measure of alignment between fund returns and the market index.   Funds that have an R2 score of nearly 1.00 track the index very closely.


1.  Lain Pardoe, Laura Simon, and Derek Young. STAT 501, Regression Methods. 1.5- The coefficient of determination, r-squared. Pennsylvania State University, Eberly College of Science, Online courses. https://onlinecourses.science.psu.edu/stat501
2.  R-squared. 2016, Investopedia http://www.investopedia.com/terms/r/r-squared.asp?lgl=no-infinite

Lead article: Stock Index Funds

January 16, 2016

The only way an individual investor can quickly invest in hundreds of different stocks is to buy shares of a stock index fund. The tremendous advantage is an immediate ownership of a diversified portfolio in one affordable investment. It’s the surest way of earning the stock market’s returns provided the correct investment is held through a series of ‘bull’ and ‘bear’ markets. Selecting the ‘correct’ fund requires only a few hours of easy research based on the following information:

INDEX. Stock index funds are passively-managed investment funds designed to imitate a stock index. The index measures the investment performance of a hypothetical portfolio of stocks. Some indices are riskier than others by virtue of the underlying securities in the hypothetical portfolio. For example, micro-cap stocks are riskier than all stocks combined by virtue of differences in turnover, liquidity, and diversification.

FUND MANAGEMENT. The investment fund is an actual portfolio of stocks that are managed for the benefit of the fund’s shareholders. Passive management is an investment style that imitates the performance of the selected index. Active management intentionally avoids imitating the index and is a more costly endeavor.

The legal structure of an index fund regulates its style of management. A unit investment trust (UIT) is bound by a trust agreement to manage a portfolio of fixed composition. The UIT has an unmanaged portfolio because there is no allowance for adjustment of composition by the manager. The open-end investment company (OEIC) operates a managed portfolio of adjustable composition. The OEIC is bound by its investment strategy to operate either a passively or actively managed fund. OEIC managers of an index fund are bound to passive management but have leeway to supplement the fund’s income by revising, lending, or borrowing a minor portion of the portfolio. These operations may increase the risk and tax burden of investment.

PRICING. The pricing mechanism of an index fund is closely regulated. Mutual funds are OEICs that trade shares at net asset value (NAV); in other words, they are priced at the fund’s net worth-per-share. The mutual fund’s share price is not quoted until the next day because the NAV is determined after trading hours from closing prices of the underlying stocks. Mutual funds are marketed through an authorized broker and guaranteed to be priced at the NAV. Exchange-traded funds (ETFs) are OEICs or UITs that trade the fund’s shares in the stock market, which means that the share price is quoted by public auction during trading hours. ETFs are traded the same way as stocks. The intraday net asset value (iNAV) and share price are continually updated and reported by the stock market. The fund’s share price is linked to the fund’s iNAV by arbitrage. Individual investors can neither participate in arbitrage nor redeem ETFs at NAV.

FEES. Managers of investment funds are compensated by charging an annual expense ratio that diminishes the NAV. Competition has decreased the expense ratio of stock index funds to only a few basis points (1 basis point = 0.01%), but beware that the expense ratios of bond index funds and actively managed mutual funds are typically higher; read the prospectus. Mutual funds are notorious for adding special fees to trades and imposing minimal holding periods; check with the broker and read the prospectus. New, small index funds are at risk for early termination when the NAV fails to grow above an estimated fifty million dollars. The expense ratios of small funds generate insufficient compensation for the fund sponsors, so they close shop.

TAXES. OEICs and UITs are registered Investment companies (RICs) that pass all income taxes to the shareholders. The amount of tax depends on dividends and capital gains earned by the fund. Managed portfolios incur a higher tax burden due to the more frequent turnover of portfolio securities. Consequently, mutual fund shareholders pay taxes on unrealized capital gains that ETF shareholders don’t have to pay. In theory, UITs are more tax efficient than OEICs.

INVESTMENT PERFORMANCE. During the 10 year period of 2006-2015, the compound annual growth rate of Standard and Poor’s 500 Total Return Index was 7.2%. In comparison, the growth rates of an index ETF (ticker: SPY) and an index mutual fund (ticker: VFINX) were 7.1% and 7.0% respectively. The slight differences in performance were due to an expense ratio, tracking error, and pricing error of the investment funds compared to the index.

OTHER INDEX FUNDS. There are indices to measure the investment performance of bonds, commodities, precious metals, and other assets. Likewise, there are mutual funds and ETFs that track the various indices. Bond index funds are managed by OEICs and require frequent turnover of the underlying bonds. The index funds for commodities, precious metals, and other assets are structured as grantor trusts, partnerships, or debt instruments. Stock index funds are generally less expensive, taxed at lower rates, and less risky than other index funds. Leveraged ETFs are exceptionally risky investments designed for same-day trading.

CONCLUSION. A broad-market stock index fund is the correct investment for earning returns from the entire stock market or a sector of the stock market. Simply choose an established, reputable index for the particular market that interests you. Then choose an established, reputable mutual fund or ETF that imitates the index. Use screeners or reputable fund families to select appropriate funds. Verify the fund’s expense ratio, extra fees (if any), NAV, longevity, and passive management by reading the prospectus and/or research reports. XTF.com is a free and excellent rating service for screening and assessing ETFs. Cross check your research with a trusted broker.

Investment strategy of the SmallTrades ETF Portfolio

February 14, 2014

An index ETF is designed to capture the investment returns from a financial market.  The SmallTrades ETF Portfolio (“Portfolio”) uses index ETFs to invest in several financial markets.  The goal of the Portfolio is to earn returns at a faster rate than possible by investing in risk-free bonds or the broad market of U.S. stocks, thereby ensuring that the accumulation of returns outpaces the inflation of prices in the American economy.  Success is measured by the following benchmark indices:

Investment strategy

The Portfolio is a high-risk, high-return investment in ETFs that duplicate well-established market indices for global stocks, U.S. bonds, U.S. real estate investment trusts, and gold bullion.  Twenty five percent of the portfolio’s market value is allocated to each index.  The ETFs generate at least 99% of the portfolio’s value and any remaining value is stored in a money market fund.  The ETFs will be held indefinitely except when faced with the advantage of replacing one with a more suitable ETF for the same index.

Table of holdings

ETF trading symbol Market Allocation
 AGG   U.S. bonds 25%
 GLD   Gold bullion 12.5%
 SGOL     Gold bullion 12.5%
 VNQ     U.S. real estate investment trusts 25%
 VT  Global stocks 25%

Expected return

Unfortunately there is no 50-100 year history of ETF performance that enables the forecast of an expected return.  To compensate for this limitation, two models were used to test the allocation plan shown in the table of holdings.  In one model of the 15-year recovery from the 1997 Asian Financial Crisis, the allocation plan outperformed the U.S. stock market.  In the other model of the 5-year recovery from the 2008 Global Financial Crisis, the allocation plan underperformed the U.S. stock market.  Among both time periods, the lowest return of the model portfolio was 8.5%.

  • MARKETS portfolio of financial-market returns from 1997 to 2011: The global-stocks market was simulated by a mixture of 75% U.S. large capitalization stocks and 25% emerging markets stocks.  Trading and management fees were excluded from the model.  The annualized return of the portfolio was 8.5% in comparison to the 5.7% annualized return of U.S. large capitalization stocks.
  • ETF portfolio of historical prices from 2008-2013: Trading fees, but not management fees, were included in the calculations (– management fees are charged in the primary market before ETFs are listed in the stock market).  The annualized return of the portfolio was 10.9% in comparison to the 17.8% annualized return of SPY, an ETF that tracks the Standard & Poor’s 500 Total Return.

Risk management

The holding period will be at least 5 years.  Fluctuation in market prices is the main risk of investing in index ETFs.  The likelihood of incurring a loss from a declining market decreases as the length of the holding period increases (– e.g., the risk of loss from stocks and bonds declines by 50% as the length of the holding period increases from 1 to 5 years; and, the risk declines by 80% when the holding period is extended to 10 years (1)).

The Portfolio will be rebalanced as needed to maintain the allocation plan within an acceptable limit of 28% error.  The Portfolio is concentrated in 4 markets and losses may occur when one or several markets decline.  The 25% allocation plan assigns equal weightings to each financial market in order to smooth the effect of market declines.  After accounting for trading fees, the strategy of rebalancing a large allocation error is more cost-effective than using a rebalancing schedule.

The Portfolio holdings are investable, have established reputations, charge low management fees, and are safely structured.  Although there’s no guarantee that the index ETFs will sustain their historical performance, the stock market, bond market, and real estate market ETFs provide diversified investments in underlying assets.  The risk of investing in these ETFs is lower than the risk of investing in an underlying asset.  Gold bullion ETFs are non-diversified investments in the volatile gold market.  Gold bullion is theoretically susceptible to physical damage by theft or fire.  This risk is diminished by investing in two funds, GLD and SGOL, that store the bullion in separate vaults located in London and Lucerne.

The investor’s tax burden can be reduced by holding these index ETFs in a tax-deferred retirement account.

Copyright © 2013 Douglas R. Knight


1.           James B. Cloonan, A lifetime strategy for investing.  American Association of Individual Investors, Chicago, 201

#ETF Scorecard, Vanguard Total World Stock ETF (VT: nyse)

January 31, 2014

The Vanguard Total World Stock ETF (VT) is an index fund that holds stocks and REITs issued by companies in the emerging and developed markets. Stocks from the frontier markets are excluded by the Fund. The following chart shows that VT is an established fund which efficiently manages its stock portfolio with the good prospect of sustaining its operations:


The following scorecard rates VT as a wealthy, tax efficient fund with several risks: 1) market volatility. 2) potential management error. 3) fluctuating exchange rates for foreign currency.



The FTSE All-World Index is derived from the FTSE Global Equity Index Series (GEIS), which covers 98% of the world’s investable market capitalizations. The FTSE All-World Index is a market-capitalization weighted index of the large- and mid-cap stocks listed in developed and emerging markets; frontier markets are excluded. The stocks are selected and weighted to ensure that the GEIS is an ‘investable’ index.

Fund operations

VT operated a $3 billion, diversified portfolio of 800 stocks in the year 2013. Most of the stocks had large capitalizations (77% large cap, 13% mid cap, 10% small cap) and most were issued in developed markets. The regional distribution of stock issuers was greatest in North America & Europe (78%) followed by Asia (19%), Latin America (2%), and Africa (1%).

According to the ETF.com website (1), VT’s major competitors in 2013 were ACWI, ACIM, ACWV, HECO, and ONEF. Among these, VT offered the lowest annual expense ratio, 0.19%. VT, ACWI, and ACIM operated in very similar ways to match the performance of their market indices; their returns were tax-efficient. In comparison, ACWV, HECO, and ONEF sought to outperform the global equities market.

The following chart was found in the ETF.com website (1). Visual inspection of the chart gives an impression that the net asset value (NAV) of VT’s portfolio closely tracked the performance of its index (the underlying FTSE index) and the market segment’s index (MSCI All World Investable Markets + Frontier).


According to the ETF.com website (1), VT’s operations were less transparent than the competitors’ due to Vanguard’s practice of reporting holdings on a monthly rather than daily basis. Similar to other competitors, VT lent its portfolio holdings to help offset the Fund’s expenses. Institutional investors incurred a higher cost for buying creation units from VT than from other Funds.


VT is a good long-term investment.

#01. http://www.etf.com/, © ETF.com 2014

#ETFscorecard_SPY, SPDR S&P 500 ETF

July 12, 2013

SPY was the first exchange-traded index fund sold in the U.S. Stock Market.   Today’s investment goal remains the same from inception: to earn returns, before expenses, that correspond to the price and yield performance of the S&P 500 Total Return Index.  The S&P 500 index measures the intraday value of the 500 largest stocks listed in U.S. stock exchanges.  SPY’s annual expense ratio is 0.09% and the Fund is considered to be tax-efficient.   It is structured as a unit investment trust (UIT) to protect the Fund from management error.  The following profile and scorecard support a long-term investment in SPY.





Copyright © 2013 Douglas R. Knight

#ETFscorecard_VWO, Vanguard FTSE Emerging Markets ETF

June 28, 2013

VWO is an index fund that invests in stocks issued by companies in the emerging markets.  The following profile shows that VWO is an established fund that operates at a low rate of turnover.


The VWO scorecard (below) reveals a wealthy, experienced index fund that offers tax-efficient returns.  The risks to underperformance are 1) market uncertainty and volatility, 2) erroneous judgment in management of the portfolio holdings, and 3) unfavorable exchange rates for foreign currency.


Fund operations

The Fund is a registered investment company for tax purposes.  The annual expense ratio is 0.18% and the net assets are about $46 billion.  The Fund’s strategy is to invest 95% of assets in stocks of the index diversified across industrial sectors (financial 27%, energy 13%, technology 11%, basic materials 10%, etc.) and regions of emerging markets (China 19%, Taiwan 13%, Brazil 12%, India 8%, South Africa 8%, Russia, 6%, other).  Dividends are distributed quarterly.

The FTSE Transition Index currently tracks ~800 stocks from emerging markets, including South Korea.  In 2014, the “transition index” will be replaced by an FTSE Index that excludes South Korea.

RISKS:  Emerging market stocks may be more volatile and less liquid than domestic stocks.  Emerging markets are less regulated than developed markets.  Foreign countries have different regulatory mechanisms and risks of disaster.  Foreign currency may decline in value, lowering the stock values.

VWO is a good investment for diversifying your ETF portfolio.

#ETFscorecard_VNQ, Vanguard REIT ETF

June 28, 2013

VNQ is an index fund that invests in U.S. real estate properties by purchasing shares of real estate investment trusts (REITs).  The following profile shows that VNQ is an established fund that operates at a low rate of turnover.


The VNQ scorecard (below) reveals a wealthy, experienced index fund that invests in a well-developed market for REITs.  The fund may be tax inefficient when cash distributions are taxed as ordinary income.  The risks to underperformance are 1) erroneous judgment in management of the portfolio holdings, and 2) generic risks of investing in the real estate market.



Fund operations

The Fund is a registered investment company for tax purposes and issues quarterly dividends.  The annual expense ratio is 0.1% and the net assets are valued at approximately $17 billion dollars.

The benchmark Index measures the performance of 85% of the U.S. Equity REIT market (~116 REITs) and is rebalanced quarterly.  The equity REITs are diversified among residential and commercial properties.

Real estate is an illiquid asset, but equity REITs are easily traded in the stock market.  Equity REITs own and manage real estate.  They must receive 75% of income from rents and sales and they must distribute 90% of taxable income to shareholders.  Equity REITs earn income by attracting tenants, renewing leases, and financing property purchases/improvements.  REIT stocks are typically small and mid-cap sized.

The main investment risks are: 1) concentrated investment in the REITs/real estate industries, and 2) competing interest rates may attract investors away from REITs.

VNQ is a good investment for diversifying your ETF portfolio.

#ETFscorecard_AGG, iShares Core Total U.S. Bond Market ETF

June 28, 2013

AGG holds a portfolio of investment-grade U.S. bonds and distributes monthly dividends.  The following profile shows that AGG is an established fund that operates at a high rate of turnover.


The AGG scorecard (below) reveals a wealthy, experienced index fund that invests in a well-developed market for bonds.  The fund is tax inefficient due to the high rate of turnover of portfolio holdings.  The risks to portfolio underperformance are 1) erroneous sampling of the bond index, 2) erroneous judgment in management of the portfolio holdings, and 3) generic risks of investing in the bond market.


Fund operations

AGG is a registered investment company for tax purposes.  Its strategy is to invest 95% of capital in a diversified basket of U.S. investment grade bonds that serve as a representative sample of the benchmark index.  The portfolio’s profile is that of an average A credit rating of the issuers, average intermediate term bonds, average 4.86% effective duration, average 4.06% weighted coupon, and average $107.46 weighted price. The remaining 5% of capital resides in cash-equivalent securities and bonds excluded from the index.  Fund management may lend up to 33% of the underlying securities to outside investors.  High portfolio turnover rate will increase the Fund’s operating expenses.

The benchmark Index measures the performance of the total U.S. investment grade bond market.  The bonds must be USD denominated, non-convertible, and have a fixed rate.  The Index is updated monthly.

Fluctuating interest rates in the bond market may reduce the investment performance of the Fund.  In the case of declining interest rates, the Fund may replace Called bonds with those of lower interest rates.  During periods of rising interest rates, long-term bonds with low interest rates will effectively reduce the Fund’s income. Rising interest rates can also lower the market value of the bonds.  A portion of the Fund’s mortgage-backed securities are not issued by government agencies and are therefore not protected against default.

AGG is a good investment for diversifying your ETF portfolio.


April 21, 2013

(updated 7/31/2013)

The Small Trades Portfolio Designer is used to test model portfolios that hold 1-9 sectors of financial market returns plus a cash supply of U.S. dollars.  The program is pre-loaded with monthly returns computed from broad market indices during the 15 year period of 1997 to 2011.  You create the model portfolio by entering an allocation plan, investment amount, and rebalancing strategy.  The results are displayed in tables and charts on the same worksheet. You have the option of assessing the impact of trading costs and investment fund fees on portfolio returns.  The program can be downloaded for free by clicking here: SmallTradesPortfolioDESIGNER.

Allocation plan

At the top of the worksheet, each class of securities is labeled according to a unique combination of market region, market sector, and asset class.


Consider, for example, funding a portfolio that is 54% invested in large-cap U.S. stocks, 36% invested in U.S. bonds and 10% stored in cash.   For every $100 invested, $54 are allocated to U.S. large-cap stocks, $36 to U.S. bonds, and $10 to a cash reserve.  The allocation plan consists of weighting factors 0.54/0.36/0.10 [the article designing a buy-and-hold portfolio offers advice on creating allocation plans relevant to your investment goal].  The following entries are made next to the appropriate labels:


Rebalancing strategy

designer3Suppose the portfolio is funded with $10,000 [comment: lower payments might be less efficient investments when factoring in the costs of trading fees and expense ratios].  Two methods of rebalancing the portfolio are scheduled (e.g., every year) and signaled.  Suppose you wish to test the signaled method by choosing “no schedule” from the pull down list of the “Rebalance schedule” cell and “signal 3” from the pull down list of the “Rebalance signal” cell.   “Signal 3” is a command to rebalance the portfolio when market forces unbalance the portfolio to an unacceptable degree of error.  The result is an intermittent series of rebalancing episodes that modify the historical returns.  “Signal 1” and “signal 2” evoke a different number of rebalancing episodes by modifying the boundary for unacceptable allocation error.  It’s an empirical process for finding the best result.

Investment costs


The “risk-free bond rate” is used to calculate the Sharpe ratio.  I recommend a rate that estimates the risk free return for the holding period of the test portfolio (e.g., a 10 year Treasury Note at inception of the portfolio).  The default bond rate is 2.98% for the 15 year period of this program.  Trading fees and annual expense ratios always reduce investment returns, sometimes by a considerable amount.  Assess these by entering the typical trading fee charged by your broker and an estimated annual expense ratio derived from investment funds and advisor’s fees.  Or consider testing the default costs of $10 for trading and 1% for an annual expense ratio.  These entries are left blank for this tutorial.


The historical returns are summarized by statistics and charts for the  “Unbalanced” (“buy-and-hold”) and “Rebalanced” portfolio. The outcomes of the “Unbalanced” and “Rebalanced” portfolio would be identical without a rebalancing strategy [furthermore, a portfolio of one asset cannot be rebalanced].  In the following table, “CAGR” is the annualized growth rate of the portfolio’s accumulated returns.  “Sharpe ratio” is the average annual investment return adjusted for market fluctuations.   A negative Sharpe ratio implies that risk-free U.S. government bonds are better investments.  Higher values of CAGR and Sharpe are preferred.  The “final value” is the portfolio’s market value at the end of the investment period.


Chart 1 shows the returns based on test conditions.  The market fluctuations ultimately reach the final values shown in the table.  An effective rebalancing strategy creates a gap between both curves.


Rebalanced portfolio

Rebalancing may not improve the investment performance of a portfolio.  However in this example, the signaled rebalancing strategy outperformed the unbalanced portfolio (CAGR 6.59% is better than CAGR 5.65%).  Not shown is that scheduled rebalancing “every 3 years” also outperformed the unbalanced portfolio (CAGR 6.38% vs CAGR 5.65%).  In this tutorial, the result of selecting “signal 3” for the signaled strategy generated a 37.7% boundary error labeled as the “rebalance signal” in the program.


“Signal 3” also triggered 4 rebalance episodes over 15 years (chart 2) when there were no trading costs at inception or rebalance.


Warning messages

The next chart uses red arrows to show the location of warning messages.  These disappear when satisfactory entries are made in the program.  Be aware that the “asset allocations” must total 100% or else the blue-lettered message “Allocations are incomplete” reminds you to check the entries.



The investable securities of the program’s market sectors are index funds, stocks, bonds, real estate investment trusts (REITs), and commodities futures. Index funds are particularly good substitutions for market sectors of the model portfolio.

Test other model portfolios.  The 60/40 Stock-Bond Portfolio, exclusive of a 10% cash holding, is a favorite of many investors.  The 60/40 unbalanced portfolio’s 6.07% “CAGR” and 0.29 “Sharpe ratio” provides a standard for comparison with other allocation plans.  Try creating higher returns by experimenting with different allocations.  Consult the article designing a buy-and-hold portfolio for advice on creating allocation plans relevant to your investment goal.

Apply the rebalancing strategy.  Either the scheduled or signaled strategy can be used to rebalance a portfolio of index ETFs that match the allocation plan of a model portfolio.  The scheduled strategy is straight forward.  Simply rebalance the ETFs according the best schedule determined by this program.  The signaled strategy is not straight forward.  It requires transcribing  data from this program to the Small Trades Portfolio REBALANCER program in the following way:

1. Enter the “Rebalance signal” from the Results of this Designer program into step 1 of the Rebalancer program.  In this example, the correct entry would be 37.7%.

2. Result 1 of the Rebalancer program will display a “Rebalance” message when any of the portfolio’s ETFs satisfies criteria for correction.


A leap of faith is needed to apply the model portfolio to your investment goals.  This program is based on recent 15-year returns and your best bet is to assume that the next 15 years will provide a different investment performance due to market uncertainty.  Even so, I don’t know any investor who completely ignores history.

This program tests strategies for rebalancing a model portfolio.  I know of no other program that provides such information!

The potential impact of trading fees and fund expense ratios is considerable when many portfolio holdings are rebalanced frequently and the expense ratios are high [that’s why respected authors recommend minimizing costs by seeking high-quality, no-fee, no-load investments].  A good rebalancing strategy should augment the expected return of the unbalanced portfolio.

You can download this program free of charge by clicking on SmallTradesPortfolioDESIGNER.  If the program inspires your investing for the betterment of self and society, consider giving a tax-deductible contribution to your favorite charity or my favorite charity.

Copyright © 2013 Douglas R. Knight  

Hey Kids, you can become rich (but it requires work)

March 29, 2013

Everybody should save for retirement.  Retirement is when a person stops working for a living and starts spending money from savings accounts.  Retired people can live in comfort and enjoy their spare time if they stay healthy and save enough money.  As a young person, you can plan on retiring with a lot of money if you invest it for a long time and get a good education.

Investing occurs in banks and companies who belong to the world’s financial system.  Investing is the process of giving money to people who pay back more than you gave them.  You make your money ‘grow’ by reinvesting all the extra money returned to you.  The money that you invest is called the principal.  You can lend the principal or use it to buy stock.  People who borrow the principal make a promise to pay it back with extra money called interest.  People who keep the principal give you shares of stock in a business or investment fund.  When you own stock, the business or investment fund may occasionally share their profits by paying you money called dividends or cash distributions.  You can sell stock for either more or less money than the amount of principal that you paid, depending on how much money the buyer is willing to pay1.  The longer you wait to sell a good stock, the better your chance of making a profit.

One of the important goals of investing is to retire with enough money to live comfortably.  You have about 50 years before retirement, which is a big advantage if you start investing now.  Suppose you invest $1 a year in the stock market and reinvest all the extra money returned to you (this is a good method of investment called “compounding”!).  In 50 years you could expect to have $464 by investing only $51 of your own money.  Investing $100 a year in the same way will get you $46,444 for payments that add up to $5,100.  If you invest $2,160 a year for 50 years, you could receive $1,000,000 (one million dollars) by paying $110,160.  Becoming rich is possible by managing money wisely, investing regularly, and getting a good job after graduation from school.  [You can begin with small payments and increase them when you get a good job!  Click on this Investment Returns calculator to create your own plan].

Many people in the financial system are honest, but there’s always the chance you can lose money from making a bad investment, paying too many fees to professional investors, or dealing with a dishonest person.  That’s why you need good advice from people you trust (parents, reference librarians, books, accountants, etc.)2.  There are four important steps to investing for 50 years:

(1)    SAVE money now

(2)    INVEST in stocks

(3)    PROTECT your investments

(4)    DIVERSIFY your portfolio

SAVE money now

Now is the time to begin saving money in a bank account that pays interest.  Your money is safer in the bank than at home.   Plan on saving at least 10% of the money you earn from allowance, gift money, and job money (10% of a dollar is ten cents)3.  Later on you will use your savings to invest in stocks and pay for other important things.  Ask your parent or guardian to open a bank account for you so that you can save money to invest.

Advice: Don’t spend money on things you don’t need.  Fun is something that you definitely need, but don’t spend too much money on having fun.

Advice: Save money for the rest your life.

INVEST in stocks

Use the money that you save to invest in stocks.  The way to start investing is to open an an investment account with the help of your parent or guardian.  Think of your first investment account as a retirement account and later on start your own Individual Retirement Account or 401k Plan when you get a regular job.  You want the manager of your investment account to prepare tax statements and send you periodic statements on the account’s value.

The best way to invest in stocks for 50 years is to buy shares of an index ETF or index mutual fund that invests in most of the stocks listed in the U.S. stock market.  Be sure to enroll in the index fund’s automatic reinvestment plan to ensure growth of your investment4.  I know at least three ways to start investing in the stock market [please see the Appendix at the end of this post].   You can also find stock and index fund dealers through an online search of stock brokers (e.g., Online Stock Trading Review, NASDAQ).

Advice: Be a thrifty investor.  Use an automatic reinvestment plan to accumulate wealth from the stock market and never pay unnecessary fees1-4.

Advice: Be a thrifty investor.  Plan to invest your earned income in an Individual Retirement Account and take advantage of the 401k Plan offered by your employer1-4.

PROTECT your investments

Right now your parents, banker, and investment account manager help protect your savings and investments.  But when you become an adult you should build walls of protection against losing money and review your investments.  The strongest walls of protection are employment, money management, and insurance.

  • Employment provides money to live in comfort.
  • Planning is needed to pay bills, save money for emergencies, and continue investing.
  • Insurance is needed to pay for unusual costs of health care and costly disasters.

Review your investments at least once a year to be sure nothing is missing and that they are performing as expected.  Take advantage of any new knowledge about investing that can help you reach your goal.  You will get better at reviewing your investments with practice and study.

Advice: Be a wise planner.  Don’t spend your retirement savings on other things1-3.

DIVERSIFY your portfolio

All the investments that you own are called an investment portfolio.  When you become an adult, be sure to diversify your portfolio to avoid losing money to the financial system.  Diversify means to own a mixture of financial assets such as stocks and bonds.  Many good investors put 60% of their money in stock index funds and 40% in bond index funds1-4.


With good advice and planning you can save for retirement and get a good education.  Investing for retirement is a goal worth having.  Start now so that your investments have plenty of time to grow.  Invest just 10% of your money for retirement and use the other 90% for other things, including saving for a good education.

After graduation from high school consider getting a college education or enrolling in a technical training program to prepare for a career.  A good job will allow you to invest more money as you get older and you will be rewarded with a lot more money for the effort.  You don’t have enough time to save all the money needed to pay for a college education.  You are going to need help, so start asking for help now. Read good books and ask for advice from people you trust.

Good Books

1.       Fred Barbash, Investing Your Money (Exploring Business and Finance).  Chelsea House Publishers, Philadelphia, 2001.  [The best book for pre-teen readers]

2.       Tim Olson, The Teenage Investor. McGraw-Hill, 2003.  [A reputable and inspirational book for teenagers]

3.       George S. Clason. The Richest Man in Babylon. Penguin Books, New York  © 1955, .., 1926. [A good explanation of money management for teenagers]

4.       John C. Bogle, The Little Book of Common Sense Investing.  John Wiley & Sons, Inc. Hoboken, 2007. [The best book about stock index funds for college students]


I know at least three ways to start investing in the stock market.   The first is by opening a brokerage account at a discount brokerage firm.  I use Charles Schwab & Co., Inc., as an example because their representatives are helpful and give good advice on the telephone (877-673-7970).

  • Schwab requires your parent’s email address and charges $100 to open the account.  Your $100 deposit can be invested right away or saved in Schwab’s bank until you’re ready to start investing.  Their bank pays interest on all deposits.  Schwab does not charge any fee to invest in its index ETFs or index mutual funds.  Otherwise, a variety of fees may be charged for other mutual funds (Schwab’s representative can explain those fees).  Schwab charges an $8.95 commission to sell shares of a stock or shares of an ETF issued by a different company.

Second, buy an index fund from a mutual fund company.  I use the Vanguard Group, Inc., as an example because their representatives are helpful and give good advice on the telephone (800-319-4254).

  • Vanguard charges between $1,000 and $3,000 to invest in a Vanguard mutual fund.  The price depends on the fund you select.  Additional investments can be made for $100. Vanguard’s representative can help you select a mutual fund.

Third, make a direct purchase of stock.  I use GE Stock Direct as an example because the General Electric Company (GE) is a famous stock that pays dividends.  GE Stock Direct is accessible through the Computershare Trust Company, N.A. (800-522-6645).

  • GE Stock Direct charges $7.50 to open the account and at least $250 for the initial purchase of GE stock.  Additional purchases of $10-$10,000 can be made weekly.  The share price is the average of the trading day’s high and low share prices.  The purchase fee is $1 per electronic transfer from your bank or $3 for your mailed check.  GE Stock Direct also charges a redemption fee of $10 + $0.15/share to sell shares of stock.  The selling price is the “same day’s price” before 2:00 pm EST or the current market price on the next day after 2:00 pm EST.  GE Stock Direct will transfer your shares to another person at no charge either in the form of certificates in the name of the recipient or to the recipient’s account.  The transfer agent is the BNY Mellon.  GE Stock Direct’s operating structure is designed for long term investment that makes it impossible to participate in day trading.

Schwab, Vanguard, and GE Stock Direct commonly operate in the following ways:

  • Children must open a custodial account with their parent or guardian.  The child must have a social security number.
  • Dollar cost averaging is encouraged by the vendor
  • Automatic reinvestment plans are offered free of charge.
  • Tax and Account statements are sent to an email address provided by you.  Beware that GE Stock Direct does not send tax statements; the shareholder must keep own tax records by saving all account statements.
  • Tax-deferred retirement accounts can be opened when the owner starts receiving earned income.  A maximum $5,500 can be invested every year.  GE Stock Direct does not offer tax-deferred accounts.
  • Shares are held in book-entry form

Copyright © 2013 Douglas R. Knight

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