Mutual Funds and Index Funds (Preliminary Version)

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Bogle's Arithmetic to Compare Expenses and Performance of Actively Managed

Mutual Funds and Index Funds (Preliminary Version)

Floyd Vest, March 2014

This article is based on Bogle, John C., "The Arithmetic of "All-In" Investment Expenses," Financial Analysts Journal, Jan./Feb., 2014, Vol. 70, No. 1:13-21. The reader needs a copy of this article in hand to follow our discussion and complete the exercises. Go to . Click on FAJ. Do a search for Bogle in this publication. The article has only ten pages including the abstract. The abstract and PDF copy are free. (See the Side Bar Notes for more on the Financial Analyst Journal.)

Investment expenses. Bogle reviews some of the research on stock fund expenses and performance. He describes and estimates several types of expenses and presents them in

Table 1: All-In Investment Expenses for Retirement Plan Investors.

For the following exercises, show your work. Label answers, numbers, and variables.

When appropriate answer in complete sentences. When appropriate give some code and commentary.

Exercise #1. Summarize Bogle's summary of research on fund expenses and performance.

Exercise #2. Describe each of Bogle's four types of expenses for actively managed stock funds and index funds. Explain his method of estimating each. Discuss the summary in Table 1. What percentage of no load fund investors incur some kind of load expense? What percentage of mutual fund investors buy load funds? Give a guess. What is the average load?

Exercise #3. Discuss the top of Table 2 giving returns and costs. Discuss the assumptions and calculations.

Preparing for retirement.

Exercise #4. Apply the two returns to Bogle's 30-year old investor to get her After 10 years accumulations, and her After 40 years accumulations. Give a general approach for after n years. The first step will be to discover Bogle's time line. See the article in this course "The Mathematics of Financial and Social Responsibility" which presents different time lines and savings formulas. You may prefer calculating with a computer program or a spreadsheet.

Exercise #5. Discuss and check the numbers in Bogle's discussion of advantages of the index fund. See page 17. Give Bogle's comparison.

Exercise #6. Use the formula for P1 on page 174 of the above article in this course to calculate from age 70 to age 100 (30 years) the optimal first year withdrawal under the two returns of 4.73% and 6.94% with 3% inflation and Bogle's 40 year accumulations. Compare these in the manner used by Bogle. What is a shortcoming of this approach to calculating required funds and available withdrawals (the Sequencing effect)?

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Exercise #7. From Exercise #6, calculate the total sum of annual retirement incomes for each case. Do a comparison of Bogle's type.

Exercise #8. If P1 gives the optimal distribution under the assumptions with 100% efficiency, what is the efficiency of the 4% Rule? With the above constant average returns and inflation, how much does the 4% Rule leave on the table at age 100?

Exercise #9. Scott and Watson claim their Floor-Leverage Rule for Retirement is 98% efficient. Read and summarize the investment strategy given in their Abstract and Summary. See the Financial Analysts Journal at .

Exercise #10. Scott and Watson used geared funds. See ProShares UltraPro S&P500, Ticker UPRO, at finance. and calculate its annual return from mid February, 2011 to Mid February 2014. Calculate the return for the S&P 500, Ticker ^GSPC. How do geared funds work? How do they achieve leverage? See .

Exercise #11. Geared funds' returns are calculated daily and compounded daily. For a two day upward trend of 10%, 10%, when the benchmark (S&P500) gains 21%, the 2x Fund gains 44%. For a downward trend of 10%, 10%, when the benchmark (S&P500) loses 19% in two days, the 2x Fund loses 36%. Do the calculations to verify this. See , Geared Funds Performance.

Exercise #12. See other articles in this course on retirement withdrawals and expense ratios. Summarize.

Exercise #13. Who is John C. Bogle? Summarize his significance and history. You can find information in his article and get a good summary by searching the internet. See and .

Exercise #14. For Table 2, what does Bogle mean by "Retirement Plan Investors" and their investment programs and income taxes? Discuss. For tax favored retirement savings plans, see several articles in this course including the recent "Health Savings Accounts," Jan. 2014. See the Side Bar Notes.

Taxes and Taxable Investors.

Exercise #15. Summarize taxation for mutual funds and Bogle's tax expense numbers. Check them against Morningstar, Vanguard, and American Funds.

Exercise #16. Do the calculations and reproduce the graphs and numbers in Figure 1.

Real vs Nominal Returns.

Exercise #17. Give two formulas that people use for real returns. What has been the rate of inflation in the recent years before 2014?

Counter Productive Investor Behavior.

Exercise #18. Describe Counterproductive investor behavior and its financial results. How do mutual fund investors in general differ from those in index funds?

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Reconciliation.

Exercise #19. Describe "survivorship bias." What percentage of funds survived? What type of funds? What is the historical underperformance resulting from discontinued funds?

Exercise #20. Make up examples of the relative significance the effect of low and higher expenses on the short term and the long term investments.

Exercise #21. How are load fees charged on load funds? Sometimes they are designated as A shares, B shares, and C shares.

Exercise #22. Who is William F. Sharpe? How are his writings used in articles in this course? See .

Exercise #23. Will the 4% rule work with recent (1999 to 2012) poor and bad performance of stock returns and current problems with bonds? See Kitchens, "Are Safe Withdrawal Rates Still Relevant in Today's Low-Return Environment?" Sept. 2013 at . It is free. Summarize parts of the article. He provides examples of the sequencing effect (the ups and down of the retirement portfolio during retirement).

Exercise #24. Who are Chartered Financial Analysts? What do they do? What do they study? Do a search on the internet. See and . Also see the Occupational Outlook Handbook: US ... . See .

Exercise #25. AAII's Dividend Investing newsletter reported Total Returns over 40 years from 1972 to 2013 and that for stocks with no dividends, the growth was 107%, for stocks with fixed dividends, the growth was 1,707%, and for stocks with rising dividends, the growth was 4,312%. By investing in rising dividend stocks over fixed dividend stocks, you would have increased your gains by an average off 33% each year. Do some math with these examples. Can you make the 33% work. See the articles in this course "High Dividend Yields on Stocks, and Low Interest Rates on CDs and Bonds," and "Dividend Growth."

Exercise #26. In discussing the sequencing effect, Money magazine, March 2014 says that using the 4% rule and starting with $1M, your retirement fund balance could reach $2M at some point before it drops off. Give a reasonable but optimistic example with an average inflation rate I and a rate of return r which would produce this effect at some point over 30 years. You could do a graph. At what year does your graph max out?

Exercise #27. According to Forbes, March, 2014, a 65 year old retiree can secure income with a deferred income life time annuity which costs $85,000 at age 65, and which starting at age 85, pays $5000 per month for life. At $60,000 per year, what interest rate does it pay to age 90, to age 95, to age 100. You may need to use a Solver. Describe your method including some code and commentary.

Exercise #28. For the Vanguard Total Stock Market Index Fund, there are about 5000 stocks on the market. How does the fund manage these stocks? What is the expense ratio for Admiral shares (ticker VTSAX) and for Investor shares? How much must be invested in the fund to qualify for Admiral shares?

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Exercise #29. Under "Reconcilliation", by how much do the adjusted average annual returns of actively managed large cap funds lag the adjusted Total Stock Market Index Fund? What about the 10 year comparison on page 18?

Exercise #30. For $10,000 invested for 40 years in a managed stock fund, calculate the accumulation before taxes and the accumulation after taxes. Discuss the significance. Do the same for the index fund.

Exercise #31. Under "Counterproductive investor behavior", what is asset-weighted return earned by investors? See the article in this course, "Time Weighted Returns versus Dollar Weighted Returns," Feb. 2013.

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Side Bar Notes:

Six types of retirement funding and spending are described in Forbes magazine, March 2014, p. 80. One is a ladder of bonds held to maturity. Another is the 4% and similar rules.

See the Dynamic strategy at T. Rowe Price. There is the Basket strategy (Scott and Watson's floor-leverage version is an example). Also, Social Security (See the articles in this course on Social Security.)

The Financial Analyst Journal is published by the Chartered Financial Analyst Institute (CFA Institute). See .

Of the 20 largest stock mutual funds ? only one outperformed the S&P500 in the last five years, only three in the last three years, and only five in the last year, through Jan. 31, 2014 (Kiplinger's Personal Finance, 4/2014, p. 43).

A stock picker's formula. Seagate (STX, $53) still sells for 10 times estimated earnings for the next year (P/E = 10). Analysts expect earnings in the following year to rise by 11.2%, and the stock has a 3.3% dividend. The sum of 11.2% + 3.3% = 14.5% which is way more than the P/E of 10. Seagate is fairly priced and may even be a bargain. P is price and E is earnings per share. P/E is price divided by earnings per share. Formula: Compare the sum of expected rise in earnings (11.2%) plus dividend yield (3.3%) to P/E (10). (Kiplinger's Personal Finance, 4/2014, p. 38). Was Seagate a good investment? See finance.. (See "Stock Pricing Models," Jan. 2014 in this course.)

Vanguard Total Stock Market ETF (VTI) holds 3,657 stocks. (Kiplinger's, Personal Finance, 4/2014, p.20)

Zero percent tax rate. For married couples with a taxable income of $72,500 or less, the income tax rate for capital gains and qualified dividends is 0% (Kiplinger's Personal Finance, 4/2014, p. 53).

A Retirement Savers Tax Credit up to $1000 may be taken by investors whose income qualifies. It can even be invested in a Roth IRA (Kiplinger's Personal Finance, 4.2014, p. 62). For this topic at , type in "Retirement Savers Tax Credit."

A bond fund which can't lose money is offered in a government saving program - a MyRA offered by some employers. It is a Roth IRA and is invested in the government Thrift

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Savings Plan G Fund recently earning between 1.47% and 2.97% (More than any money market fund and more than some five year CDs). (Kiplinger's Personal Finance, 4/14, p. 62) See for MyRA. See "US Government Thrift Savings Plan (TSP)", Jan. 2013 in this course.

Hedge funds: From March 1997 to Dec. 2013, adding a 33% exposure of hedge funds would have reduced the return of the standard unmanaged 60/40 portfolio by an annualized 0.6% with a modest reduction in risk. A typical hedge fund charges 2% in fees plus 20% of any profit. The 2,257 funds in Bloomberg's Hedge Fund Aggregate Index averaged 7.4% for 2013 while a 50/50 portfolio of index funds returned 10.41% at a lower risk. The S&P500 Index returned 32.39%. The sum of $2.25 trillion is invested in hedge funds. If all the money that's ever been in hedge funds had been invested in Treasury bills, the result would have been tice as good (Scott Burns, Denton Record Chronicle, Feb. 9, 2014).

Retirement money. Only 45% of recent retirees think their money needs to last at least 20 years (Money, Jan./Feb. 2012 p. 27).

Complaint that Bogle owns managed funds. He has ownes Vanguard Wellington (VWELX) in which he invested during 1951 when he first went to work for Vanguard. He supports his Number Two son by investing in the son's Bogle Small Cap Growth Fund (BOGLX).

Income taxes and Social Security. For a Social Security retiree with a related spousal benefit, a typical Social Security benefit starts at $23,343. For this couple with "total income" of $59,343, the tax bill is $2561. Add another $6000 brings the "total income" to $65,343 and the tax bill increases to $4256, and increase of $1695. This is a marginal tax rate on the last $6000 of 28.2%. A non Social Security couple needs a taxable income of more than $146,400 to pay a 28% marginal rate (Scott Burns, Denton Record Chronicle, March 2, 2014). Estimate their "total income." Use a tax program to check Scott's figures. (See the article in this course, "Income Taxes on Social Security," March 2012.)

Comparison of average 10 total returns ending Dec. 31, 2013. For large-cap stock funds, average 7.4%; Vanguard Total Stock Market Index Inv. (VTSMX) average 7.9%. For mid-cap stock funds, average 9.4%; Vanguard Mid-Cap Index Inv. (VIMSX) average 9.9%. For smallcap stock funds, average 9.2%; Vanguard Small-Cap Index Inv. (NAESX) average 10.2%. Vanguard S&P 500 Index Inv. (VFINX) average 7.2%. (AAII Journal, Feb. 2014). For largecap stock funds, 49 out of 107 out performed the Vanguard Total Stock Market Index Inv. For load funds, returns were not adjusted for sales load fees. Vanguard funds are no load funds. For VTSMX, for Investor shares the expense ratio is .17% and for Admiral shares, it is .05%. Ten thousand dollars invested is required for Admiral shares. There were listed funds without a ten year history. There were no discontinued funds listed. Variable annuity stock funds were not listed. The stock funds in the US government Thrift Savings Plan were not listed. There are large companies which have stock funds reserved for their employees. If the averages were calculated back to 1999, they wouldn't be as good. See the article in this course, "Annual Total Return Table for the S&P 500 Index of Stocks."

References:

For a free course in financial mathematics, with emphasis on personal finance, for upper high school and undergraduate college, see and click on the box and register.

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They will email you a password. Just click on an article in the annotated bibliography, download it, and teach it. Unit 1: The Basics of Mathematics of Finance, Unit 2: Managing Your Money, Unit 3: Long-term Financial Planning, Unit 4: Investing in Stocks and Bonds, Unit 5: Investing in Real Estate, Unit 6: Solving Financial Formulas for Interest Rate. Unit 7: More Advanced or Technical (For about ten articles in this area, see the UMAP Journal at COMAP.)

Count the number of articles in this course that are basic to this article.

Your school library may provide an on line portal to the above magazines

and all articles in the journals. You may even have access at your home computer.

For high expense ratios, see in this course "Investing in Tax Deferred Variable Annuities," 7/13.

Teacher's Note: Divide some of the Exercises among students and have them provide a written report to the class.

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