Graham, the arithmetic, and a plan
Benjamin Graham's defensive investor, Bogle's "relentless rules of humble arithmetic", and the plan he suggests: one investor's reasoned view.
FinanceBogle ch. 16–18About 5 min: 3 reading, 2 practiceUpdated
General education, not financial advice.
- Summarise Bogle's argument in a few steps
- Connect it to Graham's defensive investor
- Describe Bogle's own suggested plan and explain why it is his view, not a rule for everyone
Common-sense investing: the case for index funds: lesson 13 of 13
- Bogle ch. 1
- The Gotrocks family 4 min
- Bogle ch. 2
- Where stock returns come from 5 min
- Bogle ch. 3
- Owning the whole market 4 min
- Bogle ch. 4
- Costs and the market return 3 min
- Bogle ch. 5
- Fund returns versus investor returns 6 min
- Bogle ch. 6
- Taxes are costs too 5 min
- Bogle ch. 7
- When future returns are lower 5 min
- Bogle ch. 8–9
- Why past winners rarely repeat 5 min
- Bogle ch. 10
- Paying for advice 5 min
- Bogle ch. 11–12
- Costs go on forever 5 min
- Bogle ch. 13
- Bonds and money-market funds 4 min
- Bogle ch. 14–15
- New indexes and ETFs 5 min
- Bogle ch. 16–18
- Graham, the arithmetic, and a plan 5 min
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Pairs with Bogle, The Little Book of Common Sense Investing (2007), chapters 16–18, "What Would Benjamin Graham Have Thought about Indexing?", "The Relentless Rules of Humble Arithmetic" and "What Should I Do Now?"
What it is
Graham's defensive investor. In The Intelligent Investor (1949), Benjamin Graham said most people lack the time or inclination to treat investing as a business. They should be defensive investors: diversify, keep it simple, and resist the temptation to chase extra return. Bogle argues the index fund, invented decades later, is exactly that approach.
The relentless rules. Bogle's whole book rests on a few steps you've now worked through:
- Over the long run, stock returns come from the businesses: dividends plus earnings growth.
- In the short run, emotions (changes in the P/E ratio) dominate, but they tend to even out.
- Before costs, investors as a group earn the market return. After costs, they earn less, by exactly what they pay.
- Timing and fund-switching cost investors more again.
- Costs and taxes persist; past winners don't. So owning the whole market at low cost is, in his view, the most reliable approach.
Bogle's plan. In his last chapter he suggests: hold the broad stock and bond markets through low-cost index funds, and stay the course. If you want to gamble, keep it to a small "funny money" account, no more than about 5% of your investments, and compare its results honestly with your "serious money". For the mix of bonds and stocks, his personal rule of thumb is a bond share roughly equal to your age (or perhaps your age minus 10), though he says himself there are no hard-and-fast rules and that most experts think it too conservative.
Quick check
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What did Graham mean by a "defensive" investor?
- Graham's defensive investor also owns shares
Show answer
Someone who keeps investing simple and diversified, without trying to outsmart the market. Defensive = simple, diversified, patient.
Why it matters
Bogle's argument is one of the most influential in modern investing, and much of it is plain arithmetic you can check yourself. His plan, though, is one person's choice: how much to hold in stocks or bonds depends on your goals, your time horizon, your income and how you would cope with a big fall. That is for each person (perhaps with professional help) to decide.
Worked example
The arithmetic in one picture. Suppose the market returns 7% a year for 30 years, and 10,000 is invested.
- Market return, no costs: 10,000 × 1.07³⁰ ≈ 76,100.
- Index fund at 0.1%: 6.9% a year → about 74,000.
- Typical active fund at 1.5%, plus 1 point lost to bad timing: 4.5% a year → about 37,500.
Every number here is an assumption, so try your own in the calculator. The point is Bogle's: the gap comes almost entirely from costs and behaviour, which you can see in advance, not from predictions.
Common mistake
Treating any one investor's rule of thumb as a rule for you. "Bonds equal to your age" or "5% for fun" are Bogle's personal guides, offered with his own caveats. The arithmetic is general; the plan is personal.
Key terms
- defensive investor
- Graham's term for someone who invests simply and avoids speculation
- the relentless rules of humble arithmetic
- Bogle's phrase for: returns minus costs equals what investors keep
- serious money / funny money
- Bogle's split between long-term savings and a small amount for speculation
- stay the course
- keep to a sensible plan through good and bad markets
- asset allocation
- how money is divided between stocks, bonds and cash
Practise the key terms
Tap a card to turn it over. 5 cards.
| Front | Back |
|---|---|
| defensive investor | Graham's term for someone who invests simply and avoids speculation |
| the relentless rules of humble arithmetic | Bogle's phrase for: returns minus costs equals what investors keep |
| serious money / funny money | Bogle's split between long-term savings and a small amount for speculation |
| stay the course | keep to a sensible plan through good and bad markets |
| asset allocation | how money is divided between stocks, bonds and cash |
Practice
Sort it
Is this part of Bogle's arithmetic (true for everyone), or his personal plan (a choice)?
Investors as a group earn the market return minus costs
Follows from owning the market together.Show answer
Arithmetic. Follows from owning the market together.
Hold bonds roughly equal to your age
His rule of thumb, with caveats.Show answer
Personal plan. His rule of thumb, with caveats.
Costs taken every year compound over time
Compounding.Show answer
Arithmetic. Compounding.
Keep no more than 5% for speculation
His suggestion.Show answer
Personal plan. His suggestion.
A fund's time-weighted return can differ from its investors' return
It depends on cash flows.Show answer
Arithmetic. It depends on cash flows.
Quick quiz
Tap an answer to check it.
In Bogle's view, what are the two things that most reduce what investors keep?
- They matter, but costs and behaviour are his main themes
Show answer
Costs, and bad timing or fund-switching. His arithmetic: market return − costs − behaviour gap.
Why does this course present Bogle's plan as one person's view?
- It isn't judged wrong; it's personal
Show answer
Because the right mix depends on each person's goals, time and tolerance for risk. The arithmetic is general; the plan is personal.
In short
- Graham: most investors should be defensive, simple and diversified.
- Bogle's arithmetic: returns come from businesses; costs and behaviour decide what investors keep.
- His plan: broad low-cost index funds, stay the course, at most a small "funny money" account.
- The arithmetic applies to everyone; the plan is one investor's reasoned choice.
Mastery check
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Check yourself
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Put Bogle's argument in one sentence.
Show answer
Investors as a group earn the market's return minus their costs, so owning the whole market at low cost and holding it is, in his view, the most reliable approach.
What is Bogle's "funny money" account?
Show answer
A small amount, no more than about 5% of investments, for speculation, kept apart from serious long-term money.
Why isn't "bonds equal to your age" a rule for everyone?
Show answer
It's Bogle's personal rule of thumb; he says there are no hard-and-fast rules, and the right mix depends on each person's situation.
Further reading
- John C. Bogle, The Little Book of Common Sense Investing (John Wiley & Sons, 2007), chapters 16–18.
- Benjamin Graham, The Intelligent Investor: the next path on Studyfern.
- Investor.gov: Asset Allocation, the U.S. SEC's beginners' guide.
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