Modern Portfolio Theory and Practice

Modern Portfolio Theory and Practice

-or-Get Rich Slow

-or-Why the Real Mutual Fund

Scandal is Legal

David RoodmanSummer 2007

Lesson 1: Do save/invest

• Have 3-6 months of expenses in cash– Split between money market and short-term bond

fund

• Save in tax-favored vehicles early and often– For savings made early in life, the subsidy is large

– A window of opportunity closes every 12/31.

• If you lack 401(k)/403(b) access, favor Roths.

One-time saving of $1000 pre-tax income: rate of return=6%, marginal tax rate=33%

$0

$1,000

$2,000

$3,000

$4,000

$5,000

$6,000

$7,000

$8,000

0 5 10 15 20 25 30 35 40 45

Year

Aft

er-

tax

va

lue

IRA/401(k)/403(b) Regular taxed account

Grows 6%/year

Grows 4%/year

Modern Portfolio Theory (Harry Markowitz, 1952)

• Universe of investible securities characterized by 3 sets of numbers:– Expected return of each security (say, per

month)

– Standard deviation of future (monthly) returns

– A correlation matrix for expected returns.

• Investor’s task: choose portfolio that maximizes expected total return for a given level of “risk” (standard deviation of overall portfolio return)

MPT, cont’d• Diversification principle:

– Suppose Netzoot and Zipcom are tech stocks that have an expected return of 10%/year and an s.d. of return of 4%, and have an expected correlation of 0.5. Then a 50/50 portfolio of the two will have:

• expected return = 10%• s.d. of return =3.47% (of portfolio=3/4 of of either)• Same return, lower risk!

– 90/10 bond/stock portfolio less risky than 100% bond

• Lesson 2: Diversify. Own some of everything.

Can diversification eliminate risk?• No. There is an irreducible component of

variation in returns that is shared by all stocks. No amount of diversification will eliminate it because all stocks have it: market risk. Stocks tend to rise and fall together.

• Model: rIBM=+rmarket constants

• In theory, embodies the only component of risk investors care about: systemic or market risk. Variation not explained by this model, idiosyncratic risk, does not matter because it washes out in a diversified portfolio.

MPT, cont’d• Markowitz developed algorithm to pick

optimal portfolio for given level of risk

• We don’t know expected return, s.d. of return, future correlations.

• Can try using past values as estimators.

• Applied his algorithm to this information.

• Didn’t work so well: weird portfolios or unremarkable returns.

Efficient market hypothesis (Eugene Fama, 1965, Chicago dissertation)

• Market is a “random walk”: “efficient”• “Efficient” does not mean prices are correct.• Rather: all available information is already incorporated into

stock prices• Changes in prices caused only by unpredictable arrivals of

new information, or pure noise in trading• Beating the market is impossible except by chance• “Research” by stock & bond analysts is a waste of time• Monkeys throwing darts at stock page do as well on average

EMH, cont’d• Backed by lots of empirical evidence that

investors/mutual funds rarely beat the market consistently—no more than should happen by chance

• Think of it this way: ~90% of trading by large institutions with same information and methods. Can’t all be above average.

• Lesson 3: Practice humility

Daily % change in AT&T stock vs. previous % change, ~1998-2003

-20

-10

01

02

0e

( ch

ange

| X

)

-20 -10 0 10 20e( Lchange | X )

coef = -.02811832, se = .02827494, t = -.99

3 forms of EMH1. Weak: all past market prices and data are

reflected in securities prices today. Technical analysis useless.

2. Semistrong: all publicly available information is reflected. Fundamental analysis useless.

3. Strong: all information is reflected. Even insider information useless.

I believe it is prudent in general to invest as if all are true (unless you have inside information!)

http://www.investorhome.com/emh.htm

Implications• The investment advice industry is a huge

waste. To a first approximation, it adds no value. Indeed, it reduces value by sucking out $ billions.

• High-priced stock-pickers who work for “actively managed” mutual funds are mostly rip-offs for investors

• Expense rate on good index fund: ~0.25%

• On typical “active” fund: 0.75-2.0%

One-time saving of $1000: rate of return=6%

$0

$1,000

$2,000

$3,000

$4,000

$5,000

$6,000

$7,000

$8,000

$9,000

$10,000

0 5 10 15 20 25 30 35 40 45

Year

Aft

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Expenses=0.25%/year

Expenses=1.25%/year

Why should they tell you?• Fund companies with actively managed funds

benefit from myth• Brokers get trading commissions• Money magazines carry fund ads• TV channels and web sites must pretend to

relevance• Market imperfection: people don’t notice 1-

2%/year expense when earnings are volatile or high, and documentation is in fine print

Lesson 4: minimize turnover

When you or your fund manager buy and sell it:

• Creates taxable capital gains (if in taxable account)

• Incurs trading commissions

• Incurs losses because of bid-ask spread (not counted in expense ratios)

DALBAR survey of investors,1984-2002

• Average investor’s return on stocks: 2.57%/year. Turns $1000 into $1620

• S&P 500: 12.22%/year: $8940• Inflation: 3.14%/year• I.e., average investor turned $1000 into $900

after inflation• S&P 500 turned $1000 into $5000 after infl.• Partly expenses; partly performance chasing• Big scandal in a country with a looming

retirement crisis!

http://www.dalbarinc.com/content/printerfriendly.asp?page=2003071601

Expenses:

• Vanguard S&P 500 index fund: 0.18%/year

• Calvert “socially responsible” U.S. equity fund (class C shares): 2.10%/year

Is this socially responsible?

An indignant question

Capital Asset Pricing Model (Sharpe and others, ~1964)

• If every investor has all of Markowitz’s information about future returns and applies his algorithm, then in the equilibrium, all investors will split their $ between risk-free asset and the same portfolio of all other assets.

• i.e., outside of cash holdings, everyone will have 1% IBM, 2% AT&T, etc.

• Ergo, the market will be 1% IBM, 2% AT&T,….

• Ergo, everyone will own an index of the market.

Index mutual funds• Sharpe’s model unrealistic, but helped create

idea of index mutual funds

• Commonsense ideas of diversification, humility, low turnover, and low cost argue for index funds

• First ones started ~1973. Vanguard and State Street(?).

• They don’t call me the Index guy for nothing.

• Or: more generally, passive asset class investing

Interim conclusions• Theoretical index fund covers all assets: foreign,

domestic, stock, bond, housing• Real ones only cover subclasses• Lesson 5: Put your $ in a few very low-cost mutual

funds, preferably index funds, covering all asset classes• Exact allocation that is best is a bit unclear because we do

not believe Sharpe• Lesson 6: Obsess over expenses• Buy and hold. Minimize trading• Lesson 7: Exercise discipline. Never panic.• You will nearly match the market and beat most investors

Two things to ponder:1. Risk vs. return

• Truism that the two go together

• What is the evidence?

• A generalization, not an iron law

• There may be exceptions

• No plausible theory says market will always accurately price risk since it is substantially unknowable and market itself creates price risk

Geometric

From Malkiel, Random Walk Down Wall Street

Two things to ponder:2. Herd behavior

• Bubbles and panics older than securities markets– Dutch tulipmania in early 1600s

• Occur when people buy because the price has gone up, on the dangerous notion that past return predicts future return.

• Buying causes appreciation, and vice versa…• Milder form: all actors unwittingly follow same

strategy and reassured by results in short run—hedge funds today?

• Don’t manias violate EMH?

Definitions• Growth stocks: high-priced compared to

current book value or earnings• Value stocks: opposite• Large-cap stocks: shares in big companies• Small-cap stocks: shares in small

companies

Growth stocks called that because market evidently expects strong earnings growth

Value is a marketing euphemism?

Fama & French 1992• For each year in 1962-89, built simulated portfolios

of U.S. stocks: growth, value, large, small, sorted by decile

• 3 deciles on value end beat 3 growth deciles 5%/yr• Good companies make bad investments and v.v.• Small beat large (not news)• Overall market return each year and small-large and

value-growth return differences are factors• The 3 factors explain ~95% of the cross-sectional

variation in mutual fund returns

From Robert Haugen, The New Finance: The Case against Efficient Markets, based on Fama & French 1992

Here’s where it gets weird• Other research finds same value-growth pattern before

1960, and abroad.• Warren Buffet, Peter Lynch are value investors• But value stocks have had a lower standard deviation of

returns than growth stocks: lower risk, higher returns!• According to EMH, Fama & French 1992 (new info.)

should have sent $ pouring into value stocks, resulting in huge one-time gain, but lower returns to value stocks thereafter. Free lunches should not persist.

• I read this in 1999, during “new economy” growth stock craze: exact opposite was happening.

• (Maybe has happened now??)

From Robert Haugen, The New Finance: The Case against Efficient Markets, based on Fama & French 1992

Beta

100 Most-Cited Researchers in Economics

SOURCE: ISI Essential Science Indicators        Web based product from the September 1, 2002 update covering a ten year plus six month period, January 1992 - June 30,

2002.

RANK SCIENTIST PAPERS CITATIONS CITATIONSPER PAPER

1 SHLEIFER, A 50 1,717 34.34

2 FAMA, EF 20 1,242 62.10

3 LEVINE, R 22 1,205 54.77

4 KAHNEMAN, D 16 1,122 70.12

5 VISHNY, RW 23 1,043 45.35

6 MURPHY, KM 20 984 49.20

7 TVERSKY, A 13 901 69.31

8 SALAIMARTIN, X(*) 19 894 47.05

9 FRENCH, KR 14 881 62.93

10 ANDREWS, DWK 27 856 31.70

What’s going on?• Fama says: some unobserved risk factor looms over

these “distressed” value companies. Their true but unmeasured high risk is compensated by high returns.

• I don’t buy it. They actually were riskier for 30 years but racked up much higher returns and lower volatility?

• Fama is stuck. Maybe no Nobel

• More plausible explanations come out of new field of behavioral finance, which he attacks rather vituperatively

• “Value premium” may be a permanent artifact of investor irrationality, i.e., human nature

My conclusion• EMH is probably mostly true

• Lesson 8: But the evidence on value stock outperformance (and maybe small stock outperformance) seems strong enough that I favor “tilting”– E.g., instead of 50/50 value-growth, do 75/25.

• No one is saying value does systematically worse, so risk of long-term under-performance seems low

Lesson 9:Vanguard is the best• Essentially a cooperative• No incentive to take $ from customers and give it to

own shareholders• Extremely low expenses• Wide selection of index and other funds• 500 index fund now the world’s largest mutual fund.• From 0 in early 1970s, Vanguard has become largest

mutual fund company in the world.• Also good:

– DFA (founded by Fama and others)—but for-profit and for millionaires

– TIAA-CREF—non-profit, low-expenses, but few options WITH TIAA-CREF CANNOT DO WHAT I DID

What I did• Chose % allocations to different asset classes,

covering as many as possible.

• Put more abroad (33%) than is standard

• “Tilted” toward small and value (and small value)

• 70% stock, 30% bond (conventional for my age)

• Just funds, no individual stocks

• Rebalance once/year

• Manage my IRA and wife’s, Vanguard, TIAA-CREF, etc., as a unit

Allocations% of category % of total

Stock 67.7% 67.7%U.S. stock 66.7% 45.1%

U.S. large 25.0% 11.3%U.S. large value 75.0% 8.5%U.S. large growth 25.0% 2.8%

U.S. small 75.0% 33.9%U.S. small value 60.0% 20.3%U.S. small growth 20.0% 6.8%U.S. REIT 20.0% 6.8%

International stock 33.3% 22.6%EAFE stock 66.67% 9.4%

EAFE large 25.0% 3.8%EAFE large value 75.0% 2.8%

Europe large value 50.0% 1.4%Pacific large value 50.0% 1.4%

EAFE large growth 25.0% 0.9%Europe large growth 50.0% 0.5%Pacific large growth 50.0% 0.5%

EAFE small 75.0% 5.6%EAFE small value 50.0% 5.6%EAFE small growth 50.0% 5.6%

Emerging markets 33.3% 7.5%

Bond 29.0% 29.0%U.S. bond, non-TIPS 50.0% 14.5%TIPS 16.7% 4.8%EAFE bond 33.3% 9.7%

Metals 3.3% 3.3%

Data collection• Database with daily price data and full

transaction history. All distributions and fees counted

• Maintain benchmark based on some Vanguard single-fund solutions that implement standard investment book pie charts via index funds (LifeStrategy, Target funds)

Daily Monthly Annualized Portfolio 0.0333% 0.594% 0.921% 2.75% 8.30% 91.74% Benchmark 0.0144% 0.773% 0.506% 2.98% 2.93% 26.59%

Real returns, 8/19/99–10/24/07

–

Bottom line

• My returns should continue to be less volatile.

• Mostly likely: continuing gains relative to benchmark or parity

• My wife and I can afford to die a half a year later

Pos ition nam eTotal return

Total return real

Annualized return

Annualized return

realVanguard Precious Metals Fund 492.1% 402.1% 35.8% 32.0%Vanguard Em erging Mkts Stock Index 280.1% 204.7% 17.8% 14.6%Vanguard International Explorer 211.9% 169.3% 23.9% 20.5%Vanguard Sm all Cap Value Index 147.2% 98.2% 11.7% 8.7%Vanguard International Value 116.4% 73.5% 9.9% 7.0%Vanguard Sm all Cap Index 115.3% 72.6% 9.8% 6.9%TIAA real es tate 79.8% 54.5% 11.2% 8.2%Am erican Century International Bond Fund 79.9% 54.4% 11.1% 8.1%CREF global fund 72.2% 47.9% 10.3% 7.3%Vanguard Total Intl Stock Index 75.4% 40.8% 7.1% 4.3%Vanguard Value Index 59.0% 40.1% 12.4% 8.9%Vanguard Inflation-Protected Secs 67.3% 39.6% 7.6% 4.9%Vanguard Windsor 67.7% 39.4% 8.1% 5.1%Vanguard Total Bond Market Index 48.2% 27.6% 7.4% 4.5%CREF inflation-linked bond 45.6% 25.1% 7.0% 4.1%Vanguard Growth and Incom e 31.3% 22.5% 11.6% 8.5%CREF bond fund 31.4% 12.9% 5.1% 2.2%Vanguard Pacific Stock Index 29.9% 5.8% 3.5% 0.7%

Total return on some funds in the portfolio

Note: Not all funds held all 8 years.

“Having spent nearly a decade writing about investment management for the little guy, I have come to the conclusion that I no longer believe in the basic premise of my public persona—a surreal cross between Harry Markowitz and Johnny Appleseed, as a friend put it.

“A decade ago, I really did believe that the average investor could do it himself. After all, the flesh was willing, the vehicles were available, and the math wasn’t that hard.

“I was wrong. Having emailed and spoken to thousands of investors over the years, I’ve come to the sad conclusion that only a tiny minority, at most one percent, are capable of pulling it off.”

-- William J. Bernstein, Efficient Frontier, Winter 2003

http://www.efficientfrontier.com/ef/103/probable.htm

For more• www.indexfunds.com and www.ifa.com

• www.efficientfrontier.com

• Haugen, The New Finance

• Malkiel, Random Walk Down Wall Street

• Bogle, Common Sense on Mutual Funds

• Ellis, Winning the Loser’s Game

• Bernstein, The Intelligent Asset Allocator