Investment Decisions

Fin 434September 25, 2006

By the end of this lecture, you should be able to:

Be able to explain basic portfolio theory

The value of diversificationHow to evaluate risk/return trade-offWhat do consumers actually do?

Explain different classes of investmentsThe special case of company stock

Why do firms offer it?How does it affect retiree well-being?

A Quick Review of Investment Theory

Investor attitudes toward risk

Risk vs. return

What risk matters?

Historical returns

Your Risk Attitude - 1Suppose you have $10,000 to invest. Option A: Invest $10,000 in risk-free securities, have $10,500 for sure next yearOption B: Invest $10,000 in asset B. There is 50% chance that you will have $12,000 next year, and 50% chance of $9,000. Option C: Invest $10,000 in asset C. There is 50% chance you will have $21,000 next year, and 50% chance that you will have 0.Which would you choose?

Expected Values

Let Xi = outcome i (i = 1 … N)

If all out comes equally likely and independent,then expected value = Xev = (1/N)*Xi

More generally, if Pi is the probability of outcome Xi, then the expected value is

i

n

ii XP

1

Variance

Variance of a sample

Standard deviation = = square root of varianceVariance and standard deviation provide a measure of how disperse a distribution of outcomes is

n

ievi XX

n 1

22 )(1

1

Uncertain Outcomes

Xev

Same meanDifferent variance

Choice Between the Three Portfolios

Option A: $10,500 for sure next year

Option B: 50/50 chance of $12k or $9k

Option C: 50/50 chance of $21k or $0

Risk AversionMost investors are risk averse. What does this mean?

For a given level of risk, individuals prefer the investment option with the highest expected return

For a given level of expected return, individuals prefer the investment option with the least risk

Your Risk Attitude - 2Suppose you have $10,000 to invest. Option D: Invest $10,000 in risk-free securities, have $10,500 for sure next yearOption E: Invest $10,000 in asset E. There is 50% chance that you will have $12,000 next year, and 50% chance of $9,500. Option F: Invest $10,000 in asset F. There is 50% chance you will have $30,000 next year, and 50% chance that you will have 0.Which would you choose?

Choice Between the Three Portfolios

Option D: $10,500 for sure next year

Option E: 50/50 chance of $12k or $9.5k

Option F: 50/50 chance of $30k or $0

Financial Market Equilibrium

Investors require higher return in order to be willing to hold riskier assetsIn other words, there is a trade-off between risk and reward

Riskier assets have higher expected returnsHigher expected returns are associated with higher level of riskBut, does all risk matter?

Does Market Reward All Risk?

A financial asset has two types of risk

Systematic / Market / Non-diversifiable• Risk that is correlated with market so

that diversifying does not get rid of it

Idiosyncratic / Unique / Diversifiable• Unique to the firm, uncorrelated with

market, and thus can diversify it away

Diversification

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Number of Securities

Po

rtfo

lio

Sta

nd

ard

De

via

tio

n

Market risk

Unique risk

Portfolio Theory

Adding more securities to a portfolio will generally make the portfolio less risky

Of all the possible portfolios, some of them are efficient and some are not. An efficient portfolio is one that maximizes the level of return for a given level of risk

Minimum Variance PortfoliosExpected Return

Risk

Min. Variance portfoliosA

B

Choosing An Optimal PortfolioExpected Return

Risk

rf

Min. Variance portfolios

Market portfolio

Portfolio Choice

Portfolio theory suggests that everyone should hold some combination of the market portfolio and the risk-free asset

We really only need one mutual fund – a market index fund

The relative shares in risky vs. risk-free portfolio depends on attitudes toward risk

Types of Investments

StocksDebt / BondsMoney marketREITSMutual Funds

What Do 401(k) Participants Believe?

0 1 2 3 4

U.S. Treasury Bonds

Corporate Bonds

Money Market

Company Stock

Diversified Stock Fund

Perceived Risk

Historical Returns(Real returns from 1926-2000)

Real Return (%)

Std. Dev ()

Small Co. Stocks

13.8 43.3

Large Co. Stocks

9.7 20.2

Corp Bonds 3.0 8.7*

Govt Bonds 2.7 9.4

T-Bills 0.8 3.2•This probably understates true variance due to survivor bias•Corp bonds considered riskier than gov’t due to default risk

Relative RiskOur class’s

Risk ratingIndividual company stock 4.34Diversified stock fund 2.81Corporate bond fund 2.68Government bond fund

0.90Money market fund 2.10

(Scale = 0 if no risk, 5 if most risk)

Most risky

Leastrisky

Asset Allocation in 401(k)s (%)(EBRI / ICI 2001)

Age Group

Equity

Co Stock

Bal. Funds

Bond Funds

MM / GICs

Other

20 – 29

61 15 9 4 8 2

30 – 39

60 18 8 4 8 2

40 – 49

55 20 8 4 11 2

50 – 59

49 19 8 5 16 3

60 – 69

40 16 8 8 25 4

All 51 19 8 5 15 2

Stocks

Common Stocks Ownership of a share of a company

Preferred StocksA hybrid stock/bond instrumentMore regular dividend paymentsRights are senior to common stock holders in case of bankruptcy

DebtIssued when corporations, federal, state and local governments need to borrow moneyBond buyer is loaning money to bond issuer, usually at set interest rate and durationKnown as “fixed income” securities because the amount of income (interest) is set when bond is sold

Four Common Bond IssuersFederal government – issues government bonds or “Treasuries”

Varying maturitiesAlso offer inflation indexed bonds

Other government agenciesEx: Federal Nat’l Mortgage Assn (Fannie Mae)

Corporate BondsHigher interest than gov’t due to default risk “Junk bonds” – high yield bonds issued by low credit quality companies (below investment grade)

State & Local “Munis”Free from federal income tax

Federal Gov’t DebtTreasury bills or “T-bills”: Short term government bonds with maturities of 13, 26 or 52 weeks. Treasury notes: Intermediate term securities with maturities of 2, 5 and 10 yearsTreasury bonds: Long-term securities with longer maturities (longest used to be 30 years, but US gov’t stopped issuing 30 years recently)Treasury Inflation Protected Securities (TIPS): pay fixed % plus inflation

Money MarketMoney Market: invests in very short term and extremely low risk assetsExample: Holdings of Vanguard Prime Money Market Fund as of 5/31/2005

43.3% in Certificates of Deposit (CDs)32.2% in Commercial Paper (very short term debt from corporations – high credit quality)19.5% in short term debt from U.S. government4.9% in “other”

REITs

“Real Estate Investment Trusts”Special form of equity that allows investors to own small pieces of a large group of real estate propertiesRequired to pay out 95% of earnings in the form of dividends to shareholders

Mutual Funds

Can buy a diversified portfolio with a single purchaseActively managed funds: fund managers try to pick stocks with a goal of outperforming the market

Higher expense fees

Passively managed funds: hold portfolio that tries to mirror the market index

Ex: S&P 500 portfolioTend to have substantially lower expenses

Evidence on Fund Mgmt

Very little evidence to support the notion that actively managed mutual funds are able to outperform passively managed fundsAlso little evidence to support the notion that there is much persistence in fund manager performance

How Do Investors Behave?

Fair amount of evidence that investors “sort of” understand diversification, but are not very sophisticatedTend to follow “naïve diversification strategies”

1/N allocation, where N = # of choicesThis means you may be able to affect equity mix by choice of funds!

This Class’ Investment Choices2 stock choices + 3 “safer” choices

MM fundTreasury bondsCorp BondsUS StockInt’l stock

Allocated ____% to stocks

3 stock choices + 2 “safer” choices

MM fundTreasury bondsUS Stock (large)US Stock (small)Int’l stock

Allocated ___% to stocks

Replacing bond fund with equity fund …

How Do Investors Behave?Evidence also suggests that people rarely rebalance their portfoliosExample:

Initially put 50% in bonds, 50% in stocks. After 10 years, stocks have gone up faster, now have 35% bonds, 65% stocks. If 50/50 was optimal portfolio, then should rebalanceYet most investors do not rebalance.

Special Case of Company Stock

Many large 401(k) plans offer company stock as an investment option

42% of participants59% of account balances

Nov 2001 Co. Stock Holdings

P&G 95%Sherwin-Will. 92%Abbott Labs 90%Pfizer 86%BB&T 82%Anheuser-Busch 82%Coca-Cola82%

GE 77%Texas Instr. 76%Wm. Wrigley 76%Williams 75%McDonalds 74%

At its peak, Enron was at 60% of assets

Restrictions on Co. Stock

ERISA prohibits defined benefit plans from holding more than 10 percent of plan assets in company stockThere are no such restrictions on 401(k) plans – firm is permitted to match in company stock, and there are no caps on total investment in company stock

Enron and Other Failures

Fall 2001 – shortly after 9/11Enron’s stock “implodes”From March 2000 to December 2001, Enron’s stock price fell 99.6% !!!At its peak, 60% of pension assets were in Enron stock (closer to 40% around time things went really bad)

Enron was not unique

Company Price % change

3/00-12/01

Co. Stock as % of pension

assets

Polaroid -99.6 19

Enron -99.6 41

Global Crossing

-97.5 16

Lucent Technol.

-89.2 16

North. Telecom

-86.6 30Plus several others!

More Enron Details

Diversification restrictionsMatch in company stockEmployees made own contributions in company stock“Blackout period” during vendor change

THE IMPLICATIONS OF ENRON

Response to Enron

Lawmakers began to call for new regulation

Boxer / Corzine – cap at 20%• What would this do to match policy?

PBGC coverage of DC plans • Could be disastrous! Why?

Some more measured approachesAllowing diversification out of employer stockRestrictions on blackout periodsFacilitating more investment advice

Company Match Policy

Many companies not only offer company stock as an investment option, but they make their match in company stock as wellPrior to post-Enron legislation, participants often were restricted in their ability to diversify their match out of company stock

Effects of Match Policy

Employees that work for plans that match in company stock tend to put more of their own contributions in company stock

Why?

Why Use Co. Stock?

Why NOT Use Co. Stock?

BP Amoco Case

The Setting

August 11, 1998: Amoco and BP announce mergerNow it is January 1999Combined plan would have 40,000 employees and $7 billion in assetsHow to integrate defined contribution pension assets for US employees?What investment options to choose?

Comparing BP & Amoco Pensions

Pre-merger BP Pre-merger Amoco

Size

Inv. Style

Inv. Choices

Goal

Costs

Active vs. Passive

Active – “Beat the market”Passive – replicate market indexActive involves:

Stock picking, research, more trading, possibly higher risks than indexCosts may reach 100 b.p.Note: Expense ratios generally net of trading costs, which may be another 100 b.p.!

How Pick Investment Choices?

Seeking high returnsSeeking low riskCan we achieve both?

CAPMIn CAPM terms, “beta” tells us how much an individual security varies with the portfolio, i.e., the market risk

(Ri – Rf) = (Rm – Rf) + i

• Ri = return on asset i• Rm = return on market• Rf = return on risk free asset i = idiosyncratic risk (mean = 0)

Only market risk is “priced” or rewarded by the market

Higher higher expected return

CAPME[Ri]

i

Rf

1.0

Rm

CAPM in Practice

Run regression of excess returns on a constant and the market’s excess return

(Ri – Rf) = i + i (Rm – Rf) + i

According to CAPMAverage i will be equal to zero

i will measure market risk – if market goes up by 1%, security i goes up by i%

Var(i) measures idiosyncratic risk

Meaning of Alpha

(Ri – Rf) = i + i (Rm – Rf) + i

What if i > 0?

What if i < 0?

What is i supposed to measure?

Remember GM’s “alpha strategy”?

CAPME[Ri]

i

Rf

1.0

Rm

i<0i>0

Pre-Merger Investment Options

What are the alphas on the BP funds like?

What were the BP fund expense ratios like?

What role did company stock play?

Performance Persistence

The Peter Lynch experiment:Our penny flipping exercise

Why is it so hard to beat the market?

How Many Funds?

Is one fund enough?

Safe Harbor provisions

Ruey: increase number of core investment options to “cover wide region of risk-return spectrum”

What would you do?

What did they do?