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![Page 1: Muddy Points from Thursday FICA v. FICO? Define. The best-known and most widely used credit score model in the United States, the FICO score is calculated.](https://reader038.fdocuments.us/reader038/viewer/2022110208/56649dbf5503460f94ab32a8/html5/thumbnails/1.jpg)
Muddy Points from Thursday• FICA v. FICO? Define.
• The best-known and most widely used credit score model in the United States, the FICO score is calculated statistically, with information from a consumer's credit files.
• The score is sold by FICO, the company.
• FICO was founded in 1956 as Fair, Isaac and Company by engineer Bill Fair and mathematician Earl Isaac.
• Traded on the NYSE.
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Muddy Points
• FICA
• Federal Insurance Contributions Act:– US Federal payroll tax imposed on both
employees and employers
– to fund Social Security and Medicare
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Muddy Points
• If my econ class is only a semester long, how much detail do I need to spend on Annuity and Compound Interest equations?
• Economics course:– Assume:
• High school• Responsible for PFL as well as straight economics
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Standard 3: EconomicsGrade Level Expectation: High School
5. Analyze strategic spending, saving, and investment options to achieve the objectives of diversification, liquidity, income and growth.
– Selected Evidence Outcomes & 21st Century Skills:
• Investments available for diversified portfolio• How economic cycles affect financial decisions• Investments to achieve liquidity, growth, income.• How compound interest manifests in investment and
debt situations.
Invest
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Muddy Points
• Please provide recommended reading list for PFL instructors, including:– Case studies of individuals who have found
great earning success.• I do not know of resource to suggest.
– Background information on how to motivate students toward rational financial choices.• If the students have opportunity to make money, they
are likely motivated.
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Muddy Points
• Why are index funds capable of such low fees?
– Do not have to hire high cost portfolio managers and researchers who pick the stocks.• Merely buy the stocks in the Index
– e.g., the S&P 500
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Muddy Points
• Can we go over Wednesday’s [tax calculation] homework?
– No!
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Hultstrom Household • Wage and Salary Income: $20,000 • Other Income: $0 • Purchases of Goods and Services: $15,000 • Value of Land and House: $0 (renters) • Income Tax: $1000 + ($10,000 x .20) =
$3000 • Payroll Tax: $20,000 x .06 =
$1200 • Sales Taxes: $15,000 x .05 = $750 • Property Tax: $0 x .01 = $0 • Total Taxes: $3000
+ $1200 + $750 + $0 = $4950 • Net Income (after tax): $20,000 - $4950 = $15,050 • Saving: $15,050 - $15,000 = $50
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Rodriguez Household • Wage and Salary Income: $60,000 • Other Income: $0 • Purchases of Goods and Services: $36,000 • Value of Land and House: $100,000
• Income Tax: $7000 + ($20,000 x .25) = $12,000
• Detail behind this tax calculation?
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Rodriguez Household • Wage and Salary Income: $60,000 • Other Income: $0 • Purchases of Goods and Services: $36,000 • Value of Land and House: $100,000• Income Tax: $7000 + ($20,000 x .25) = $12,000
How calculate the $12,000 income tax?
$1000 + $6000 + $5000
10% of 1st $10,000 20% of next $30,000 25% of last $20,000
$7000 + 25% on income
from $40K to $100K
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Rodriguez Household
• Wage and Salary Income: $60,000 • Other Income: $0 • Purchases of Goods and Services: $36,000 • Value of Land and House: $100,000• Income Tax: $7000 + ($20,000 x .25) = $12,000 • Payroll Tax: $60,000 x .06 = $3600 • Sales Taxes: $36,000 x .05 = $1800 • Property Tax: $100,000 x .01 = $1000 • Total Taxes: $12000 + $3600 + $1800 + $1000 = $18,400 • Net Income (after tax): $60,000 - $18,400 = $41,600 • Saving: $41,600 - $36,000 = $5,600
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Jones Household
• Wage and Salary Income: $200,000 • Other Income (interest & dividends): $50,000• Purchases of Goods and Services: $140,000 • Value of Land and House: $1,000,000 • Income Tax: $22,000 + ($150,000 x .30) =
$67,000 • Payroll Tax: $100,000 x .06 =
$6,000 • Sales Taxes: $140,000 x .05 =
$7,000 • Property Tax: $1,000,000 x .01 =
$10,000 • Total Taxes: $67000 + $6000 + $7000 + $10000 =
$90,000 • Net Income (after tax): $250,000 - $90,000 =
$160,000 • Saving: $160,000 - $140,000 =
$20,000
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Proportional, Progressive, or Regressive?
• Income Tax: all income
Hultstrom HH% Rodriguez HH Jones HH
$3000 $12000 $67000
3000/20000 = 15%
12,000 /60,000 = 20%
67,000/250,000 = 26.8%
Progressive
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Proportional, Progressive, or Regressive?
• Payroll Tax: wage & salary income
• Payroll Tax: all income– Regressive if there is any other income
• Since no payroll tax paid on other income
Hultstrom HH Rodriguez HH Jones HH
$1200 $3600 $6000
1200/20000 = 6% 3600/60000 = 6% 6000/200000 = 3%
Proportional, up to $100K
Regressive over $100K
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Proportional, Progressive, or Regressive?
• Sales Tax: on purchases of goods & services
• Sales Tax: on all income
Hultstrom HH Rodriguez HH Jones HH
$750 $1800 $7000
750/15000 = 5% 1800/36000= 5% 7000/140000 = 5%
Proportional
Hultstrom HH Rodriguez HH Jones HH
$750 $1800 $7000
750/20000 = 3.75% 1800/60000= 3% 7000/250000 = 2.8%
Regressive
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Muddy Points
• Do you have practice problems for the formulas?– YES … see the Handout that was on your table
this AM.
• Good resource to read more about these?– Wikipedia “time value of money”
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Practice with Time Value of Money(#1)
• Inherit $10,000. – Invest at 8% for 40 years.
– Therefore: Pn = P0(1+i)n = 10,000(1.08)40
– Table A-3: n = 40, i = 8%
Factor: 21.725
Pn = P(Factor) = $10,000 (21.725) = $217,250
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Practice with Time Value of Money(#2)
• IRA has grown from $10,000 to $19,672 in 10 years. – Find the “total return” (or CAGR).
– Therefore: Pn = P0(1+i)n
– 19,672 = 10,000(1 + i)10
– Table A-3: n = 10, but we don’t know i.
But we do know that: Pn = P0(Factor) … therefore
Factor = Pn/P0 = $19,672/$10,000 = 1.9672
Read across n = 10, looking for Factor = 1.9672
Result: i = 7%
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Practice with Time Value of Money(#3)
• Find present value of $100,000 received 5 years from today.
• P0 = Pn/(1+i)n = 100,000/(1.12)5
• Or, using Table A-1:
– n = 5 and i = 12%
– Factor: 0.5674– Thus, P(Factor) = $100,000(0.5674)– = $56,740.
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Five-Year Annuity
1 2 3 4 5
P(1+i)4 + P(1+i)3 + P(1+i)2 + P(1+i)1 + P
i
1 i)(1P P Annuity of Value
n
n
Factor in Table A-4 for n & i
Year:
P P P P P
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Statement 9• At age 18, you decide not to
purchase vending machine soft drinks &save $1.50 a day.
• You invest this $1.50 a day at 8% annual interest until you are 67.
• At age 67, your savings are almost $150,000.– Because of the power of compound
interest, small savings can make a difference, • about $300,000 in this case.
• False Save
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50-Year Annuity
19 20 ……. 67 68
P(1+i)49 + P(1+i)48 + … + P(1+i)1 + P
0.08
1 0.08)(1P P Annuity of Value
50
50
Factor in Table for n & i
Age:
P = $547.50
P P P P P
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Use Annuity Table to Calculate• Annuity:
– n = 50 years – i = 8%
– Factor: from the table:• 573.77
– Annual annuity:• 365 x $1.50 = $547.50
• Value of Annuity = P (Factor)
= $547.50 (573.77) = $314,139
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Two Volunteers?Eat one at a time.
After eating each one, note on piece of paper how good each successive one tastes – use of ranking of:
10 = absolutely delicious - the best 9 = really good, but not as good as a 10 8 = quite good, but not as high as a 9 . . . and so on … 3 = only fair 2 = mediocre 1 = less than a 2 0 = my lowest taste ranking – no more satisfaction eating
Like these?
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Life is Full of Gambles:The Economics of Risk
• Go skiing – Risk breaking your leg
• Drive to work– Risk an auto accident
• Live in a house– Risk a fire
• Savings in stock market– Risk a fall in stock prices
• Savings in bonds– Risk a rise in interest rates
• Invest U.S. T-bills– Risk rapid inflation & loss
of purchasing power
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A Bet Anyone?
• A third party will flip a coin:– heads, I pay you $1,000– tails, you pay me $1,000
• Anyone want to play?
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Risk Aversion• Most people would reject this bet
• Why?
• Most people are risk averse– dislike bad things happening to them
– But more specifically,
– dislike bad things more than they like comparable good things
– That is, • the pain of losing $1,000 > pleasure from winning $1,000
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Data from Our Volunteer
• “Law of Diminishing Marginal Utility” – or, diminishing marginal satisfaction
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The cartoons even address marginal utility!
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Definition
• Marginal benefit (utility, satisfaction):
• the added benefit gained from one more unit– let’s assume your ranking (1 to 10) is also
your marginal utility or satisfaction received from each cup
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Another Example from Previous Experiment
• For Reese’s Butter Cups• How much you like (0 – 10) each added cup
– Last class volunteer ate 5 cups … • data next slide
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Quantity
Marginal Benefit
Total Utility
1 10 10
2 8 18
3 6 24
4 4 28
5 1 29
6 0 29
Marginal and Total Utility
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Utility
35
30
25
20
15
10
5
0
Quantity of Cups
0 1 2 3 4 5 6
Q MB TU
1 10 10
2 8 18
3 6 24
4 4 28
5 1 29
6 0 29
Diminishing marginal utility … total utility rises, but at
diminishing rate
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Utility
35
30
25
20
15
10
5
0
Wealth0 1 2 3 4 5 6
Total utility
Suppose we measure wealth on the horizontal axis
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Risk Aversion is Common• Most people have diminishing marginal utility
basis for risk aversion in most people
• Logic:– Dollar gained when income is low adds more to utility than a
dollar gained when income is high
– Having an additional dollar matters more when facing hard times than when things are good
– Insurance: transfers a dollar from • high-income states (where it is valued less) to • low-income states (where it is valued more)
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Dealing with Risk Aversion
• 1. Buy Insurance:
– Person facing risk pays a fee to insurance company• Which agrees to accept all or part of financial risk
– Types of insurance:• Health, Automobile, Homeowner (Renter), Disability, Life• Living too long (fee paid today, annuity until die)
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Insurance ActivityThe Insurance Game:
Is Insurance Worth Buying?
• Divide into 9 Groups of 4 each (one 3)
• Distribute:– One complete deck of cards to each Group
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The Situation
• You are a young single person – earning an annual income of $24,000– living in a rented apartment
• You will have to decide:– What types of insurance, if any, you want to buy
• and what level of coverage for each type
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Risk: Possibility of Financial Loss
• Risks you face: displayed on Visual 10 – 1 – Visual shows what could happen to you
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Activity Procedure
• Each person select insurance & level of coverage– Applies throughout the activity
• Each year:– A card is randomly drawn in each group
what happens that year to each person in group– e.g., “8” drawn each person needed:
» 10 office visits ($200 x 10) + $6,000 hospital
= $8,000, if no health insurance
– Note: replace the card into deck for the next year’s draw
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Activity Procedure(continued)
• “Double” card events (e.g, “K-K”): – only occur if that card is drawn in consecutive years
• possible in year 2 and beyond, for example:
– Year 1: K drawn major fire causes $4K damages
– Year 2: K drawn K - K has occurred
one-year major disability costing $24,000 in income
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Activity 10 – 1: Insurance • Different types (5) of insurance from which to choose:
– Health– Automobile – Renter’s – Disability– Life
• Within each, several options for amounts of coverage– As coverage rises premium rises due to higher insurance
company payout– NOTE: premiums shown are annual, covering you one year
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Types of Insurance & Terms• Health
– Co-pay: amount you pay for each office visit– Hospitalization: insurance company pays % shown
• Automobile– Deductible: amount you must pay due to accident
• Insurance company pays anything above deductible– combine comprehensive and collision for simplicity
• Liability: protects from damages you cause others up to amount shown
– you are responsible for additional
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Types of Insurance• Renter’s Insurance
– Deductible: amount you have to pay on loss• Insurance company covers above deductible• Covers: loss of personal property
• Disability Insurance– Each unit coverage pays $500 /mo for lost income
• Maximum of 4 units = $2,000/month $24,000/year
• Life Insurance– Each unit pays beneficiaries $10,000
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Weigh Benefit vs. Cost in Making Insurance Decision
B(X) C(X)
Reduce losses when “bad things” happen to you
- see Activity 10 – 1
Insurance Premiums you pay
- see Activity 10 – 1
Forgetting anything …??
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• Choice involves cost» choosing is refusing
» choose to buy insurance» refuse to invest $ spent on premiums
» suppose could earn 10%» $1,000 on premium® $100 return foregone
Key Economic Concept Revisited
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Weigh Benefit vs. Cost in Making Insurance Decision
B(X) C(X)
Lower losses when “bad things” happen
- see Activity 10 – 1
Insurance Premiums paid
+Lost Return on Premium
In our example: $1,000(1 + 0.10) = $1,100
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Now Ready to Complete Activity 10 – 1
• Decide what types & levels of coverage you desire– RESTRICTION: ALL states require basic liability
coverage with car insurance, so you must choose at least Option 3
• Since no way of knowing what will happen to you, there is no exact right amount of insurance
– Goal: buy enough coverage to protect yourself from losses, but not so much that you end up spending far more on insurance than it is worth.
• Compare B(X) v. C(X) & make choice with which you are comfortable
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Activity 10 – 2
• Enter the Total Annual Insurance Premiums (bottom of Activity 10 – 1) for every year in Column (1) of Activity 10 – 2. – i.e., premium is constant throughout
• Then, complete Column (2) for every year– opportunity cost constant throughout
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Your Life is About to Begin• Each year – shuffle the deck, then one person in
each group draw one card at random– Each person in group experiences same event
depicted in Visual 10 – 1. – Then:
• Fill in Column (3) –actual loss if you had no insurance• Fill in Column (4) – actual loss if you had insurance
– Same event for all in group, but since not same coverage, Column (4) may differ for each member
– Each group is experiencing a different “life”
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Conduct 8 Years
• Completing Columns (3) – (4) after each year’s draw
• After completing 8 years:– Sum the values in Column (4)– Fill in the blanks at the bottom of Activity 10 – 2
• Questions?• Begin . . .
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Activity Debrief
• Who is really happy that you bought the insurance you did?
• Who wishes you would have purchased a lot less insurance?
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The Nature of Insurance
• If you experienced particularly costly events, likely happy if you bought a lot of insurance– Losses without insurance would have been much bigger
• If you experienced fairly inexpensive events, likely unhappy if you bought a lot of insurance– Losses without insurance would have been much less.
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Premiums Based on Expected Payouts of Insurance Company
(plus operating cost and profit)
• Thus,– There must be some people who pay more in
premiums than they get back in claims• and perhaps feeling they shouldn’t have purchased so
much coverage
– The insurance company uses this extra premium to pay the claims of those who pay less in premiums than claims.
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Insurance
• Every insurance contract is a gamble:
– Possible that you will not have accident
– Most years you pay premium• get nothing in return, except peace of mind
– Insurance company counting on fact that most people will not make claims• or they couldn’t survive
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Insurance & the Economy
• Insurance:– Does not eliminate risk
• but spreads it around
– For example:• Owning fire insurance does not reduce the risk of losing
your home in fire– You could suffer “moral hazard” – take less care due to insurance
• But if the unlucky event occurs, – the insurance compensates you
• Risk shared among thousands of insured people
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Simple Insurance Example• Assume:
– 100 young people all face the same risk of loss• statistically, only 1 accident occurs per year• if an accident occurs, the injured party has an accident loss
of $2,000– such a loss is catastrophic for one person to bear
• Idea: let’s spread the risk (insurance)– Since one accident occurs per year
• Our “society” incurs a loss of $2,000 per year• So,
– each of the 100 people pay an “insurance premium” of:» $20 per year
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A Little More Reality
• The “society” decides that the burden of administering their internal insurance plan is too great – getting collections of premiums, etc.
• So, one person (an entrepreneur) says, •
“I’ll handle all the details if you pay me $500 per year.”
• Now, what happens to the premiums?– $2,500/100 = $25
– Greater than the expected loss of each person:• (Prob of accident) x ($ loss if accident) = 0.01($2,000) = $20
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What Should We Insure?
• Since cost of insurance > expected loss• NOT a fair game!• Insurance is NOT a fair bet!
– So, most economists recommend insurance for:• large potential losses where you will be severely impacted
if accident occurs – catastrophic loss– e.g., Cancer or Liability
• But don’t necessarily insure small risk events– that you could self-insure
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Over-insure?
• 34.4% of new-car buyers bought extended-warranty– up from 23.5% in 1999
• With the average car dealer now losing money (or making little) on each car sale, selling extended warranties is an important source of dealer profits– 65% of respondents said they spent significantly more for the
new-car warranty than they got back in repair savings
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Early Retirement• Less time to build nest egg• More time to live off nest egg
– (But, studies find people who retire earlier live shorter lives)
→ early retirement is a risky choice
later retirement is less risky choice
• Retirement Data from the Department of Labor Statistics
• This trend is likely to continue going forward.
Age Range Labor Force Participation Rate (%)
1988 2012
55 – 64 54.6 64.5
65 – 74 16.0 26.8
Over 75 4.3 7.6
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Problem:
Criteria
Risk Return Liquidity Income
Bonds
Stock
Savings Acct
How to Invest My Savings
Alternatives
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Risk• . . . comes in many forms
– Liquidity risk, default risk, purchasing power risk
• . . . In this session we’ll only address a couple more types
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Purchasing Power Risk
• Inflation risk
– T-bills (zero-coupon) have very little volatility risk
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Recent 10-Year Period2002–2011
0.50
$3
2002 2004 2006 2008 2010
$1.20
1
• Treasury bills 1.8
Past performance is no guarantee of future results. Hypothetical value of $1 invested at the beginning of 2002. Assumes reinvestment of income and no transaction costs or taxes. This is for illustrative purposes only and not indicative of any investment. An investment cannot be made directly in an index. © 2012 Morningstar. All Rights Reserved. 3/1/2012
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Purchasing Power Risk
• Inflation risk
– T-bills (zero-coupon) have very little volatility risk, but • May not keep up with inflation
Lose purchasing power.
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Recent 10-Year Period2002–2011
0.50
$3
2002 2004 2006 2008 2010
$1.20
1
• Treasury bills
$1.28
• Inflation 2.5
1.8
Past performance is no guarantee of future results. Hypothetical value of $1 invested at the beginning of 2002. Assumes reinvestment of income and no transaction costs or taxes. This is for illustrative purposes only and not indicative of any investment. An investment cannot be made directly in an index. © 2012 Morningstar. All Rights Reserved. 3/1/2012
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Purchasing Power Risk
• Inflation risk
– T-bills (zero-coupon) have very little volatility risk, but • May not keep up with inflation
Lose purchasing power.
– Coupon bonds also face inflation
interest rate risk
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0.10
1
10
100
1,000
1926 1936 1946 1956 1966 1976 1986 1996 2006
Stocks, Bonds, Bills, & Inflation: 1926–2012
• Govt bonds 5.7• Treasury bills 3.56
$21
Past performance is no guarantee of future results. Hypothetical value of $1 invested at the beginning of 1926. Assumes reinvestment of income and no transaction costs or taxes. This is for illustrative purposes only and not indicative of any investment. An investment cannot be made directly in an index. © 2012 Morningstar. All Rights Reserved. 3/1/2012
Ibbotson® SBBI®
CAGR (%)
$10,000
$123
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Why Do So Many Fear the Stock Market?
• It’s a dangerous, volatile place – … thousands of sophisticated
traders and brokers lurk to steal your hard-earned money!
• Many call it “gambling!”• But maybe the real source of
fear is . . .
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Adults Invested in the Stock Market
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Market Volatility Risk
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1
1926 1936 1946 1956 1966 1976 1986 1996 2006
Smooth and Steady: 1926–2012
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1
1926 1936 1946 1956 1966 1976 1986 1996 2006
A Bumpy Ride: 1926–2012
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Why Would Anyone Take This Risk?
In High School saving for college
In college and now need the money
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Another spot to conduct this
activity
• Raise the benefit
– Now, B(X) > C(X),
• Choose the bar with the reward!
–where B(X) = benefit of action X
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Key Economic Concept
People respond to incentives
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Would You Ride a Bull?
– For $5?– for $50?– for $500?– for $5,000?– for $50,000?
• Likely to get more risk takers as the reward rises!
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Since Choice has a Cost
• Why choose it?
• People choose X if:
•B(X) > C(X)
B(X) C(X)
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Greater Return . . . ® accept the risk of:
– Riding the Bull
– Riding the
Roller Coaster
… or
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0.101926 1936 1946 1956 1966 1976 1986 1996 2006
Stocks and Bills: 1926–2012
$21
• Large stocks 9.8
• Treasury bills 3.56
CAGR (%)
$3,533
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Strategies for Dealing with Risk
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Strategies for Dealing with Risk
Time
$
1. Market Timing: Buy low, sell high!
Try to take advantage of volatility by “timing”
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How Do Investors Fare?(Study by Dalbar, Inc.)
• 1984 – 2000:– S&P 500 (geometric mean ≡ total return) + 16.3%– Avg stock mutual fund investor (IRR): +
5.3%
• What’s happening?
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Mutual Fund Merry-Go-Round• Possible explanation:
– Investors lack discipline to “buy and hold”• Chase the HOT fund, but
–This year’s star is next year’s dog
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Hot-Hand Fallacy: Chasing Fund Performance
© 2011 Morningstar. All Rights Reserved. 3/1/2011
$10,000 in Mutual Fund
Cash flows
10-year mutual fund total return = 6.94%
–3
0
1
2
3
4
5
$6 billion
–1
20082001 2002 2003 2004 2005 2006 2007 20090
10
20
25
40
$45k
35
30
15
5
2010
–2
10-year average investor return = – 20.24%
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Dangers of Market Timing1926–2009
$2,573
0
500
1,000
1,500
2,000
2,500
$3,000
S&P 500
$19.66
S&P minus best
37/1,008 months
$20.53
Treasury bills
$1.00 invested in 1926 in S&P 500
© 2010 Morningstar. All Rights Reserved. 3/1/2010 Ibbotson® SBBI®
$1(1.098)84
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Advice Worth Heeding!
• “I’ve seen people get famous for being right once in a row.”
• “Smart investing doesn’t consist of buying good things, but rather of buying things well. Price is what matters most for investment success.”
• Howard Marks
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Can you predict this?!
Market Timing?
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Geometric Mean – Common Use• Mutual funds & financial analysts refer to as:
– “total return”– “compound annual growth rate” (CAGR)
• a time-weighted rate of return
• nothing added or withdrawn during the period
• e.g., started with $1.00 . . . – did not deposit or withdraw
– did not withdraw any interest or dividends
Reasonable measure of mutual fund management because it ignores variables that are outside the manager’s control
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Is Geometric Return Good for Evaluating Individual Investor Performance?
• Total return: – computed by assuming that investors deposit
money at the beginning of the period – and pursue a buy-&-hold strategy
• Many investors deposit & withdraw funds– i.e., many investors do NOT buy & hold– need a “dollar-weighted” rate of return
• that takes into account the flow of funds in & out
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Example: Investor Facts• Purchased 100 shares of mutual fund @ $20• During 1st year, fund’s P rises by 30%, to $26• Begin of 2nd year, purchase 200 shares @ $26• During 2nd year, P fell by 4% to end @ $24.96• End year 2: investor sells all shares @ $24.96
Summary
Begin Year 1 Begin Year 2 End Year 2Deposit: $2,000 Deposit: $5,200 Withdraw: $7,488
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Evaluating the Fund Manager
• Use geometric return≡ Total Return
≡ time-weighted return
• Year 1: +30%
• Year 2: - 4%
• Thus, $1(1+.3)(1-.04) = $1.248
• To solve for total return:
• $1(1+ig)2 = 1.248
• 1 + ig = 1.248(0.5) = 1.117
• Thus, ig = 0.117, or 11.7%Reasonable measure of mutual fund management because it ignores variables outside the manager’s control
$1(1+i1)(1+i2)
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Is Total Return a Good Measure of Our Investor’s Performance?
• When there are cash flows into & out of an account, – we must use “internal rate of return” (IRR) calculation.
• Definition of IRR: – The rate of interest that satisfies the condition that
the sum of the present value of the outflows
is equal to the sum of the present value of the inflows.– Math Behind the Market, p. 60
– or – the interest rate that makes the net present value of an
investment equal zero.
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Setting Up IRR
Begin Year 1 Begin Year 2 End Year 2
Deposit: $2,000 Deposit: $5,200 Withdraw: $7,488
0)1(
488,7$
)1(
200,5$
)1(
000,2$210
iii
NPV
• The interest rate that makes the net present value = 0
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Solution
• This particular problem could be solved by using quadratic formula, however– Many more complicated problems must be
solved through computer iteration
• Using Microsoft Excel:• IRR = IRR(-2,000, -5,200, 7,488) = 0.031
– i.e, the investor earned 3.1% per year IRR
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Total Return v. Investor Return
• In this example,– the geometric return (total return) is:
• 11.7%– time-weighted, assumes buy-and-hold by investor
– the IRR (Investor Return on Morningstar) is:• 3.1%
– a dollar-weighted return
• Why such a significant difference?– Many investors chase hot funds ...
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Recall: Investor Facts• Purchased 100 shares of mutual fund @ $20• During 1st year, fund’s P rises by 30%, to $26• Begin of 2nd year, purchase 200 shares @ $26• During 2nd year, P fell by 4% to end @ $24.96• End year 2: investor sells all shares @ $24.96
• Chase what’s hot … – first year: 30% return: buy, buy, buy– second year: - 4% return– end 2nd year: it’s down: sell, sell, sell
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Study by Dalbar, Inc.
• Geometric mean return: S&P 500 recent 20 year period (1988 – 2008) – ≈ 12%
• i.e., if buy and hold, earn 12% annual rate of return
• Average investor return (IRR) – takes into account inflow & outflow
• i.e., chasing hot funds!
– ≈ 4%
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Prudent Strategies to Deal with Risk
2. Invest for the Long Term
. . . if you think long-term, the ups exceed the downs.
or, spread risk over more years!
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0.10
1
10
100
1,000
$10,000
1926 1936 1946 1956 1966 1976 1986 1996 2006
12.1% • Small stocks
Ibbotson® SBBI®
Small Stocks 1926–2010
© 2011 Morningstar. All Rights Reserved. 3/1/2011
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Which gray circle is bigger?
Which gray bar is longer?
Are the gray horizontal lines
parallel?
What Do You See?© 2011 Morningstar. All Rights Reserved. 3/1/2011
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They are the same size
They are the same size
The horizontal lines are parallel
Key Insight from Behavioral Economics:
Humans Don’t Always View Things Rationally© 2011 Morningstar. All Rights Reserved. 3/1/2011
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Focus on short-term instead of long-term risk
Result: Time-inconsistent behavior Interest in long term but act short term
Overly sensitive to recent volatility
Act as though time horizon far shorter than it is
Short-Term Focus
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When shown a distribution of 1-year returns
When shown a distribution of 30-year returns
Stocks
Short-Term Focus
Source:
Shlomo Benartzi and Richard H. Thaler, “Risk Aversion or Myopia? Choices in Repeated Gambles and Retirement Investments,” March 1999.
40%
60%
10%
90%
Bonds
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Reduction of Risk Over Time1926–2006
Small stocks Large stocks Government bonds Treasury bills
-60
-30
0
30
60
90
120
150%
1-year
Holding period
5-year 20-year 1-year 5-year 20-year 1-year 5-year 20-year 1-year 5-year 20-year
12.7%10.4% 5.4%
3.7%
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1926–2009
GeometricReturn
Arithmeticannualreturn
StandardDeviation
12.3%
17.4%
5.8%
3.8%
3.1%
Treasurybills
3.7% 3.1%
Large stocks
Governmentbonds
Inflation
9.8%
5.4%
3.0%
20.5%
9.6%
4.2%
–90%0
90%
Small stocks*
11.9% 32.8%
*Small company stock total return (1933) = 142.9%.
Histograms
Largest Standard Deviation?Smallest Standard Deviation?
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Nominal GDP & the S&P 500
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Prudent Strategies to Deal with Risk
• All money in one stock?– Could spill all the eggs
Don’t Put All Your Eggs in One Basket
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It Can Be Tempting!
• All Your Eggs in One Basket? – Great if you “hit it big”
• Wal-Mart–If you had purchased $1,000 of Wal-Mart
stock in 1970 at its IPO –held it through 1999, would have grown to:
» over $6,000,000!
• Not so great if things go south– Enron
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Prudent Strategies to Deal with Risk
• Diversify across asset class– Stocks and bonds
• Diversify within asset class– Stock from different
industries
Don’t Put All Your Eggs in One Basket
3. Diversify
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Benefit of Diversification
Time
$
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Cost of Diversification
Time
$
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$9.31
$6.25
$3.72
$20
10
11987 1992 1997 2002
Diversified Portfolios 1987–2006
11.8%
9.6%
6.8%
• Portfolio 1 (100% Stocks)
• Portfolio 2 (50% Stocks, 50% Bonds)
• Portfolio 3 (100% Bonds – 5 yr.)
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A Bull Market
• “Characterized by optimism, investor confidence and expectations that strong results will continue.
• The use of “Bull” to describe markets comes from the way bulls attack their opponents. A bull thrusts its horns up into the air. These actions are metaphors for the movement of a market. If the trend is up, it’s a “bull market.”
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A Bear Market
• Downward trend in the market that investors believe will continue in the long run, which, in turn, perpetuates the spiral.
• Downturn of 20% or more in multiple broad market indexes, such as the DJIA or S&P 500, over at least a two-month period– not to be confused with a correction
• a short-term trend with duration < two months
A bear will swipe its paws downward upon its unfortunate
prey
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Diversification – Cost & Benefit$3,000 Bull market
2,500
2,000
1,500
1,000
5001996 1997 1998 1999 2000 2001 2002
250
500
750
1,000
1,250
$1,500
$1,181
$2,555
$624
$1,484
$1,763
$985
• Stocks
• 50/50 portfolio
• Bonds
Bear market
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Risk & Return Diagram12
10
8
6
45 7 9 11 13 15 17
Return (%)
Risk (% standard deviation)
100% Bonds
100% Stocks
8.4
60% Stocks 40% Bonds
?
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Risk & Return Diagram12
10
8
6
45 7 9 11 13 15 17
Return (%)
Risk (% standard deviation)
100% Bonds
100% Stocks
8.4
60% Stocks 40% Bonds
?
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12
10
8
6
45 7 9 11 13 15 17
Return (%)
Risk (% standard deviation)
100% Bonds
100% Stocks
8.460% Stocks 40% Bonds
5.92
• The Efficient Frontier
If there were no benefit from diversification, then we would lie upon this linear combination of
bonds and stocks
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Actual Stock Market: 1970–200613
12
11
10
910 11 12 13 14 15 16 17
100% Stocks
80% Stocks, 20% Bonds
100% Bonds
60% Stocks, 40% Bonds
50% Stocks, 50% Bonds
25% Stocks, 75% Bonds
Return (%)
Risk (% standard deviation)
Efficient frontier
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What Makes This Work?
• How can we combine stocks and bonds
– and get a portfolio mean return that is the weighted average of the stocks and bonds
– but the standard deviation (volatility) is lower than either stocks or bonds?
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Correlation is High in Crisis
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Diversified Portfolios in Various Market ConditionsPerformance during and after select bear markets
• Past performance is no guarantee of future results. Diversified portfolio: 35% stocks, 40% bonds, 25% Treasury bills. Hypothetical value of $1,000 invested at the beginning of January 1973 and Nov 2007, respectively. This is for illustrative purposes only and not indicative of any investment. An investment cannot be made directly in an index. © 2011 Morningstar. All Rights Reserved. 3/1/2011
Mid-1970s recession (1973–76) 2007 bear market & aftermath (Nov 2007–Dec 2010)
$1,150
$1,014
$1,072
$872
$1,250
1,000
750
250 Jan1973
Jan1974
Jan1975
Jan1976
Nov 2007
Nov 2008
Nov2009
Nov 2010
• Stocks
• Diversified portfolio
500 35% stocks, 40% bonds, and 25% Treasury bills
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Risk & Stock Diversification
1 2 4 6 8 16 30 50 100 1000
Number of stocks in portfolio
Market Risk
Diversifiable Risk
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Too Much of a Good Thing?
• Diversification has benefits, but …
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Over-Diversification?
• Peter Lynch refers to “di-worse-ification”
– mutual funds might purchase so many separate companies
• Selecting companies lower on value list–dilutes return
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How Achieve Diversification?
• Passive management approach– “index funds”
• Achieve “market” rate of return– Slightly below, due to cost
• Active management approach– Assumes can “beat the market”
– Tough to do.
– Higher costs due to portfolio selection
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“Beauty Contest”
• Rules of the Game:– Each player will select a number from 0 to 100– Winner is the player whose number is closest to
the number that is 70% of the average of all player chosen numbers.
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Active Management
• A. Do it yourself:– Adequate diversification requires > $50,000
– NASD survey• People overestimate their abilities/understanding
– Expensive hobby – why do it yourself?• Maybe you can beat the market!?• You want to learn for later career• You simply have fun with it
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Active Management
• B. Professional management
– Investment adviser• Typical fee: 1% of asset value
–Mutual fund
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Diversify with Mutual Funds
• Mutual fund pools investors’ money
• Puts it into the markets on your behalf– you own small amounts of many different assets
• Good way to avoid the risk that comes from owning any one asset
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Picking Mutual Funds?
• Check on web sites for fund– e.g., Fidelity.com, Vanguard.com, Roycefunds.com
• Factors to consider:– Longevity/stability of fund managers– Management investment philosophy
• Long-term focus; not over diversified– Management track record– Expense ratios: preferably less than average of 1.5%– Portfolio turnover: preferably below 20%– Preference for “no load” funds
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Small Sample of Funds
• Locate names of funds through– Recommendations
• From other friends• From Wall Street Journal, or other articles
– Search recommendations by:• Morningstar.com• Other firm
– Then, review web page of fund for information . . . • Not necessarily recommended,
– although appeared satisfactory at one time
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Equity Income Fund
• Objective:– provide substantial dividend income as well as
long-term capital appreciation through investments in common stocks of established companies.• Turnover rate: 12% of fund
– % of fund bought and sold during year
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Fund Performance(through March 2013)
• T. Rowe Price:– 5-year total return:
5.5%– 10-year total return:
9.0%– Since 1985:
11.0%
• Benchmark: S&P 500– 5-year total return: 6.0%– 10-year total return:
8.0%– Since 1985:
10.5%Minimum amount required to open an account: $2,500
IRA minimum: $1,000
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Investment Philosophy• This fund offers a relatively conservative, value-oriented way to
pursue substantial dividend income and long-term capital growth potential.
• It invests in common stocks of established firms that are expected to pay above-average dividends.
• By investing in stocks that appear to be out of favor or undervalued, the fund should be less volatile than one investing in growth stocks.
• If, as the manager expects, the underpriced holdings regain favor in the marketplace, their stock prices may rise—providing capital appreciation opportunities.
• The value approach carries the risk that the market will not recognize a security’s true worth for a long time, or that a stock judged to be undervalued may actually be appropriately priced.
Price/earnings or P/E ratio: 13.8
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Top 10 Holdings• AT&T • Apache • Chevron • Exxon Mobil • General Electric • International Paper • JPMorgan Chase • Royal Dutch Shell • US Bancorp • Wells Fargo
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• Financials 20.3% • Industrials & Busn Services 14.0%• Energy 13.8% • Consumer Discretionary 10.4% • Information Technology 8.0% • Health Care 6.9% • Utilities 5.9% • Consumer Staples 5.6% • Materials 4.6% • Telecommunication Services 3.8%
Sector Diversification
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Portfolio Manager
• Brian C. Rogers • B.A., Harvard College • M.B.A., Harvard Business School
– Managed Fund Since: 10/31/1985
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To Summarize
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• How much one saves out of income
Three Key Variables Pn = (1 + i)n P0
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Three Key Variables
PN = (1 + i)n P0
• Interest rate, i–Compound interest is
powerful
–e.g., consider 2 cases: one-time investment of $10,000 for 40 years
– A invested at 8%
– B invested at 5%
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Power of Compounding: Importance of i2010 - 2050
Years invested:Amount Contributed:Rate of return:
$0
$50,000
$100,000
$150,000
$200,000
$250,000
$300,000
$10,000
$217,245
Investment B 40
$10,0008%
$10,000
$70,400
Investment A40
$10,0005%
PN = P0(1+i)n
= $10,000(1.05)40
PN = $10,000(1.08)40
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0.10
1
10
100
1,000
$10,000
1926 1936 1946 1956 1966 1976 1986 1996 2006
$2,982
$21
9.9%• Large stocks
• T-bills 3.6%
Ibbotson® SBBI®
142 times greater!
U.S. T-Bills & S&P 500, 1926–2010
2.7 times greater
© 2011 Morningstar. All Rights Reserved. 3/1/2011
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0.10
1
10
100
1,000
$10,000
1926 1936 1946 1956 1966 1976 1986 1996 2006
Ibbotson® SBBI®
Have Been Focused on Market Volatility Risk
Can avoid volatility risk with T-Bills
© 2011 Morningstar. All Rights Reserved. 3/1/2011
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0.10
1
10
100
1,000
$10,000
1926 1936 1946 1956 1966 1976 1986 1996 2006
$21
• T-bills 3.6
Compound Annual Return (%)
$12
• Inflation 3.0
Ibbotson® SBBI®
• Inflation risk
– maintain purchasing power
However, “Every Choice Has a Cost!”
© 2011 Morningstar. All Rights Reserved. 3/1/2011
• Real return 0.6
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0.10
1
10
100
1,000
$10,000
1926 1936 1946 1956 1966 1976 1986 1996 2006
Dealing with Inflation Risk?Mind the Gap in Rates of Return
$2,982
$21
$12
12.1% 9.95.5
$93
• Small stocks
• Gov’t bonds
• Inflation
• Large stocks
• T-bills 3.6
$16,055
3.0
Ibbotson® SBBI® © 2011 Morningstar. All Rights Reserved. 3/1/2011
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Two Key Variables PN = (1 + i)n P0
• Interest rate, i • Length of investment, n– Start early to benefit from
compounding
– Consider investors A & B– Both invest in S&P 500:
• A invests $2,000 per year from 1990 - 1999, then watches grow.
• B invests $4,000 per year from 2000 - 2009.
– Note: these are “annuities”
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Power of Compounding: Importance of n
Years contributing: 10
Annual contribution: $2,000
Years contributing: 10
Annual amount contributed: $4,000
Investor BInvestor A
$40,000
$42,118$20,000
$60,759
0
20
40
60
80
100
120
$140k
1990 – 2009 2000 – 2009
Investor A Investor B
Invested in S&P 500
Invested in S&P 500
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Two Key Messages from Compound Interest Story
• Save and Invest . . .
– Early• Consider . . .
– Stocks
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Conclusion
• Take a long-term perspective• Reinvest interest, dividends• Do not remove principal• Don’t chase the hot fund!
• Recognize the importance of:• Starting early, and• Minding the gap – pay attention to rates of return
– some stocks (via mutual/index funds) in portfolio
• Diversify– Through mutual funds
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