Transcript Lecture4 - UCSB Economics

Introduction to Economics
Elements of Personal Finance
Llad Phillips
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4. Thursday, Oct 8, Lecture Four: "Markowitz Efficiency
Portfolio Analysis"
Wall Street Journal Video, Guide to Money and Markets
( on reserve in Kerr Hall)
Markowitz Efficient Portfolio Analysis
Reading Assignment:
Guide to Understanding Personal Finance, Ch. 5, "Investing"
O’Sullivan and Sheffrin: Ch. 4, “Supply, Demand and Market
Equilibrium”
emphasis: the law of demand and market supply
Problems O & S Text
p. 78: 1, 2, 3, 4, 5, 6, 7
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Outline: Lecture Four
Video Guide to Money and Markets
 Interest rate, % per year, APR
 Determinants of Personal Income (cont.)
 Markowitz Efficient Portfolio Analysis

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Interest Rate Per Year On A Loan
Example: One Payment
 loan
amount: $1000
 annual interest rate: 10%
 one payment at the end of the year
pay
back principal: $1,000
pay the interest on $1000 for a year: $100
 principal*interest
rate = interest
 $1000*0.1 = $100
total
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payment due: $1100
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Interest Rate Per Year On A Loan
Example: Twelve Monthly Payments
 loan
amount: $1000
 annual interest rate: 10%
 Twelve Monthly Payments
pay
back principal of $1000
pay interest on the amount owed
 declining
amount owed since you pay back
some principal each month, until balance of
principal owed is zero after twelve payments
 use Excel’s PMT function to calculate
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one payment of principal
plus interest at the end
of the year
Principal
$1000
Declining
Balance,
12 monthly
payments
one Time
year
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Twelve Monthly Payments
loan
interest rate, per year
monthly payments
1000
10%
12
($87.92)
total payments
-1054.99
interest
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54.99
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Determinants of Personal Income
Life Cycle Model
 Learning and Earning
 Your Market Wage Depends on

 your

human capital
Allocating your time between Learning and
Earning
 24
hour endowment
 your tastes for learning versus earning
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Earnings
$480
Opportunities for trading leisure
for earnings (income) at a rate,
$20 per hour, the market wage,
determined by your stock of human
capital(step one of the paradigm:
describing the alternatives for choice)
$0
0 hours
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24 hours
Leisure
(learning)
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Choosing Between Learning and
Earning
How much time for learning?
 How much time for earning?
 This choice, like all choices depends on
your tastes

 Do
you want to earn and consume now?
 Do you want to learn, earn more in the future,
and consume more in the future?
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Economists Assume You Can
make Comparisons

example: more leisure and less income
versus less leisure and more income
 recall
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Lecture One: an Altima Vs. a Taurus
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Economists Assume You Can
Make Tradeoffs

How much income will you demand to give
up your leisure?
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Depicting your tastes graphically: iso-preference or
indifference curves
Earnings
$480
Iso-Preference Curves:
You value all points on
a curve equally(step two of
the paradigm: valuing the
alternatives for choice)
$0
0 hours
24 hours Leisure
(learning)
Depicting your tastes graphically
Earnings
low value
$480
high
Iso-Preference Curves:
You value all points on
a curve equally
high value
$0
0 hours
Leisure
24 hours (learning)
The choice between leisure and earning now:picking the
best alternative
Earnings
high
$480
alternatives
$0
0 hours
Iso-Preference Curves:
You value all points on
a curve equally
high value
low value
24 hours
Leisure
(learning)
Individual’s Supply of Labor
Earnings
low value
$480
$180
for 9 hrs
of work
high
Optimum
high value
Leisure
(learning)
$0
0 hours
15 hours
of leisure
24 hours
Personal Investing
How do you choose between stocks or
bonds as a personal investment?
 How do you choose between mutual funds?
 Are stocks and bonds too risky? Should you
keep your money in cash or gold?

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Example: UC Funds

Suppose you invest up to $9,500 per year in
a tax sheltered 403(b) plan
 you
have to save $9,500, but you would have to
pay income taxes if you took it as income

UC investment alternatives
 guaranteed
insurance contract(GIC)
 savings fund
 money market fund
 bond fund
 stock index fund
 multi-asset fund
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Investment Concepts
 monthly
return for June 1998 on an asset
price(June)
- price(May) + dividends
 price(June)
- price(May): capital gain(loss)
 dividends(interest): income from stocks(bonds)
 monthly
rate of return for June 1998
[price(June)
- price(May) +
dividends]/price(May)
 in
%, multiply by 100
• annual rate: multiply by 12
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Example: UC Funds/Mutual Funds
 Sources
of information on UC funds
monthly,
quarterly, annual, etc. rates of return
 internet:
http://www.ucop.edu/bencom/rs/perform.html
 Notice, a publication of the UC Academic Senate
 Source
of Information on Mutual Funds
quarterly
 The
Wall Street Journal, Mutual Funds Quarterly
Review, e.g. extra section in July 3, 1997 Journal
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UC Funds: Monthly Rate of Return
8
6
2
97.05
97.03
97.01
96.11
96.09
96.07
96.05
96.03
96.01
-2
95.11
0
95.09
Rate
4
Equity
Insurance
-4
-6
Year:Month
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UC Funds: Equity Vs. Insurance

Insurance
 steady
at a rate of
return of about 0.6
per month or 7.2%
per year
 does not vary much
 never negative
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
Equity
 rate
of return varies
a lot from month to
month
 range of rates of
return from about
plus 8% in Nov. ‘96
to minus 5% in July
‘96
 can turn negative: 7
months out of 22
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UC Funds Monthly Rate of Return
0.7
0.6
0.4
0.3
Insurance
Money Market
Savings
0.2
0.1
97.05
97.03
97.01
96.11
96.09
96.07
96.05
96.03
96.01
95.11
0
95.09
Rate
0.5
Year:Month
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UC Funds: Monthly Rates of Return
8
Bond
Equity
Multi-Asset
6
2
97.05
97.03
97.01
96.11
96.09
96.07
96.05
96.03
96.01
-2
95.11
0
95.09
Rate
4
-4
-6
Year:Month
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Two Kinds of Assets
low rate of returnlow variability
 want high rate of
return return on
average
 want low variability

 predictable
high return-high
variability
 want high rate of
return on average
 want low variability

average
return
Dilemma: which kind of asset to hold?
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Investment Principles or Maxims
 Don’t
hold
put all of your eggs in one basket
a diversified portfolio
 cash
 bonds
 stocks
 real
estate
advantage
of a mutual fund
 instead
of holding one stock, e.g. Coca-Cola, you
hold a bundle of stocks
 Choose
the asset with the highest reward
for a given level of risk
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Measures of Average Rate of Return and Variability: Mean & Std. Dev.
Date
Bond
95.09
95.1
95.11
95.12
96.01
96.02
96.03
96.04
96.05
96.06
96.07
96.08
96.09
96.1
96.11
96.12
97.01
97.02
97.03
97.04
97.05
97.06
mean
standard deviation
Equity
Insurance
2.66
2.4
3.9
2.83
-0.51
-5.42
-0.63
-0.75
0.78
1.68
0.34
0.35
4.21
7
5.56
-4.16
0.04
1.35
-3.59
2.23
2.59
2.75
4
-0.26
4.07
-0.13
3.32
2.35
-0.24
1.6
2.56
-0.12
-5.01
2.33
4.59
0.39
7.69
-1.25
4.59
0.42
-2.33
4.09
6.16
3.5
0.64
0.66
0.64
0.66
0.64
0.6
0.64
0.61
0.63
0.61
0.63
0.63
0.61
0.63
0.61
0.62
0.62
0.56
0.64
0.6
0.62
0.6
1.16
3.00
1.92
2.95
0.62
0.02
Money Market Multi-Asset
Savings
0.49
2.09
0.49
0.64
0.47
2.39
0.48
0.78
0.47
1.23
0.43
-0.12
0.45
0.02
0.43
0.62
0.44
1.27
0.44
0.5
0.46
-1.43
0.46
1.08
0.45
2.6
0.46
1.77
0.45
3.97
0.47
-1.1
0.46
1.82
0.41
0.62
0.45
-1.31
0.45
2.08
0.47
2.91
0.46
2.02
0.46
0.02
1.11
1.38
0.52
0.53
0.51
0.52
0.52
0.49
0.52
0.5
0.51
0.5
0.51
0.51
0.49
0.52
0.49
0.51
0.52
0.46
0.54
0.5
0.51
0.5
0.51
0.02
Mean Returns & Standard Deviations
UC Funds: Mean Return Vs. Risk (Standard Deviation)
2.00
Equity
1.80
1.60
Mean Return
1.40
1.20
Multi-Asset
Bond
1.00
0.80
0.60
Insurance
Savings
0.40
Money Market
0.20
0.00
0.00
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0.50
1.00
1.50
2.00
Standard Deviation
2.50
3.00
3.50
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Efficient Investment Portfolio
UC Funds: Mean Return Vs. Risk (Standard Deviation)
2.00
Equity
1.80
1.60
Mean Return
1.40
1.20
Multi-Asset
Bond
1.00
0.80
0.60
Insurance
Savings
0.40
Money Market
0.20
0.00
0.00
0.50
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1.00
1.50
2.00
Standard Deviation
2.50
3.00
3.50
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Your portfolio should be on the
efficient frontier
 But
where on the frontier?
depends
on your taste for reward and risk
 reward,
i.e. the mean rate of return is a good
 risk is a bad
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Economic Paradigm: Valuation of Mean Return and Risk
Assumption: Mean Return is Good, Risk is Bad: U =U(M,R)
better
Mean
Return,
M
worse
B
C
A
Iso - Preference Curves
Prefer B to A; Prefer B to C
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Risk, R
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Efficient Investment Portfolio
UC Funds: Mean Return Vs. Risk (Standard Deviation)
2.00
Investor A: very risk averse
1.80
Equity
1.60
Mean Return
1.40
1.20
Multi-Asset
Bond
1.00
0.80
0.60
Insurance
Savings
0.40
Money Market
0.20
0.00
0.00
0.50
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1.00
1.50
2.00
Standard Deviation
2.50
3.00
3.50
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Efficient Investment Portfolio
UC Funds: Mean Return Vs. Risk (Standard Deviation)
2.00
Investor B: not very risk averse
Equity
1.80
1.60
Mean Return
1.40
1.20
Multi-Asset
Bond
1.00
0.80
0.60
Insurance
Savings
0.40
Money Market
0.20
0.00
0.00
0.50
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1.00
1.50
2.00
Standard Deviation
2.50
3.00
3.50
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Efficient UC Investment Portfolio
 f*insurance
where
contract + (1-f)*equity fund
f can range from zero to one
example:
50:50, i.e one half of your nest egg
is invested in the Insurance Contract and the
other half is invested in the Equity Fund.
• mean return: 1/2 *0.62 + 1/2*1.92 = 1.27 % per
month
• expected risk(standard deviation: 1/2*0.02 +
1/2*3.02 =1.52
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–exercise: show that this mean portfolio return
–and expected risk lie on the efficient frontier
– connecting the insurance contract and the
–equity fund
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Summary-Vocabulary-Concepts






Markowitz Portfolio
Analysis
stock index fund
bond fund
money market fund
guaranteed insurance
contract
monthly rate of return
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





capital gains
dividends
mean rate of return on
an asset
risk of holding an asset
a risk averse person
investment portfolio
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Return
-5
-10
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98.07
98.05
98.03
98.01
97.11
97.09
97.07
97.05
97.03
97.01
96.11
96.09
96.07
96.05
96.03
96.01
95.11
95.09
UC Funds: Monthly Rates of Return
10
5
0
Bond
Equity
-15
Date
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