Investing 101
Lecture 4
Basic Portfolio Building
Review

Explain supply and demand?

What is GDP?

What are Consumer/Producer surplus? Reservation
Price?

What is an interest rate?

What is an exchange rate?
Does anyone have anything to share?

Stock update?

Anything special happening in life?

Anyone have any questions on unrelated
random financial topics?
I don’t expect to get through all of today’s
material in two hours, may stay 15 min and/or
go into next day.

Main Teaching Points

Variance and standard deviation

Security market line (SML)

Capital allocation line (CAL)

Capital assets pricing model (CAPM)

Covariance and correlation

Diligent asset allocation

Pulling it all together.
Warning





There are lots of slides in today’s class.
Many of them are pictures and graphs.
If you are a spatial mathematician you will
want to pay close attention.
There are some eqns you do NOT have to
understand them, so if they confuse you do
your best to block them out.
Lets get started we have A LOT to learn and
much to pull together.
All the stats you will ever need to know
Empirical Rule

Has anyone heard of it???

68 95 99

The key to risk in stocks.
The Security Market Line
Risk
GOOG
SBUX
TELUS
Risk
Free
Return
Asset Allocation

Asset Allocation is the portfolio choice among
broad investment classes:




One risky asset and one risk-free asset
Two risky assets
Two risky assets and one risk-free asset
Many risky assets and one risk-free asset
Asset Classes

Risky Assets

Stocks (S&P Comp. Index)



Bonds




Mean Real Return: 10%
Standard Deviation: 20%
Mean Real Return: 4%
Standard Deviation: 10%
Correlation with Real Stock Return: 0.2
T-Bills (Risk-free asset)

Real Return: 1%
Portfolio of Risk-Free Asset and
Risky Asset

What is the expected return and the standard
deviation of a portfolio that invests:


w in stocks
1-w in the risk-free asset?
Capital Allocation Line

Expected Return of Portfolio:
E (r P )  wE (r S )  1  wr F

Standard Deviation of Portfolio:
 P  w S

Substituting for w, gives the Capital
Allocation Line (CAL):
E (r P )  r F 
E (r S )  r F
S
P
Capital Allocation Line
E(r)
P
rf
0
r
Capital Allocation Line
E(r)
The Capital
Allocation Line
P
rf
Slope = E (rp) - rf
rp
0
r
Capital Allocation Line
0.14
CAL
0.12
125% Stocks
-25% T-Bills
Expected Return
0.1
100% Stocks
0.08
0.06
50% Stocks
50% T-Bills
0.04
0.02
100% T-Bills
0
0
0.05
0.1
0.15
0.2
Standard Deviation
0.25
0.3
0.35
Capital Allocation Line


The Capital Allocation Line shows the riskreturn combinations available by changing the
proportion invested in a risk-free asset and a
risky asset
The slope of the CAL is the reward-tovariability ratio
Capital Assets Pricing Model





Now that we know that different stocks hold
different levels of risk, we can use this
knowledge to price the stocks.
We use CAPM to find the rate at which to
discount the future dividends of a stock.
Perpetuity stock = D1/k
Growth stock = D1/k-g
Where D = dividend, g = growth, k = discount
rate.
CAPM Equation



k = rf + B(Rm-rf)
Where rf = Risk free rate Rm = Return of the
market and B = beta.
Beta is the correlation b/w the returns of the
market and the returns of the stock.
R stock
RMkt
Risk Aversion




Now the question is, which risk-return
combination along the CAL do you want?
To answer this we need to bring your
preferences for risk into the picture
We will use indifference curves to represent
risk aversion
Indifference curves represent utility functions
Indifference Curves
u=3
E(r)
u=2
B
u=1
N Van
A
C
Surrey
0
r
Asset Allocation



Now we can combine the indifference
curves with the capital allocation line
If investors are maximizing their utility,
they will choose the highest possible
indifference curve
The highest curve is tangent to the CAL
Asset Allocation
E(r)
CAL
P
r
f
0
Indifference
Curves
r
Portfolio Frontier with Stocks
and Bonds
0.14
-50% Bonds / 150% Stocks
0.12
0% Bonds / 100% Stocks
Expected Return
0.1
0.08
0.06
86% Bonds / 14% Stocks
100% Bonds / 0% Stocks
0.04
0.02
150% Bonds / -50% Stocks
0
0
0.05
0.1
0.15
0.2
Standard Deviation
0.25
0.3
0.35
Portfolio Frontier




The portfolio frontier depicts the feasible portfolio
choices for investors holding stocks and bonds
The minimum variance portfolio includes 86% bonds
and 14% stocks
Portfolios below the minimum variance portfolio are
inefficient
The portfolio frontier above the minimum variance
portfolio is called ‘efficient frontier’
Correlation: Two Risky Assets


To see the importance of correlation, we will look
at the set of feasible portfolios under three
different assumptions:
 1) ρAB = 1
 2) ρAB = -1
 3) ρAB = 0
Then we will discuss the intermediate cases
Perfect Correlation
E(r)
A
B
0
(r)
Perfect Correlation
E(r)
A
AB= 1
B
0
(r)
Perfect Negative Correlation
E(r)
A
AB= -1
0
AB= 1
B
(r)
No Correlation
E(r)
AB= 0
A
AB= -1
0
AB= 1
B
(r)
Portfolio Frontiers with Different
Asset Correlations
0.14
Expected Return
0.12
0.1
0.08
0.06
0.04
0.02
=1
0
0
=0.75
0.1
=0
=-1
0.2
Standard Deviation
0.3
0.4
Asset Allocation with Risk-Free
Asset

Introducing a risk-free asset besides stocks and
bonds improves the investment opportunities
Capital Allocation Lines using
Stocks and Bonds
0.14
0.12
Stocks
Expected Return
0.1
0.08
0.06
Bonds
0.04
0.02
100% T-Bills
0
0
0.05
0.1
0.15
0.2
Standard Deviation
0.25
0.3
0.35
Optimal Capital Allocation Line
0.14
-50% T-Bills
78% Bonds
72% Stocks
Expected Return
0.12
0.1
0.08
52% Bonds / 48% Stocks
50% T-Bills
26% Bonds
24% Stocks
0.06
0.04
0.02
100% T-bills
0
0
0.05
0.1
0.15
0.2
Standard Deviation
0.25
0.3
0.35
Portfolio Frontier with Three
Risky Assets
0.2
0.18
Expected Return
0.16
Small Stocks
0.14
0.12
0.1
Large Stocks
0.08
0.06
0.04
Bonds
0.02
0
0
0.1
0.2
0.3
Standard Deviation
0.4
0.5
Portfolio Frontier with Many
Risky Assets
0.2
CAL
0.18
Expected Return
0.16
YHOO
0.14
0.12
MSFT
0.1
0.08 Tangency
Portfolio
0.06
GE
Corp-Bonds
T-Bonds
0.04
0.02
0
Gold
0
0.1
0.2
0.3
Standard Deviation
0.4
0.5
Diversification


“It is part of a wise man … not to venture all
his eggs in one basket”
- Miguel de Cervantes
“Put all your eggs in one basket and watch that
basket”
- Mark Twain
The Benefits of Diversification

The variance of the return of a portfolio that includes
N different assets depends on the weight w and on the
covariances :
N
N
Var (rP )   wi w j Cov(ri , rj )
i 1 j 1
 w1w1Cov(r1 , r1 )  w1w2Cov(r1 , r2 )    w1wN Cov(r1 , rN )
 w2 w1Cov(r2 , r1 )  w2 w2Cov(r2 , r2 )    w2 wN Cov(r2 , rN )

 wN w1Cov(rN , r1 )  wN w2Cov(rN , r2 )    wN wN Cov(rN , rN )
Diversification

The standard deviation of a portfolio tends to
decrease as more risky assets are added to the
portfolio
Std. Deviation
Of Portfolio
Firm-specific Risk
Market Risk
Number of Securities
Questions?