investing 101 lecture 4 basic portfolio building
TRANSCRIPT
Investing 101Investing 101
Lecture 4Lecture 4
Basic Portfolio BuildingBasic Portfolio Building
ReviewReview Explain supply and demand?Explain supply and demand?
What is GDP?What is GDP?
What are Consumer/Producer surplus? Reservation What are Consumer/Producer surplus? Reservation Price?Price?
What is an interest rate?What is an interest rate?
What is an exchange rate?What is an exchange rate?
Does anyone have anything to share?Does anyone have anything to share?
Stock update?Stock update?
Anything special happening in life?Anything special happening in life?
Anyone have any questions on unrelated Anyone have any questions on unrelated random financial topics?random financial topics?
I don’t expect to get through all of today’s I don’t expect to get through all of today’s material in two hours, may stay 15 min and/or material in two hours, may stay 15 min and/or go into next day.go into next day.
Main Teaching PointsMain Teaching Points Variance and standard deviationVariance and standard deviation
Security market line (SML)Security market line (SML)
Capital allocation line (CAL)Capital allocation line (CAL)
Capital assets pricing model (CAPM)Capital assets pricing model (CAPM)
Covariance and correlationCovariance and correlation
Diligent asset allocationDiligent asset allocation
Pulling it all together.Pulling it all together.
WarningWarning
There are lots of slides in today’s class. There are lots of slides in today’s class. Many of them are pictures and graphs.Many of them are pictures and graphs. If you are a spatial mathematician you will If you are a spatial mathematician you will
want to pay close attention.want to pay close attention. There are some eqns you do NOT have to There are some eqns you do NOT have to
understand them, so if they confuse you do understand them, so if they confuse you do your best to block them out. your best to block them out.
Lets get started we have A LOT to learn and Lets get started we have A LOT to learn and much to pull together.much to pull together.
All the stats you will ever need to knowAll the stats you will ever need to know
Empirical RuleEmpirical Rule
Has anyone heard of it???Has anyone heard of it???
68 95 9968 95 99
The key to risk in stocks.The key to risk in stocks.
The Security Market LineThe Security Market LineRisk
Return
SBUX
GOOG
TELUS
Risk Free
Asset AllocationAsset Allocation
Asset Allocation is the portfolio choice among Asset Allocation is the portfolio choice among broad investment classes:broad investment classes: One risky asset and one risk-free assetOne risky asset and one risk-free asset Two risky assetsTwo risky assets Two risky assets and one risk-free assetTwo risky assets and one risk-free asset Many risky assets and one risk-free assetMany risky assets and one risk-free asset
Asset ClassesAsset Classes
Risky AssetsRisky Assets Stocks (S&P Comp. Index)Stocks (S&P Comp. Index)
Mean Real Return: 10%Mean Real Return: 10% Standard Deviation: 20%Standard Deviation: 20%
BondsBonds Mean Real Return: 4%Mean Real Return: 4% Standard Deviation: 10%Standard Deviation: 10% Correlation with Real Stock Return: 0.2Correlation with Real Stock Return: 0.2
T-Bills (Risk-free asset)T-Bills (Risk-free asset) Real Return: 1%Real Return: 1%
Portfolio of Risk-Free Asset and Portfolio of Risk-Free Asset and Risky AssetRisky Asset
What is the expected return and the standard What is the expected return and the standard deviation of a portfolio that invests:deviation of a portfolio that invests: ww in stocks in stocks 1-1-ww in the risk-free asset? in the risk-free asset?
Capital Allocation LineCapital Allocation Line
Expected Return of Portfolio:Expected Return of Portfolio:
Standard Deviation of Portfolio:Standard Deviation of Portfolio:
Substituting for Substituting for ww, gives the Capital , gives the Capital Allocation Line (CAL):Allocation Line (CAL):
FSP rwrwErE 1)()(
SP w
PS
FSFP rrErrE
)(
)(
Capital Allocation LineCapital Allocation Line
rr
E(r)E(r)
00
PP
rr ff
Capital Allocation LineCapital Allocation Line
rr
E(r)E(r)
00
PP
rr ff Slope = Slope = E (rE (rpp) - r) - rff
rrpp
The Capital The Capital Allocation LineAllocation Line
Capital Allocation LineCapital Allocation Line
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Standard Deviation
Exp
ecte
d R
etur
n
100% Stocks
100% T-Bills
50% Stocks50% T-Bills
CAL
125% Stocks-25% T-Bills
Capital Allocation LineCapital Allocation Line
The Capital Allocation Line shows the risk-The Capital Allocation Line shows the risk-return combinations available by changing the return combinations available by changing the proportion invested in a risk-free asset and a proportion invested in a risk-free asset and a risky assetrisky asset
The slope of the CAL is the reward-to-The slope of the CAL is the reward-to-variability ratiovariability ratio
Capital Assets Pricing ModelCapital Assets Pricing Model
Now that we know that different stocks hold Now that we know that different stocks hold different levels of risk, we can use this different levels of risk, we can use this knowledge to price the stocks.knowledge to price the stocks.
We use CAPM to find the rate at which to We use CAPM to find the rate at which to discount the future dividends of a stock. discount the future dividends of a stock.
Perpetuity stock = D1/k Perpetuity stock = D1/k Growth stock = D1/k-gGrowth stock = D1/k-g Where D = dividend, g = growth, k = discount Where D = dividend, g = growth, k = discount
rate.rate.
CAPM EquationCAPM Equation
k = rf + B(Rm-rf) k = rf + B(Rm-rf) Where rf = Risk free rate Rm = Return of the Where rf = Risk free rate Rm = Return of the
market and B = beta. market and B = beta. Beta is the correlation b/w the returns of the Beta is the correlation b/w the returns of the
market and the returns of the stock. market and the returns of the stock.
RMkt
R stock
Risk AversionRisk Aversion Now the question is, which risk-return Now the question is, which risk-return
combination along the CAL do you want?combination along the CAL do you want? To answer this we need to bring your To answer this we need to bring your
preferences for risk into the picturepreferences for risk into the picture We will use indifference curves to represent We will use indifference curves to represent
risk aversionrisk aversion Indifference curves represent utility functionsIndifference curves represent utility functions
Indifference CurvesIndifference Curves
rr
E(r)E(r)
00
u=3u=3
u=2u=2
u=1u=1
AA
BB
CC
Surrey
N Van
Asset AllocationAsset Allocation
Now we can combine the indifference Now we can combine the indifference curves with the capital allocation linecurves with the capital allocation line
If investors are maximizing their utility, If investors are maximizing their utility, they will choose the highest possible they will choose the highest possible indifference curveindifference curve
The highest curve is tangent to the CALThe highest curve is tangent to the CAL
Asset AllocationAsset Allocation
rr
E(r)E(r)
00
PP
ff
CALCAL
IndifferenceIndifferenceCurvesCurves
rr
Portfolio Frontier with Stocks Portfolio Frontier with Stocks and Bondsand Bonds
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Standard Deviation
Exp
ecte
d R
etur
n
100% Bonds / 0% Stocks
0% Bonds / 100% Stocks
86% Bonds / 14% Stocks
150% Bonds / -50% Stocks
-50% Bonds / 150% Stocks
Portfolio FrontierPortfolio Frontier
The portfolio frontier depicts the feasible portfolio The portfolio frontier depicts the feasible portfolio choices for investors holding stocks and bondschoices for investors holding stocks and bonds
The minimum variance portfolio includes 86% bonds The minimum variance portfolio includes 86% bonds and 14% stocksand 14% stocks
Portfolios below the minimum variance portfolio are Portfolios below the minimum variance portfolio are inefficientinefficient
The portfolio frontier above the minimum variance The portfolio frontier above the minimum variance portfolio is called ‘efficient frontier’portfolio is called ‘efficient frontier’
Correlation: Correlation: Two Risky AssetsTwo Risky Assets To see the importance of correlation, we will look To see the importance of correlation, we will look
at the set of feasible portfolios under three at the set of feasible portfolios under three different assumptions:different assumptions: 1) 1) ρρABAB = 1 = 1 2) 2) ρρABAB = -1 = -1 3) 3) ρρABAB = 0 = 0
Then we will discuss the intermediate casesThen we will discuss the intermediate cases
Perfect CorrelationPerfect Correlation
(r)(r)
E(r)E(r)
00
AA
BB
Perfect CorrelationPerfect Correlation
(r)(r)
E(r)E(r)
00
AA
BB
ABAB= 1= 1
(r)(r)
E(r)E(r)
00
AA
BB
ABAB== 11
Perfect Negative CorrelationPerfect Negative Correlation
ABAB= -1= -1
No CorrelationNo Correlation
(r)(r)
E(r)E(r)
AA
BB
ABAB= 1= 1
ABAB
= 0= 0
ABAB= -1= -1
00
Portfolio Frontiers with Different Portfolio Frontiers with Different Asset CorrelationsAsset Correlations
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 0.1 0.2 0.3 0.4
Standard Deviation
Exp
ect
ed
Re
turn
=-1=0=0.75=1
Asset Allocation with Risk-Free Asset Allocation with Risk-Free AssetAsset
Introducing a risk-free asset besides stocks and Introducing a risk-free asset besides stocks and bonds improves the investment opportunitiesbonds improves the investment opportunities
Capital Allocation Lines using Capital Allocation Lines using Stocks and BondsStocks and Bonds
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Standard Deviation
Exp
ecte
d R
etur
n
Bonds
Stocks
100% T-Bills
Optimal Capital Allocation LineOptimal Capital Allocation Line
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Standard Deviation
Exp
ecte
d R
etur
n
52% Bonds / 48% Stocks
100% T-bills
50% T-Bills26% Bonds24% Stocks
-50% T-Bills78% Bonds72% Stocks
Portfolio Frontier with Three Portfolio Frontier with Three Risky AssetsRisky Assets
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0 0.1 0.2 0.3 0.4 0.5
Standard Deviation
Exp
ect
ed
Re
turn
Bonds
Large Stocks
Small Stocks
Portfolio Frontier with Many Portfolio Frontier with Many Risky AssetsRisky Assets
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0 0.1 0.2 0.3 0.4 0.5
Standard Deviation
Exp
ect
ed
Re
turn
T-Bonds
YHOO
Corp-Bonds
MSFT
GE
Gold
TangencyPortfolio
CAL
DiversificationDiversification
““It is part of a wise man … not to venture all It is part of a wise man … not to venture all his eggs in one basket” his eggs in one basket”
- Miguel de Cervantes- Miguel de Cervantes
““Put all your eggs in one basket and watch that Put all your eggs in one basket and watch that basket” basket”
- Mark Twain- Mark Twain
The Benefits of DiversificationThe Benefits of Diversification The variance of the return of a portfolio that includes The variance of the return of a portfolio that includes NN different assets depends on the weight different assets depends on the weight ww and on the and on the covariances :covariances :
),(),(),(
),(),(),(
),(),(),(
),()(
2211
2222221212
1121211111
1 1
NNNNNNNN
NN
NN
N
i
N
jjijiP
rrCovwwrrCovwwrrCovww
rrCovwwrrCovwwrrCovww
rrCovwwrrCovwwrrCovww
rrCovwwrVar
DiversificationDiversification
The standard deviation of a portfolio tends to The standard deviation of a portfolio tends to decrease as more risky assets are added to the decrease as more risky assets are added to the portfolioportfolio
Number of Securities
Std. DeviationOf Portfolio
Market Risk
Firm-specific Risk
Questions?Questions?