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?