Investment

Theory

Alexandre

Corhay

Review

Return on a

Portfolio

Predicted

Return and

Variance

Beneﬁts of

Diversiﬁcation

M-V Opt.

and the

Profile

Frontier

Investment Theory

Portfolio Theory

Alexandre Corhay

Sauder School of Business

University or college of Britich columbia

P-F with

Risky

Possessions Only

Limits of

Diversiﬁcation

P-F using a

Riskless

Advantage

Tangent

Profile

Property

Copyright laws c 2012 J. Bena, H. Kung, A. Pavlova and G. Vayanos

1 / 46

Overview of the Lecture

Expense

Theory

Alexandre

Corhay

Big question: How to choose a stock collection?

Overview

one particular

Return on a

Portfolio

Expected

Return and

Variance

Beneﬁts of

Diversiﬁcation

Return over a Portfolio

a couple of

Expected Go back and Difference of a Profile

3

Beneﬁts of Diversiﬁcation

4

Mean-Variance Optimization plus the Portfolio Frontier

Portfolio Frontier with Risky Assets Only

5

• Two Possessions

• Hardship deals

• Much more than Two Property

M-V Choose.

and the

Profile

Frontier

P-F with

High-risk

Assets Just

Limits of

Diversiﬁcation

six

Limits of Diversiﬁcation: Organized vs . Idiosyncratic risk

six

Portfolio Frontier with a Riskless Asset

8

An Important Home of the Tangent Portfolio

P-F with a

Riskless

Asset

Tangent

Portfolio

House

2 / 46

Return on a Stock portfolio

Investment

Theory

Alexandre

Corhay

Overview

Return on a

Portfolio

Expected

Go back and

Difference

Determine the return on the stock profile given the returns on the individual stocks.

• Look at a portfolio including X1 dollars in Disney and X2 dollars in

IBM.

• The value of the portfolio in date zero is Back button = X1 + X2.

• The importance of the collection at date 1 is

Beneﬁts of

Diversiﬁcation

M-V Opt.

and the

Portfolio

Frontier

P-F with

Risky

Resources Only

Limits of

Diversiﬁcation

P-F having a

Riskless

Asset

Tangent

Collection

Property

X1 (1 + R1 ) + X2 (1 & R2 ),

where R1 is the go back on Disney and R2 the return on APPLE between schedules 0 and 1 .

• The go back on the collection is

Ur

=

=

X1 (1 + R1 ) + X2 (1 + R2 ) − X

By

X1

X2

R1 &

R2.

X

X

several / 46

Portfolio Dumbbells

Investment

Theory

• The portfolio weight loads are

Alexandre

Corhay

w1 =

Review

Return over a

Portfolio

Anticipated

Return and

Variance

X2

.

X

3rd there�s r = w1 R1 + w2 R2.

It is a measured average of the returns within the individual shares. • Even more generally, the return on a portfolio with N stocks and options is N

R=

Limits of

Diversiﬁcation

Tangent

Portfolio

Property

w2 =

• The go back on the collection is

P-F with

Risky

Assets Just

P-F using a

Riskless

Asset

and

They will represent the fraction of portfolio value invested in each stock. That they sum to at least one.

Beneﬁts of

Diversiﬁcation

M-V Opt.

and the

Portfolio

Frontier

X1

By

wn R n,

n=1

where

wn =

Xn

.

X

four / 46

Example you

Investment

Theory

Alexandre

Corhay

Overview

Go back on a

Collection

Expected

Go back and

Difference

Beneﬁts of

Diversiﬁcation

M-V Opt.

as well as the

Portfolio

Frontier

P-F with

Risky

Possessions Only

Figure out the go back on a stock portfolio consisting of 300 dollar in Disney and hundred buck in APPLE.

• We have

w1 sama dengan

300

sama dengan 0. 75

400

w2 =

75

= zero. 25.

four hundred

and

• The go back on the profile is

R = 0. 75 × R1 + 0. 25 × R2.

Limits of

Diversiﬁcation

P-F with a

Riskless

Asset

Tangent

Portfolio

Property

5 as well as 46

Case 2

Purchase

Theory

Alexandre

Corhay

Review

Return on the

Portfolio

Anticipated

Return and

Variance

Beneﬁts of

Diversiﬁcation

M-V Choose.

and the

Collection

Frontier

Begin with the same amount of initial capital $400. Rather than buying $22.99 of IBM, we promote short $100 of IBM. Compute the return for the portfolio. • What are short sales?

• How to compute the return on the portfolio that involves short sales?

P-F with

High-risk

Assets Simply

Limits of

Diversiﬁcation

P-F with a

Riskless

Asset

Tangent

Portfolio

Home

6 as well as 46

Exactly what are Short...