MENGUKUR RISIKO, KESEIMBANGAN UNTUK

PASAR DENGAN ASET YANG BERISIKO

NAMA:

ANISA LISTYA (01022681519017)

SASKIA JAMILAH K (01022681519011)

Pemilihan Asset Berisiko

Higher mean return is preferred. Less variation in return is preferred

(less risk). Preferences are represented by a

utility function U(,). U as mean return . U as risk .

Preferences over Risky Assets

Mean Return,

St. Dev. of Return,

Preferred Higher mean return is a good.Higher risk is a bad.

dd

UU

//

Budget Constraints for Risky Assets

Two assets. Risk-free asset’s rate-or-return is rf .

Risky stock’s rate-or-return is ms if state s occurs, with prob. s .

Risky stock’s mean rate-of-return is

r mm s ss

S

.

1

Budget Constraints for Risky Assets

A bundle containing some of the risky stock and some of the risk-free asset is a portfolio.

x is the fraction of wealth used to buy the risky stock.

Given x, the portfolio’s av. rate-of-return is r xr x rx m f ( ) .1

Budget Constraints for Risky Assets

r xr x rx m f ( ) .1

x = 0 r rx f and x = 1 r rx m .

Since stock is risky and risk is a bad, for stockto be purchased must have r rm f .

So portfolio’s expected rate-of-return rises with x(more stock in the portfolio).

Measuring Risk

Quantitatively, how risky is an asset? Depends upon how the asset’s value

depends upon other assets’ values. E.g. Asset A’s value is $60 with

chance 1/4 and $20 with chance 3/4. Pay at most $30 for asset A.

Measuring Risk

Asset A’s value is $60 with chance 1/4 and $20 with chance 3/4.

Asset B’s value is $20 when asset A’s value is $60 and is $60 when asset A’s value is $20 (perfect negative correlation of values).

Pay up to $40 > $30 for a 50-50 mix of assets A and B.

Measuring Risk

Asset A’s risk relative to risk in the whole stock market is measured by

Arisk of asset A

risk of whole market .

AAcovariance(

variance(

r rr

m

m

, ))

where is the market’s rate-of-returnand is asset A’s rate-of-return.rA

rm

Measuring Risk

asset A’s return is not perfectly correlated with the whole market’s return and so it can be used to build a lower risk portfolio.

1 1 A .

A 1

Equilibrium in Risky Asset Markets

At equilibrium, all assets’ risk-adjusted rates-of-return must be equal.

How do we adjust for riskiness?

Equilibrium in Risky Asset Markets

Riskiness of asset A relative to total market risk is A.

Total market risk is m.

So total riskiness of asset A is Am. Price of risk is

So cost of asset A’s risk is pAm.

pr rm f

m

.

Equilibrium in Risky Asset Markets

Risk adjustment for asset A is

Risk adjusted rate-of-return for asset A is

pr r

r rmm f

mm m f

A A A

( ).

r r rm fA A ( ).

Equilibrium in Risky Asset Markets

At equilibrium, all risk adjusted rates-of-return for all assets are equal.

The risk-free asset’s = 0 so its adjusted rate-of-return is just

Hence,

for every risky asset A.

r r r r

r r r r

f m f

f m f

A A

A Ai.e.

( )

( )

rf .

Equilibrium in Risky Asset Markets

That at equilibrium in asset markets is the main result of the Capital Asset Pricing Model (CAPM), a model used extensively to study financial markets.

r r r rf m fA A ( )

Q & A

1. 2 3

TERIMA KASIH