“International Finance and Payments” Course III: “International financial portfolios theory” Lect. Cristian PĂUN Email: [email protected] [email protected]@ase.ro

“International Finance and Payments”

Course III:Course III:

““International financial portfolios theoryInternational financial portfolios theory””

Lect. Cristian PĂUNLect. Cristian PĂUN

Email: Email: [email protected]

URL: http://www.finint.ase.roURL: http://www.finint.ase.ro

Academy of Economic Studies

Faculty of International Business and Economics

Course 3: International Financial Portfolios Theory

2

International Financial Markets and Institutions - review

• the main components of the IFS are: financial markets, financial institutions and financial instruments;

• financial markets: money markets and capital markets (the differences);

• internal financial resources vs. external financial resources;

• direct financing vs. indirect financing;

• financial institutions: international financial institutions, government agencies, depositary institutions and investment institutions

• financial instruments: direct investment and indirect investment instruments;

• direct investment instruments: money market instruments and capital market instruments

• money market instruments: T-bills, REPO, negotiable DC, commercial papers, forward contracts;

• capital market instruments: fixed income instruments, variable income instruments, derivatives.


3

Risk and return in international finance• Knight definition: risk is the decisional situation in which we can associate o probability to future events (uncertainty and certainty)

• Main critics:

• it is difficult to make a difference between the three decisional situations;

• it is very difficult to determine the risk level for an investment based on the capacity of probabilistic associations;

• a too simplistic approach;

• high subjectivity in the probabilistic association process (some investors can consider an event as a risky one and others as an uncertain one based on different analytical capacities).

• Other risk definitions:• “Risk is the possibility that the returns be lower than expected” (Mehr Hedges);

• “Risk is the possible return variability caused by an uncertain further event” (Dorfman);

• “Risk is the incertitude about future possible losses” (Redja)


4

Incertitude and risk factors:• lack of perfect information;• impossibility to make a correct prediction in case of future events;• incapacity to identify all the alternatives for your decision;• the future events are usually unique;• the investors profile;• impossibility to control all factors or events;• time pressure.

•higher risk implies usually higher expected return;

• the relation between the utility of an investment return and the return is not a linear one (decreasing marginal utility - u(w)>0 and u(w)<0) – Bernoulli

• if an investor prefers an investment p instead an investment q than U(p) is higher than U(q) – Neumann & Morgenstern

• if we have to chose between two investment p an q, the utility of a linear combination is equal with the amount of the utility for each alternative:

U( p + (1- )q) = U(p) + (1-)U(q) for each (0, 1)

Risk and return relation:


5

A. Markovitz Model


6

Markovitz Model Hypothesis:

1. Expected profit is normally distributed;

2. Investors are seeking in every moment for their profit maximization;

3. Investors have a decreasing marginal utility of their wealth;

4. The variability of the probable profits is the proper measure for the level of

risk assumed by the investors;

5. The investment decision is based on risk & return profile;

6. The investors usually prefer higher profits at a given level of risk;

7. The investors usually prefer lower risk at a given level of the expected

return;

8. Investors have a limited time for their investment decision.


7

Expected return

it

1tti

ti

1ti

P

DPPRET

qk

qk

4k3k

4k3k

2k1k

2k1kik R...

p...

RR

pp

RR

ppR

n1,ini

q1,ii

n

q1,i2iq1,i1i

q1,iiq1,ii

21

port

E(R

p

w

...E(RE(R

...pp

...ww

R

)))

q

1i iik Rp)E(R

n

1i iiport )E(Rw)E(R

- initial assumption


8

Expected return - example

Individual expected return

p

Security A Security B

w(A) E(Rport)Ri Ri

0.02 10% 10% 0 10.00%

0.08 12% 11% 0.1 11.10%

0.11 14% 13% 0.2 13.20%

0.12 16% 17% 0.3 16.70%

0.15 18% 19% 0.4 18.60%

0.17 20% 21% 0.5 20.50%

0.13 22% 23% 0.6 22.40%

0.09 24% 24% 0.7 24.00%

0.07 26% 25% 0.8 25.80%

0.06 28% 26% 0.9 27.80%

1.00 19.2% 19.4% 1 19.24%


9

Variance, covariance and correlation

)E(RR...

p...

)E(RR)E(RR

pp)E(RR

iqk

qk

i2ki1k

2k1kiik

2 iii2 RERpσ

iii RERpσ The measure of a risk in case of an individual security

Variance properties:

1. var (constant)= 0

2. var (c x z) = c2 x var (z)

3. var (x + y) = var (x) + var (y) + cov (x, y)


10

Variance, covariance and correlation (cont.)

)E(RR)E(RRpCov jjx

N

1x

iixiij

Covariance properties:

1. cov(y, xi)= c1*cov(y,x1)+c2* cov(y,x2)+...cn* cov(y,xn) when

y= c1*x1+c2*x2+...cn*xn

2. cov(x,y) = cov(y,x)

3. cov(c * x, y)=c*cov(x,y)

)E(RRp)E(RRp

)E(RR)E(RRp

disp(y)disp(x)

y)cov(x,y)correl(x,

yi

yii

xi

xii

yi

yi

xi

xii

Interpretation:

• correl(x,y) = 0 – x is independent of y

• correl(x,y)=1 – x is total dependent of y

• correl(x,y) – negative means inverse relation between x and y


11

p

Security A Security B

w(A) E(Rport) StDev(Port)Ri Ri

0.02 10.00% 10.00% 0.00% 10.00% 0.0035

0.08 12.00% 11.00% 10.00% 11.10% 0.0241

0.11 14.00% 13.00% 20.00% 13.20% 0.0320

0.12 16.00% 17.00% 30.00% 16.70% 0.0366

0.15 18.00% 19.00% 40.00% 18.60% 0.0391

0.17 20.00% 21.00% 50.00% 20.50% 0.0399

0.13 22.00% 23.00% 60.00% 22.40% 0.0391

0.09 24.00% 24.00% 70.00% 24.00% 0.0366

0.07 26.00% 25.00% 80.00% 25.80% 0.0320

0.06 28.00% 26.00% 90.00% 27.80% 0.0241

1.00 19.2% 19.4% 100.00% 19.24% 0.0037

Variance A 0.00366667

Variance B 0.00349889

Covariance 0.00317

Correlation 0.98336775

(8) covww2σw σ

(7) covww2σw σ

n

1i

n

1jijji

2i

2iportofoliu

n

1i

n

1jijji

2i

2iportofoliu

2

n

1i iiport )E(Rw)E(R


12

Measuring the return distribution:

A B

E(Ra) E(Rb)

loss profit

loss profit

Return distribution for two investments with the same variation

3iii3 )E(rrpM

U(r) = E(r) – a0 x σ2 + a1 x M3 – a2 x M4 + a3 x M5 - ....


13

Deriving Efficient Frontier:

A

B

C

A

B

C

Combination between A, B

and C

rf

Here is impossible to find a portfolio

Standard deviation

High risk / High return

Medium risk / Medium return

Low risk / Low return

Inefficient portfolios

Efficient Frontier of a market


14

Optimal portfolio using Markovitz Model:

Efficient Frontier

CAL1

CAL2

CAL3

rf

Optimal portfolio

Efficient Frontier

CAL

Optimal risky portfolio

M

Investment

Debt

Risk

Expected return

Optimal portfolio:

Max{f(P)}=Max{[E(rP) - rF]/σP}


15

Markovitz model (two assets example):

E(Ri) StDev Cov(A,B)Security A 7% 0.12Security B 14% 0.2

W(A) StDev E(Ri)0% 0.04 14.00%10% 0.03 13.30%20% 0.03 12.60%30% 0.02 11.90%40% 0.02 11.20%50% 0.02 10.50%60% 0.02 9.80%70% 0.01 9.10%80% 0.01 8.40%90% 0.01 7.70%

100% 0.01 7.00%

0.0087

E(Ri)

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%

16.00%

0.00 0.01 0.02 0.03 0.04 0.05

E(Ri)


16

Optimal portfolio using utility function:

k 0.8A 5

Correl -0.7W(A) 15.57%W(B) 84.43%

Uport= E(rport) - σport2 x Aver x k,

(A)w(B)w

σσcorel2σσAk

B)corel(A,σσσAverk)E(r)E(r(A)w

optopt

BAABB2

A2

BAB2

BAopt

1

Aver – coefficient that measures the level of risk aversion for an investor

Optimal = Highest return at the lowest level of risk

More risk averse investor: Less risk averse investor:

k 0.8A 20

Correl -0.7W(A) 30.48%W(B) 69.52%


17

Z1= 50000

Z2= 150000

P E(ret) U

1 50000 10.82

0.9 60000 10.93

0.8 70000 11.04

0.7 80000 11.15

0.6 90000 11.26

0.5 100000 11.37

0.4 110000 11.48

0.3 120000 11.59

0.2 130000 11.70

0.1 140000 11.81

0 150000 11.92

Risk averse investor:U(R) = Σ Pn lnRi

U(100000)=11.51

U(150000)=11.92

U(50000)=10.82

E(U(z))=11.37

z

50000 USD profit utility

50.000 USD loss utility

U(100000)=11.51

z1 z2E(z)

100.000 USD

50.000 USD

150.000 USD

p=1/2

p=1/2


18

Risk lover investor:

U(150000)=2250

Profit utility

E(U(z))=1250

U(50000)=250

U(100000)=1000

E(z) z2z1

Loss utility

C(z)

Z1= 50000

Z2= 150000

P E(ret) U

1 50000 250

0.9 60000 450

0.8 70000 650

0.7 80000 850

0.6 90000 1050

0.5 100000 1250

0.4 110000 1450

0.3 120000 1650

0.2 130000 1850

0.1 140000 2050

0 150000 2250

U(100000)=1000

U(z) = K

1zp n

ii , n=2, k=10


19

Markovitz Model and risk aversion:

Risk

Expected return

Risk lovers

Risk averse

P

InvestmentDebt

Efficient Frontier


20

Conclusions:

• using historical data we can assign probabilities for returns in case of securities;

• expectation in case of returns are based on average value of probabilistic returns;

• we have only one optimal risky portfolio on efficient frontier;

• Markovitz Model is quite complicated to be applied on international markets or in case of complex portfolios;

• Markovitz approach improved the portfolio selection;

• the singleness of the optimal portfolio explains the development of new financial markets (pension funds, investment funds, life insurance policies)

• Markovitz Model takes into consideration the investors attitude against the risk;


21

B. Capital Asset Pricing Model


22

CAPM hypothesis:

• there are many investors on financial markets (incapacity to have a major influence on security pricing);

• limited time to take an investment decision (“myopic” behavior);

• we have risky instruments and risk free rate instruments;

• we have no transaction costs or taxes in case of investment transactions;

• all investors have a rational behavior (maximize their returns);

• all investors analyze investment alternatives in the same way (the return expectation are homogenous);

• market portfolio => optimal portfolio;

• risk premium = Rm – RFR

• risk measure: beta coefficient


23

CAPM Equation:

Rf

Rm

Ei

Betaβi=1

Risk premium

Securities with a higher risk than market risk

Securities with a lower risk than market risk

2M

iMi

)r,R(Cov


24

Problems with CAPM:

• we have a distinction between systemic and non-systemic risk;

• CAPM is a simple model and easy to use;

• we have no risk free rate instruments on a financial market;

• it is difficult to construct the optimal risky portfolio (market portfolio);

• market is not the only risk factor with impact on the expected return (company dimension, transaction costs);

• market index approximation;

• CAPM is a static model focused on expected return at a moment t;

• there was a lot of tests on the relevance of the CAPM (Roll, Fama & MacBeth, Banz, Jensen);

• is difficult to develop a global CAPM;


25

Alternatives of the CAPM:

),(FRRRE Mimfiii A. CAPM and transaction costs:

B. CAPM and companies dimension (Banz, 1981):

C. CAPM and non-tradable assets (Mayers, 1972):

D. Single factor model:

iMiii RR


26

C. Arbitrage Pricing Theory


27

APT Model Hypothesis:

• factorial models can explain expected returns;

• arbitrage opportunities = zero investment portfolios;

• arbitrage opportunities occur when the law of one price is violated

• financial markets are perfect with a law volatility;

• rational equilibrium market prices move to rule out arbitrage opportunities;

• violation of the no arbitrage condition is the strongest form of market irrationality

• the way of exploiting arbitrage opportunities does not depend on risk aversion


28

APT Equation:

i

K

1k

kikii

iKiK22i11iii

Fr

F...FFr

KiK22i11iii ...)r(E

Risk factors:

1. Chen, Ross and Roll APT Model

2. Fama & French APT Model

3. Morgan Stanley APT Model

4. Salomon Smith Barney APT Model

Systematic risk Non-systematic risk


29

Chen, Ross and Roll APT Model (original APT):1. Industrial production (reflects changes in cash flow expectations)2. Yield spread btw high risk and low risk corporate bonds (reflects

changes in risk preferences)3. Difference between short-and long-term interest rate (reflects shifts in

time preferences)4. Unanticipated inflation5. Expected inflation (less important)

Fama & French APT Model :1. Market

2. Company size

3. Book-to-market factor


30

Morgan Stanley APT Model:

Salomon Smith Barney APT Model

GDP growth1. Long-term interest rates2. Foreign exchange (Yen, Euro, Pound basket)3. Market Factor4. Commodities or oil price index

1. Market trend2. Economic growth3. Credit quality4. Interest rates5. Inflation shocks6. Small cap premium


31

Problems with APT:

• Existence of arbitrage opportunities (single price violation);

• It is difficult to identify a proper set of risk factors (this factors should be uncorrelated and expected returns for all securities should be sensitive to them);

• Singleness of the risk factors selection;

• The applicability of the model to real world;

• The stability of the relationship between expected return and risk factors during a longer period of time;

• The independence between risk factors for a determined period of time;

• Modification in terms of expected return sensitivity to risk factors;


32

Final Conclusions:• the most important financial resources are obtained trough international capital markets by issuing bonds or stocks;

• when a company chose to issue securities on international markets it is very important to understand investors behavior;

• investment decision is based on risk and expected return analysis;

• we have different theories in case of risk & return valuation:

• Markovitz: mean for expected return and variance for risk

• CAPM: linear relation between expected return and risk, risk is evaluated based on a specific indicator;

• APT: linear relation between expected return and a lot of risk factors;

• we have an utility function associated to expected returns;

• we have different risk attitudes (aversion, preference, indifference);

• we have arbitrage opportunities when we have different prices and return to the same categories of securities.

Documents

“International Finance and Payments” Course III: “International financial portfolios theory” Lect. Cristian PĂUN Email: [email protected] [email protected]@ase.ro